1,1,279,0,5.477752," ","integrate(x**2*(e*x+d)*(-e**2*x**2+d**2)**(1/2),x)","d \left(\begin{cases} - \frac{i d^{4} \operatorname{acosh}{\left(\frac{e x}{d} \right)}}{8 e^{3}} + \frac{i d^{3} x}{8 e^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{3 i d x^{3}}{8 \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + \frac{i e^{2} x^{5}}{4 d \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{d^{4} \operatorname{asin}{\left(\frac{e x}{d} \right)}}{8 e^{3}} - \frac{d^{3} x}{8 e^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{3 d x^{3}}{8 \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} - \frac{e^{2} x^{5}}{4 d \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} & \text{otherwise} \end{cases}\right) + e \left(\begin{cases} - \frac{2 d^{4} \sqrt{d^{2} - e^{2} x^{2}}}{15 e^{4}} - \frac{d^{2} x^{2} \sqrt{d^{2} - e^{2} x^{2}}}{15 e^{2}} + \frac{x^{4} \sqrt{d^{2} - e^{2} x^{2}}}{5} & \text{for}\: e \neq 0 \\\frac{x^{4} \sqrt{d^{2}}}{4} & \text{otherwise} \end{cases}\right)"," ",0,"d*Piecewise((-I*d**4*acosh(e*x/d)/(8*e**3) + I*d**3*x/(8*e**2*sqrt(-1 + e**2*x**2/d**2)) - 3*I*d*x**3/(8*sqrt(-1 + e**2*x**2/d**2)) + I*e**2*x**5/(4*d*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (d**4*asin(e*x/d)/(8*e**3) - d**3*x/(8*e**2*sqrt(1 - e**2*x**2/d**2)) + 3*d*x**3/(8*sqrt(1 - e**2*x**2/d**2)) - e**2*x**5/(4*d*sqrt(1 - e**2*x**2/d**2)), True)) + e*Piecewise((-2*d**4*sqrt(d**2 - e**2*x**2)/(15*e**4) - d**2*x**2*sqrt(d**2 - e**2*x**2)/(15*e**2) + x**4*sqrt(d**2 - e**2*x**2)/5, Ne(e, 0)), (x**4*sqrt(d**2)/4, True))","C",0
2,1,830,0,17.834813," ","integrate(x**4*(e*x+d)*(-e**2*x**2+d**2)**(3/2),x)","d^{3} \left(\begin{cases} - \frac{i d^{6} \operatorname{acosh}{\left(\frac{e x}{d} \right)}}{16 e^{5}} + \frac{i d^{5} x}{16 e^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{i d^{3} x^{3}}{48 e^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{5 i d x^{5}}{24 \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + \frac{i e^{2} x^{7}}{6 d \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{d^{6} \operatorname{asin}{\left(\frac{e x}{d} \right)}}{16 e^{5}} - \frac{d^{5} x}{16 e^{4} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{d^{3} x^{3}}{48 e^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{5 d x^{5}}{24 \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} - \frac{e^{2} x^{7}}{6 d \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} & \text{otherwise} \end{cases}\right) + d^{2} e \left(\begin{cases} - \frac{8 d^{6} \sqrt{d^{2} - e^{2} x^{2}}}{105 e^{6}} - \frac{4 d^{4} x^{2} \sqrt{d^{2} - e^{2} x^{2}}}{105 e^{4}} - \frac{d^{2} x^{4} \sqrt{d^{2} - e^{2} x^{2}}}{35 e^{2}} + \frac{x^{6} \sqrt{d^{2} - e^{2} x^{2}}}{7} & \text{for}\: e \neq 0 \\\frac{x^{6} \sqrt{d^{2}}}{6} & \text{otherwise} \end{cases}\right) - d e^{2} \left(\begin{cases} - \frac{5 i d^{8} \operatorname{acosh}{\left(\frac{e x}{d} \right)}}{128 e^{7}} + \frac{5 i d^{7} x}{128 e^{6} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{5 i d^{5} x^{3}}{384 e^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{i d^{3} x^{5}}{192 e^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{7 i d x^{7}}{48 \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + \frac{i e^{2} x^{9}}{8 d \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{5 d^{8} \operatorname{asin}{\left(\frac{e x}{d} \right)}}{128 e^{7}} - \frac{5 d^{7} x}{128 e^{6} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{5 d^{5} x^{3}}{384 e^{4} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{d^{3} x^{5}}{192 e^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{7 d x^{7}}{48 \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} - \frac{e^{2} x^{9}}{8 d \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} & \text{otherwise} \end{cases}\right) - e^{3} \left(\begin{cases} - \frac{16 d^{8} \sqrt{d^{2} - e^{2} x^{2}}}{315 e^{8}} - \frac{8 d^{6} x^{2} \sqrt{d^{2} - e^{2} x^{2}}}{315 e^{6}} - \frac{2 d^{4} x^{4} \sqrt{d^{2} - e^{2} x^{2}}}{105 e^{4}} - \frac{d^{2} x^{6} \sqrt{d^{2} - e^{2} x^{2}}}{63 e^{2}} + \frac{x^{8} \sqrt{d^{2} - e^{2} x^{2}}}{9} & \text{for}\: e \neq 0 \\\frac{x^{8} \sqrt{d^{2}}}{8} & \text{otherwise} \end{cases}\right)"," ",0,"d**3*Piecewise((-I*d**6*acosh(e*x/d)/(16*e**5) + I*d**5*x/(16*e**4*sqrt(-1 + e**2*x**2/d**2)) - I*d**3*x**3/(48*e**2*sqrt(-1 + e**2*x**2/d**2)) - 5*I*d*x**5/(24*sqrt(-1 + e**2*x**2/d**2)) + I*e**2*x**7/(6*d*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (d**6*asin(e*x/d)/(16*e**5) - d**5*x/(16*e**4*sqrt(1 - e**2*x**2/d**2)) + d**3*x**3/(48*e**2*sqrt(1 - e**2*x**2/d**2)) + 5*d*x**5/(24*sqrt(1 - e**2*x**2/d**2)) - e**2*x**7/(6*d*sqrt(1 - e**2*x**2/d**2)), True)) + d**2*e*Piecewise((-8*d**6*sqrt(d**2 - e**2*x**2)/(105*e**6) - 4*d**4*x**2*sqrt(d**2 - e**2*x**2)/(105*e**4) - d**2*x**4*sqrt(d**2 - e**2*x**2)/(35*e**2) + x**6*sqrt(d**2 - e**2*x**2)/7, Ne(e, 0)), (x**6*sqrt(d**2)/6, True)) - d*e**2*Piecewise((-5*I*d**8*acosh(e*x/d)/(128*e**7) + 5*I*d**7*x/(128*e**6*sqrt(-1 + e**2*x**2/d**2)) - 5*I*d**5*x**3/(384*e**4*sqrt(-1 + e**2*x**2/d**2)) - I*d**3*x**5/(192*e**2*sqrt(-1 + e**2*x**2/d**2)) - 7*I*d*x**7/(48*sqrt(-1 + e**2*x**2/d**2)) + I*e**2*x**9/(8*d*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (5*d**8*asin(e*x/d)/(128*e**7) - 5*d**7*x/(128*e**6*sqrt(1 - e**2*x**2/d**2)) + 5*d**5*x**3/(384*e**4*sqrt(1 - e**2*x**2/d**2)) + d**3*x**5/(192*e**2*sqrt(1 - e**2*x**2/d**2)) + 7*d*x**7/(48*sqrt(1 - e**2*x**2/d**2)) - e**2*x**9/(8*d*sqrt(1 - e**2*x**2/d**2)), True)) - e**3*Piecewise((-16*d**8*sqrt(d**2 - e**2*x**2)/(315*e**8) - 8*d**6*x**2*sqrt(d**2 - e**2*x**2)/(315*e**6) - 2*d**4*x**4*sqrt(d**2 - e**2*x**2)/(105*e**4) - d**2*x**6*sqrt(d**2 - e**2*x**2)/(63*e**2) + x**8*sqrt(d**2 - e**2*x**2)/9, Ne(e, 0)), (x**8*sqrt(d**2)/8, True))","C",0
3,1,775,0,17.170100," ","integrate(x**3*(e*x+d)*(-e**2*x**2+d**2)**(3/2),x)","d^{3} \left(\begin{cases} - \frac{2 d^{4} \sqrt{d^{2} - e^{2} x^{2}}}{15 e^{4}} - \frac{d^{2} x^{2} \sqrt{d^{2} - e^{2} x^{2}}}{15 e^{2}} + \frac{x^{4} \sqrt{d^{2} - e^{2} x^{2}}}{5} & \text{for}\: e \neq 0 \\\frac{x^{4} \sqrt{d^{2}}}{4} & \text{otherwise} \end{cases}\right) + d^{2} e \left(\begin{cases} - \frac{i d^{6} \operatorname{acosh}{\left(\frac{e x}{d} \right)}}{16 e^{5}} + \frac{i d^{5} x}{16 e^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{i d^{3} x^{3}}{48 e^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{5 i d x^{5}}{24 \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + \frac{i e^{2} x^{7}}{6 d \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{d^{6} \operatorname{asin}{\left(\frac{e x}{d} \right)}}{16 e^{5}} - \frac{d^{5} x}{16 e^{4} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{d^{3} x^{3}}{48 e^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{5 d x^{5}}{24 \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} - \frac{e^{2} x^{7}}{6 d \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} & \text{otherwise} \end{cases}\right) - d e^{2} \left(\begin{cases} - \frac{8 d^{6} \sqrt{d^{2} - e^{2} x^{2}}}{105 e^{6}} - \frac{4 d^{4} x^{2} \sqrt{d^{2} - e^{2} x^{2}}}{105 e^{4}} - \frac{d^{2} x^{4} \sqrt{d^{2} - e^{2} x^{2}}}{35 e^{2}} + \frac{x^{6} \sqrt{d^{2} - e^{2} x^{2}}}{7} & \text{for}\: e \neq 0 \\\frac{x^{6} \sqrt{d^{2}}}{6} & \text{otherwise} \end{cases}\right) - e^{3} \left(\begin{cases} - \frac{5 i d^{8} \operatorname{acosh}{\left(\frac{e x}{d} \right)}}{128 e^{7}} + \frac{5 i d^{7} x}{128 e^{6} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{5 i d^{5} x^{3}}{384 e^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{i d^{3} x^{5}}{192 e^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{7 i d x^{7}}{48 \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + \frac{i e^{2} x^{9}}{8 d \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{5 d^{8} \operatorname{asin}{\left(\frac{e x}{d} \right)}}{128 e^{7}} - \frac{5 d^{7} x}{128 e^{6} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{5 d^{5} x^{3}}{384 e^{4} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{d^{3} x^{5}}{192 e^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{7 d x^{7}}{48 \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} - \frac{e^{2} x^{9}}{8 d \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} & \text{otherwise} \end{cases}\right)"," ",0,"d**3*Piecewise((-2*d**4*sqrt(d**2 - e**2*x**2)/(15*e**4) - d**2*x**2*sqrt(d**2 - e**2*x**2)/(15*e**2) + x**4*sqrt(d**2 - e**2*x**2)/5, Ne(e, 0)), (x**4*sqrt(d**2)/4, True)) + d**2*e*Piecewise((-I*d**6*acosh(e*x/d)/(16*e**5) + I*d**5*x/(16*e**4*sqrt(-1 + e**2*x**2/d**2)) - I*d**3*x**3/(48*e**2*sqrt(-1 + e**2*x**2/d**2)) - 5*I*d*x**5/(24*sqrt(-1 + e**2*x**2/d**2)) + I*e**2*x**7/(6*d*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (d**6*asin(e*x/d)/(16*e**5) - d**5*x/(16*e**4*sqrt(1 - e**2*x**2/d**2)) + d**3*x**3/(48*e**2*sqrt(1 - e**2*x**2/d**2)) + 5*d*x**5/(24*sqrt(1 - e**2*x**2/d**2)) - e**2*x**7/(6*d*sqrt(1 - e**2*x**2/d**2)), True)) - d*e**2*Piecewise((-8*d**6*sqrt(d**2 - e**2*x**2)/(105*e**6) - 4*d**4*x**2*sqrt(d**2 - e**2*x**2)/(105*e**4) - d**2*x**4*sqrt(d**2 - e**2*x**2)/(35*e**2) + x**6*sqrt(d**2 - e**2*x**2)/7, Ne(e, 0)), (x**6*sqrt(d**2)/6, True)) - e**3*Piecewise((-5*I*d**8*acosh(e*x/d)/(128*e**7) + 5*I*d**7*x/(128*e**6*sqrt(-1 + e**2*x**2/d**2)) - 5*I*d**5*x**3/(384*e**4*sqrt(-1 + e**2*x**2/d**2)) - I*d**3*x**5/(192*e**2*sqrt(-1 + e**2*x**2/d**2)) - 7*I*d*x**7/(48*sqrt(-1 + e**2*x**2/d**2)) + I*e**2*x**9/(8*d*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (5*d**8*asin(e*x/d)/(128*e**7) - 5*d**7*x/(128*e**6*sqrt(1 - e**2*x**2/d**2)) + 5*d**5*x**3/(384*e**4*sqrt(1 - e**2*x**2/d**2)) + d**3*x**5/(192*e**2*sqrt(1 - e**2*x**2/d**2)) + 7*d*x**7/(48*sqrt(1 - e**2*x**2/d**2)) - e**2*x**9/(8*d*sqrt(1 - e**2*x**2/d**2)), True))","A",0
4,1,653,0,12.266969," ","integrate(x**2*(e*x+d)*(-e**2*x**2+d**2)**(3/2),x)","d^{3} \left(\begin{cases} - \frac{i d^{4} \operatorname{acosh}{\left(\frac{e x}{d} \right)}}{8 e^{3}} + \frac{i d^{3} x}{8 e^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{3 i d x^{3}}{8 \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + \frac{i e^{2} x^{5}}{4 d \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{d^{4} \operatorname{asin}{\left(\frac{e x}{d} \right)}}{8 e^{3}} - \frac{d^{3} x}{8 e^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{3 d x^{3}}{8 \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} - \frac{e^{2} x^{5}}{4 d \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} & \text{otherwise} \end{cases}\right) + d^{2} e \left(\begin{cases} - \frac{2 d^{4} \sqrt{d^{2} - e^{2} x^{2}}}{15 e^{4}} - \frac{d^{2} x^{2} \sqrt{d^{2} - e^{2} x^{2}}}{15 e^{2}} + \frac{x^{4} \sqrt{d^{2} - e^{2} x^{2}}}{5} & \text{for}\: e \neq 0 \\\frac{x^{4} \sqrt{d^{2}}}{4} & \text{otherwise} \end{cases}\right) - d e^{2} \left(\begin{cases} - \frac{i d^{6} \operatorname{acosh}{\left(\frac{e x}{d} \right)}}{16 e^{5}} + \frac{i d^{5} x}{16 e^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{i d^{3} x^{3}}{48 e^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{5 i d x^{5}}{24 \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + \frac{i e^{2} x^{7}}{6 d \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{d^{6} \operatorname{asin}{\left(\frac{e x}{d} \right)}}{16 e^{5}} - \frac{d^{5} x}{16 e^{4} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{d^{3} x^{3}}{48 e^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{5 d x^{5}}{24 \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} - \frac{e^{2} x^{7}}{6 d \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} & \text{otherwise} \end{cases}\right) - e^{3} \left(\begin{cases} - \frac{8 d^{6} \sqrt{d^{2} - e^{2} x^{2}}}{105 e^{6}} - \frac{4 d^{4} x^{2} \sqrt{d^{2} - e^{2} x^{2}}}{105 e^{4}} - \frac{d^{2} x^{4} \sqrt{d^{2} - e^{2} x^{2}}}{35 e^{2}} + \frac{x^{6} \sqrt{d^{2} - e^{2} x^{2}}}{7} & \text{for}\: e \neq 0 \\\frac{x^{6} \sqrt{d^{2}}}{6} & \text{otherwise} \end{cases}\right)"," ",0,"d**3*Piecewise((-I*d**4*acosh(e*x/d)/(8*e**3) + I*d**3*x/(8*e**2*sqrt(-1 + e**2*x**2/d**2)) - 3*I*d*x**3/(8*sqrt(-1 + e**2*x**2/d**2)) + I*e**2*x**5/(4*d*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (d**4*asin(e*x/d)/(8*e**3) - d**3*x/(8*e**2*sqrt(1 - e**2*x**2/d**2)) + 3*d*x**3/(8*sqrt(1 - e**2*x**2/d**2)) - e**2*x**5/(4*d*sqrt(1 - e**2*x**2/d**2)), True)) + d**2*e*Piecewise((-2*d**4*sqrt(d**2 - e**2*x**2)/(15*e**4) - d**2*x**2*sqrt(d**2 - e**2*x**2)/(15*e**2) + x**4*sqrt(d**2 - e**2*x**2)/5, Ne(e, 0)), (x**4*sqrt(d**2)/4, True)) - d*e**2*Piecewise((-I*d**6*acosh(e*x/d)/(16*e**5) + I*d**5*x/(16*e**4*sqrt(-1 + e**2*x**2/d**2)) - I*d**3*x**3/(48*e**2*sqrt(-1 + e**2*x**2/d**2)) - 5*I*d*x**5/(24*sqrt(-1 + e**2*x**2/d**2)) + I*e**2*x**7/(6*d*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (d**6*asin(e*x/d)/(16*e**5) - d**5*x/(16*e**4*sqrt(1 - e**2*x**2/d**2)) + d**3*x**3/(48*e**2*sqrt(1 - e**2*x**2/d**2)) + 5*d*x**5/(24*sqrt(1 - e**2*x**2/d**2)) - e**2*x**7/(6*d*sqrt(1 - e**2*x**2/d**2)), True)) - e**3*Piecewise((-8*d**6*sqrt(d**2 - e**2*x**2)/(105*e**6) - 4*d**4*x**2*sqrt(d**2 - e**2*x**2)/(105*e**4) - d**2*x**4*sqrt(d**2 - e**2*x**2)/(35*e**2) + x**6*sqrt(d**2 - e**2*x**2)/7, Ne(e, 0)), (x**6*sqrt(d**2)/6, True))","C",0
5,1,580,0,12.058521," ","integrate(x*(e*x+d)*(-e**2*x**2+d**2)**(3/2),x)","d^{3} \left(\begin{cases} \frac{x^{2} \sqrt{d^{2}}}{2} & \text{for}\: e^{2} = 0 \\- \frac{\left(d^{2} - e^{2} x^{2}\right)^{\frac{3}{2}}}{3 e^{2}} & \text{otherwise} \end{cases}\right) + d^{2} e \left(\begin{cases} - \frac{i d^{4} \operatorname{acosh}{\left(\frac{e x}{d} \right)}}{8 e^{3}} + \frac{i d^{3} x}{8 e^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{3 i d x^{3}}{8 \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + \frac{i e^{2} x^{5}}{4 d \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{d^{4} \operatorname{asin}{\left(\frac{e x}{d} \right)}}{8 e^{3}} - \frac{d^{3} x}{8 e^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{3 d x^{3}}{8 \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} - \frac{e^{2} x^{5}}{4 d \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} & \text{otherwise} \end{cases}\right) - d e^{2} \left(\begin{cases} - \frac{2 d^{4} \sqrt{d^{2} - e^{2} x^{2}}}{15 e^{4}} - \frac{d^{2} x^{2} \sqrt{d^{2} - e^{2} x^{2}}}{15 e^{2}} + \frac{x^{4} \sqrt{d^{2} - e^{2} x^{2}}}{5} & \text{for}\: e \neq 0 \\\frac{x^{4} \sqrt{d^{2}}}{4} & \text{otherwise} \end{cases}\right) - e^{3} \left(\begin{cases} - \frac{i d^{6} \operatorname{acosh}{\left(\frac{e x}{d} \right)}}{16 e^{5}} + \frac{i d^{5} x}{16 e^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{i d^{3} x^{3}}{48 e^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{5 i d x^{5}}{24 \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + \frac{i e^{2} x^{7}}{6 d \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{d^{6} \operatorname{asin}{\left(\frac{e x}{d} \right)}}{16 e^{5}} - \frac{d^{5} x}{16 e^{4} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{d^{3} x^{3}}{48 e^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{5 d x^{5}}{24 \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} - \frac{e^{2} x^{7}}{6 d \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} & \text{otherwise} \end{cases}\right)"," ",0,"d**3*Piecewise((x**2*sqrt(d**2)/2, Eq(e**2, 0)), (-(d**2 - e**2*x**2)**(3/2)/(3*e**2), True)) + d**2*e*Piecewise((-I*d**4*acosh(e*x/d)/(8*e**3) + I*d**3*x/(8*e**2*sqrt(-1 + e**2*x**2/d**2)) - 3*I*d*x**3/(8*sqrt(-1 + e**2*x**2/d**2)) + I*e**2*x**5/(4*d*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (d**4*asin(e*x/d)/(8*e**3) - d**3*x/(8*e**2*sqrt(1 - e**2*x**2/d**2)) + 3*d*x**3/(8*sqrt(1 - e**2*x**2/d**2)) - e**2*x**5/(4*d*sqrt(1 - e**2*x**2/d**2)), True)) - d*e**2*Piecewise((-2*d**4*sqrt(d**2 - e**2*x**2)/(15*e**4) - d**2*x**2*sqrt(d**2 - e**2*x**2)/(15*e**2) + x**4*sqrt(d**2 - e**2*x**2)/5, Ne(e, 0)), (x**4*sqrt(d**2)/4, True)) - e**3*Piecewise((-I*d**6*acosh(e*x/d)/(16*e**5) + I*d**5*x/(16*e**4*sqrt(-1 + e**2*x**2/d**2)) - I*d**3*x**3/(48*e**2*sqrt(-1 + e**2*x**2/d**2)) - 5*I*d*x**5/(24*sqrt(-1 + e**2*x**2/d**2)) + I*e**2*x**7/(6*d*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (d**6*asin(e*x/d)/(16*e**5) - d**5*x/(16*e**4*sqrt(1 - e**2*x**2/d**2)) + d**3*x**3/(48*e**2*sqrt(1 - e**2*x**2/d**2)) + 5*d*x**5/(24*sqrt(1 - e**2*x**2/d**2)) - e**2*x**7/(6*d*sqrt(1 - e**2*x**2/d**2)), True))","A",0
6,1,580,0,12.179707," ","integrate(x*(e*x+d)*(-e**2*x**2+d**2)**(3/2),x)","d^{3} \left(\begin{cases} \frac{x^{2} \sqrt{d^{2}}}{2} & \text{for}\: e^{2} = 0 \\- \frac{\left(d^{2} - e^{2} x^{2}\right)^{\frac{3}{2}}}{3 e^{2}} & \text{otherwise} \end{cases}\right) + d^{2} e \left(\begin{cases} - \frac{i d^{4} \operatorname{acosh}{\left(\frac{e x}{d} \right)}}{8 e^{3}} + \frac{i d^{3} x}{8 e^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{3 i d x^{3}}{8 \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + \frac{i e^{2} x^{5}}{4 d \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{d^{4} \operatorname{asin}{\left(\frac{e x}{d} \right)}}{8 e^{3}} - \frac{d^{3} x}{8 e^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{3 d x^{3}}{8 \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} - \frac{e^{2} x^{5}}{4 d \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} & \text{otherwise} \end{cases}\right) - d e^{2} \left(\begin{cases} - \frac{2 d^{4} \sqrt{d^{2} - e^{2} x^{2}}}{15 e^{4}} - \frac{d^{2} x^{2} \sqrt{d^{2} - e^{2} x^{2}}}{15 e^{2}} + \frac{x^{4} \sqrt{d^{2} - e^{2} x^{2}}}{5} & \text{for}\: e \neq 0 \\\frac{x^{4} \sqrt{d^{2}}}{4} & \text{otherwise} \end{cases}\right) - e^{3} \left(\begin{cases} - \frac{i d^{6} \operatorname{acosh}{\left(\frac{e x}{d} \right)}}{16 e^{5}} + \frac{i d^{5} x}{16 e^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{i d^{3} x^{3}}{48 e^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{5 i d x^{5}}{24 \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + \frac{i e^{2} x^{7}}{6 d \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{d^{6} \operatorname{asin}{\left(\frac{e x}{d} \right)}}{16 e^{5}} - \frac{d^{5} x}{16 e^{4} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{d^{3} x^{3}}{48 e^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{5 d x^{5}}{24 \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} - \frac{e^{2} x^{7}}{6 d \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} & \text{otherwise} \end{cases}\right)"," ",0,"d**3*Piecewise((x**2*sqrt(d**2)/2, Eq(e**2, 0)), (-(d**2 - e**2*x**2)**(3/2)/(3*e**2), True)) + d**2*e*Piecewise((-I*d**4*acosh(e*x/d)/(8*e**3) + I*d**3*x/(8*e**2*sqrt(-1 + e**2*x**2/d**2)) - 3*I*d*x**3/(8*sqrt(-1 + e**2*x**2/d**2)) + I*e**2*x**5/(4*d*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (d**4*asin(e*x/d)/(8*e**3) - d**3*x/(8*e**2*sqrt(1 - e**2*x**2/d**2)) + 3*d*x**3/(8*sqrt(1 - e**2*x**2/d**2)) - e**2*x**5/(4*d*sqrt(1 - e**2*x**2/d**2)), True)) - d*e**2*Piecewise((-2*d**4*sqrt(d**2 - e**2*x**2)/(15*e**4) - d**2*x**2*sqrt(d**2 - e**2*x**2)/(15*e**2) + x**4*sqrt(d**2 - e**2*x**2)/5, Ne(e, 0)), (x**4*sqrt(d**2)/4, True)) - e**3*Piecewise((-I*d**6*acosh(e*x/d)/(16*e**5) + I*d**5*x/(16*e**4*sqrt(-1 + e**2*x**2/d**2)) - I*d**3*x**3/(48*e**2*sqrt(-1 + e**2*x**2/d**2)) - 5*I*d*x**5/(24*sqrt(-1 + e**2*x**2/d**2)) + I*e**2*x**7/(6*d*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (d**6*asin(e*x/d)/(16*e**5) - d**5*x/(16*e**4*sqrt(1 - e**2*x**2/d**2)) + d**3*x**3/(48*e**2*sqrt(1 - e**2*x**2/d**2)) + 5*d*x**5/(24*sqrt(1 - e**2*x**2/d**2)) - e**2*x**7/(6*d*sqrt(1 - e**2*x**2/d**2)), True))","A",0
7,1,469,0,22.410894," ","integrate((e*x+d)*(-e**2*x**2+d**2)**(3/2)/x,x)","d^{3} \left(\begin{cases} \frac{d^{2}}{e x \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} - d \operatorname{acosh}{\left(\frac{d}{e x} \right)} - \frac{e x}{\sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\- \frac{i d^{2}}{e x \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} + i d \operatorname{asin}{\left(\frac{d}{e x} \right)} + \frac{i e x}{\sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} & \text{otherwise} \end{cases}\right) + d^{2} e \left(\begin{cases} - \frac{i d^{2} \operatorname{acosh}{\left(\frac{e x}{d} \right)}}{2 e} - \frac{i d x}{2 \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + \frac{i e^{2} x^{3}}{2 d \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{d^{2} \operatorname{asin}{\left(\frac{e x}{d} \right)}}{2 e} + \frac{d x \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}}{2} & \text{otherwise} \end{cases}\right) - d e^{2} \left(\begin{cases} \frac{x^{2} \sqrt{d^{2}}}{2} & \text{for}\: e^{2} = 0 \\- \frac{\left(d^{2} - e^{2} x^{2}\right)^{\frac{3}{2}}}{3 e^{2}} & \text{otherwise} \end{cases}\right) - e^{3} \left(\begin{cases} - \frac{i d^{4} \operatorname{acosh}{\left(\frac{e x}{d} \right)}}{8 e^{3}} + \frac{i d^{3} x}{8 e^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{3 i d x^{3}}{8 \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + \frac{i e^{2} x^{5}}{4 d \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{d^{4} \operatorname{asin}{\left(\frac{e x}{d} \right)}}{8 e^{3}} - \frac{d^{3} x}{8 e^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{3 d x^{3}}{8 \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} - \frac{e^{2} x^{5}}{4 d \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} & \text{otherwise} \end{cases}\right)"," ",0,"d**3*Piecewise((d**2/(e*x*sqrt(d**2/(e**2*x**2) - 1)) - d*acosh(d/(e*x)) - e*x/sqrt(d**2/(e**2*x**2) - 1), Abs(d**2/(e**2*x**2)) > 1), (-I*d**2/(e*x*sqrt(-d**2/(e**2*x**2) + 1)) + I*d*asin(d/(e*x)) + I*e*x/sqrt(-d**2/(e**2*x**2) + 1), True)) + d**2*e*Piecewise((-I*d**2*acosh(e*x/d)/(2*e) - I*d*x/(2*sqrt(-1 + e**2*x**2/d**2)) + I*e**2*x**3/(2*d*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (d**2*asin(e*x/d)/(2*e) + d*x*sqrt(1 - e**2*x**2/d**2)/2, True)) - d*e**2*Piecewise((x**2*sqrt(d**2)/2, Eq(e**2, 0)), (-(d**2 - e**2*x**2)**(3/2)/(3*e**2), True)) - e**3*Piecewise((-I*d**4*acosh(e*x/d)/(8*e**3) + I*d**3*x/(8*e**2*sqrt(-1 + e**2*x**2/d**2)) - 3*I*d*x**3/(8*sqrt(-1 + e**2*x**2/d**2)) + I*e**2*x**5/(4*d*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (d**4*asin(e*x/d)/(8*e**3) - d**3*x/(8*e**2*sqrt(1 - e**2*x**2/d**2)) + 3*d*x**3/(8*sqrt(1 - e**2*x**2/d**2)) - e**2*x**5/(4*d*sqrt(1 - e**2*x**2/d**2)), True))","C",0
8,1,386,0,8.182227," ","integrate((e*x+d)*(-e**2*x**2+d**2)**(3/2)/x**2,x)","d^{3} \left(\begin{cases} \frac{i d}{x \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + i e \operatorname{acosh}{\left(\frac{e x}{d} \right)} - \frac{i e^{2} x}{d \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\- \frac{d}{x \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} - e \operatorname{asin}{\left(\frac{e x}{d} \right)} + \frac{e^{2} x}{d \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} & \text{otherwise} \end{cases}\right) + d^{2} e \left(\begin{cases} \frac{d^{2}}{e x \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} - d \operatorname{acosh}{\left(\frac{d}{e x} \right)} - \frac{e x}{\sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\- \frac{i d^{2}}{e x \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} + i d \operatorname{asin}{\left(\frac{d}{e x} \right)} + \frac{i e x}{\sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} & \text{otherwise} \end{cases}\right) - d e^{2} \left(\begin{cases} - \frac{i d^{2} \operatorname{acosh}{\left(\frac{e x}{d} \right)}}{2 e} - \frac{i d x}{2 \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + \frac{i e^{2} x^{3}}{2 d \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{d^{2} \operatorname{asin}{\left(\frac{e x}{d} \right)}}{2 e} + \frac{d x \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}}{2} & \text{otherwise} \end{cases}\right) - e^{3} \left(\begin{cases} \frac{x^{2} \sqrt{d^{2}}}{2} & \text{for}\: e^{2} = 0 \\- \frac{\left(d^{2} - e^{2} x^{2}\right)^{\frac{3}{2}}}{3 e^{2}} & \text{otherwise} \end{cases}\right)"," ",0,"d**3*Piecewise((I*d/(x*sqrt(-1 + e**2*x**2/d**2)) + I*e*acosh(e*x/d) - I*e**2*x/(d*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (-d/(x*sqrt(1 - e**2*x**2/d**2)) - e*asin(e*x/d) + e**2*x/(d*sqrt(1 - e**2*x**2/d**2)), True)) + d**2*e*Piecewise((d**2/(e*x*sqrt(d**2/(e**2*x**2) - 1)) - d*acosh(d/(e*x)) - e*x/sqrt(d**2/(e**2*x**2) - 1), Abs(d**2/(e**2*x**2)) > 1), (-I*d**2/(e*x*sqrt(-d**2/(e**2*x**2) + 1)) + I*d*asin(d/(e*x)) + I*e*x/sqrt(-d**2/(e**2*x**2) + 1), True)) - d*e**2*Piecewise((-I*d**2*acosh(e*x/d)/(2*e) - I*d*x/(2*sqrt(-1 + e**2*x**2/d**2)) + I*e**2*x**3/(2*d*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (d**2*asin(e*x/d)/(2*e) + d*x*sqrt(1 - e**2*x**2/d**2)/2, True)) - e**3*Piecewise((x**2*sqrt(d**2)/2, Eq(e**2, 0)), (-(d**2 - e**2*x**2)**(3/2)/(3*e**2), True))","C",0
9,1,461,0,9.533202," ","integrate((e*x+d)*(-e**2*x**2+d**2)**(3/2)/x**3,x)","d^{3} \left(\begin{cases} - \frac{d^{2}}{2 e x^{3} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{e}{2 x \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{e^{2} \operatorname{acosh}{\left(\frac{d}{e x} \right)}}{2 d} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\- \frac{i e \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{2 x} - \frac{i e^{2} \operatorname{asin}{\left(\frac{d}{e x} \right)}}{2 d} & \text{otherwise} \end{cases}\right) + d^{2} e \left(\begin{cases} \frac{i d}{x \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + i e \operatorname{acosh}{\left(\frac{e x}{d} \right)} - \frac{i e^{2} x}{d \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\- \frac{d}{x \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} - e \operatorname{asin}{\left(\frac{e x}{d} \right)} + \frac{e^{2} x}{d \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} & \text{otherwise} \end{cases}\right) - d e^{2} \left(\begin{cases} \frac{d^{2}}{e x \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} - d \operatorname{acosh}{\left(\frac{d}{e x} \right)} - \frac{e x}{\sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\- \frac{i d^{2}}{e x \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} + i d \operatorname{asin}{\left(\frac{d}{e x} \right)} + \frac{i e x}{\sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} & \text{otherwise} \end{cases}\right) - e^{3} \left(\begin{cases} - \frac{i d^{2} \operatorname{acosh}{\left(\frac{e x}{d} \right)}}{2 e} - \frac{i d x}{2 \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + \frac{i e^{2} x^{3}}{2 d \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{d^{2} \operatorname{asin}{\left(\frac{e x}{d} \right)}}{2 e} + \frac{d x \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}}{2} & \text{otherwise} \end{cases}\right)"," ",0,"d**3*Piecewise((-d**2/(2*e*x**3*sqrt(d**2/(e**2*x**2) - 1)) + e/(2*x*sqrt(d**2/(e**2*x**2) - 1)) + e**2*acosh(d/(e*x))/(2*d), Abs(d**2/(e**2*x**2)) > 1), (-I*e*sqrt(-d**2/(e**2*x**2) + 1)/(2*x) - I*e**2*asin(d/(e*x))/(2*d), True)) + d**2*e*Piecewise((I*d/(x*sqrt(-1 + e**2*x**2/d**2)) + I*e*acosh(e*x/d) - I*e**2*x/(d*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (-d/(x*sqrt(1 - e**2*x**2/d**2)) - e*asin(e*x/d) + e**2*x/(d*sqrt(1 - e**2*x**2/d**2)), True)) - d*e**2*Piecewise((d**2/(e*x*sqrt(d**2/(e**2*x**2) - 1)) - d*acosh(d/(e*x)) - e*x/sqrt(d**2/(e**2*x**2) - 1), Abs(d**2/(e**2*x**2)) > 1), (-I*d**2/(e*x*sqrt(-d**2/(e**2*x**2) + 1)) + I*d*asin(d/(e*x)) + I*e*x/sqrt(-d**2/(e**2*x**2) + 1), True)) - e**3*Piecewise((-I*d**2*acosh(e*x/d)/(2*e) - I*d*x/(2*sqrt(-1 + e**2*x**2/d**2)) + I*e**2*x**3/(2*d*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (d**2*asin(e*x/d)/(2*e) + d*x*sqrt(1 - e**2*x**2/d**2)/2, True))","C",0
10,1,457,0,8.931628," ","integrate((e*x+d)*(-e**2*x**2+d**2)**(3/2)/x**4,x)","d^{3} \left(\begin{cases} - \frac{e \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}}{3 x^{2}} + \frac{e^{3} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}}{3 d^{2}} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\- \frac{i e \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{3 x^{2}} + \frac{i e^{3} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{3 d^{2}} & \text{otherwise} \end{cases}\right) + d^{2} e \left(\begin{cases} - \frac{d^{2}}{2 e x^{3} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{e}{2 x \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{e^{2} \operatorname{acosh}{\left(\frac{d}{e x} \right)}}{2 d} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\- \frac{i e \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{2 x} - \frac{i e^{2} \operatorname{asin}{\left(\frac{d}{e x} \right)}}{2 d} & \text{otherwise} \end{cases}\right) - d e^{2} \left(\begin{cases} \frac{i d}{x \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + i e \operatorname{acosh}{\left(\frac{e x}{d} \right)} - \frac{i e^{2} x}{d \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\- \frac{d}{x \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} - e \operatorname{asin}{\left(\frac{e x}{d} \right)} + \frac{e^{2} x}{d \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} & \text{otherwise} \end{cases}\right) - e^{3} \left(\begin{cases} \frac{d^{2}}{e x \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} - d \operatorname{acosh}{\left(\frac{d}{e x} \right)} - \frac{e x}{\sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\- \frac{i d^{2}}{e x \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} + i d \operatorname{asin}{\left(\frac{d}{e x} \right)} + \frac{i e x}{\sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} & \text{otherwise} \end{cases}\right)"," ",0,"d**3*Piecewise((-e*sqrt(d**2/(e**2*x**2) - 1)/(3*x**2) + e**3*sqrt(d**2/(e**2*x**2) - 1)/(3*d**2), Abs(d**2/(e**2*x**2)) > 1), (-I*e*sqrt(-d**2/(e**2*x**2) + 1)/(3*x**2) + I*e**3*sqrt(-d**2/(e**2*x**2) + 1)/(3*d**2), True)) + d**2*e*Piecewise((-d**2/(2*e*x**3*sqrt(d**2/(e**2*x**2) - 1)) + e/(2*x*sqrt(d**2/(e**2*x**2) - 1)) + e**2*acosh(d/(e*x))/(2*d), Abs(d**2/(e**2*x**2)) > 1), (-I*e*sqrt(-d**2/(e**2*x**2) + 1)/(2*x) - I*e**2*asin(d/(e*x))/(2*d), True)) - d*e**2*Piecewise((I*d/(x*sqrt(-1 + e**2*x**2/d**2)) + I*e*acosh(e*x/d) - I*e**2*x/(d*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (-d/(x*sqrt(1 - e**2*x**2/d**2)) - e*asin(e*x/d) + e**2*x/(d*sqrt(1 - e**2*x**2/d**2)), True)) - e**3*Piecewise((d**2/(e*x*sqrt(d**2/(e**2*x**2) - 1)) - d*acosh(d/(e*x)) - e*x/sqrt(d**2/(e**2*x**2) - 1), Abs(d**2/(e**2*x**2)) > 1), (-I*d**2/(e*x*sqrt(-d**2/(e**2*x**2) + 1)) + I*d*asin(d/(e*x)) + I*e*x/sqrt(-d**2/(e**2*x**2) + 1), True))","C",0
11,1,541,0,11.056218," ","integrate((e*x+d)*(-e**2*x**2+d**2)**(3/2)/x**5,x)","d^{3} \left(\begin{cases} - \frac{d^{2}}{4 e x^{5} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{3 e}{8 x^{3} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} - \frac{e^{3}}{8 d^{2} x \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{e^{4} \operatorname{acosh}{\left(\frac{d}{e x} \right)}}{8 d^{3}} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\\frac{i d^{2}}{4 e x^{5} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} - \frac{3 i e}{8 x^{3} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} + \frac{i e^{3}}{8 d^{2} x \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} - \frac{i e^{4} \operatorname{asin}{\left(\frac{d}{e x} \right)}}{8 d^{3}} & \text{otherwise} \end{cases}\right) + d^{2} e \left(\begin{cases} - \frac{e \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}}{3 x^{2}} + \frac{e^{3} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}}{3 d^{2}} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\- \frac{i e \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{3 x^{2}} + \frac{i e^{3} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{3 d^{2}} & \text{otherwise} \end{cases}\right) - d e^{2} \left(\begin{cases} - \frac{d^{2}}{2 e x^{3} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{e}{2 x \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{e^{2} \operatorname{acosh}{\left(\frac{d}{e x} \right)}}{2 d} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\- \frac{i e \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{2 x} - \frac{i e^{2} \operatorname{asin}{\left(\frac{d}{e x} \right)}}{2 d} & \text{otherwise} \end{cases}\right) - e^{3} \left(\begin{cases} \frac{i d}{x \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + i e \operatorname{acosh}{\left(\frac{e x}{d} \right)} - \frac{i e^{2} x}{d \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\- \frac{d}{x \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} - e \operatorname{asin}{\left(\frac{e x}{d} \right)} + \frac{e^{2} x}{d \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} & \text{otherwise} \end{cases}\right)"," ",0,"d**3*Piecewise((-d**2/(4*e*x**5*sqrt(d**2/(e**2*x**2) - 1)) + 3*e/(8*x**3*sqrt(d**2/(e**2*x**2) - 1)) - e**3/(8*d**2*x*sqrt(d**2/(e**2*x**2) - 1)) + e**4*acosh(d/(e*x))/(8*d**3), Abs(d**2/(e**2*x**2)) > 1), (I*d**2/(4*e*x**5*sqrt(-d**2/(e**2*x**2) + 1)) - 3*I*e/(8*x**3*sqrt(-d**2/(e**2*x**2) + 1)) + I*e**3/(8*d**2*x*sqrt(-d**2/(e**2*x**2) + 1)) - I*e**4*asin(d/(e*x))/(8*d**3), True)) + d**2*e*Piecewise((-e*sqrt(d**2/(e**2*x**2) - 1)/(3*x**2) + e**3*sqrt(d**2/(e**2*x**2) - 1)/(3*d**2), Abs(d**2/(e**2*x**2)) > 1), (-I*e*sqrt(-d**2/(e**2*x**2) + 1)/(3*x**2) + I*e**3*sqrt(-d**2/(e**2*x**2) + 1)/(3*d**2), True)) - d*e**2*Piecewise((-d**2/(2*e*x**3*sqrt(d**2/(e**2*x**2) - 1)) + e/(2*x*sqrt(d**2/(e**2*x**2) - 1)) + e**2*acosh(d/(e*x))/(2*d), Abs(d**2/(e**2*x**2)) > 1), (-I*e*sqrt(-d**2/(e**2*x**2) + 1)/(2*x) - I*e**2*asin(d/(e*x))/(2*d), True)) - e**3*Piecewise((I*d/(x*sqrt(-1 + e**2*x**2/d**2)) + I*e*acosh(e*x/d) - I*e**2*x/(d*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (-d/(x*sqrt(1 - e**2*x**2/d**2)) - e*asin(e*x/d) + e**2*x/(d*sqrt(1 - e**2*x**2/d**2)), True))","C",0
12,1,774,0,11.364841," ","integrate((e*x+d)*(-e**2*x**2+d**2)**(3/2)/x**6,x)","d^{3} \left(\begin{cases} \frac{3 i d^{3} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{2} x^{5} + 15 e^{2} x^{7}} - \frac{4 i d e^{2} x^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{2} x^{5} + 15 e^{2} x^{7}} + \frac{2 i e^{6} x^{6} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{5} x^{5} + 15 d^{3} e^{2} x^{7}} - \frac{i e^{4} x^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{3} x^{5} + 15 d e^{2} x^{7}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{3 d^{3} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{2} x^{5} + 15 e^{2} x^{7}} - \frac{4 d e^{2} x^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{2} x^{5} + 15 e^{2} x^{7}} + \frac{2 e^{6} x^{6} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{5} x^{5} + 15 d^{3} e^{2} x^{7}} - \frac{e^{4} x^{4} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{3} x^{5} + 15 d e^{2} x^{7}} & \text{otherwise} \end{cases}\right) + d^{2} e \left(\begin{cases} - \frac{d^{2}}{4 e x^{5} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{3 e}{8 x^{3} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} - \frac{e^{3}}{8 d^{2} x \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{e^{4} \operatorname{acosh}{\left(\frac{d}{e x} \right)}}{8 d^{3}} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\\frac{i d^{2}}{4 e x^{5} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} - \frac{3 i e}{8 x^{3} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} + \frac{i e^{3}}{8 d^{2} x \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} - \frac{i e^{4} \operatorname{asin}{\left(\frac{d}{e x} \right)}}{8 d^{3}} & \text{otherwise} \end{cases}\right) - d e^{2} \left(\begin{cases} - \frac{e \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}}{3 x^{2}} + \frac{e^{3} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}}{3 d^{2}} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\- \frac{i e \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{3 x^{2}} + \frac{i e^{3} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{3 d^{2}} & \text{otherwise} \end{cases}\right) - e^{3} \left(\begin{cases} - \frac{d^{2}}{2 e x^{3} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{e}{2 x \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{e^{2} \operatorname{acosh}{\left(\frac{d}{e x} \right)}}{2 d} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\- \frac{i e \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{2 x} - \frac{i e^{2} \operatorname{asin}{\left(\frac{d}{e x} \right)}}{2 d} & \text{otherwise} \end{cases}\right)"," ",0,"d**3*Piecewise((3*I*d**3*sqrt(-1 + e**2*x**2/d**2)/(-15*d**2*x**5 + 15*e**2*x**7) - 4*I*d*e**2*x**2*sqrt(-1 + e**2*x**2/d**2)/(-15*d**2*x**5 + 15*e**2*x**7) + 2*I*e**6*x**6*sqrt(-1 + e**2*x**2/d**2)/(-15*d**5*x**5 + 15*d**3*e**2*x**7) - I*e**4*x**4*sqrt(-1 + e**2*x**2/d**2)/(-15*d**3*x**5 + 15*d*e**2*x**7), Abs(e**2*x**2/d**2) > 1), (3*d**3*sqrt(1 - e**2*x**2/d**2)/(-15*d**2*x**5 + 15*e**2*x**7) - 4*d*e**2*x**2*sqrt(1 - e**2*x**2/d**2)/(-15*d**2*x**5 + 15*e**2*x**7) + 2*e**6*x**6*sqrt(1 - e**2*x**2/d**2)/(-15*d**5*x**5 + 15*d**3*e**2*x**7) - e**4*x**4*sqrt(1 - e**2*x**2/d**2)/(-15*d**3*x**5 + 15*d*e**2*x**7), True)) + d**2*e*Piecewise((-d**2/(4*e*x**5*sqrt(d**2/(e**2*x**2) - 1)) + 3*e/(8*x**3*sqrt(d**2/(e**2*x**2) - 1)) - e**3/(8*d**2*x*sqrt(d**2/(e**2*x**2) - 1)) + e**4*acosh(d/(e*x))/(8*d**3), Abs(d**2/(e**2*x**2)) > 1), (I*d**2/(4*e*x**5*sqrt(-d**2/(e**2*x**2) + 1)) - 3*I*e/(8*x**3*sqrt(-d**2/(e**2*x**2) + 1)) + I*e**3/(8*d**2*x*sqrt(-d**2/(e**2*x**2) + 1)) - I*e**4*asin(d/(e*x))/(8*d**3), True)) - d*e**2*Piecewise((-e*sqrt(d**2/(e**2*x**2) - 1)/(3*x**2) + e**3*sqrt(d**2/(e**2*x**2) - 1)/(3*d**2), Abs(d**2/(e**2*x**2)) > 1), (-I*e*sqrt(-d**2/(e**2*x**2) + 1)/(3*x**2) + I*e**3*sqrt(-d**2/(e**2*x**2) + 1)/(3*d**2), True)) - e**3*Piecewise((-d**2/(2*e*x**3*sqrt(d**2/(e**2*x**2) - 1)) + e/(2*x*sqrt(d**2/(e**2*x**2) - 1)) + e**2*acosh(d/(e*x))/(2*d), Abs(d**2/(e**2*x**2)) > 1), (-I*e*sqrt(-d**2/(e**2*x**2) + 1)/(2*x) - I*e**2*asin(d/(e*x))/(2*d), True))","C",0
13,1,918,0,15.253824," ","integrate((e*x+d)*(-e**2*x**2+d**2)**(3/2)/x**7,x)","d^{3} \left(\begin{cases} - \frac{d^{2}}{6 e x^{7} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{5 e}{24 x^{5} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{e^{3}}{48 d^{2} x^{3} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} - \frac{e^{5}}{16 d^{4} x \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{e^{6} \operatorname{acosh}{\left(\frac{d}{e x} \right)}}{16 d^{5}} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\\frac{i d^{2}}{6 e x^{7} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} - \frac{5 i e}{24 x^{5} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} - \frac{i e^{3}}{48 d^{2} x^{3} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} + \frac{i e^{5}}{16 d^{4} x \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} - \frac{i e^{6} \operatorname{asin}{\left(\frac{d}{e x} \right)}}{16 d^{5}} & \text{otherwise} \end{cases}\right) + d^{2} e \left(\begin{cases} \frac{3 i d^{3} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{2} x^{5} + 15 e^{2} x^{7}} - \frac{4 i d e^{2} x^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{2} x^{5} + 15 e^{2} x^{7}} + \frac{2 i e^{6} x^{6} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{5} x^{5} + 15 d^{3} e^{2} x^{7}} - \frac{i e^{4} x^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{3} x^{5} + 15 d e^{2} x^{7}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{3 d^{3} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{2} x^{5} + 15 e^{2} x^{7}} - \frac{4 d e^{2} x^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{2} x^{5} + 15 e^{2} x^{7}} + \frac{2 e^{6} x^{6} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{5} x^{5} + 15 d^{3} e^{2} x^{7}} - \frac{e^{4} x^{4} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{3} x^{5} + 15 d e^{2} x^{7}} & \text{otherwise} \end{cases}\right) - d e^{2} \left(\begin{cases} - \frac{d^{2}}{4 e x^{5} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{3 e}{8 x^{3} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} - \frac{e^{3}}{8 d^{2} x \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{e^{4} \operatorname{acosh}{\left(\frac{d}{e x} \right)}}{8 d^{3}} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\\frac{i d^{2}}{4 e x^{5} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} - \frac{3 i e}{8 x^{3} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} + \frac{i e^{3}}{8 d^{2} x \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} - \frac{i e^{4} \operatorname{asin}{\left(\frac{d}{e x} \right)}}{8 d^{3}} & \text{otherwise} \end{cases}\right) - e^{3} \left(\begin{cases} - \frac{e \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}}{3 x^{2}} + \frac{e^{3} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}}{3 d^{2}} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\- \frac{i e \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{3 x^{2}} + \frac{i e^{3} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{3 d^{2}} & \text{otherwise} \end{cases}\right)"," ",0,"d**3*Piecewise((-d**2/(6*e*x**7*sqrt(d**2/(e**2*x**2) - 1)) + 5*e/(24*x**5*sqrt(d**2/(e**2*x**2) - 1)) + e**3/(48*d**2*x**3*sqrt(d**2/(e**2*x**2) - 1)) - e**5/(16*d**4*x*sqrt(d**2/(e**2*x**2) - 1)) + e**6*acosh(d/(e*x))/(16*d**5), Abs(d**2/(e**2*x**2)) > 1), (I*d**2/(6*e*x**7*sqrt(-d**2/(e**2*x**2) + 1)) - 5*I*e/(24*x**5*sqrt(-d**2/(e**2*x**2) + 1)) - I*e**3/(48*d**2*x**3*sqrt(-d**2/(e**2*x**2) + 1)) + I*e**5/(16*d**4*x*sqrt(-d**2/(e**2*x**2) + 1)) - I*e**6*asin(d/(e*x))/(16*d**5), True)) + d**2*e*Piecewise((3*I*d**3*sqrt(-1 + e**2*x**2/d**2)/(-15*d**2*x**5 + 15*e**2*x**7) - 4*I*d*e**2*x**2*sqrt(-1 + e**2*x**2/d**2)/(-15*d**2*x**5 + 15*e**2*x**7) + 2*I*e**6*x**6*sqrt(-1 + e**2*x**2/d**2)/(-15*d**5*x**5 + 15*d**3*e**2*x**7) - I*e**4*x**4*sqrt(-1 + e**2*x**2/d**2)/(-15*d**3*x**5 + 15*d*e**2*x**7), Abs(e**2*x**2/d**2) > 1), (3*d**3*sqrt(1 - e**2*x**2/d**2)/(-15*d**2*x**5 + 15*e**2*x**7) - 4*d*e**2*x**2*sqrt(1 - e**2*x**2/d**2)/(-15*d**2*x**5 + 15*e**2*x**7) + 2*e**6*x**6*sqrt(1 - e**2*x**2/d**2)/(-15*d**5*x**5 + 15*d**3*e**2*x**7) - e**4*x**4*sqrt(1 - e**2*x**2/d**2)/(-15*d**3*x**5 + 15*d*e**2*x**7), True)) - d*e**2*Piecewise((-d**2/(4*e*x**5*sqrt(d**2/(e**2*x**2) - 1)) + 3*e/(8*x**3*sqrt(d**2/(e**2*x**2) - 1)) - e**3/(8*d**2*x*sqrt(d**2/(e**2*x**2) - 1)) + e**4*acosh(d/(e*x))/(8*d**3), Abs(d**2/(e**2*x**2)) > 1), (I*d**2/(4*e*x**5*sqrt(-d**2/(e**2*x**2) + 1)) - 3*I*e/(8*x**3*sqrt(-d**2/(e**2*x**2) + 1)) + I*e**3/(8*d**2*x*sqrt(-d**2/(e**2*x**2) + 1)) - I*e**4*asin(d/(e*x))/(8*d**3), True)) - e**3*Piecewise((-e*sqrt(d**2/(e**2*x**2) - 1)/(3*x**2) + e**3*sqrt(d**2/(e**2*x**2) - 1)/(3*d**2), Abs(d**2/(e**2*x**2)) > 1), (-I*e*sqrt(-d**2/(e**2*x**2) + 1)/(3*x**2) + I*e**3*sqrt(-d**2/(e**2*x**2) + 1)/(3*d**2), True))","C",0
14,1,1037,0,16.620195," ","integrate((e*x+d)*(-e**2*x**2+d**2)**(3/2)/x**8,x)","d^{3} \left(\begin{cases} - \frac{e \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}}{7 x^{6}} + \frac{e^{3} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}}{35 d^{2} x^{4}} + \frac{4 e^{5} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}}{105 d^{4} x^{2}} + \frac{8 e^{7} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}}{105 d^{6}} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\- \frac{i e \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{7 x^{6}} + \frac{i e^{3} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{35 d^{2} x^{4}} + \frac{4 i e^{5} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{105 d^{4} x^{2}} + \frac{8 i e^{7} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{105 d^{6}} & \text{otherwise} \end{cases}\right) + d^{2} e \left(\begin{cases} - \frac{d^{2}}{6 e x^{7} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{5 e}{24 x^{5} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{e^{3}}{48 d^{2} x^{3} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} - \frac{e^{5}}{16 d^{4} x \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{e^{6} \operatorname{acosh}{\left(\frac{d}{e x} \right)}}{16 d^{5}} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\\frac{i d^{2}}{6 e x^{7} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} - \frac{5 i e}{24 x^{5} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} - \frac{i e^{3}}{48 d^{2} x^{3} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} + \frac{i e^{5}}{16 d^{4} x \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} - \frac{i e^{6} \operatorname{asin}{\left(\frac{d}{e x} \right)}}{16 d^{5}} & \text{otherwise} \end{cases}\right) - d e^{2} \left(\begin{cases} \frac{3 i d^{3} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{2} x^{5} + 15 e^{2} x^{7}} - \frac{4 i d e^{2} x^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{2} x^{5} + 15 e^{2} x^{7}} + \frac{2 i e^{6} x^{6} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{5} x^{5} + 15 d^{3} e^{2} x^{7}} - \frac{i e^{4} x^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{3} x^{5} + 15 d e^{2} x^{7}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{3 d^{3} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{2} x^{5} + 15 e^{2} x^{7}} - \frac{4 d e^{2} x^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{2} x^{5} + 15 e^{2} x^{7}} + \frac{2 e^{6} x^{6} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{5} x^{5} + 15 d^{3} e^{2} x^{7}} - \frac{e^{4} x^{4} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{3} x^{5} + 15 d e^{2} x^{7}} & \text{otherwise} \end{cases}\right) - e^{3} \left(\begin{cases} - \frac{d^{2}}{4 e x^{5} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{3 e}{8 x^{3} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} - \frac{e^{3}}{8 d^{2} x \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{e^{4} \operatorname{acosh}{\left(\frac{d}{e x} \right)}}{8 d^{3}} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\\frac{i d^{2}}{4 e x^{5} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} - \frac{3 i e}{8 x^{3} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} + \frac{i e^{3}}{8 d^{2} x \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} - \frac{i e^{4} \operatorname{asin}{\left(\frac{d}{e x} \right)}}{8 d^{3}} & \text{otherwise} \end{cases}\right)"," ",0,"d**3*Piecewise((-e*sqrt(d**2/(e**2*x**2) - 1)/(7*x**6) + e**3*sqrt(d**2/(e**2*x**2) - 1)/(35*d**2*x**4) + 4*e**5*sqrt(d**2/(e**2*x**2) - 1)/(105*d**4*x**2) + 8*e**7*sqrt(d**2/(e**2*x**2) - 1)/(105*d**6), Abs(d**2/(e**2*x**2)) > 1), (-I*e*sqrt(-d**2/(e**2*x**2) + 1)/(7*x**6) + I*e**3*sqrt(-d**2/(e**2*x**2) + 1)/(35*d**2*x**4) + 4*I*e**5*sqrt(-d**2/(e**2*x**2) + 1)/(105*d**4*x**2) + 8*I*e**7*sqrt(-d**2/(e**2*x**2) + 1)/(105*d**6), True)) + d**2*e*Piecewise((-d**2/(6*e*x**7*sqrt(d**2/(e**2*x**2) - 1)) + 5*e/(24*x**5*sqrt(d**2/(e**2*x**2) - 1)) + e**3/(48*d**2*x**3*sqrt(d**2/(e**2*x**2) - 1)) - e**5/(16*d**4*x*sqrt(d**2/(e**2*x**2) - 1)) + e**6*acosh(d/(e*x))/(16*d**5), Abs(d**2/(e**2*x**2)) > 1), (I*d**2/(6*e*x**7*sqrt(-d**2/(e**2*x**2) + 1)) - 5*I*e/(24*x**5*sqrt(-d**2/(e**2*x**2) + 1)) - I*e**3/(48*d**2*x**3*sqrt(-d**2/(e**2*x**2) + 1)) + I*e**5/(16*d**4*x*sqrt(-d**2/(e**2*x**2) + 1)) - I*e**6*asin(d/(e*x))/(16*d**5), True)) - d*e**2*Piecewise((3*I*d**3*sqrt(-1 + e**2*x**2/d**2)/(-15*d**2*x**5 + 15*e**2*x**7) - 4*I*d*e**2*x**2*sqrt(-1 + e**2*x**2/d**2)/(-15*d**2*x**5 + 15*e**2*x**7) + 2*I*e**6*x**6*sqrt(-1 + e**2*x**2/d**2)/(-15*d**5*x**5 + 15*d**3*e**2*x**7) - I*e**4*x**4*sqrt(-1 + e**2*x**2/d**2)/(-15*d**3*x**5 + 15*d*e**2*x**7), Abs(e**2*x**2/d**2) > 1), (3*d**3*sqrt(1 - e**2*x**2/d**2)/(-15*d**2*x**5 + 15*e**2*x**7) - 4*d*e**2*x**2*sqrt(1 - e**2*x**2/d**2)/(-15*d**2*x**5 + 15*e**2*x**7) + 2*e**6*x**6*sqrt(1 - e**2*x**2/d**2)/(-15*d**5*x**5 + 15*d**3*e**2*x**7) - e**4*x**4*sqrt(1 - e**2*x**2/d**2)/(-15*d**3*x**5 + 15*d*e**2*x**7), True)) - e**3*Piecewise((-d**2/(4*e*x**5*sqrt(d**2/(e**2*x**2) - 1)) + 3*e/(8*x**3*sqrt(d**2/(e**2*x**2) - 1)) - e**3/(8*d**2*x*sqrt(d**2/(e**2*x**2) - 1)) + e**4*acosh(d/(e*x))/(8*d**3), Abs(d**2/(e**2*x**2)) > 1), (I*d**2/(4*e*x**5*sqrt(-d**2/(e**2*x**2) + 1)) - 3*I*e/(8*x**3*sqrt(-d**2/(e**2*x**2) + 1)) + I*e**3/(8*d**2*x*sqrt(-d**2/(e**2*x**2) + 1)) - I*e**4*asin(d/(e*x))/(8*d**3), True))","C",0
15,1,1159,0,22.545147," ","integrate((e*x+d)*(-e**2*x**2+d**2)**(3/2)/x**9,x)","d^{3} \left(\begin{cases} - \frac{d^{2}}{8 e x^{9} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{7 e}{48 x^{7} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{e^{3}}{192 d^{2} x^{5} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{5 e^{5}}{384 d^{4} x^{3} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} - \frac{5 e^{7}}{128 d^{6} x \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{5 e^{8} \operatorname{acosh}{\left(\frac{d}{e x} \right)}}{128 d^{7}} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\\frac{i d^{2}}{8 e x^{9} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} - \frac{7 i e}{48 x^{7} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} - \frac{i e^{3}}{192 d^{2} x^{5} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} - \frac{5 i e^{5}}{384 d^{4} x^{3} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} + \frac{5 i e^{7}}{128 d^{6} x \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} - \frac{5 i e^{8} \operatorname{asin}{\left(\frac{d}{e x} \right)}}{128 d^{7}} & \text{otherwise} \end{cases}\right) + d^{2} e \left(\begin{cases} - \frac{e \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}}{7 x^{6}} + \frac{e^{3} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}}{35 d^{2} x^{4}} + \frac{4 e^{5} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}}{105 d^{4} x^{2}} + \frac{8 e^{7} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}}{105 d^{6}} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\- \frac{i e \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{7 x^{6}} + \frac{i e^{3} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{35 d^{2} x^{4}} + \frac{4 i e^{5} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{105 d^{4} x^{2}} + \frac{8 i e^{7} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{105 d^{6}} & \text{otherwise} \end{cases}\right) - d e^{2} \left(\begin{cases} - \frac{d^{2}}{6 e x^{7} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{5 e}{24 x^{5} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{e^{3}}{48 d^{2} x^{3} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} - \frac{e^{5}}{16 d^{4} x \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{e^{6} \operatorname{acosh}{\left(\frac{d}{e x} \right)}}{16 d^{5}} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\\frac{i d^{2}}{6 e x^{7} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} - \frac{5 i e}{24 x^{5} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} - \frac{i e^{3}}{48 d^{2} x^{3} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} + \frac{i e^{5}}{16 d^{4} x \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} - \frac{i e^{6} \operatorname{asin}{\left(\frac{d}{e x} \right)}}{16 d^{5}} & \text{otherwise} \end{cases}\right) - e^{3} \left(\begin{cases} \frac{3 i d^{3} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{2} x^{5} + 15 e^{2} x^{7}} - \frac{4 i d e^{2} x^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{2} x^{5} + 15 e^{2} x^{7}} + \frac{2 i e^{6} x^{6} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{5} x^{5} + 15 d^{3} e^{2} x^{7}} - \frac{i e^{4} x^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{3} x^{5} + 15 d e^{2} x^{7}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{3 d^{3} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{2} x^{5} + 15 e^{2} x^{7}} - \frac{4 d e^{2} x^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{2} x^{5} + 15 e^{2} x^{7}} + \frac{2 e^{6} x^{6} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{5} x^{5} + 15 d^{3} e^{2} x^{7}} - \frac{e^{4} x^{4} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{3} x^{5} + 15 d e^{2} x^{7}} & \text{otherwise} \end{cases}\right)"," ",0,"d**3*Piecewise((-d**2/(8*e*x**9*sqrt(d**2/(e**2*x**2) - 1)) + 7*e/(48*x**7*sqrt(d**2/(e**2*x**2) - 1)) + e**3/(192*d**2*x**5*sqrt(d**2/(e**2*x**2) - 1)) + 5*e**5/(384*d**4*x**3*sqrt(d**2/(e**2*x**2) - 1)) - 5*e**7/(128*d**6*x*sqrt(d**2/(e**2*x**2) - 1)) + 5*e**8*acosh(d/(e*x))/(128*d**7), Abs(d**2/(e**2*x**2)) > 1), (I*d**2/(8*e*x**9*sqrt(-d**2/(e**2*x**2) + 1)) - 7*I*e/(48*x**7*sqrt(-d**2/(e**2*x**2) + 1)) - I*e**3/(192*d**2*x**5*sqrt(-d**2/(e**2*x**2) + 1)) - 5*I*e**5/(384*d**4*x**3*sqrt(-d**2/(e**2*x**2) + 1)) + 5*I*e**7/(128*d**6*x*sqrt(-d**2/(e**2*x**2) + 1)) - 5*I*e**8*asin(d/(e*x))/(128*d**7), True)) + d**2*e*Piecewise((-e*sqrt(d**2/(e**2*x**2) - 1)/(7*x**6) + e**3*sqrt(d**2/(e**2*x**2) - 1)/(35*d**2*x**4) + 4*e**5*sqrt(d**2/(e**2*x**2) - 1)/(105*d**4*x**2) + 8*e**7*sqrt(d**2/(e**2*x**2) - 1)/(105*d**6), Abs(d**2/(e**2*x**2)) > 1), (-I*e*sqrt(-d**2/(e**2*x**2) + 1)/(7*x**6) + I*e**3*sqrt(-d**2/(e**2*x**2) + 1)/(35*d**2*x**4) + 4*I*e**5*sqrt(-d**2/(e**2*x**2) + 1)/(105*d**4*x**2) + 8*I*e**7*sqrt(-d**2/(e**2*x**2) + 1)/(105*d**6), True)) - d*e**2*Piecewise((-d**2/(6*e*x**7*sqrt(d**2/(e**2*x**2) - 1)) + 5*e/(24*x**5*sqrt(d**2/(e**2*x**2) - 1)) + e**3/(48*d**2*x**3*sqrt(d**2/(e**2*x**2) - 1)) - e**5/(16*d**4*x*sqrt(d**2/(e**2*x**2) - 1)) + e**6*acosh(d/(e*x))/(16*d**5), Abs(d**2/(e**2*x**2)) > 1), (I*d**2/(6*e*x**7*sqrt(-d**2/(e**2*x**2) + 1)) - 5*I*e/(24*x**5*sqrt(-d**2/(e**2*x**2) + 1)) - I*e**3/(48*d**2*x**3*sqrt(-d**2/(e**2*x**2) + 1)) + I*e**5/(16*d**4*x*sqrt(-d**2/(e**2*x**2) + 1)) - I*e**6*asin(d/(e*x))/(16*d**5), True)) - e**3*Piecewise((3*I*d**3*sqrt(-1 + e**2*x**2/d**2)/(-15*d**2*x**5 + 15*e**2*x**7) - 4*I*d*e**2*x**2*sqrt(-1 + e**2*x**2/d**2)/(-15*d**2*x**5 + 15*e**2*x**7) + 2*I*e**6*x**6*sqrt(-1 + e**2*x**2/d**2)/(-15*d**5*x**5 + 15*d**3*e**2*x**7) - I*e**4*x**4*sqrt(-1 + e**2*x**2/d**2)/(-15*d**3*x**5 + 15*d*e**2*x**7), Abs(e**2*x**2/d**2) > 1), (3*d**3*sqrt(1 - e**2*x**2/d**2)/(-15*d**2*x**5 + 15*e**2*x**7) - 4*d*e**2*x**2*sqrt(1 - e**2*x**2/d**2)/(-15*d**2*x**5 + 15*e**2*x**7) + 2*e**6*x**6*sqrt(1 - e**2*x**2/d**2)/(-15*d**5*x**5 + 15*d**3*e**2*x**7) - e**4*x**4*sqrt(1 - e**2*x**2/d**2)/(-15*d**3*x**5 + 15*d*e**2*x**7), True))","C",0
16,1,177,0,5.254340," ","integrate(x**2*(e*x+d)/(-e**2*x**2+d**2)**(1/2),x)","d \left(\begin{cases} - \frac{i d^{2} \operatorname{acosh}{\left(\frac{e x}{d} \right)}}{2 e^{3}} - \frac{i d x \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}}{2 e^{2}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{d^{2} \operatorname{asin}{\left(\frac{e x}{d} \right)}}{2 e^{3}} - \frac{d x}{2 e^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{x^{3}}{2 d \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} & \text{otherwise} \end{cases}\right) + e \left(\begin{cases} - \frac{2 d^{2} \sqrt{d^{2} - e^{2} x^{2}}}{3 e^{4}} - \frac{x^{2} \sqrt{d^{2} - e^{2} x^{2}}}{3 e^{2}} & \text{for}\: e \neq 0 \\\frac{x^{4}}{4 \sqrt{d^{2}}} & \text{otherwise} \end{cases}\right)"," ",0,"d*Piecewise((-I*d**2*acosh(e*x/d)/(2*e**3) - I*d*x*sqrt(-1 + e**2*x**2/d**2)/(2*e**2), Abs(e**2*x**2/d**2) > 1), (d**2*asin(e*x/d)/(2*e**3) - d*x/(2*e**2*sqrt(1 - e**2*x**2/d**2)) + x**3/(2*d*sqrt(1 - e**2*x**2/d**2)), True)) + e*Piecewise((-2*d**2*sqrt(d**2 - e**2*x**2)/(3*e**4) - x**2*sqrt(d**2 - e**2*x**2)/(3*e**2), Ne(e, 0)), (x**4/(4*sqrt(d**2)), True))","C",0
17,1,184,0,9.707516," ","integrate(x**2*(e*x+d)/(-e**2*x**2+d**2)**(3/2),x)","d \left(\begin{cases} \frac{i \operatorname{acosh}{\left(\frac{e x}{d} \right)}}{e^{3}} - \frac{i x}{d e^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\- \frac{\operatorname{asin}{\left(\frac{e x}{d} \right)}}{e^{3}} + \frac{x}{d e^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} & \text{otherwise} \end{cases}\right) + e \left(\begin{cases} \tilde{\infty} x^{4} & \text{for}\: \left(d = 0 \vee d = - \sqrt{e^{2} x^{2}} \vee d = \sqrt{e^{2} x^{2}}\right) \wedge \left(d = - \sqrt{e^{2} x^{2}} \vee d = \sqrt{e^{2} x^{2}} \vee e = 0\right) \\\frac{x^{4}}{4 \left(d^{2}\right)^{\frac{3}{2}}} & \text{for}\: e = 0 \\\frac{2 d^{2}}{e^{4} \sqrt{d^{2} - e^{2} x^{2}}} - \frac{x^{2}}{e^{2} \sqrt{d^{2} - e^{2} x^{2}}} & \text{otherwise} \end{cases}\right)"," ",0,"d*Piecewise((I*acosh(e*x/d)/e**3 - I*x/(d*e**2*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (-asin(e*x/d)/e**3 + x/(d*e**2*sqrt(1 - e**2*x**2/d**2)), True)) + e*Piecewise((zoo*x**4, (Eq(d, 0) | Eq(d, sqrt(e**2*x**2)) | Eq(d, -sqrt(e**2*x**2))) & (Eq(e, 0) | Eq(d, sqrt(e**2*x**2)) | Eq(d, -sqrt(e**2*x**2)))), (x**4/(4*(d**2)**(3/2)), Eq(e, 0)), (2*d**2/(e**4*sqrt(d**2 - e**2*x**2)) - x**2/(e**2*sqrt(d**2 - e**2*x**2)), True))","C",0
18,1,231,0,9.883257," ","integrate(x**2*(e*x+d)/(-e**2*x**2+d**2)**(5/2),x)","d \left(\begin{cases} \frac{i x^{3}}{- 3 d^{5} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}} + 3 d^{3} e^{2} x^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\- \frac{x^{3}}{- 3 d^{5} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}} + 3 d^{3} e^{2} x^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} & \text{otherwise} \end{cases}\right) + e \left(\begin{cases} \frac{2 d^{2}}{- 3 d^{2} e^{4} \sqrt{d^{2} - e^{2} x^{2}} + 3 e^{6} x^{2} \sqrt{d^{2} - e^{2} x^{2}}} - \frac{3 e^{2} x^{2}}{- 3 d^{2} e^{4} \sqrt{d^{2} - e^{2} x^{2}} + 3 e^{6} x^{2} \sqrt{d^{2} - e^{2} x^{2}}} & \text{for}\: e \neq 0 \\\frac{x^{4}}{4 \left(d^{2}\right)^{\frac{5}{2}}} & \text{otherwise} \end{cases}\right)"," ",0,"d*Piecewise((I*x**3/(-3*d**5*sqrt(-1 + e**2*x**2/d**2) + 3*d**3*e**2*x**2*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (-x**3/(-3*d**5*sqrt(1 - e**2*x**2/d**2) + 3*d**3*e**2*x**2*sqrt(1 - e**2*x**2/d**2)), True)) + e*Piecewise((2*d**2/(-3*d**2*e**4*sqrt(d**2 - e**2*x**2) + 3*e**6*x**2*sqrt(d**2 - e**2*x**2)) - 3*e**2*x**2/(-3*d**2*e**4*sqrt(d**2 - e**2*x**2) + 3*e**6*x**2*sqrt(d**2 - e**2*x**2)), Ne(e, 0)), (x**4/(4*(d**2)**(5/2)), True))","C",0
19,1,2004,0,66.418282," ","integrate(x**7*(e*x+d)/(-e**2*x**2+d**2)**(7/2),x)","d \left(\begin{cases} \frac{16 d^{6}}{5 d^{4} e^{8} \sqrt{d^{2} - e^{2} x^{2}} - 10 d^{2} e^{10} x^{2} \sqrt{d^{2} - e^{2} x^{2}} + 5 e^{12} x^{4} \sqrt{d^{2} - e^{2} x^{2}}} - \frac{40 d^{4} e^{2} x^{2}}{5 d^{4} e^{8} \sqrt{d^{2} - e^{2} x^{2}} - 10 d^{2} e^{10} x^{2} \sqrt{d^{2} - e^{2} x^{2}} + 5 e^{12} x^{4} \sqrt{d^{2} - e^{2} x^{2}}} + \frac{30 d^{2} e^{4} x^{4}}{5 d^{4} e^{8} \sqrt{d^{2} - e^{2} x^{2}} - 10 d^{2} e^{10} x^{2} \sqrt{d^{2} - e^{2} x^{2}} + 5 e^{12} x^{4} \sqrt{d^{2} - e^{2} x^{2}}} - \frac{5 e^{6} x^{6}}{5 d^{4} e^{8} \sqrt{d^{2} - e^{2} x^{2}} - 10 d^{2} e^{10} x^{2} \sqrt{d^{2} - e^{2} x^{2}} + 5 e^{12} x^{4} \sqrt{d^{2} - e^{2} x^{2}}} & \text{for}\: e \neq 0 \\\frac{x^{8}}{8 \left(d^{2}\right)^{\frac{7}{2}}} & \text{otherwise} \end{cases}\right) + e \left(\begin{cases} - \frac{210 i d^{7} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}} \operatorname{acosh}{\left(\frac{e x}{d} \right)}}{- 60 d^{5} e^{9} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}} + 120 d^{3} e^{11} x^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}} - 60 d e^{13} x^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + \frac{105 \pi d^{7} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}}{- 60 d^{5} e^{9} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}} + 120 d^{3} e^{11} x^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}} - 60 d e^{13} x^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + \frac{210 i d^{6} e x}{- 60 d^{5} e^{9} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}} + 120 d^{3} e^{11} x^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}} - 60 d e^{13} x^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + \frac{420 i d^{5} e^{2} x^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}} \operatorname{acosh}{\left(\frac{e x}{d} \right)}}{- 60 d^{5} e^{9} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}} + 120 d^{3} e^{11} x^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}} - 60 d e^{13} x^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{210 \pi d^{5} e^{2} x^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}}{- 60 d^{5} e^{9} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}} + 120 d^{3} e^{11} x^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}} - 60 d e^{13} x^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{490 i d^{4} e^{3} x^{3}}{- 60 d^{5} e^{9} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}} + 120 d^{3} e^{11} x^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}} - 60 d e^{13} x^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{210 i d^{3} e^{4} x^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}} \operatorname{acosh}{\left(\frac{e x}{d} \right)}}{- 60 d^{5} e^{9} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}} + 120 d^{3} e^{11} x^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}} - 60 d e^{13} x^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + \frac{105 \pi d^{3} e^{4} x^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}}{- 60 d^{5} e^{9} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}} + 120 d^{3} e^{11} x^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}} - 60 d e^{13} x^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + \frac{322 i d^{2} e^{5} x^{5}}{- 60 d^{5} e^{9} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}} + 120 d^{3} e^{11} x^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}} - 60 d e^{13} x^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{30 i e^{7} x^{7}}{- 60 d^{5} e^{9} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}} + 120 d^{3} e^{11} x^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}} - 60 d e^{13} x^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\- \frac{105 d^{7} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}} \operatorname{asin}{\left(\frac{e x}{d} \right)}}{30 d^{5} e^{9} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}} - 60 d^{3} e^{11} x^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}} + 30 d e^{13} x^{4} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{105 d^{6} e x}{30 d^{5} e^{9} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}} - 60 d^{3} e^{11} x^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}} + 30 d e^{13} x^{4} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{210 d^{5} e^{2} x^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}} \operatorname{asin}{\left(\frac{e x}{d} \right)}}{30 d^{5} e^{9} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}} - 60 d^{3} e^{11} x^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}} + 30 d e^{13} x^{4} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} - \frac{245 d^{4} e^{3} x^{3}}{30 d^{5} e^{9} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}} - 60 d^{3} e^{11} x^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}} + 30 d e^{13} x^{4} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} - \frac{105 d^{3} e^{4} x^{4} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}} \operatorname{asin}{\left(\frac{e x}{d} \right)}}{30 d^{5} e^{9} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}} - 60 d^{3} e^{11} x^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}} + 30 d e^{13} x^{4} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{161 d^{2} e^{5} x^{5}}{30 d^{5} e^{9} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}} - 60 d^{3} e^{11} x^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}} + 30 d e^{13} x^{4} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} - \frac{15 e^{7} x^{7}}{30 d^{5} e^{9} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}} - 60 d^{3} e^{11} x^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}} + 30 d e^{13} x^{4} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} & \text{otherwise} \end{cases}\right)"," ",0,"d*Piecewise((16*d**6/(5*d**4*e**8*sqrt(d**2 - e**2*x**2) - 10*d**2*e**10*x**2*sqrt(d**2 - e**2*x**2) + 5*e**12*x**4*sqrt(d**2 - e**2*x**2)) - 40*d**4*e**2*x**2/(5*d**4*e**8*sqrt(d**2 - e**2*x**2) - 10*d**2*e**10*x**2*sqrt(d**2 - e**2*x**2) + 5*e**12*x**4*sqrt(d**2 - e**2*x**2)) + 30*d**2*e**4*x**4/(5*d**4*e**8*sqrt(d**2 - e**2*x**2) - 10*d**2*e**10*x**2*sqrt(d**2 - e**2*x**2) + 5*e**12*x**4*sqrt(d**2 - e**2*x**2)) - 5*e**6*x**6/(5*d**4*e**8*sqrt(d**2 - e**2*x**2) - 10*d**2*e**10*x**2*sqrt(d**2 - e**2*x**2) + 5*e**12*x**4*sqrt(d**2 - e**2*x**2)), Ne(e, 0)), (x**8/(8*(d**2)**(7/2)), True)) + e*Piecewise((-210*I*d**7*sqrt(-1 + e**2*x**2/d**2)*acosh(e*x/d)/(-60*d**5*e**9*sqrt(-1 + e**2*x**2/d**2) + 120*d**3*e**11*x**2*sqrt(-1 + e**2*x**2/d**2) - 60*d*e**13*x**4*sqrt(-1 + e**2*x**2/d**2)) + 105*pi*d**7*sqrt(-1 + e**2*x**2/d**2)/(-60*d**5*e**9*sqrt(-1 + e**2*x**2/d**2) + 120*d**3*e**11*x**2*sqrt(-1 + e**2*x**2/d**2) - 60*d*e**13*x**4*sqrt(-1 + e**2*x**2/d**2)) + 210*I*d**6*e*x/(-60*d**5*e**9*sqrt(-1 + e**2*x**2/d**2) + 120*d**3*e**11*x**2*sqrt(-1 + e**2*x**2/d**2) - 60*d*e**13*x**4*sqrt(-1 + e**2*x**2/d**2)) + 420*I*d**5*e**2*x**2*sqrt(-1 + e**2*x**2/d**2)*acosh(e*x/d)/(-60*d**5*e**9*sqrt(-1 + e**2*x**2/d**2) + 120*d**3*e**11*x**2*sqrt(-1 + e**2*x**2/d**2) - 60*d*e**13*x**4*sqrt(-1 + e**2*x**2/d**2)) - 210*pi*d**5*e**2*x**2*sqrt(-1 + e**2*x**2/d**2)/(-60*d**5*e**9*sqrt(-1 + e**2*x**2/d**2) + 120*d**3*e**11*x**2*sqrt(-1 + e**2*x**2/d**2) - 60*d*e**13*x**4*sqrt(-1 + e**2*x**2/d**2)) - 490*I*d**4*e**3*x**3/(-60*d**5*e**9*sqrt(-1 + e**2*x**2/d**2) + 120*d**3*e**11*x**2*sqrt(-1 + e**2*x**2/d**2) - 60*d*e**13*x**4*sqrt(-1 + e**2*x**2/d**2)) - 210*I*d**3*e**4*x**4*sqrt(-1 + e**2*x**2/d**2)*acosh(e*x/d)/(-60*d**5*e**9*sqrt(-1 + e**2*x**2/d**2) + 120*d**3*e**11*x**2*sqrt(-1 + e**2*x**2/d**2) - 60*d*e**13*x**4*sqrt(-1 + e**2*x**2/d**2)) + 105*pi*d**3*e**4*x**4*sqrt(-1 + e**2*x**2/d**2)/(-60*d**5*e**9*sqrt(-1 + e**2*x**2/d**2) + 120*d**3*e**11*x**2*sqrt(-1 + e**2*x**2/d**2) - 60*d*e**13*x**4*sqrt(-1 + e**2*x**2/d**2)) + 322*I*d**2*e**5*x**5/(-60*d**5*e**9*sqrt(-1 + e**2*x**2/d**2) + 120*d**3*e**11*x**2*sqrt(-1 + e**2*x**2/d**2) - 60*d*e**13*x**4*sqrt(-1 + e**2*x**2/d**2)) - 30*I*e**7*x**7/(-60*d**5*e**9*sqrt(-1 + e**2*x**2/d**2) + 120*d**3*e**11*x**2*sqrt(-1 + e**2*x**2/d**2) - 60*d*e**13*x**4*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (-105*d**7*sqrt(1 - e**2*x**2/d**2)*asin(e*x/d)/(30*d**5*e**9*sqrt(1 - e**2*x**2/d**2) - 60*d**3*e**11*x**2*sqrt(1 - e**2*x**2/d**2) + 30*d*e**13*x**4*sqrt(1 - e**2*x**2/d**2)) + 105*d**6*e*x/(30*d**5*e**9*sqrt(1 - e**2*x**2/d**2) - 60*d**3*e**11*x**2*sqrt(1 - e**2*x**2/d**2) + 30*d*e**13*x**4*sqrt(1 - e**2*x**2/d**2)) + 210*d**5*e**2*x**2*sqrt(1 - e**2*x**2/d**2)*asin(e*x/d)/(30*d**5*e**9*sqrt(1 - e**2*x**2/d**2) - 60*d**3*e**11*x**2*sqrt(1 - e**2*x**2/d**2) + 30*d*e**13*x**4*sqrt(1 - e**2*x**2/d**2)) - 245*d**4*e**3*x**3/(30*d**5*e**9*sqrt(1 - e**2*x**2/d**2) - 60*d**3*e**11*x**2*sqrt(1 - e**2*x**2/d**2) + 30*d*e**13*x**4*sqrt(1 - e**2*x**2/d**2)) - 105*d**3*e**4*x**4*sqrt(1 - e**2*x**2/d**2)*asin(e*x/d)/(30*d**5*e**9*sqrt(1 - e**2*x**2/d**2) - 60*d**3*e**11*x**2*sqrt(1 - e**2*x**2/d**2) + 30*d*e**13*x**4*sqrt(1 - e**2*x**2/d**2)) + 161*d**2*e**5*x**5/(30*d**5*e**9*sqrt(1 - e**2*x**2/d**2) - 60*d**3*e**11*x**2*sqrt(1 - e**2*x**2/d**2) + 30*d*e**13*x**4*sqrt(1 - e**2*x**2/d**2)) - 15*e**7*x**7/(30*d**5*e**9*sqrt(1 - e**2*x**2/d**2) - 60*d**3*e**11*x**2*sqrt(1 - e**2*x**2/d**2) + 30*d*e**13*x**4*sqrt(1 - e**2*x**2/d**2)), True))","B",0
20,1,1821,0,62.080921," ","integrate(x**6*(e*x+d)/(-e**2*x**2+d**2)**(7/2),x)","d \left(\begin{cases} - \frac{30 i d^{5} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}} \operatorname{acosh}{\left(\frac{e x}{d} \right)}}{- 30 d^{5} e^{7} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}} + 60 d^{3} e^{9} x^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}} - 30 d e^{11} x^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + \frac{15 \pi d^{5} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}}{- 30 d^{5} e^{7} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}} + 60 d^{3} e^{9} x^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}} - 30 d e^{11} x^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + \frac{30 i d^{4} e x}{- 30 d^{5} e^{7} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}} + 60 d^{3} e^{9} x^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}} - 30 d e^{11} x^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + \frac{60 i d^{3} e^{2} x^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}} \operatorname{acosh}{\left(\frac{e x}{d} \right)}}{- 30 d^{5} e^{7} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}} + 60 d^{3} e^{9} x^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}} - 30 d e^{11} x^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{30 \pi d^{3} e^{2} x^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}}{- 30 d^{5} e^{7} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}} + 60 d^{3} e^{9} x^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}} - 30 d e^{11} x^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{70 i d^{2} e^{3} x^{3}}{- 30 d^{5} e^{7} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}} + 60 d^{3} e^{9} x^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}} - 30 d e^{11} x^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{30 i d e^{4} x^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}} \operatorname{acosh}{\left(\frac{e x}{d} \right)}}{- 30 d^{5} e^{7} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}} + 60 d^{3} e^{9} x^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}} - 30 d e^{11} x^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + \frac{15 \pi d e^{4} x^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}}{- 30 d^{5} e^{7} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}} + 60 d^{3} e^{9} x^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}} - 30 d e^{11} x^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + \frac{46 i e^{5} x^{5}}{- 30 d^{5} e^{7} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}} + 60 d^{3} e^{9} x^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}} - 30 d e^{11} x^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\- \frac{15 d^{5} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}} \operatorname{asin}{\left(\frac{e x}{d} \right)}}{15 d^{5} e^{7} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}} - 30 d^{3} e^{9} x^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}} + 15 d e^{11} x^{4} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{15 d^{4} e x}{15 d^{5} e^{7} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}} - 30 d^{3} e^{9} x^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}} + 15 d e^{11} x^{4} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{30 d^{3} e^{2} x^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}} \operatorname{asin}{\left(\frac{e x}{d} \right)}}{15 d^{5} e^{7} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}} - 30 d^{3} e^{9} x^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}} + 15 d e^{11} x^{4} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} - \frac{35 d^{2} e^{3} x^{3}}{15 d^{5} e^{7} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}} - 30 d^{3} e^{9} x^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}} + 15 d e^{11} x^{4} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} - \frac{15 d e^{4} x^{4} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}} \operatorname{asin}{\left(\frac{e x}{d} \right)}}{15 d^{5} e^{7} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}} - 30 d^{3} e^{9} x^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}} + 15 d e^{11} x^{4} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{23 e^{5} x^{5}}{15 d^{5} e^{7} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}} - 30 d^{3} e^{9} x^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}} + 15 d e^{11} x^{4} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} & \text{otherwise} \end{cases}\right) + e \left(\begin{cases} \frac{16 d^{6}}{5 d^{4} e^{8} \sqrt{d^{2} - e^{2} x^{2}} - 10 d^{2} e^{10} x^{2} \sqrt{d^{2} - e^{2} x^{2}} + 5 e^{12} x^{4} \sqrt{d^{2} - e^{2} x^{2}}} - \frac{40 d^{4} e^{2} x^{2}}{5 d^{4} e^{8} \sqrt{d^{2} - e^{2} x^{2}} - 10 d^{2} e^{10} x^{2} \sqrt{d^{2} - e^{2} x^{2}} + 5 e^{12} x^{4} \sqrt{d^{2} - e^{2} x^{2}}} + \frac{30 d^{2} e^{4} x^{4}}{5 d^{4} e^{8} \sqrt{d^{2} - e^{2} x^{2}} - 10 d^{2} e^{10} x^{2} \sqrt{d^{2} - e^{2} x^{2}} + 5 e^{12} x^{4} \sqrt{d^{2} - e^{2} x^{2}}} - \frac{5 e^{6} x^{6}}{5 d^{4} e^{8} \sqrt{d^{2} - e^{2} x^{2}} - 10 d^{2} e^{10} x^{2} \sqrt{d^{2} - e^{2} x^{2}} + 5 e^{12} x^{4} \sqrt{d^{2} - e^{2} x^{2}}} & \text{for}\: e \neq 0 \\\frac{x^{8}}{8 \left(d^{2}\right)^{\frac{7}{2}}} & \text{otherwise} \end{cases}\right)"," ",0,"d*Piecewise((-30*I*d**5*sqrt(-1 + e**2*x**2/d**2)*acosh(e*x/d)/(-30*d**5*e**7*sqrt(-1 + e**2*x**2/d**2) + 60*d**3*e**9*x**2*sqrt(-1 + e**2*x**2/d**2) - 30*d*e**11*x**4*sqrt(-1 + e**2*x**2/d**2)) + 15*pi*d**5*sqrt(-1 + e**2*x**2/d**2)/(-30*d**5*e**7*sqrt(-1 + e**2*x**2/d**2) + 60*d**3*e**9*x**2*sqrt(-1 + e**2*x**2/d**2) - 30*d*e**11*x**4*sqrt(-1 + e**2*x**2/d**2)) + 30*I*d**4*e*x/(-30*d**5*e**7*sqrt(-1 + e**2*x**2/d**2) + 60*d**3*e**9*x**2*sqrt(-1 + e**2*x**2/d**2) - 30*d*e**11*x**4*sqrt(-1 + e**2*x**2/d**2)) + 60*I*d**3*e**2*x**2*sqrt(-1 + e**2*x**2/d**2)*acosh(e*x/d)/(-30*d**5*e**7*sqrt(-1 + e**2*x**2/d**2) + 60*d**3*e**9*x**2*sqrt(-1 + e**2*x**2/d**2) - 30*d*e**11*x**4*sqrt(-1 + e**2*x**2/d**2)) - 30*pi*d**3*e**2*x**2*sqrt(-1 + e**2*x**2/d**2)/(-30*d**5*e**7*sqrt(-1 + e**2*x**2/d**2) + 60*d**3*e**9*x**2*sqrt(-1 + e**2*x**2/d**2) - 30*d*e**11*x**4*sqrt(-1 + e**2*x**2/d**2)) - 70*I*d**2*e**3*x**3/(-30*d**5*e**7*sqrt(-1 + e**2*x**2/d**2) + 60*d**3*e**9*x**2*sqrt(-1 + e**2*x**2/d**2) - 30*d*e**11*x**4*sqrt(-1 + e**2*x**2/d**2)) - 30*I*d*e**4*x**4*sqrt(-1 + e**2*x**2/d**2)*acosh(e*x/d)/(-30*d**5*e**7*sqrt(-1 + e**2*x**2/d**2) + 60*d**3*e**9*x**2*sqrt(-1 + e**2*x**2/d**2) - 30*d*e**11*x**4*sqrt(-1 + e**2*x**2/d**2)) + 15*pi*d*e**4*x**4*sqrt(-1 + e**2*x**2/d**2)/(-30*d**5*e**7*sqrt(-1 + e**2*x**2/d**2) + 60*d**3*e**9*x**2*sqrt(-1 + e**2*x**2/d**2) - 30*d*e**11*x**4*sqrt(-1 + e**2*x**2/d**2)) + 46*I*e**5*x**5/(-30*d**5*e**7*sqrt(-1 + e**2*x**2/d**2) + 60*d**3*e**9*x**2*sqrt(-1 + e**2*x**2/d**2) - 30*d*e**11*x**4*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (-15*d**5*sqrt(1 - e**2*x**2/d**2)*asin(e*x/d)/(15*d**5*e**7*sqrt(1 - e**2*x**2/d**2) - 30*d**3*e**9*x**2*sqrt(1 - e**2*x**2/d**2) + 15*d*e**11*x**4*sqrt(1 - e**2*x**2/d**2)) + 15*d**4*e*x/(15*d**5*e**7*sqrt(1 - e**2*x**2/d**2) - 30*d**3*e**9*x**2*sqrt(1 - e**2*x**2/d**2) + 15*d*e**11*x**4*sqrt(1 - e**2*x**2/d**2)) + 30*d**3*e**2*x**2*sqrt(1 - e**2*x**2/d**2)*asin(e*x/d)/(15*d**5*e**7*sqrt(1 - e**2*x**2/d**2) - 30*d**3*e**9*x**2*sqrt(1 - e**2*x**2/d**2) + 15*d*e**11*x**4*sqrt(1 - e**2*x**2/d**2)) - 35*d**2*e**3*x**3/(15*d**5*e**7*sqrt(1 - e**2*x**2/d**2) - 30*d**3*e**9*x**2*sqrt(1 - e**2*x**2/d**2) + 15*d*e**11*x**4*sqrt(1 - e**2*x**2/d**2)) - 15*d*e**4*x**4*sqrt(1 - e**2*x**2/d**2)*asin(e*x/d)/(15*d**5*e**7*sqrt(1 - e**2*x**2/d**2) - 30*d**3*e**9*x**2*sqrt(1 - e**2*x**2/d**2) + 15*d*e**11*x**4*sqrt(1 - e**2*x**2/d**2)) + 23*e**5*x**5/(15*d**5*e**7*sqrt(1 - e**2*x**2/d**2) - 30*d**3*e**9*x**2*sqrt(1 - e**2*x**2/d**2) + 15*d*e**11*x**4*sqrt(1 - e**2*x**2/d**2)), True)) + e*Piecewise((16*d**6/(5*d**4*e**8*sqrt(d**2 - e**2*x**2) - 10*d**2*e**10*x**2*sqrt(d**2 - e**2*x**2) + 5*e**12*x**4*sqrt(d**2 - e**2*x**2)) - 40*d**4*e**2*x**2/(5*d**4*e**8*sqrt(d**2 - e**2*x**2) - 10*d**2*e**10*x**2*sqrt(d**2 - e**2*x**2) + 5*e**12*x**4*sqrt(d**2 - e**2*x**2)) + 30*d**2*e**4*x**4/(5*d**4*e**8*sqrt(d**2 - e**2*x**2) - 10*d**2*e**10*x**2*sqrt(d**2 - e**2*x**2) + 5*e**12*x**4*sqrt(d**2 - e**2*x**2)) - 5*e**6*x**6/(5*d**4*e**8*sqrt(d**2 - e**2*x**2) - 10*d**2*e**10*x**2*sqrt(d**2 - e**2*x**2) + 5*e**12*x**4*sqrt(d**2 - e**2*x**2)), Ne(e, 0)), (x**8/(8*(d**2)**(7/2)), True))","C",0
21,1,1739,0,73.139616," ","integrate(x**5*(e*x+d)/(-e**2*x**2+d**2)**(7/2),x)","d \left(\begin{cases} \frac{8 d^{4}}{15 d^{4} e^{6} \sqrt{d^{2} - e^{2} x^{2}} - 30 d^{2} e^{8} x^{2} \sqrt{d^{2} - e^{2} x^{2}} + 15 e^{10} x^{4} \sqrt{d^{2} - e^{2} x^{2}}} - \frac{20 d^{2} e^{2} x^{2}}{15 d^{4} e^{6} \sqrt{d^{2} - e^{2} x^{2}} - 30 d^{2} e^{8} x^{2} \sqrt{d^{2} - e^{2} x^{2}} + 15 e^{10} x^{4} \sqrt{d^{2} - e^{2} x^{2}}} + \frac{15 e^{4} x^{4}}{15 d^{4} e^{6} \sqrt{d^{2} - e^{2} x^{2}} - 30 d^{2} e^{8} x^{2} \sqrt{d^{2} - e^{2} x^{2}} + 15 e^{10} x^{4} \sqrt{d^{2} - e^{2} x^{2}}} & \text{for}\: e \neq 0 \\\frac{x^{6}}{6 \left(d^{2}\right)^{\frac{7}{2}}} & \text{otherwise} \end{cases}\right) + e \left(\begin{cases} - \frac{30 i d^{5} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}} \operatorname{acosh}{\left(\frac{e x}{d} \right)}}{- 30 d^{5} e^{7} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}} + 60 d^{3} e^{9} x^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}} - 30 d e^{11} x^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + \frac{15 \pi d^{5} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}}{- 30 d^{5} e^{7} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}} + 60 d^{3} e^{9} x^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}} - 30 d e^{11} x^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + \frac{30 i d^{4} e x}{- 30 d^{5} e^{7} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}} + 60 d^{3} e^{9} x^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}} - 30 d e^{11} x^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + \frac{60 i d^{3} e^{2} x^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}} \operatorname{acosh}{\left(\frac{e x}{d} \right)}}{- 30 d^{5} e^{7} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}} + 60 d^{3} e^{9} x^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}} - 30 d e^{11} x^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{30 \pi d^{3} e^{2} x^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}}{- 30 d^{5} e^{7} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}} + 60 d^{3} e^{9} x^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}} - 30 d e^{11} x^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{70 i d^{2} e^{3} x^{3}}{- 30 d^{5} e^{7} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}} + 60 d^{3} e^{9} x^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}} - 30 d e^{11} x^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{30 i d e^{4} x^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}} \operatorname{acosh}{\left(\frac{e x}{d} \right)}}{- 30 d^{5} e^{7} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}} + 60 d^{3} e^{9} x^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}} - 30 d e^{11} x^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + \frac{15 \pi d e^{4} x^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}}{- 30 d^{5} e^{7} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}} + 60 d^{3} e^{9} x^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}} - 30 d e^{11} x^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + \frac{46 i e^{5} x^{5}}{- 30 d^{5} e^{7} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}} + 60 d^{3} e^{9} x^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}} - 30 d e^{11} x^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\- \frac{15 d^{5} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}} \operatorname{asin}{\left(\frac{e x}{d} \right)}}{15 d^{5} e^{7} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}} - 30 d^{3} e^{9} x^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}} + 15 d e^{11} x^{4} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{15 d^{4} e x}{15 d^{5} e^{7} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}} - 30 d^{3} e^{9} x^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}} + 15 d e^{11} x^{4} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{30 d^{3} e^{2} x^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}} \operatorname{asin}{\left(\frac{e x}{d} \right)}}{15 d^{5} e^{7} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}} - 30 d^{3} e^{9} x^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}} + 15 d e^{11} x^{4} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} - \frac{35 d^{2} e^{3} x^{3}}{15 d^{5} e^{7} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}} - 30 d^{3} e^{9} x^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}} + 15 d e^{11} x^{4} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} - \frac{15 d e^{4} x^{4} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}} \operatorname{asin}{\left(\frac{e x}{d} \right)}}{15 d^{5} e^{7} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}} - 30 d^{3} e^{9} x^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}} + 15 d e^{11} x^{4} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{23 e^{5} x^{5}}{15 d^{5} e^{7} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}} - 30 d^{3} e^{9} x^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}} + 15 d e^{11} x^{4} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} & \text{otherwise} \end{cases}\right)"," ",0,"d*Piecewise((8*d**4/(15*d**4*e**6*sqrt(d**2 - e**2*x**2) - 30*d**2*e**8*x**2*sqrt(d**2 - e**2*x**2) + 15*e**10*x**4*sqrt(d**2 - e**2*x**2)) - 20*d**2*e**2*x**2/(15*d**4*e**6*sqrt(d**2 - e**2*x**2) - 30*d**2*e**8*x**2*sqrt(d**2 - e**2*x**2) + 15*e**10*x**4*sqrt(d**2 - e**2*x**2)) + 15*e**4*x**4/(15*d**4*e**6*sqrt(d**2 - e**2*x**2) - 30*d**2*e**8*x**2*sqrt(d**2 - e**2*x**2) + 15*e**10*x**4*sqrt(d**2 - e**2*x**2)), Ne(e, 0)), (x**6/(6*(d**2)**(7/2)), True)) + e*Piecewise((-30*I*d**5*sqrt(-1 + e**2*x**2/d**2)*acosh(e*x/d)/(-30*d**5*e**7*sqrt(-1 + e**2*x**2/d**2) + 60*d**3*e**9*x**2*sqrt(-1 + e**2*x**2/d**2) - 30*d*e**11*x**4*sqrt(-1 + e**2*x**2/d**2)) + 15*pi*d**5*sqrt(-1 + e**2*x**2/d**2)/(-30*d**5*e**7*sqrt(-1 + e**2*x**2/d**2) + 60*d**3*e**9*x**2*sqrt(-1 + e**2*x**2/d**2) - 30*d*e**11*x**4*sqrt(-1 + e**2*x**2/d**2)) + 30*I*d**4*e*x/(-30*d**5*e**7*sqrt(-1 + e**2*x**2/d**2) + 60*d**3*e**9*x**2*sqrt(-1 + e**2*x**2/d**2) - 30*d*e**11*x**4*sqrt(-1 + e**2*x**2/d**2)) + 60*I*d**3*e**2*x**2*sqrt(-1 + e**2*x**2/d**2)*acosh(e*x/d)/(-30*d**5*e**7*sqrt(-1 + e**2*x**2/d**2) + 60*d**3*e**9*x**2*sqrt(-1 + e**2*x**2/d**2) - 30*d*e**11*x**4*sqrt(-1 + e**2*x**2/d**2)) - 30*pi*d**3*e**2*x**2*sqrt(-1 + e**2*x**2/d**2)/(-30*d**5*e**7*sqrt(-1 + e**2*x**2/d**2) + 60*d**3*e**9*x**2*sqrt(-1 + e**2*x**2/d**2) - 30*d*e**11*x**4*sqrt(-1 + e**2*x**2/d**2)) - 70*I*d**2*e**3*x**3/(-30*d**5*e**7*sqrt(-1 + e**2*x**2/d**2) + 60*d**3*e**9*x**2*sqrt(-1 + e**2*x**2/d**2) - 30*d*e**11*x**4*sqrt(-1 + e**2*x**2/d**2)) - 30*I*d*e**4*x**4*sqrt(-1 + e**2*x**2/d**2)*acosh(e*x/d)/(-30*d**5*e**7*sqrt(-1 + e**2*x**2/d**2) + 60*d**3*e**9*x**2*sqrt(-1 + e**2*x**2/d**2) - 30*d*e**11*x**4*sqrt(-1 + e**2*x**2/d**2)) + 15*pi*d*e**4*x**4*sqrt(-1 + e**2*x**2/d**2)/(-30*d**5*e**7*sqrt(-1 + e**2*x**2/d**2) + 60*d**3*e**9*x**2*sqrt(-1 + e**2*x**2/d**2) - 30*d*e**11*x**4*sqrt(-1 + e**2*x**2/d**2)) + 46*I*e**5*x**5/(-30*d**5*e**7*sqrt(-1 + e**2*x**2/d**2) + 60*d**3*e**9*x**2*sqrt(-1 + e**2*x**2/d**2) - 30*d*e**11*x**4*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (-15*d**5*sqrt(1 - e**2*x**2/d**2)*asin(e*x/d)/(15*d**5*e**7*sqrt(1 - e**2*x**2/d**2) - 30*d**3*e**9*x**2*sqrt(1 - e**2*x**2/d**2) + 15*d*e**11*x**4*sqrt(1 - e**2*x**2/d**2)) + 15*d**4*e*x/(15*d**5*e**7*sqrt(1 - e**2*x**2/d**2) - 30*d**3*e**9*x**2*sqrt(1 - e**2*x**2/d**2) + 15*d*e**11*x**4*sqrt(1 - e**2*x**2/d**2)) + 30*d**3*e**2*x**2*sqrt(1 - e**2*x**2/d**2)*asin(e*x/d)/(15*d**5*e**7*sqrt(1 - e**2*x**2/d**2) - 30*d**3*e**9*x**2*sqrt(1 - e**2*x**2/d**2) + 15*d*e**11*x**4*sqrt(1 - e**2*x**2/d**2)) - 35*d**2*e**3*x**3/(15*d**5*e**7*sqrt(1 - e**2*x**2/d**2) - 30*d**3*e**9*x**2*sqrt(1 - e**2*x**2/d**2) + 15*d*e**11*x**4*sqrt(1 - e**2*x**2/d**2)) - 15*d*e**4*x**4*sqrt(1 - e**2*x**2/d**2)*asin(e*x/d)/(15*d**5*e**7*sqrt(1 - e**2*x**2/d**2) - 30*d**3*e**9*x**2*sqrt(1 - e**2*x**2/d**2) + 15*d*e**11*x**4*sqrt(1 - e**2*x**2/d**2)) + 23*e**5*x**5/(15*d**5*e**7*sqrt(1 - e**2*x**2/d**2) - 30*d**3*e**9*x**2*sqrt(1 - e**2*x**2/d**2) + 15*d*e**11*x**4*sqrt(1 - e**2*x**2/d**2)), True))","B",0
22,1,418,0,63.868921," ","integrate(x**4*(e*x+d)/(-e**2*x**2+d**2)**(7/2),x)","d \left(\begin{cases} - \frac{i x^{5}}{5 d^{7} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}} - 10 d^{5} e^{2} x^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}} + 5 d^{3} e^{4} x^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{x^{5}}{5 d^{7} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}} - 10 d^{5} e^{2} x^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}} + 5 d^{3} e^{4} x^{4} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} & \text{otherwise} \end{cases}\right) + e \left(\begin{cases} \frac{8 d^{4}}{15 d^{4} e^{6} \sqrt{d^{2} - e^{2} x^{2}} - 30 d^{2} e^{8} x^{2} \sqrt{d^{2} - e^{2} x^{2}} + 15 e^{10} x^{4} \sqrt{d^{2} - e^{2} x^{2}}} - \frac{20 d^{2} e^{2} x^{2}}{15 d^{4} e^{6} \sqrt{d^{2} - e^{2} x^{2}} - 30 d^{2} e^{8} x^{2} \sqrt{d^{2} - e^{2} x^{2}} + 15 e^{10} x^{4} \sqrt{d^{2} - e^{2} x^{2}}} + \frac{15 e^{4} x^{4}}{15 d^{4} e^{6} \sqrt{d^{2} - e^{2} x^{2}} - 30 d^{2} e^{8} x^{2} \sqrt{d^{2} - e^{2} x^{2}} + 15 e^{10} x^{4} \sqrt{d^{2} - e^{2} x^{2}}} & \text{for}\: e \neq 0 \\\frac{x^{6}}{6 \left(d^{2}\right)^{\frac{7}{2}}} & \text{otherwise} \end{cases}\right)"," ",0,"d*Piecewise((-I*x**5/(5*d**7*sqrt(-1 + e**2*x**2/d**2) - 10*d**5*e**2*x**2*sqrt(-1 + e**2*x**2/d**2) + 5*d**3*e**4*x**4*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (x**5/(5*d**7*sqrt(1 - e**2*x**2/d**2) - 10*d**5*e**2*x**2*sqrt(1 - e**2*x**2/d**2) + 5*d**3*e**4*x**4*sqrt(1 - e**2*x**2/d**2)), True)) + e*Piecewise((8*d**4/(15*d**4*e**6*sqrt(d**2 - e**2*x**2) - 30*d**2*e**8*x**2*sqrt(d**2 - e**2*x**2) + 15*e**10*x**4*sqrt(d**2 - e**2*x**2)) - 20*d**2*e**2*x**2/(15*d**4*e**6*sqrt(d**2 - e**2*x**2) - 30*d**2*e**8*x**2*sqrt(d**2 - e**2*x**2) + 15*e**10*x**4*sqrt(d**2 - e**2*x**2)) + 15*e**4*x**4/(15*d**4*e**6*sqrt(d**2 - e**2*x**2) - 30*d**2*e**8*x**2*sqrt(d**2 - e**2*x**2) + 15*e**10*x**4*sqrt(d**2 - e**2*x**2)), Ne(e, 0)), (x**6/(6*(d**2)**(7/2)), True))","C",0
23,1,337,0,20.547566," ","integrate(x**3*(e*x+d)/(-e**2*x**2+d**2)**(7/2),x)","d \left(\begin{cases} - \frac{2 d^{2}}{15 d^{4} e^{4} \sqrt{d^{2} - e^{2} x^{2}} - 30 d^{2} e^{6} x^{2} \sqrt{d^{2} - e^{2} x^{2}} + 15 e^{8} x^{4} \sqrt{d^{2} - e^{2} x^{2}}} + \frac{5 e^{2} x^{2}}{15 d^{4} e^{4} \sqrt{d^{2} - e^{2} x^{2}} - 30 d^{2} e^{6} x^{2} \sqrt{d^{2} - e^{2} x^{2}} + 15 e^{8} x^{4} \sqrt{d^{2} - e^{2} x^{2}}} & \text{for}\: e \neq 0 \\\frac{x^{4}}{4 \left(d^{2}\right)^{\frac{7}{2}}} & \text{otherwise} \end{cases}\right) + e \left(\begin{cases} - \frac{i x^{5}}{5 d^{7} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}} - 10 d^{5} e^{2} x^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}} + 5 d^{3} e^{4} x^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{x^{5}}{5 d^{7} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}} - 10 d^{5} e^{2} x^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}} + 5 d^{3} e^{4} x^{4} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} & \text{otherwise} \end{cases}\right)"," ",0,"d*Piecewise((-2*d**2/(15*d**4*e**4*sqrt(d**2 - e**2*x**2) - 30*d**2*e**6*x**2*sqrt(d**2 - e**2*x**2) + 15*e**8*x**4*sqrt(d**2 - e**2*x**2)) + 5*e**2*x**2/(15*d**4*e**4*sqrt(d**2 - e**2*x**2) - 30*d**2*e**6*x**2*sqrt(d**2 - e**2*x**2) + 15*e**8*x**4*sqrt(d**2 - e**2*x**2)), Ne(e, 0)), (x**4/(4*(d**2)**(7/2)), True)) + e*Piecewise((-I*x**5/(5*d**7*sqrt(-1 + e**2*x**2/d**2) - 10*d**5*e**2*x**2*sqrt(-1 + e**2*x**2/d**2) + 5*d**3*e**4*x**4*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (x**5/(5*d**7*sqrt(1 - e**2*x**2/d**2) - 10*d**5*e**2*x**2*sqrt(1 - e**2*x**2/d**2) + 5*d**3*e**4*x**4*sqrt(1 - e**2*x**2/d**2)), True))","B",0
24,1,513,0,21.307925," ","integrate(x**2*(e*x+d)/(-e**2*x**2+d**2)**(7/2),x)","d \left(\begin{cases} - \frac{5 i d^{2} x^{3}}{15 d^{9} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}} - 30 d^{7} e^{2} x^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}} + 15 d^{5} e^{4} x^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + \frac{2 i e^{2} x^{5}}{15 d^{9} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}} - 30 d^{7} e^{2} x^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}} + 15 d^{5} e^{4} x^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{5 d^{2} x^{3}}{15 d^{9} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}} - 30 d^{7} e^{2} x^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}} + 15 d^{5} e^{4} x^{4} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} - \frac{2 e^{2} x^{5}}{15 d^{9} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}} - 30 d^{7} e^{2} x^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}} + 15 d^{5} e^{4} x^{4} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} & \text{otherwise} \end{cases}\right) + e \left(\begin{cases} - \frac{2 d^{2}}{15 d^{4} e^{4} \sqrt{d^{2} - e^{2} x^{2}} - 30 d^{2} e^{6} x^{2} \sqrt{d^{2} - e^{2} x^{2}} + 15 e^{8} x^{4} \sqrt{d^{2} - e^{2} x^{2}}} + \frac{5 e^{2} x^{2}}{15 d^{4} e^{4} \sqrt{d^{2} - e^{2} x^{2}} - 30 d^{2} e^{6} x^{2} \sqrt{d^{2} - e^{2} x^{2}} + 15 e^{8} x^{4} \sqrt{d^{2} - e^{2} x^{2}}} & \text{for}\: e \neq 0 \\\frac{x^{4}}{4 \left(d^{2}\right)^{\frac{7}{2}}} & \text{otherwise} \end{cases}\right)"," ",0,"d*Piecewise((-5*I*d**2*x**3/(15*d**9*sqrt(-1 + e**2*x**2/d**2) - 30*d**7*e**2*x**2*sqrt(-1 + e**2*x**2/d**2) + 15*d**5*e**4*x**4*sqrt(-1 + e**2*x**2/d**2)) + 2*I*e**2*x**5/(15*d**9*sqrt(-1 + e**2*x**2/d**2) - 30*d**7*e**2*x**2*sqrt(-1 + e**2*x**2/d**2) + 15*d**5*e**4*x**4*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (5*d**2*x**3/(15*d**9*sqrt(1 - e**2*x**2/d**2) - 30*d**7*e**2*x**2*sqrt(1 - e**2*x**2/d**2) + 15*d**5*e**4*x**4*sqrt(1 - e**2*x**2/d**2)) - 2*e**2*x**5/(15*d**9*sqrt(1 - e**2*x**2/d**2) - 30*d**7*e**2*x**2*sqrt(1 - e**2*x**2/d**2) + 15*d**5*e**4*x**4*sqrt(1 - e**2*x**2/d**2)), True)) + e*Piecewise((-2*d**2/(15*d**4*e**4*sqrt(d**2 - e**2*x**2) - 30*d**2*e**6*x**2*sqrt(d**2 - e**2*x**2) + 15*e**8*x**4*sqrt(d**2 - e**2*x**2)) + 5*e**2*x**2/(15*d**4*e**4*sqrt(d**2 - e**2*x**2) - 30*d**2*e**6*x**2*sqrt(d**2 - e**2*x**2) + 15*e**8*x**4*sqrt(d**2 - e**2*x**2)), Ne(e, 0)), (x**4/(4*(d**2)**(7/2)), True))","C",0
25,1,432,0,22.679085," ","integrate(x*(e*x+d)/(-e**2*x**2+d**2)**(7/2),x)","d \left(\begin{cases} \frac{1}{5 d^{4} e^{2} \sqrt{d^{2} - e^{2} x^{2}} - 10 d^{2} e^{4} x^{2} \sqrt{d^{2} - e^{2} x^{2}} + 5 e^{6} x^{4} \sqrt{d^{2} - e^{2} x^{2}}} & \text{for}\: e \neq 0 \\\frac{x^{2}}{2 \left(d^{2}\right)^{\frac{7}{2}}} & \text{otherwise} \end{cases}\right) + e \left(\begin{cases} - \frac{5 i d^{2} x^{3}}{15 d^{9} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}} - 30 d^{7} e^{2} x^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}} + 15 d^{5} e^{4} x^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + \frac{2 i e^{2} x^{5}}{15 d^{9} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}} - 30 d^{7} e^{2} x^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}} + 15 d^{5} e^{4} x^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{5 d^{2} x^{3}}{15 d^{9} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}} - 30 d^{7} e^{2} x^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}} + 15 d^{5} e^{4} x^{4} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} - \frac{2 e^{2} x^{5}}{15 d^{9} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}} - 30 d^{7} e^{2} x^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}} + 15 d^{5} e^{4} x^{4} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} & \text{otherwise} \end{cases}\right)"," ",0,"d*Piecewise((1/(5*d**4*e**2*sqrt(d**2 - e**2*x**2) - 10*d**2*e**4*x**2*sqrt(d**2 - e**2*x**2) + 5*e**6*x**4*sqrt(d**2 - e**2*x**2)), Ne(e, 0)), (x**2/(2*(d**2)**(7/2)), True)) + e*Piecewise((-5*I*d**2*x**3/(15*d**9*sqrt(-1 + e**2*x**2/d**2) - 30*d**7*e**2*x**2*sqrt(-1 + e**2*x**2/d**2) + 15*d**5*e**4*x**4*sqrt(-1 + e**2*x**2/d**2)) + 2*I*e**2*x**5/(15*d**9*sqrt(-1 + e**2*x**2/d**2) - 30*d**7*e**2*x**2*sqrt(-1 + e**2*x**2/d**2) + 15*d**5*e**4*x**4*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (5*d**2*x**3/(15*d**9*sqrt(1 - e**2*x**2/d**2) - 30*d**7*e**2*x**2*sqrt(1 - e**2*x**2/d**2) + 15*d**5*e**4*x**4*sqrt(1 - e**2*x**2/d**2)) - 2*e**2*x**5/(15*d**9*sqrt(1 - e**2*x**2/d**2) - 30*d**7*e**2*x**2*sqrt(1 - e**2*x**2/d**2) + 15*d**5*e**4*x**4*sqrt(1 - e**2*x**2/d**2)), True))","A",0
26,1,604,0,24.406337," ","integrate((e*x+d)/(-e**2*x**2+d**2)**(7/2),x)","d \left(\begin{cases} - \frac{15 i d^{4} x}{15 d^{11} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}} - 30 d^{9} e^{2} x^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}} + 15 d^{7} e^{4} x^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + \frac{20 i d^{2} e^{2} x^{3}}{15 d^{11} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}} - 30 d^{9} e^{2} x^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}} + 15 d^{7} e^{4} x^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{8 i e^{4} x^{5}}{15 d^{11} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}} - 30 d^{9} e^{2} x^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}} + 15 d^{7} e^{4} x^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{15 d^{4} x}{15 d^{11} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}} - 30 d^{9} e^{2} x^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}} + 15 d^{7} e^{4} x^{4} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} - \frac{20 d^{2} e^{2} x^{3}}{15 d^{11} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}} - 30 d^{9} e^{2} x^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}} + 15 d^{7} e^{4} x^{4} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{8 e^{4} x^{5}}{15 d^{11} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}} - 30 d^{9} e^{2} x^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}} + 15 d^{7} e^{4} x^{4} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} & \text{otherwise} \end{cases}\right) + e \left(\begin{cases} \frac{1}{5 d^{4} e^{2} \sqrt{d^{2} - e^{2} x^{2}} - 10 d^{2} e^{4} x^{2} \sqrt{d^{2} - e^{2} x^{2}} + 5 e^{6} x^{4} \sqrt{d^{2} - e^{2} x^{2}}} & \text{for}\: e \neq 0 \\\frac{x^{2}}{2 \left(d^{2}\right)^{\frac{7}{2}}} & \text{otherwise} \end{cases}\right)"," ",0,"d*Piecewise((-15*I*d**4*x/(15*d**11*sqrt(-1 + e**2*x**2/d**2) - 30*d**9*e**2*x**2*sqrt(-1 + e**2*x**2/d**2) + 15*d**7*e**4*x**4*sqrt(-1 + e**2*x**2/d**2)) + 20*I*d**2*e**2*x**3/(15*d**11*sqrt(-1 + e**2*x**2/d**2) - 30*d**9*e**2*x**2*sqrt(-1 + e**2*x**2/d**2) + 15*d**7*e**4*x**4*sqrt(-1 + e**2*x**2/d**2)) - 8*I*e**4*x**5/(15*d**11*sqrt(-1 + e**2*x**2/d**2) - 30*d**9*e**2*x**2*sqrt(-1 + e**2*x**2/d**2) + 15*d**7*e**4*x**4*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (15*d**4*x/(15*d**11*sqrt(1 - e**2*x**2/d**2) - 30*d**9*e**2*x**2*sqrt(1 - e**2*x**2/d**2) + 15*d**7*e**4*x**4*sqrt(1 - e**2*x**2/d**2)) - 20*d**2*e**2*x**3/(15*d**11*sqrt(1 - e**2*x**2/d**2) - 30*d**9*e**2*x**2*sqrt(1 - e**2*x**2/d**2) + 15*d**7*e**4*x**4*sqrt(1 - e**2*x**2/d**2)) + 8*e**4*x**5/(15*d**11*sqrt(1 - e**2*x**2/d**2) - 30*d**9*e**2*x**2*sqrt(1 - e**2*x**2/d**2) + 15*d**7*e**4*x**4*sqrt(1 - e**2*x**2/d**2)), True)) + e*Piecewise((1/(5*d**4*e**2*sqrt(d**2 - e**2*x**2) - 10*d**2*e**4*x**2*sqrt(d**2 - e**2*x**2) + 5*e**6*x**4*sqrt(d**2 - e**2*x**2)), Ne(e, 0)), (x**2/(2*(d**2)**(7/2)), True))","C",0
27,1,2378,0,41.141238," ","integrate((e*x+d)/x/(-e**2*x**2+d**2)**(7/2),x)","d \left(\begin{cases} \frac{46 i d^{6} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}}{30 d^{13} - 90 d^{11} e^{2} x^{2} + 90 d^{9} e^{4} x^{4} - 30 d^{7} e^{6} x^{6}} + \frac{15 d^{6} \log{\left(\frac{e^{2} x^{2}}{d^{2}} \right)}}{30 d^{13} - 90 d^{11} e^{2} x^{2} + 90 d^{9} e^{4} x^{4} - 30 d^{7} e^{6} x^{6}} - \frac{30 d^{6} \log{\left(\frac{e x}{d} \right)}}{30 d^{13} - 90 d^{11} e^{2} x^{2} + 90 d^{9} e^{4} x^{4} - 30 d^{7} e^{6} x^{6}} + \frac{30 i d^{6} \operatorname{asin}{\left(\frac{d}{e x} \right)}}{30 d^{13} - 90 d^{11} e^{2} x^{2} + 90 d^{9} e^{4} x^{4} - 30 d^{7} e^{6} x^{6}} - \frac{70 i d^{4} e^{2} x^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}}{30 d^{13} - 90 d^{11} e^{2} x^{2} + 90 d^{9} e^{4} x^{4} - 30 d^{7} e^{6} x^{6}} - \frac{45 d^{4} e^{2} x^{2} \log{\left(\frac{e^{2} x^{2}}{d^{2}} \right)}}{30 d^{13} - 90 d^{11} e^{2} x^{2} + 90 d^{9} e^{4} x^{4} - 30 d^{7} e^{6} x^{6}} + \frac{90 d^{4} e^{2} x^{2} \log{\left(\frac{e x}{d} \right)}}{30 d^{13} - 90 d^{11} e^{2} x^{2} + 90 d^{9} e^{4} x^{4} - 30 d^{7} e^{6} x^{6}} - \frac{90 i d^{4} e^{2} x^{2} \operatorname{asin}{\left(\frac{d}{e x} \right)}}{30 d^{13} - 90 d^{11} e^{2} x^{2} + 90 d^{9} e^{4} x^{4} - 30 d^{7} e^{6} x^{6}} + \frac{30 i d^{2} e^{4} x^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}}{30 d^{13} - 90 d^{11} e^{2} x^{2} + 90 d^{9} e^{4} x^{4} - 30 d^{7} e^{6} x^{6}} + \frac{45 d^{2} e^{4} x^{4} \log{\left(\frac{e^{2} x^{2}}{d^{2}} \right)}}{30 d^{13} - 90 d^{11} e^{2} x^{2} + 90 d^{9} e^{4} x^{4} - 30 d^{7} e^{6} x^{6}} - \frac{90 d^{2} e^{4} x^{4} \log{\left(\frac{e x}{d} \right)}}{30 d^{13} - 90 d^{11} e^{2} x^{2} + 90 d^{9} e^{4} x^{4} - 30 d^{7} e^{6} x^{6}} + \frac{90 i d^{2} e^{4} x^{4} \operatorname{asin}{\left(\frac{d}{e x} \right)}}{30 d^{13} - 90 d^{11} e^{2} x^{2} + 90 d^{9} e^{4} x^{4} - 30 d^{7} e^{6} x^{6}} - \frac{15 e^{6} x^{6} \log{\left(\frac{e^{2} x^{2}}{d^{2}} \right)}}{30 d^{13} - 90 d^{11} e^{2} x^{2} + 90 d^{9} e^{4} x^{4} - 30 d^{7} e^{6} x^{6}} + \frac{30 e^{6} x^{6} \log{\left(\frac{e x}{d} \right)}}{30 d^{13} - 90 d^{11} e^{2} x^{2} + 90 d^{9} e^{4} x^{4} - 30 d^{7} e^{6} x^{6}} - \frac{30 i e^{6} x^{6} \operatorname{asin}{\left(\frac{d}{e x} \right)}}{30 d^{13} - 90 d^{11} e^{2} x^{2} + 90 d^{9} e^{4} x^{4} - 30 d^{7} e^{6} x^{6}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{46 d^{6} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}}{30 d^{13} - 90 d^{11} e^{2} x^{2} + 90 d^{9} e^{4} x^{4} - 30 d^{7} e^{6} x^{6}} + \frac{15 d^{6} \log{\left(\frac{e^{2} x^{2}}{d^{2}} \right)}}{30 d^{13} - 90 d^{11} e^{2} x^{2} + 90 d^{9} e^{4} x^{4} - 30 d^{7} e^{6} x^{6}} - \frac{30 d^{6} \log{\left(\sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}} + 1 \right)}}{30 d^{13} - 90 d^{11} e^{2} x^{2} + 90 d^{9} e^{4} x^{4} - 30 d^{7} e^{6} x^{6}} + \frac{15 i \pi d^{6}}{30 d^{13} - 90 d^{11} e^{2} x^{2} + 90 d^{9} e^{4} x^{4} - 30 d^{7} e^{6} x^{6}} - \frac{70 d^{4} e^{2} x^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}}{30 d^{13} - 90 d^{11} e^{2} x^{2} + 90 d^{9} e^{4} x^{4} - 30 d^{7} e^{6} x^{6}} - \frac{45 d^{4} e^{2} x^{2} \log{\left(\frac{e^{2} x^{2}}{d^{2}} \right)}}{30 d^{13} - 90 d^{11} e^{2} x^{2} + 90 d^{9} e^{4} x^{4} - 30 d^{7} e^{6} x^{6}} + \frac{90 d^{4} e^{2} x^{2} \log{\left(\sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}} + 1 \right)}}{30 d^{13} - 90 d^{11} e^{2} x^{2} + 90 d^{9} e^{4} x^{4} - 30 d^{7} e^{6} x^{6}} - \frac{45 i \pi d^{4} e^{2} x^{2}}{30 d^{13} - 90 d^{11} e^{2} x^{2} + 90 d^{9} e^{4} x^{4} - 30 d^{7} e^{6} x^{6}} + \frac{30 d^{2} e^{4} x^{4} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}}{30 d^{13} - 90 d^{11} e^{2} x^{2} + 90 d^{9} e^{4} x^{4} - 30 d^{7} e^{6} x^{6}} + \frac{45 d^{2} e^{4} x^{4} \log{\left(\frac{e^{2} x^{2}}{d^{2}} \right)}}{30 d^{13} - 90 d^{11} e^{2} x^{2} + 90 d^{9} e^{4} x^{4} - 30 d^{7} e^{6} x^{6}} - \frac{90 d^{2} e^{4} x^{4} \log{\left(\sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}} + 1 \right)}}{30 d^{13} - 90 d^{11} e^{2} x^{2} + 90 d^{9} e^{4} x^{4} - 30 d^{7} e^{6} x^{6}} + \frac{45 i \pi d^{2} e^{4} x^{4}}{30 d^{13} - 90 d^{11} e^{2} x^{2} + 90 d^{9} e^{4} x^{4} - 30 d^{7} e^{6} x^{6}} - \frac{15 e^{6} x^{6} \log{\left(\frac{e^{2} x^{2}}{d^{2}} \right)}}{30 d^{13} - 90 d^{11} e^{2} x^{2} + 90 d^{9} e^{4} x^{4} - 30 d^{7} e^{6} x^{6}} + \frac{30 e^{6} x^{6} \log{\left(\sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}} + 1 \right)}}{30 d^{13} - 90 d^{11} e^{2} x^{2} + 90 d^{9} e^{4} x^{4} - 30 d^{7} e^{6} x^{6}} - \frac{15 i \pi e^{6} x^{6}}{30 d^{13} - 90 d^{11} e^{2} x^{2} + 90 d^{9} e^{4} x^{4} - 30 d^{7} e^{6} x^{6}} & \text{otherwise} \end{cases}\right) + e \left(\begin{cases} - \frac{15 i d^{4} x}{15 d^{11} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}} - 30 d^{9} e^{2} x^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}} + 15 d^{7} e^{4} x^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + \frac{20 i d^{2} e^{2} x^{3}}{15 d^{11} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}} - 30 d^{9} e^{2} x^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}} + 15 d^{7} e^{4} x^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{8 i e^{4} x^{5}}{15 d^{11} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}} - 30 d^{9} e^{2} x^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}} + 15 d^{7} e^{4} x^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{15 d^{4} x}{15 d^{11} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}} - 30 d^{9} e^{2} x^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}} + 15 d^{7} e^{4} x^{4} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} - \frac{20 d^{2} e^{2} x^{3}}{15 d^{11} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}} - 30 d^{9} e^{2} x^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}} + 15 d^{7} e^{4} x^{4} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{8 e^{4} x^{5}}{15 d^{11} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}} - 30 d^{9} e^{2} x^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}} + 15 d^{7} e^{4} x^{4} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} & \text{otherwise} \end{cases}\right)"," ",0,"d*Piecewise((46*I*d**6*sqrt(-1 + e**2*x**2/d**2)/(30*d**13 - 90*d**11*e**2*x**2 + 90*d**9*e**4*x**4 - 30*d**7*e**6*x**6) + 15*d**6*log(e**2*x**2/d**2)/(30*d**13 - 90*d**11*e**2*x**2 + 90*d**9*e**4*x**4 - 30*d**7*e**6*x**6) - 30*d**6*log(e*x/d)/(30*d**13 - 90*d**11*e**2*x**2 + 90*d**9*e**4*x**4 - 30*d**7*e**6*x**6) + 30*I*d**6*asin(d/(e*x))/(30*d**13 - 90*d**11*e**2*x**2 + 90*d**9*e**4*x**4 - 30*d**7*e**6*x**6) - 70*I*d**4*e**2*x**2*sqrt(-1 + e**2*x**2/d**2)/(30*d**13 - 90*d**11*e**2*x**2 + 90*d**9*e**4*x**4 - 30*d**7*e**6*x**6) - 45*d**4*e**2*x**2*log(e**2*x**2/d**2)/(30*d**13 - 90*d**11*e**2*x**2 + 90*d**9*e**4*x**4 - 30*d**7*e**6*x**6) + 90*d**4*e**2*x**2*log(e*x/d)/(30*d**13 - 90*d**11*e**2*x**2 + 90*d**9*e**4*x**4 - 30*d**7*e**6*x**6) - 90*I*d**4*e**2*x**2*asin(d/(e*x))/(30*d**13 - 90*d**11*e**2*x**2 + 90*d**9*e**4*x**4 - 30*d**7*e**6*x**6) + 30*I*d**2*e**4*x**4*sqrt(-1 + e**2*x**2/d**2)/(30*d**13 - 90*d**11*e**2*x**2 + 90*d**9*e**4*x**4 - 30*d**7*e**6*x**6) + 45*d**2*e**4*x**4*log(e**2*x**2/d**2)/(30*d**13 - 90*d**11*e**2*x**2 + 90*d**9*e**4*x**4 - 30*d**7*e**6*x**6) - 90*d**2*e**4*x**4*log(e*x/d)/(30*d**13 - 90*d**11*e**2*x**2 + 90*d**9*e**4*x**4 - 30*d**7*e**6*x**6) + 90*I*d**2*e**4*x**4*asin(d/(e*x))/(30*d**13 - 90*d**11*e**2*x**2 + 90*d**9*e**4*x**4 - 30*d**7*e**6*x**6) - 15*e**6*x**6*log(e**2*x**2/d**2)/(30*d**13 - 90*d**11*e**2*x**2 + 90*d**9*e**4*x**4 - 30*d**7*e**6*x**6) + 30*e**6*x**6*log(e*x/d)/(30*d**13 - 90*d**11*e**2*x**2 + 90*d**9*e**4*x**4 - 30*d**7*e**6*x**6) - 30*I*e**6*x**6*asin(d/(e*x))/(30*d**13 - 90*d**11*e**2*x**2 + 90*d**9*e**4*x**4 - 30*d**7*e**6*x**6), Abs(e**2*x**2/d**2) > 1), (46*d**6*sqrt(1 - e**2*x**2/d**2)/(30*d**13 - 90*d**11*e**2*x**2 + 90*d**9*e**4*x**4 - 30*d**7*e**6*x**6) + 15*d**6*log(e**2*x**2/d**2)/(30*d**13 - 90*d**11*e**2*x**2 + 90*d**9*e**4*x**4 - 30*d**7*e**6*x**6) - 30*d**6*log(sqrt(1 - e**2*x**2/d**2) + 1)/(30*d**13 - 90*d**11*e**2*x**2 + 90*d**9*e**4*x**4 - 30*d**7*e**6*x**6) + 15*I*pi*d**6/(30*d**13 - 90*d**11*e**2*x**2 + 90*d**9*e**4*x**4 - 30*d**7*e**6*x**6) - 70*d**4*e**2*x**2*sqrt(1 - e**2*x**2/d**2)/(30*d**13 - 90*d**11*e**2*x**2 + 90*d**9*e**4*x**4 - 30*d**7*e**6*x**6) - 45*d**4*e**2*x**2*log(e**2*x**2/d**2)/(30*d**13 - 90*d**11*e**2*x**2 + 90*d**9*e**4*x**4 - 30*d**7*e**6*x**6) + 90*d**4*e**2*x**2*log(sqrt(1 - e**2*x**2/d**2) + 1)/(30*d**13 - 90*d**11*e**2*x**2 + 90*d**9*e**4*x**4 - 30*d**7*e**6*x**6) - 45*I*pi*d**4*e**2*x**2/(30*d**13 - 90*d**11*e**2*x**2 + 90*d**9*e**4*x**4 - 30*d**7*e**6*x**6) + 30*d**2*e**4*x**4*sqrt(1 - e**2*x**2/d**2)/(30*d**13 - 90*d**11*e**2*x**2 + 90*d**9*e**4*x**4 - 30*d**7*e**6*x**6) + 45*d**2*e**4*x**4*log(e**2*x**2/d**2)/(30*d**13 - 90*d**11*e**2*x**2 + 90*d**9*e**4*x**4 - 30*d**7*e**6*x**6) - 90*d**2*e**4*x**4*log(sqrt(1 - e**2*x**2/d**2) + 1)/(30*d**13 - 90*d**11*e**2*x**2 + 90*d**9*e**4*x**4 - 30*d**7*e**6*x**6) + 45*I*pi*d**2*e**4*x**4/(30*d**13 - 90*d**11*e**2*x**2 + 90*d**9*e**4*x**4 - 30*d**7*e**6*x**6) - 15*e**6*x**6*log(e**2*x**2/d**2)/(30*d**13 - 90*d**11*e**2*x**2 + 90*d**9*e**4*x**4 - 30*d**7*e**6*x**6) + 30*e**6*x**6*log(sqrt(1 - e**2*x**2/d**2) + 1)/(30*d**13 - 90*d**11*e**2*x**2 + 90*d**9*e**4*x**4 - 30*d**7*e**6*x**6) - 15*I*pi*e**6*x**6/(30*d**13 - 90*d**11*e**2*x**2 + 90*d**9*e**4*x**4 - 30*d**7*e**6*x**6), True)) + e*Piecewise((-15*I*d**4*x/(15*d**11*sqrt(-1 + e**2*x**2/d**2) - 30*d**9*e**2*x**2*sqrt(-1 + e**2*x**2/d**2) + 15*d**7*e**4*x**4*sqrt(-1 + e**2*x**2/d**2)) + 20*I*d**2*e**2*x**3/(15*d**11*sqrt(-1 + e**2*x**2/d**2) - 30*d**9*e**2*x**2*sqrt(-1 + e**2*x**2/d**2) + 15*d**7*e**4*x**4*sqrt(-1 + e**2*x**2/d**2)) - 8*I*e**4*x**5/(15*d**11*sqrt(-1 + e**2*x**2/d**2) - 30*d**9*e**2*x**2*sqrt(-1 + e**2*x**2/d**2) + 15*d**7*e**4*x**4*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (15*d**4*x/(15*d**11*sqrt(1 - e**2*x**2/d**2) - 30*d**9*e**2*x**2*sqrt(1 - e**2*x**2/d**2) + 15*d**7*e**4*x**4*sqrt(1 - e**2*x**2/d**2)) - 20*d**2*e**2*x**3/(15*d**11*sqrt(1 - e**2*x**2/d**2) - 30*d**9*e**2*x**2*sqrt(1 - e**2*x**2/d**2) + 15*d**7*e**4*x**4*sqrt(1 - e**2*x**2/d**2)) + 8*e**4*x**5/(15*d**11*sqrt(1 - e**2*x**2/d**2) - 30*d**9*e**2*x**2*sqrt(1 - e**2*x**2/d**2) + 15*d**7*e**4*x**4*sqrt(1 - e**2*x**2/d**2)), True))","C",0
28,1,2404,0,31.224953," ","integrate((e*x+d)/x**2/(-e**2*x**2+d**2)**(7/2),x)","d \left(\begin{cases} \frac{5 d^{6} e \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}}{- 5 d^{14} + 15 d^{12} e^{2} x^{2} - 15 d^{10} e^{4} x^{4} + 5 d^{8} e^{6} x^{6}} - \frac{30 d^{4} e^{3} x^{2} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}}{- 5 d^{14} + 15 d^{12} e^{2} x^{2} - 15 d^{10} e^{4} x^{4} + 5 d^{8} e^{6} x^{6}} + \frac{40 d^{2} e^{5} x^{4} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}}{- 5 d^{14} + 15 d^{12} e^{2} x^{2} - 15 d^{10} e^{4} x^{4} + 5 d^{8} e^{6} x^{6}} - \frac{16 e^{7} x^{6} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}}{- 5 d^{14} + 15 d^{12} e^{2} x^{2} - 15 d^{10} e^{4} x^{4} + 5 d^{8} e^{6} x^{6}} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\\frac{5 i d^{6} e \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{- 5 d^{14} + 15 d^{12} e^{2} x^{2} - 15 d^{10} e^{4} x^{4} + 5 d^{8} e^{6} x^{6}} - \frac{30 i d^{4} e^{3} x^{2} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{- 5 d^{14} + 15 d^{12} e^{2} x^{2} - 15 d^{10} e^{4} x^{4} + 5 d^{8} e^{6} x^{6}} + \frac{40 i d^{2} e^{5} x^{4} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{- 5 d^{14} + 15 d^{12} e^{2} x^{2} - 15 d^{10} e^{4} x^{4} + 5 d^{8} e^{6} x^{6}} - \frac{16 i e^{7} x^{6} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{- 5 d^{14} + 15 d^{12} e^{2} x^{2} - 15 d^{10} e^{4} x^{4} + 5 d^{8} e^{6} x^{6}} & \text{otherwise} \end{cases}\right) + e \left(\begin{cases} \frac{46 i d^{6} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}}{30 d^{13} - 90 d^{11} e^{2} x^{2} + 90 d^{9} e^{4} x^{4} - 30 d^{7} e^{6} x^{6}} + \frac{15 d^{6} \log{\left(\frac{e^{2} x^{2}}{d^{2}} \right)}}{30 d^{13} - 90 d^{11} e^{2} x^{2} + 90 d^{9} e^{4} x^{4} - 30 d^{7} e^{6} x^{6}} - \frac{30 d^{6} \log{\left(\frac{e x}{d} \right)}}{30 d^{13} - 90 d^{11} e^{2} x^{2} + 90 d^{9} e^{4} x^{4} - 30 d^{7} e^{6} x^{6}} + \frac{30 i d^{6} \operatorname{asin}{\left(\frac{d}{e x} \right)}}{30 d^{13} - 90 d^{11} e^{2} x^{2} + 90 d^{9} e^{4} x^{4} - 30 d^{7} e^{6} x^{6}} - \frac{70 i d^{4} e^{2} x^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}}{30 d^{13} - 90 d^{11} e^{2} x^{2} + 90 d^{9} e^{4} x^{4} - 30 d^{7} e^{6} x^{6}} - \frac{45 d^{4} e^{2} x^{2} \log{\left(\frac{e^{2} x^{2}}{d^{2}} \right)}}{30 d^{13} - 90 d^{11} e^{2} x^{2} + 90 d^{9} e^{4} x^{4} - 30 d^{7} e^{6} x^{6}} + \frac{90 d^{4} e^{2} x^{2} \log{\left(\frac{e x}{d} \right)}}{30 d^{13} - 90 d^{11} e^{2} x^{2} + 90 d^{9} e^{4} x^{4} - 30 d^{7} e^{6} x^{6}} - \frac{90 i d^{4} e^{2} x^{2} \operatorname{asin}{\left(\frac{d}{e x} \right)}}{30 d^{13} - 90 d^{11} e^{2} x^{2} + 90 d^{9} e^{4} x^{4} - 30 d^{7} e^{6} x^{6}} + \frac{30 i d^{2} e^{4} x^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}}{30 d^{13} - 90 d^{11} e^{2} x^{2} + 90 d^{9} e^{4} x^{4} - 30 d^{7} e^{6} x^{6}} + \frac{45 d^{2} e^{4} x^{4} \log{\left(\frac{e^{2} x^{2}}{d^{2}} \right)}}{30 d^{13} - 90 d^{11} e^{2} x^{2} + 90 d^{9} e^{4} x^{4} - 30 d^{7} e^{6} x^{6}} - \frac{90 d^{2} e^{4} x^{4} \log{\left(\frac{e x}{d} \right)}}{30 d^{13} - 90 d^{11} e^{2} x^{2} + 90 d^{9} e^{4} x^{4} - 30 d^{7} e^{6} x^{6}} + \frac{90 i d^{2} e^{4} x^{4} \operatorname{asin}{\left(\frac{d}{e x} \right)}}{30 d^{13} - 90 d^{11} e^{2} x^{2} + 90 d^{9} e^{4} x^{4} - 30 d^{7} e^{6} x^{6}} - \frac{15 e^{6} x^{6} \log{\left(\frac{e^{2} x^{2}}{d^{2}} \right)}}{30 d^{13} - 90 d^{11} e^{2} x^{2} + 90 d^{9} e^{4} x^{4} - 30 d^{7} e^{6} x^{6}} + \frac{30 e^{6} x^{6} \log{\left(\frac{e x}{d} \right)}}{30 d^{13} - 90 d^{11} e^{2} x^{2} + 90 d^{9} e^{4} x^{4} - 30 d^{7} e^{6} x^{6}} - \frac{30 i e^{6} x^{6} \operatorname{asin}{\left(\frac{d}{e x} \right)}}{30 d^{13} - 90 d^{11} e^{2} x^{2} + 90 d^{9} e^{4} x^{4} - 30 d^{7} e^{6} x^{6}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{46 d^{6} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}}{30 d^{13} - 90 d^{11} e^{2} x^{2} + 90 d^{9} e^{4} x^{4} - 30 d^{7} e^{6} x^{6}} + \frac{15 d^{6} \log{\left(\frac{e^{2} x^{2}}{d^{2}} \right)}}{30 d^{13} - 90 d^{11} e^{2} x^{2} + 90 d^{9} e^{4} x^{4} - 30 d^{7} e^{6} x^{6}} - \frac{30 d^{6} \log{\left(\sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}} + 1 \right)}}{30 d^{13} - 90 d^{11} e^{2} x^{2} + 90 d^{9} e^{4} x^{4} - 30 d^{7} e^{6} x^{6}} + \frac{15 i \pi d^{6}}{30 d^{13} - 90 d^{11} e^{2} x^{2} + 90 d^{9} e^{4} x^{4} - 30 d^{7} e^{6} x^{6}} - \frac{70 d^{4} e^{2} x^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}}{30 d^{13} - 90 d^{11} e^{2} x^{2} + 90 d^{9} e^{4} x^{4} - 30 d^{7} e^{6} x^{6}} - \frac{45 d^{4} e^{2} x^{2} \log{\left(\frac{e^{2} x^{2}}{d^{2}} \right)}}{30 d^{13} - 90 d^{11} e^{2} x^{2} + 90 d^{9} e^{4} x^{4} - 30 d^{7} e^{6} x^{6}} + \frac{90 d^{4} e^{2} x^{2} \log{\left(\sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}} + 1 \right)}}{30 d^{13} - 90 d^{11} e^{2} x^{2} + 90 d^{9} e^{4} x^{4} - 30 d^{7} e^{6} x^{6}} - \frac{45 i \pi d^{4} e^{2} x^{2}}{30 d^{13} - 90 d^{11} e^{2} x^{2} + 90 d^{9} e^{4} x^{4} - 30 d^{7} e^{6} x^{6}} + \frac{30 d^{2} e^{4} x^{4} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}}{30 d^{13} - 90 d^{11} e^{2} x^{2} + 90 d^{9} e^{4} x^{4} - 30 d^{7} e^{6} x^{6}} + \frac{45 d^{2} e^{4} x^{4} \log{\left(\frac{e^{2} x^{2}}{d^{2}} \right)}}{30 d^{13} - 90 d^{11} e^{2} x^{2} + 90 d^{9} e^{4} x^{4} - 30 d^{7} e^{6} x^{6}} - \frac{90 d^{2} e^{4} x^{4} \log{\left(\sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}} + 1 \right)}}{30 d^{13} - 90 d^{11} e^{2} x^{2} + 90 d^{9} e^{4} x^{4} - 30 d^{7} e^{6} x^{6}} + \frac{45 i \pi d^{2} e^{4} x^{4}}{30 d^{13} - 90 d^{11} e^{2} x^{2} + 90 d^{9} e^{4} x^{4} - 30 d^{7} e^{6} x^{6}} - \frac{15 e^{6} x^{6} \log{\left(\frac{e^{2} x^{2}}{d^{2}} \right)}}{30 d^{13} - 90 d^{11} e^{2} x^{2} + 90 d^{9} e^{4} x^{4} - 30 d^{7} e^{6} x^{6}} + \frac{30 e^{6} x^{6} \log{\left(\sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}} + 1 \right)}}{30 d^{13} - 90 d^{11} e^{2} x^{2} + 90 d^{9} e^{4} x^{4} - 30 d^{7} e^{6} x^{6}} - \frac{15 i \pi e^{6} x^{6}}{30 d^{13} - 90 d^{11} e^{2} x^{2} + 90 d^{9} e^{4} x^{4} - 30 d^{7} e^{6} x^{6}} & \text{otherwise} \end{cases}\right)"," ",0,"d*Piecewise((5*d**6*e*sqrt(d**2/(e**2*x**2) - 1)/(-5*d**14 + 15*d**12*e**2*x**2 - 15*d**10*e**4*x**4 + 5*d**8*e**6*x**6) - 30*d**4*e**3*x**2*sqrt(d**2/(e**2*x**2) - 1)/(-5*d**14 + 15*d**12*e**2*x**2 - 15*d**10*e**4*x**4 + 5*d**8*e**6*x**6) + 40*d**2*e**5*x**4*sqrt(d**2/(e**2*x**2) - 1)/(-5*d**14 + 15*d**12*e**2*x**2 - 15*d**10*e**4*x**4 + 5*d**8*e**6*x**6) - 16*e**7*x**6*sqrt(d**2/(e**2*x**2) - 1)/(-5*d**14 + 15*d**12*e**2*x**2 - 15*d**10*e**4*x**4 + 5*d**8*e**6*x**6), Abs(d**2/(e**2*x**2)) > 1), (5*I*d**6*e*sqrt(-d**2/(e**2*x**2) + 1)/(-5*d**14 + 15*d**12*e**2*x**2 - 15*d**10*e**4*x**4 + 5*d**8*e**6*x**6) - 30*I*d**4*e**3*x**2*sqrt(-d**2/(e**2*x**2) + 1)/(-5*d**14 + 15*d**12*e**2*x**2 - 15*d**10*e**4*x**4 + 5*d**8*e**6*x**6) + 40*I*d**2*e**5*x**4*sqrt(-d**2/(e**2*x**2) + 1)/(-5*d**14 + 15*d**12*e**2*x**2 - 15*d**10*e**4*x**4 + 5*d**8*e**6*x**6) - 16*I*e**7*x**6*sqrt(-d**2/(e**2*x**2) + 1)/(-5*d**14 + 15*d**12*e**2*x**2 - 15*d**10*e**4*x**4 + 5*d**8*e**6*x**6), True)) + e*Piecewise((46*I*d**6*sqrt(-1 + e**2*x**2/d**2)/(30*d**13 - 90*d**11*e**2*x**2 + 90*d**9*e**4*x**4 - 30*d**7*e**6*x**6) + 15*d**6*log(e**2*x**2/d**2)/(30*d**13 - 90*d**11*e**2*x**2 + 90*d**9*e**4*x**4 - 30*d**7*e**6*x**6) - 30*d**6*log(e*x/d)/(30*d**13 - 90*d**11*e**2*x**2 + 90*d**9*e**4*x**4 - 30*d**7*e**6*x**6) + 30*I*d**6*asin(d/(e*x))/(30*d**13 - 90*d**11*e**2*x**2 + 90*d**9*e**4*x**4 - 30*d**7*e**6*x**6) - 70*I*d**4*e**2*x**2*sqrt(-1 + e**2*x**2/d**2)/(30*d**13 - 90*d**11*e**2*x**2 + 90*d**9*e**4*x**4 - 30*d**7*e**6*x**6) - 45*d**4*e**2*x**2*log(e**2*x**2/d**2)/(30*d**13 - 90*d**11*e**2*x**2 + 90*d**9*e**4*x**4 - 30*d**7*e**6*x**6) + 90*d**4*e**2*x**2*log(e*x/d)/(30*d**13 - 90*d**11*e**2*x**2 + 90*d**9*e**4*x**4 - 30*d**7*e**6*x**6) - 90*I*d**4*e**2*x**2*asin(d/(e*x))/(30*d**13 - 90*d**11*e**2*x**2 + 90*d**9*e**4*x**4 - 30*d**7*e**6*x**6) + 30*I*d**2*e**4*x**4*sqrt(-1 + e**2*x**2/d**2)/(30*d**13 - 90*d**11*e**2*x**2 + 90*d**9*e**4*x**4 - 30*d**7*e**6*x**6) + 45*d**2*e**4*x**4*log(e**2*x**2/d**2)/(30*d**13 - 90*d**11*e**2*x**2 + 90*d**9*e**4*x**4 - 30*d**7*e**6*x**6) - 90*d**2*e**4*x**4*log(e*x/d)/(30*d**13 - 90*d**11*e**2*x**2 + 90*d**9*e**4*x**4 - 30*d**7*e**6*x**6) + 90*I*d**2*e**4*x**4*asin(d/(e*x))/(30*d**13 - 90*d**11*e**2*x**2 + 90*d**9*e**4*x**4 - 30*d**7*e**6*x**6) - 15*e**6*x**6*log(e**2*x**2/d**2)/(30*d**13 - 90*d**11*e**2*x**2 + 90*d**9*e**4*x**4 - 30*d**7*e**6*x**6) + 30*e**6*x**6*log(e*x/d)/(30*d**13 - 90*d**11*e**2*x**2 + 90*d**9*e**4*x**4 - 30*d**7*e**6*x**6) - 30*I*e**6*x**6*asin(d/(e*x))/(30*d**13 - 90*d**11*e**2*x**2 + 90*d**9*e**4*x**4 - 30*d**7*e**6*x**6), Abs(e**2*x**2/d**2) > 1), (46*d**6*sqrt(1 - e**2*x**2/d**2)/(30*d**13 - 90*d**11*e**2*x**2 + 90*d**9*e**4*x**4 - 30*d**7*e**6*x**6) + 15*d**6*log(e**2*x**2/d**2)/(30*d**13 - 90*d**11*e**2*x**2 + 90*d**9*e**4*x**4 - 30*d**7*e**6*x**6) - 30*d**6*log(sqrt(1 - e**2*x**2/d**2) + 1)/(30*d**13 - 90*d**11*e**2*x**2 + 90*d**9*e**4*x**4 - 30*d**7*e**6*x**6) + 15*I*pi*d**6/(30*d**13 - 90*d**11*e**2*x**2 + 90*d**9*e**4*x**4 - 30*d**7*e**6*x**6) - 70*d**4*e**2*x**2*sqrt(1 - e**2*x**2/d**2)/(30*d**13 - 90*d**11*e**2*x**2 + 90*d**9*e**4*x**4 - 30*d**7*e**6*x**6) - 45*d**4*e**2*x**2*log(e**2*x**2/d**2)/(30*d**13 - 90*d**11*e**2*x**2 + 90*d**9*e**4*x**4 - 30*d**7*e**6*x**6) + 90*d**4*e**2*x**2*log(sqrt(1 - e**2*x**2/d**2) + 1)/(30*d**13 - 90*d**11*e**2*x**2 + 90*d**9*e**4*x**4 - 30*d**7*e**6*x**6) - 45*I*pi*d**4*e**2*x**2/(30*d**13 - 90*d**11*e**2*x**2 + 90*d**9*e**4*x**4 - 30*d**7*e**6*x**6) + 30*d**2*e**4*x**4*sqrt(1 - e**2*x**2/d**2)/(30*d**13 - 90*d**11*e**2*x**2 + 90*d**9*e**4*x**4 - 30*d**7*e**6*x**6) + 45*d**2*e**4*x**4*log(e**2*x**2/d**2)/(30*d**13 - 90*d**11*e**2*x**2 + 90*d**9*e**4*x**4 - 30*d**7*e**6*x**6) - 90*d**2*e**4*x**4*log(sqrt(1 - e**2*x**2/d**2) + 1)/(30*d**13 - 90*d**11*e**2*x**2 + 90*d**9*e**4*x**4 - 30*d**7*e**6*x**6) + 45*I*pi*d**2*e**4*x**4/(30*d**13 - 90*d**11*e**2*x**2 + 90*d**9*e**4*x**4 - 30*d**7*e**6*x**6) - 15*e**6*x**6*log(e**2*x**2/d**2)/(30*d**13 - 90*d**11*e**2*x**2 + 90*d**9*e**4*x**4 - 30*d**7*e**6*x**6) + 30*e**6*x**6*log(sqrt(1 - e**2*x**2/d**2) + 1)/(30*d**13 - 90*d**11*e**2*x**2 + 90*d**9*e**4*x**4 - 30*d**7*e**6*x**6) - 15*I*pi*e**6*x**6/(30*d**13 - 90*d**11*e**2*x**2 + 90*d**9*e**4*x**4 - 30*d**7*e**6*x**6), True))","C",0
29,1,2691,0,35.059883," ","integrate((e*x+d)/x**3/(-e**2*x**2+d**2)**(7/2),x)","d \left(\begin{cases} - \frac{30 i d^{8} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}}{60 d^{15} x^{2} - 180 d^{13} e^{2} x^{4} + 180 d^{11} e^{4} x^{6} - 60 d^{9} e^{6} x^{8}} + \frac{322 i d^{6} e^{2} x^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}}{60 d^{15} x^{2} - 180 d^{13} e^{2} x^{4} + 180 d^{11} e^{4} x^{6} - 60 d^{9} e^{6} x^{8}} + \frac{105 d^{6} e^{2} x^{2} \log{\left(\frac{e^{2} x^{2}}{d^{2}} \right)}}{60 d^{15} x^{2} - 180 d^{13} e^{2} x^{4} + 180 d^{11} e^{4} x^{6} - 60 d^{9} e^{6} x^{8}} - \frac{210 d^{6} e^{2} x^{2} \log{\left(\frac{e x}{d} \right)}}{60 d^{15} x^{2} - 180 d^{13} e^{2} x^{4} + 180 d^{11} e^{4} x^{6} - 60 d^{9} e^{6} x^{8}} + \frac{210 i d^{6} e^{2} x^{2} \operatorname{asin}{\left(\frac{d}{e x} \right)}}{60 d^{15} x^{2} - 180 d^{13} e^{2} x^{4} + 180 d^{11} e^{4} x^{6} - 60 d^{9} e^{6} x^{8}} - \frac{490 i d^{4} e^{4} x^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}}{60 d^{15} x^{2} - 180 d^{13} e^{2} x^{4} + 180 d^{11} e^{4} x^{6} - 60 d^{9} e^{6} x^{8}} - \frac{315 d^{4} e^{4} x^{4} \log{\left(\frac{e^{2} x^{2}}{d^{2}} \right)}}{60 d^{15} x^{2} - 180 d^{13} e^{2} x^{4} + 180 d^{11} e^{4} x^{6} - 60 d^{9} e^{6} x^{8}} + \frac{630 d^{4} e^{4} x^{4} \log{\left(\frac{e x}{d} \right)}}{60 d^{15} x^{2} - 180 d^{13} e^{2} x^{4} + 180 d^{11} e^{4} x^{6} - 60 d^{9} e^{6} x^{8}} - \frac{630 i d^{4} e^{4} x^{4} \operatorname{asin}{\left(\frac{d}{e x} \right)}}{60 d^{15} x^{2} - 180 d^{13} e^{2} x^{4} + 180 d^{11} e^{4} x^{6} - 60 d^{9} e^{6} x^{8}} + \frac{210 i d^{2} e^{6} x^{6} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}}{60 d^{15} x^{2} - 180 d^{13} e^{2} x^{4} + 180 d^{11} e^{4} x^{6} - 60 d^{9} e^{6} x^{8}} + \frac{315 d^{2} e^{6} x^{6} \log{\left(\frac{e^{2} x^{2}}{d^{2}} \right)}}{60 d^{15} x^{2} - 180 d^{13} e^{2} x^{4} + 180 d^{11} e^{4} x^{6} - 60 d^{9} e^{6} x^{8}} - \frac{630 d^{2} e^{6} x^{6} \log{\left(\frac{e x}{d} \right)}}{60 d^{15} x^{2} - 180 d^{13} e^{2} x^{4} + 180 d^{11} e^{4} x^{6} - 60 d^{9} e^{6} x^{8}} + \frac{630 i d^{2} e^{6} x^{6} \operatorname{asin}{\left(\frac{d}{e x} \right)}}{60 d^{15} x^{2} - 180 d^{13} e^{2} x^{4} + 180 d^{11} e^{4} x^{6} - 60 d^{9} e^{6} x^{8}} - \frac{105 e^{8} x^{8} \log{\left(\frac{e^{2} x^{2}}{d^{2}} \right)}}{60 d^{15} x^{2} - 180 d^{13} e^{2} x^{4} + 180 d^{11} e^{4} x^{6} - 60 d^{9} e^{6} x^{8}} + \frac{210 e^{8} x^{8} \log{\left(\frac{e x}{d} \right)}}{60 d^{15} x^{2} - 180 d^{13} e^{2} x^{4} + 180 d^{11} e^{4} x^{6} - 60 d^{9} e^{6} x^{8}} - \frac{210 i e^{8} x^{8} \operatorname{asin}{\left(\frac{d}{e x} \right)}}{60 d^{15} x^{2} - 180 d^{13} e^{2} x^{4} + 180 d^{11} e^{4} x^{6} - 60 d^{9} e^{6} x^{8}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{30 d^{8} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}}{- 60 d^{15} x^{2} + 180 d^{13} e^{2} x^{4} - 180 d^{11} e^{4} x^{6} + 60 d^{9} e^{6} x^{8}} - \frac{322 d^{6} e^{2} x^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}}{- 60 d^{15} x^{2} + 180 d^{13} e^{2} x^{4} - 180 d^{11} e^{4} x^{6} + 60 d^{9} e^{6} x^{8}} - \frac{105 d^{6} e^{2} x^{2} \log{\left(\frac{e^{2} x^{2}}{d^{2}} \right)}}{- 60 d^{15} x^{2} + 180 d^{13} e^{2} x^{4} - 180 d^{11} e^{4} x^{6} + 60 d^{9} e^{6} x^{8}} + \frac{210 d^{6} e^{2} x^{2} \log{\left(\sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}} + 1 \right)}}{- 60 d^{15} x^{2} + 180 d^{13} e^{2} x^{4} - 180 d^{11} e^{4} x^{6} + 60 d^{9} e^{6} x^{8}} - \frac{105 i \pi d^{6} e^{2} x^{2}}{- 60 d^{15} x^{2} + 180 d^{13} e^{2} x^{4} - 180 d^{11} e^{4} x^{6} + 60 d^{9} e^{6} x^{8}} + \frac{490 d^{4} e^{4} x^{4} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}}{- 60 d^{15} x^{2} + 180 d^{13} e^{2} x^{4} - 180 d^{11} e^{4} x^{6} + 60 d^{9} e^{6} x^{8}} + \frac{315 d^{4} e^{4} x^{4} \log{\left(\frac{e^{2} x^{2}}{d^{2}} \right)}}{- 60 d^{15} x^{2} + 180 d^{13} e^{2} x^{4} - 180 d^{11} e^{4} x^{6} + 60 d^{9} e^{6} x^{8}} - \frac{630 d^{4} e^{4} x^{4} \log{\left(\sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}} + 1 \right)}}{- 60 d^{15} x^{2} + 180 d^{13} e^{2} x^{4} - 180 d^{11} e^{4} x^{6} + 60 d^{9} e^{6} x^{8}} + \frac{315 i \pi d^{4} e^{4} x^{4}}{- 60 d^{15} x^{2} + 180 d^{13} e^{2} x^{4} - 180 d^{11} e^{4} x^{6} + 60 d^{9} e^{6} x^{8}} - \frac{210 d^{2} e^{6} x^{6} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}}{- 60 d^{15} x^{2} + 180 d^{13} e^{2} x^{4} - 180 d^{11} e^{4} x^{6} + 60 d^{9} e^{6} x^{8}} - \frac{315 d^{2} e^{6} x^{6} \log{\left(\frac{e^{2} x^{2}}{d^{2}} \right)}}{- 60 d^{15} x^{2} + 180 d^{13} e^{2} x^{4} - 180 d^{11} e^{4} x^{6} + 60 d^{9} e^{6} x^{8}} + \frac{630 d^{2} e^{6} x^{6} \log{\left(\sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}} + 1 \right)}}{- 60 d^{15} x^{2} + 180 d^{13} e^{2} x^{4} - 180 d^{11} e^{4} x^{6} + 60 d^{9} e^{6} x^{8}} - \frac{315 i \pi d^{2} e^{6} x^{6}}{- 60 d^{15} x^{2} + 180 d^{13} e^{2} x^{4} - 180 d^{11} e^{4} x^{6} + 60 d^{9} e^{6} x^{8}} + \frac{105 e^{8} x^{8} \log{\left(\frac{e^{2} x^{2}}{d^{2}} \right)}}{- 60 d^{15} x^{2} + 180 d^{13} e^{2} x^{4} - 180 d^{11} e^{4} x^{6} + 60 d^{9} e^{6} x^{8}} - \frac{210 e^{8} x^{8} \log{\left(\sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}} + 1 \right)}}{- 60 d^{15} x^{2} + 180 d^{13} e^{2} x^{4} - 180 d^{11} e^{4} x^{6} + 60 d^{9} e^{6} x^{8}} + \frac{105 i \pi e^{8} x^{8}}{- 60 d^{15} x^{2} + 180 d^{13} e^{2} x^{4} - 180 d^{11} e^{4} x^{6} + 60 d^{9} e^{6} x^{8}} & \text{otherwise} \end{cases}\right) + e \left(\begin{cases} \frac{5 d^{6} e \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}}{- 5 d^{14} + 15 d^{12} e^{2} x^{2} - 15 d^{10} e^{4} x^{4} + 5 d^{8} e^{6} x^{6}} - \frac{30 d^{4} e^{3} x^{2} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}}{- 5 d^{14} + 15 d^{12} e^{2} x^{2} - 15 d^{10} e^{4} x^{4} + 5 d^{8} e^{6} x^{6}} + \frac{40 d^{2} e^{5} x^{4} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}}{- 5 d^{14} + 15 d^{12} e^{2} x^{2} - 15 d^{10} e^{4} x^{4} + 5 d^{8} e^{6} x^{6}} - \frac{16 e^{7} x^{6} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}}{- 5 d^{14} + 15 d^{12} e^{2} x^{2} - 15 d^{10} e^{4} x^{4} + 5 d^{8} e^{6} x^{6}} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\\frac{5 i d^{6} e \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{- 5 d^{14} + 15 d^{12} e^{2} x^{2} - 15 d^{10} e^{4} x^{4} + 5 d^{8} e^{6} x^{6}} - \frac{30 i d^{4} e^{3} x^{2} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{- 5 d^{14} + 15 d^{12} e^{2} x^{2} - 15 d^{10} e^{4} x^{4} + 5 d^{8} e^{6} x^{6}} + \frac{40 i d^{2} e^{5} x^{4} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{- 5 d^{14} + 15 d^{12} e^{2} x^{2} - 15 d^{10} e^{4} x^{4} + 5 d^{8} e^{6} x^{6}} - \frac{16 i e^{7} x^{6} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{- 5 d^{14} + 15 d^{12} e^{2} x^{2} - 15 d^{10} e^{4} x^{4} + 5 d^{8} e^{6} x^{6}} & \text{otherwise} \end{cases}\right)"," ",0,"d*Piecewise((-30*I*d**8*sqrt(-1 + e**2*x**2/d**2)/(60*d**15*x**2 - 180*d**13*e**2*x**4 + 180*d**11*e**4*x**6 - 60*d**9*e**6*x**8) + 322*I*d**6*e**2*x**2*sqrt(-1 + e**2*x**2/d**2)/(60*d**15*x**2 - 180*d**13*e**2*x**4 + 180*d**11*e**4*x**6 - 60*d**9*e**6*x**8) + 105*d**6*e**2*x**2*log(e**2*x**2/d**2)/(60*d**15*x**2 - 180*d**13*e**2*x**4 + 180*d**11*e**4*x**6 - 60*d**9*e**6*x**8) - 210*d**6*e**2*x**2*log(e*x/d)/(60*d**15*x**2 - 180*d**13*e**2*x**4 + 180*d**11*e**4*x**6 - 60*d**9*e**6*x**8) + 210*I*d**6*e**2*x**2*asin(d/(e*x))/(60*d**15*x**2 - 180*d**13*e**2*x**4 + 180*d**11*e**4*x**6 - 60*d**9*e**6*x**8) - 490*I*d**4*e**4*x**4*sqrt(-1 + e**2*x**2/d**2)/(60*d**15*x**2 - 180*d**13*e**2*x**4 + 180*d**11*e**4*x**6 - 60*d**9*e**6*x**8) - 315*d**4*e**4*x**4*log(e**2*x**2/d**2)/(60*d**15*x**2 - 180*d**13*e**2*x**4 + 180*d**11*e**4*x**6 - 60*d**9*e**6*x**8) + 630*d**4*e**4*x**4*log(e*x/d)/(60*d**15*x**2 - 180*d**13*e**2*x**4 + 180*d**11*e**4*x**6 - 60*d**9*e**6*x**8) - 630*I*d**4*e**4*x**4*asin(d/(e*x))/(60*d**15*x**2 - 180*d**13*e**2*x**4 + 180*d**11*e**4*x**6 - 60*d**9*e**6*x**8) + 210*I*d**2*e**6*x**6*sqrt(-1 + e**2*x**2/d**2)/(60*d**15*x**2 - 180*d**13*e**2*x**4 + 180*d**11*e**4*x**6 - 60*d**9*e**6*x**8) + 315*d**2*e**6*x**6*log(e**2*x**2/d**2)/(60*d**15*x**2 - 180*d**13*e**2*x**4 + 180*d**11*e**4*x**6 - 60*d**9*e**6*x**8) - 630*d**2*e**6*x**6*log(e*x/d)/(60*d**15*x**2 - 180*d**13*e**2*x**4 + 180*d**11*e**4*x**6 - 60*d**9*e**6*x**8) + 630*I*d**2*e**6*x**6*asin(d/(e*x))/(60*d**15*x**2 - 180*d**13*e**2*x**4 + 180*d**11*e**4*x**6 - 60*d**9*e**6*x**8) - 105*e**8*x**8*log(e**2*x**2/d**2)/(60*d**15*x**2 - 180*d**13*e**2*x**4 + 180*d**11*e**4*x**6 - 60*d**9*e**6*x**8) + 210*e**8*x**8*log(e*x/d)/(60*d**15*x**2 - 180*d**13*e**2*x**4 + 180*d**11*e**4*x**6 - 60*d**9*e**6*x**8) - 210*I*e**8*x**8*asin(d/(e*x))/(60*d**15*x**2 - 180*d**13*e**2*x**4 + 180*d**11*e**4*x**6 - 60*d**9*e**6*x**8), Abs(e**2*x**2/d**2) > 1), (30*d**8*sqrt(1 - e**2*x**2/d**2)/(-60*d**15*x**2 + 180*d**13*e**2*x**4 - 180*d**11*e**4*x**6 + 60*d**9*e**6*x**8) - 322*d**6*e**2*x**2*sqrt(1 - e**2*x**2/d**2)/(-60*d**15*x**2 + 180*d**13*e**2*x**4 - 180*d**11*e**4*x**6 + 60*d**9*e**6*x**8) - 105*d**6*e**2*x**2*log(e**2*x**2/d**2)/(-60*d**15*x**2 + 180*d**13*e**2*x**4 - 180*d**11*e**4*x**6 + 60*d**9*e**6*x**8) + 210*d**6*e**2*x**2*log(sqrt(1 - e**2*x**2/d**2) + 1)/(-60*d**15*x**2 + 180*d**13*e**2*x**4 - 180*d**11*e**4*x**6 + 60*d**9*e**6*x**8) - 105*I*pi*d**6*e**2*x**2/(-60*d**15*x**2 + 180*d**13*e**2*x**4 - 180*d**11*e**4*x**6 + 60*d**9*e**6*x**8) + 490*d**4*e**4*x**4*sqrt(1 - e**2*x**2/d**2)/(-60*d**15*x**2 + 180*d**13*e**2*x**4 - 180*d**11*e**4*x**6 + 60*d**9*e**6*x**8) + 315*d**4*e**4*x**4*log(e**2*x**2/d**2)/(-60*d**15*x**2 + 180*d**13*e**2*x**4 - 180*d**11*e**4*x**6 + 60*d**9*e**6*x**8) - 630*d**4*e**4*x**4*log(sqrt(1 - e**2*x**2/d**2) + 1)/(-60*d**15*x**2 + 180*d**13*e**2*x**4 - 180*d**11*e**4*x**6 + 60*d**9*e**6*x**8) + 315*I*pi*d**4*e**4*x**4/(-60*d**15*x**2 + 180*d**13*e**2*x**4 - 180*d**11*e**4*x**6 + 60*d**9*e**6*x**8) - 210*d**2*e**6*x**6*sqrt(1 - e**2*x**2/d**2)/(-60*d**15*x**2 + 180*d**13*e**2*x**4 - 180*d**11*e**4*x**6 + 60*d**9*e**6*x**8) - 315*d**2*e**6*x**6*log(e**2*x**2/d**2)/(-60*d**15*x**2 + 180*d**13*e**2*x**4 - 180*d**11*e**4*x**6 + 60*d**9*e**6*x**8) + 630*d**2*e**6*x**6*log(sqrt(1 - e**2*x**2/d**2) + 1)/(-60*d**15*x**2 + 180*d**13*e**2*x**4 - 180*d**11*e**4*x**6 + 60*d**9*e**6*x**8) - 315*I*pi*d**2*e**6*x**6/(-60*d**15*x**2 + 180*d**13*e**2*x**4 - 180*d**11*e**4*x**6 + 60*d**9*e**6*x**8) + 105*e**8*x**8*log(e**2*x**2/d**2)/(-60*d**15*x**2 + 180*d**13*e**2*x**4 - 180*d**11*e**4*x**6 + 60*d**9*e**6*x**8) - 210*e**8*x**8*log(sqrt(1 - e**2*x**2/d**2) + 1)/(-60*d**15*x**2 + 180*d**13*e**2*x**4 - 180*d**11*e**4*x**6 + 60*d**9*e**6*x**8) + 105*I*pi*e**8*x**8/(-60*d**15*x**2 + 180*d**13*e**2*x**4 - 180*d**11*e**4*x**6 + 60*d**9*e**6*x**8), True)) + e*Piecewise((5*d**6*e*sqrt(d**2/(e**2*x**2) - 1)/(-5*d**14 + 15*d**12*e**2*x**2 - 15*d**10*e**4*x**4 + 5*d**8*e**6*x**6) - 30*d**4*e**3*x**2*sqrt(d**2/(e**2*x**2) - 1)/(-5*d**14 + 15*d**12*e**2*x**2 - 15*d**10*e**4*x**4 + 5*d**8*e**6*x**6) + 40*d**2*e**5*x**4*sqrt(d**2/(e**2*x**2) - 1)/(-5*d**14 + 15*d**12*e**2*x**2 - 15*d**10*e**4*x**4 + 5*d**8*e**6*x**6) - 16*e**7*x**6*sqrt(d**2/(e**2*x**2) - 1)/(-5*d**14 + 15*d**12*e**2*x**2 - 15*d**10*e**4*x**4 + 5*d**8*e**6*x**6), Abs(d**2/(e**2*x**2)) > 1), (5*I*d**6*e*sqrt(-d**2/(e**2*x**2) + 1)/(-5*d**14 + 15*d**12*e**2*x**2 - 15*d**10*e**4*x**4 + 5*d**8*e**6*x**6) - 30*I*d**4*e**3*x**2*sqrt(-d**2/(e**2*x**2) + 1)/(-5*d**14 + 15*d**12*e**2*x**2 - 15*d**10*e**4*x**4 + 5*d**8*e**6*x**6) + 40*I*d**2*e**5*x**4*sqrt(-d**2/(e**2*x**2) + 1)/(-5*d**14 + 15*d**12*e**2*x**2 - 15*d**10*e**4*x**4 + 5*d**8*e**6*x**6) - 16*I*e**7*x**6*sqrt(-d**2/(e**2*x**2) + 1)/(-5*d**14 + 15*d**12*e**2*x**2 - 15*d**10*e**4*x**4 + 5*d**8*e**6*x**6), True))","C",0
30,1,903,0,22.732928," ","integrate(x**2*(e*x+d)/(-e**2*x**2+d**2)**(9/2),x)","d \left(\begin{cases} \frac{35 i d^{4} x^{3}}{- 105 d^{13} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}} + 315 d^{11} e^{2} x^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}} - 315 d^{9} e^{4} x^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}} + 105 d^{7} e^{6} x^{6} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{28 i d^{2} e^{2} x^{5}}{- 105 d^{13} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}} + 315 d^{11} e^{2} x^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}} - 315 d^{9} e^{4} x^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}} + 105 d^{7} e^{6} x^{6} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + \frac{8 i e^{4} x^{7}}{- 105 d^{13} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}} + 315 d^{11} e^{2} x^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}} - 315 d^{9} e^{4} x^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}} + 105 d^{7} e^{6} x^{6} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\- \frac{35 d^{4} x^{3}}{- 105 d^{13} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}} + 315 d^{11} e^{2} x^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}} - 315 d^{9} e^{4} x^{4} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}} + 105 d^{7} e^{6} x^{6} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{28 d^{2} e^{2} x^{5}}{- 105 d^{13} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}} + 315 d^{11} e^{2} x^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}} - 315 d^{9} e^{4} x^{4} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}} + 105 d^{7} e^{6} x^{6} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} - \frac{8 e^{4} x^{7}}{- 105 d^{13} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}} + 315 d^{11} e^{2} x^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}} - 315 d^{9} e^{4} x^{4} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}} + 105 d^{7} e^{6} x^{6} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} & \text{otherwise} \end{cases}\right) + e \left(\begin{cases} \frac{2 d^{2}}{- 35 d^{6} e^{4} \sqrt{d^{2} - e^{2} x^{2}} + 105 d^{4} e^{6} x^{2} \sqrt{d^{2} - e^{2} x^{2}} - 105 d^{2} e^{8} x^{4} \sqrt{d^{2} - e^{2} x^{2}} + 35 e^{10} x^{6} \sqrt{d^{2} - e^{2} x^{2}}} - \frac{7 e^{2} x^{2}}{- 35 d^{6} e^{4} \sqrt{d^{2} - e^{2} x^{2}} + 105 d^{4} e^{6} x^{2} \sqrt{d^{2} - e^{2} x^{2}} - 105 d^{2} e^{8} x^{4} \sqrt{d^{2} - e^{2} x^{2}} + 35 e^{10} x^{6} \sqrt{d^{2} - e^{2} x^{2}}} & \text{for}\: e \neq 0 \\\frac{x^{4}}{4 \left(d^{2}\right)^{\frac{9}{2}}} & \text{otherwise} \end{cases}\right)"," ",0,"d*Piecewise((35*I*d**4*x**3/(-105*d**13*sqrt(-1 + e**2*x**2/d**2) + 315*d**11*e**2*x**2*sqrt(-1 + e**2*x**2/d**2) - 315*d**9*e**4*x**4*sqrt(-1 + e**2*x**2/d**2) + 105*d**7*e**6*x**6*sqrt(-1 + e**2*x**2/d**2)) - 28*I*d**2*e**2*x**5/(-105*d**13*sqrt(-1 + e**2*x**2/d**2) + 315*d**11*e**2*x**2*sqrt(-1 + e**2*x**2/d**2) - 315*d**9*e**4*x**4*sqrt(-1 + e**2*x**2/d**2) + 105*d**7*e**6*x**6*sqrt(-1 + e**2*x**2/d**2)) + 8*I*e**4*x**7/(-105*d**13*sqrt(-1 + e**2*x**2/d**2) + 315*d**11*e**2*x**2*sqrt(-1 + e**2*x**2/d**2) - 315*d**9*e**4*x**4*sqrt(-1 + e**2*x**2/d**2) + 105*d**7*e**6*x**6*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (-35*d**4*x**3/(-105*d**13*sqrt(1 - e**2*x**2/d**2) + 315*d**11*e**2*x**2*sqrt(1 - e**2*x**2/d**2) - 315*d**9*e**4*x**4*sqrt(1 - e**2*x**2/d**2) + 105*d**7*e**6*x**6*sqrt(1 - e**2*x**2/d**2)) + 28*d**2*e**2*x**5/(-105*d**13*sqrt(1 - e**2*x**2/d**2) + 315*d**11*e**2*x**2*sqrt(1 - e**2*x**2/d**2) - 315*d**9*e**4*x**4*sqrt(1 - e**2*x**2/d**2) + 105*d**7*e**6*x**6*sqrt(1 - e**2*x**2/d**2)) - 8*e**4*x**7/(-105*d**13*sqrt(1 - e**2*x**2/d**2) + 315*d**11*e**2*x**2*sqrt(1 - e**2*x**2/d**2) - 315*d**9*e**4*x**4*sqrt(1 - e**2*x**2/d**2) + 105*d**7*e**6*x**6*sqrt(1 - e**2*x**2/d**2)), True)) + e*Piecewise((2*d**2/(-35*d**6*e**4*sqrt(d**2 - e**2*x**2) + 105*d**4*e**6*x**2*sqrt(d**2 - e**2*x**2) - 105*d**2*e**8*x**4*sqrt(d**2 - e**2*x**2) + 35*e**10*x**6*sqrt(d**2 - e**2*x**2)) - 7*e**2*x**2/(-35*d**6*e**4*sqrt(d**2 - e**2*x**2) + 105*d**4*e**6*x**2*sqrt(d**2 - e**2*x**2) - 105*d**2*e**8*x**4*sqrt(d**2 - e**2*x**2) + 35*e**10*x**6*sqrt(d**2 - e**2*x**2)), Ne(e, 0)), (x**4/(4*(d**2)**(9/2)), True))","C",0
31,1,1401,0,48.457960," ","integrate(x**2*(e*x+d)/(-e**2*x**2+d**2)**(11/2),x)","d \left(\begin{cases} - \frac{105 i d^{6} x^{3}}{315 d^{17} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}} - 1260 d^{15} e^{2} x^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}} + 1890 d^{13} e^{4} x^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}} - 1260 d^{11} e^{6} x^{6} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}} + 315 d^{9} e^{8} x^{8} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + \frac{126 i d^{4} e^{2} x^{5}}{315 d^{17} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}} - 1260 d^{15} e^{2} x^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}} + 1890 d^{13} e^{4} x^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}} - 1260 d^{11} e^{6} x^{6} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}} + 315 d^{9} e^{8} x^{8} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{72 i d^{2} e^{4} x^{7}}{315 d^{17} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}} - 1260 d^{15} e^{2} x^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}} + 1890 d^{13} e^{4} x^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}} - 1260 d^{11} e^{6} x^{6} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}} + 315 d^{9} e^{8} x^{8} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + \frac{16 i e^{6} x^{9}}{315 d^{17} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}} - 1260 d^{15} e^{2} x^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}} + 1890 d^{13} e^{4} x^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}} - 1260 d^{11} e^{6} x^{6} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}} + 315 d^{9} e^{8} x^{8} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{105 d^{6} x^{3}}{315 d^{17} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}} - 1260 d^{15} e^{2} x^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}} + 1890 d^{13} e^{4} x^{4} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}} - 1260 d^{11} e^{6} x^{6} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}} + 315 d^{9} e^{8} x^{8} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} - \frac{126 d^{4} e^{2} x^{5}}{315 d^{17} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}} - 1260 d^{15} e^{2} x^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}} + 1890 d^{13} e^{4} x^{4} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}} - 1260 d^{11} e^{6} x^{6} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}} + 315 d^{9} e^{8} x^{8} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{72 d^{2} e^{4} x^{7}}{315 d^{17} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}} - 1260 d^{15} e^{2} x^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}} + 1890 d^{13} e^{4} x^{4} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}} - 1260 d^{11} e^{6} x^{6} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}} + 315 d^{9} e^{8} x^{8} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} - \frac{16 e^{6} x^{9}}{315 d^{17} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}} - 1260 d^{15} e^{2} x^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}} + 1890 d^{13} e^{4} x^{4} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}} - 1260 d^{11} e^{6} x^{6} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}} + 315 d^{9} e^{8} x^{8} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} & \text{otherwise} \end{cases}\right) + e \left(\begin{cases} - \frac{2 d^{2}}{63 d^{8} e^{4} \sqrt{d^{2} - e^{2} x^{2}} - 252 d^{6} e^{6} x^{2} \sqrt{d^{2} - e^{2} x^{2}} + 378 d^{4} e^{8} x^{4} \sqrt{d^{2} - e^{2} x^{2}} - 252 d^{2} e^{10} x^{6} \sqrt{d^{2} - e^{2} x^{2}} + 63 e^{12} x^{8} \sqrt{d^{2} - e^{2} x^{2}}} + \frac{9 e^{2} x^{2}}{63 d^{8} e^{4} \sqrt{d^{2} - e^{2} x^{2}} - 252 d^{6} e^{6} x^{2} \sqrt{d^{2} - e^{2} x^{2}} + 378 d^{4} e^{8} x^{4} \sqrt{d^{2} - e^{2} x^{2}} - 252 d^{2} e^{10} x^{6} \sqrt{d^{2} - e^{2} x^{2}} + 63 e^{12} x^{8} \sqrt{d^{2} - e^{2} x^{2}}} & \text{for}\: e \neq 0 \\\frac{x^{4}}{4 \left(d^{2}\right)^{\frac{11}{2}}} & \text{otherwise} \end{cases}\right)"," ",0,"d*Piecewise((-105*I*d**6*x**3/(315*d**17*sqrt(-1 + e**2*x**2/d**2) - 1260*d**15*e**2*x**2*sqrt(-1 + e**2*x**2/d**2) + 1890*d**13*e**4*x**4*sqrt(-1 + e**2*x**2/d**2) - 1260*d**11*e**6*x**6*sqrt(-1 + e**2*x**2/d**2) + 315*d**9*e**8*x**8*sqrt(-1 + e**2*x**2/d**2)) + 126*I*d**4*e**2*x**5/(315*d**17*sqrt(-1 + e**2*x**2/d**2) - 1260*d**15*e**2*x**2*sqrt(-1 + e**2*x**2/d**2) + 1890*d**13*e**4*x**4*sqrt(-1 + e**2*x**2/d**2) - 1260*d**11*e**6*x**6*sqrt(-1 + e**2*x**2/d**2) + 315*d**9*e**8*x**8*sqrt(-1 + e**2*x**2/d**2)) - 72*I*d**2*e**4*x**7/(315*d**17*sqrt(-1 + e**2*x**2/d**2) - 1260*d**15*e**2*x**2*sqrt(-1 + e**2*x**2/d**2) + 1890*d**13*e**4*x**4*sqrt(-1 + e**2*x**2/d**2) - 1260*d**11*e**6*x**6*sqrt(-1 + e**2*x**2/d**2) + 315*d**9*e**8*x**8*sqrt(-1 + e**2*x**2/d**2)) + 16*I*e**6*x**9/(315*d**17*sqrt(-1 + e**2*x**2/d**2) - 1260*d**15*e**2*x**2*sqrt(-1 + e**2*x**2/d**2) + 1890*d**13*e**4*x**4*sqrt(-1 + e**2*x**2/d**2) - 1260*d**11*e**6*x**6*sqrt(-1 + e**2*x**2/d**2) + 315*d**9*e**8*x**8*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (105*d**6*x**3/(315*d**17*sqrt(1 - e**2*x**2/d**2) - 1260*d**15*e**2*x**2*sqrt(1 - e**2*x**2/d**2) + 1890*d**13*e**4*x**4*sqrt(1 - e**2*x**2/d**2) - 1260*d**11*e**6*x**6*sqrt(1 - e**2*x**2/d**2) + 315*d**9*e**8*x**8*sqrt(1 - e**2*x**2/d**2)) - 126*d**4*e**2*x**5/(315*d**17*sqrt(1 - e**2*x**2/d**2) - 1260*d**15*e**2*x**2*sqrt(1 - e**2*x**2/d**2) + 1890*d**13*e**4*x**4*sqrt(1 - e**2*x**2/d**2) - 1260*d**11*e**6*x**6*sqrt(1 - e**2*x**2/d**2) + 315*d**9*e**8*x**8*sqrt(1 - e**2*x**2/d**2)) + 72*d**2*e**4*x**7/(315*d**17*sqrt(1 - e**2*x**2/d**2) - 1260*d**15*e**2*x**2*sqrt(1 - e**2*x**2/d**2) + 1890*d**13*e**4*x**4*sqrt(1 - e**2*x**2/d**2) - 1260*d**11*e**6*x**6*sqrt(1 - e**2*x**2/d**2) + 315*d**9*e**8*x**8*sqrt(1 - e**2*x**2/d**2)) - 16*e**6*x**9/(315*d**17*sqrt(1 - e**2*x**2/d**2) - 1260*d**15*e**2*x**2*sqrt(1 - e**2*x**2/d**2) + 1890*d**13*e**4*x**4*sqrt(1 - e**2*x**2/d**2) - 1260*d**11*e**6*x**6*sqrt(1 - e**2*x**2/d**2) + 315*d**9*e**8*x**8*sqrt(1 - e**2*x**2/d**2)), True)) + e*Piecewise((-2*d**2/(63*d**8*e**4*sqrt(d**2 - e**2*x**2) - 252*d**6*e**6*x**2*sqrt(d**2 - e**2*x**2) + 378*d**4*e**8*x**4*sqrt(d**2 - e**2*x**2) - 252*d**2*e**10*x**6*sqrt(d**2 - e**2*x**2) + 63*e**12*x**8*sqrt(d**2 - e**2*x**2)) + 9*e**2*x**2/(63*d**8*e**4*sqrt(d**2 - e**2*x**2) - 252*d**6*e**6*x**2*sqrt(d**2 - e**2*x**2) + 378*d**4*e**8*x**4*sqrt(d**2 - e**2*x**2) - 252*d**2*e**10*x**6*sqrt(d**2 - e**2*x**2) + 63*e**12*x**8*sqrt(d**2 - e**2*x**2)), Ne(e, 0)), (x**4/(4*(d**2)**(11/2)), True))","C",0
32,1,102,0,8.328486," ","integrate(x**2*(-a*x+1)/(-a**2*x**2+1)**(3/2),x)","- a \left(\begin{cases} - \frac{x^{2}}{a^{2} \sqrt{- a^{2} x^{2} + 1}} + \frac{2}{a^{4} \sqrt{- a^{2} x^{2} + 1}} & \text{for}\: a \neq 0 \\\frac{x^{4}}{4} & \text{otherwise} \end{cases}\right) + \begin{cases} - \frac{i x}{a^{2} \sqrt{a^{2} x^{2} - 1}} + \frac{i \operatorname{acosh}{\left(a x \right)}}{a^{3}} & \text{for}\: \left|{a^{2} x^{2}}\right| > 1 \\\frac{x}{a^{2} \sqrt{- a^{2} x^{2} + 1}} - \frac{\operatorname{asin}{\left(a x \right)}}{a^{3}} & \text{otherwise} \end{cases}"," ",0,"-a*Piecewise((-x**2/(a**2*sqrt(-a**2*x**2 + 1)) + 2/(a**4*sqrt(-a**2*x**2 + 1)), Ne(a, 0)), (x**4/4, True)) + Piecewise((-I*x/(a**2*sqrt(a**2*x**2 - 1)) + I*acosh(a*x)/a**3, Abs(a**2*x**2) > 1), (x/(a**2*sqrt(-a**2*x**2 + 1)) - asin(a*x)/a**3, True))","A",0
33,1,558,0,13.484317," ","integrate(x**4*(e*x+d)**2/(-e**2*x**2+d**2)**(1/2),x)","d^{2} \left(\begin{cases} - \frac{3 i d^{4} \operatorname{acosh}{\left(\frac{e x}{d} \right)}}{8 e^{5}} + \frac{3 i d^{3} x}{8 e^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{i d x^{3}}{8 e^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{i x^{5}}{4 d \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{3 d^{4} \operatorname{asin}{\left(\frac{e x}{d} \right)}}{8 e^{5}} - \frac{3 d^{3} x}{8 e^{4} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{d x^{3}}{8 e^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{x^{5}}{4 d \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} & \text{otherwise} \end{cases}\right) + 2 d e \left(\begin{cases} - \frac{8 d^{4} \sqrt{d^{2} - e^{2} x^{2}}}{15 e^{6}} - \frac{4 d^{2} x^{2} \sqrt{d^{2} - e^{2} x^{2}}}{15 e^{4}} - \frac{x^{4} \sqrt{d^{2} - e^{2} x^{2}}}{5 e^{2}} & \text{for}\: e \neq 0 \\\frac{x^{6}}{6 \sqrt{d^{2}}} & \text{otherwise} \end{cases}\right) + e^{2} \left(\begin{cases} - \frac{5 i d^{6} \operatorname{acosh}{\left(\frac{e x}{d} \right)}}{16 e^{7}} + \frac{5 i d^{5} x}{16 e^{6} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{5 i d^{3} x^{3}}{48 e^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{i d x^{5}}{24 e^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{i x^{7}}{6 d \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{5 d^{6} \operatorname{asin}{\left(\frac{e x}{d} \right)}}{16 e^{7}} - \frac{5 d^{5} x}{16 e^{6} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{5 d^{3} x^{3}}{48 e^{4} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{d x^{5}}{24 e^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{x^{7}}{6 d \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} & \text{otherwise} \end{cases}\right)"," ",0,"d**2*Piecewise((-3*I*d**4*acosh(e*x/d)/(8*e**5) + 3*I*d**3*x/(8*e**4*sqrt(-1 + e**2*x**2/d**2)) - I*d*x**3/(8*e**2*sqrt(-1 + e**2*x**2/d**2)) - I*x**5/(4*d*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (3*d**4*asin(e*x/d)/(8*e**5) - 3*d**3*x/(8*e**4*sqrt(1 - e**2*x**2/d**2)) + d*x**3/(8*e**2*sqrt(1 - e**2*x**2/d**2)) + x**5/(4*d*sqrt(1 - e**2*x**2/d**2)), True)) + 2*d*e*Piecewise((-8*d**4*sqrt(d**2 - e**2*x**2)/(15*e**6) - 4*d**2*x**2*sqrt(d**2 - e**2*x**2)/(15*e**4) - x**4*sqrt(d**2 - e**2*x**2)/(5*e**2), Ne(e, 0)), (x**6/(6*sqrt(d**2)), True)) + e**2*Piecewise((-5*I*d**6*acosh(e*x/d)/(16*e**7) + 5*I*d**5*x/(16*e**6*sqrt(-1 + e**2*x**2/d**2)) - 5*I*d**3*x**3/(48*e**4*sqrt(-1 + e**2*x**2/d**2)) - I*d*x**5/(24*e**2*sqrt(-1 + e**2*x**2/d**2)) - I*x**7/(6*d*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (5*d**6*asin(e*x/d)/(16*e**7) - 5*d**5*x/(16*e**6*sqrt(1 - e**2*x**2/d**2)) + 5*d**3*x**3/(48*e**4*sqrt(1 - e**2*x**2/d**2)) + d*x**5/(24*e**2*sqrt(1 - e**2*x**2/d**2)) + x**7/(6*d*sqrt(1 - e**2*x**2/d**2)), True))","C",0
34,1,357,0,7.870838," ","integrate(x**3*(e*x+d)**2/(-e**2*x**2+d**2)**(1/2),x)","d^{2} \left(\begin{cases} - \frac{2 d^{2} \sqrt{d^{2} - e^{2} x^{2}}}{3 e^{4}} - \frac{x^{2} \sqrt{d^{2} - e^{2} x^{2}}}{3 e^{2}} & \text{for}\: e \neq 0 \\\frac{x^{4}}{4 \sqrt{d^{2}}} & \text{otherwise} \end{cases}\right) + 2 d e \left(\begin{cases} - \frac{3 i d^{4} \operatorname{acosh}{\left(\frac{e x}{d} \right)}}{8 e^{5}} + \frac{3 i d^{3} x}{8 e^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{i d x^{3}}{8 e^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{i x^{5}}{4 d \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{3 d^{4} \operatorname{asin}{\left(\frac{e x}{d} \right)}}{8 e^{5}} - \frac{3 d^{3} x}{8 e^{4} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{d x^{3}}{8 e^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{x^{5}}{4 d \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} & \text{otherwise} \end{cases}\right) + e^{2} \left(\begin{cases} - \frac{8 d^{4} \sqrt{d^{2} - e^{2} x^{2}}}{15 e^{6}} - \frac{4 d^{2} x^{2} \sqrt{d^{2} - e^{2} x^{2}}}{15 e^{4}} - \frac{x^{4} \sqrt{d^{2} - e^{2} x^{2}}}{5 e^{2}} & \text{for}\: e \neq 0 \\\frac{x^{6}}{6 \sqrt{d^{2}}} & \text{otherwise} \end{cases}\right)"," ",0,"d**2*Piecewise((-2*d**2*sqrt(d**2 - e**2*x**2)/(3*e**4) - x**2*sqrt(d**2 - e**2*x**2)/(3*e**2), Ne(e, 0)), (x**4/(4*sqrt(d**2)), True)) + 2*d*e*Piecewise((-3*I*d**4*acosh(e*x/d)/(8*e**5) + 3*I*d**3*x/(8*e**4*sqrt(-1 + e**2*x**2/d**2)) - I*d*x**3/(8*e**2*sqrt(-1 + e**2*x**2/d**2)) - I*x**5/(4*d*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (3*d**4*asin(e*x/d)/(8*e**5) - 3*d**3*x/(8*e**4*sqrt(1 - e**2*x**2/d**2)) + d*x**3/(8*e**2*sqrt(1 - e**2*x**2/d**2)) + x**5/(4*d*sqrt(1 - e**2*x**2/d**2)), True)) + e**2*Piecewise((-8*d**4*sqrt(d**2 - e**2*x**2)/(15*e**6) - 4*d**2*x**2*sqrt(d**2 - e**2*x**2)/(15*e**4) - x**4*sqrt(d**2 - e**2*x**2)/(5*e**2), Ne(e, 0)), (x**6/(6*sqrt(d**2)), True))","A",0
35,1,386,0,9.326615," ","integrate(x**2*(e*x+d)**2/(-e**2*x**2+d**2)**(1/2),x)","d^{2} \left(\begin{cases} - \frac{i d^{2} \operatorname{acosh}{\left(\frac{e x}{d} \right)}}{2 e^{3}} - \frac{i d x \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}}{2 e^{2}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{d^{2} \operatorname{asin}{\left(\frac{e x}{d} \right)}}{2 e^{3}} - \frac{d x}{2 e^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{x^{3}}{2 d \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} & \text{otherwise} \end{cases}\right) + 2 d e \left(\begin{cases} - \frac{2 d^{2} \sqrt{d^{2} - e^{2} x^{2}}}{3 e^{4}} - \frac{x^{2} \sqrt{d^{2} - e^{2} x^{2}}}{3 e^{2}} & \text{for}\: e \neq 0 \\\frac{x^{4}}{4 \sqrt{d^{2}}} & \text{otherwise} \end{cases}\right) + e^{2} \left(\begin{cases} - \frac{3 i d^{4} \operatorname{acosh}{\left(\frac{e x}{d} \right)}}{8 e^{5}} + \frac{3 i d^{3} x}{8 e^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{i d x^{3}}{8 e^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{i x^{5}}{4 d \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{3 d^{4} \operatorname{asin}{\left(\frac{e x}{d} \right)}}{8 e^{5}} - \frac{3 d^{3} x}{8 e^{4} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{d x^{3}}{8 e^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{x^{5}}{4 d \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} & \text{otherwise} \end{cases}\right)"," ",0,"d**2*Piecewise((-I*d**2*acosh(e*x/d)/(2*e**3) - I*d*x*sqrt(-1 + e**2*x**2/d**2)/(2*e**2), Abs(e**2*x**2/d**2) > 1), (d**2*asin(e*x/d)/(2*e**3) - d*x/(2*e**2*sqrt(1 - e**2*x**2/d**2)) + x**3/(2*d*sqrt(1 - e**2*x**2/d**2)), True)) + 2*d*e*Piecewise((-2*d**2*sqrt(d**2 - e**2*x**2)/(3*e**4) - x**2*sqrt(d**2 - e**2*x**2)/(3*e**2), Ne(e, 0)), (x**4/(4*sqrt(d**2)), True)) + e**2*Piecewise((-3*I*d**4*acosh(e*x/d)/(8*e**5) + 3*I*d**3*x/(8*e**4*sqrt(-1 + e**2*x**2/d**2)) - I*d*x**3/(8*e**2*sqrt(-1 + e**2*x**2/d**2)) - I*x**5/(4*d*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (3*d**4*asin(e*x/d)/(8*e**5) - 3*d**3*x/(8*e**4*sqrt(1 - e**2*x**2/d**2)) + d*x**3/(8*e**2*sqrt(1 - e**2*x**2/d**2)) + x**5/(4*d*sqrt(1 - e**2*x**2/d**2)), True))","C",0
36,1,218,0,5.616808," ","integrate(x*(e*x+d)**2/(-e**2*x**2+d**2)**(1/2),x)","d^{2} \left(\begin{cases} \frac{x^{2}}{2 \sqrt{d^{2}}} & \text{for}\: e^{2} = 0 \\- \frac{\sqrt{d^{2} - e^{2} x^{2}}}{e^{2}} & \text{otherwise} \end{cases}\right) + 2 d e \left(\begin{cases} - \frac{i d^{2} \operatorname{acosh}{\left(\frac{e x}{d} \right)}}{2 e^{3}} - \frac{i d x \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}}{2 e^{2}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{d^{2} \operatorname{asin}{\left(\frac{e x}{d} \right)}}{2 e^{3}} - \frac{d x}{2 e^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{x^{3}}{2 d \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} & \text{otherwise} \end{cases}\right) + e^{2} \left(\begin{cases} - \frac{2 d^{2} \sqrt{d^{2} - e^{2} x^{2}}}{3 e^{4}} - \frac{x^{2} \sqrt{d^{2} - e^{2} x^{2}}}{3 e^{2}} & \text{for}\: e \neq 0 \\\frac{x^{4}}{4 \sqrt{d^{2}}} & \text{otherwise} \end{cases}\right)"," ",0,"d**2*Piecewise((x**2/(2*sqrt(d**2)), Eq(e**2, 0)), (-sqrt(d**2 - e**2*x**2)/e**2, True)) + 2*d*e*Piecewise((-I*d**2*acosh(e*x/d)/(2*e**3) - I*d*x*sqrt(-1 + e**2*x**2/d**2)/(2*e**2), Abs(e**2*x**2/d**2) > 1), (d**2*asin(e*x/d)/(2*e**3) - d*x/(2*e**2*sqrt(1 - e**2*x**2/d**2)) + x**3/(2*d*sqrt(1 - e**2*x**2/d**2)), True)) + e**2*Piecewise((-2*d**2*sqrt(d**2 - e**2*x**2)/(3*e**4) - x**2*sqrt(d**2 - e**2*x**2)/(3*e**2), Ne(e, 0)), (x**4/(4*sqrt(d**2)), True))","A",0
37,1,269,0,5.044015," ","integrate((e*x+d)**2/(-e**2*x**2+d**2)**(1/2),x)","d^{2} \left(\begin{cases} \frac{\sqrt{\frac{d^{2}}{e^{2}}} \operatorname{asin}{\left(x \sqrt{\frac{e^{2}}{d^{2}}} \right)}}{\sqrt{d^{2}}} & \text{for}\: d^{2} > 0 \wedge e^{2} > 0 \\\frac{\sqrt{- \frac{d^{2}}{e^{2}}} \operatorname{asinh}{\left(x \sqrt{- \frac{e^{2}}{d^{2}}} \right)}}{\sqrt{d^{2}}} & \text{for}\: d^{2} > 0 \wedge e^{2} < 0 \\\frac{\sqrt{\frac{d^{2}}{e^{2}}} \operatorname{acosh}{\left(x \sqrt{\frac{e^{2}}{d^{2}}} \right)}}{\sqrt{- d^{2}}} & \text{for}\: d^{2} < 0 \wedge e^{2} < 0 \end{cases}\right) + 2 d e \left(\begin{cases} \frac{x^{2}}{2 \sqrt{d^{2}}} & \text{for}\: e^{2} = 0 \\- \frac{\sqrt{d^{2} - e^{2} x^{2}}}{e^{2}} & \text{otherwise} \end{cases}\right) + e^{2} \left(\begin{cases} - \frac{i d^{2} \operatorname{acosh}{\left(\frac{e x}{d} \right)}}{2 e^{3}} - \frac{i d x \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}}{2 e^{2}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{d^{2} \operatorname{asin}{\left(\frac{e x}{d} \right)}}{2 e^{3}} - \frac{d x}{2 e^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{x^{3}}{2 d \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} & \text{otherwise} \end{cases}\right)"," ",0,"d**2*Piecewise((sqrt(d**2/e**2)*asin(x*sqrt(e**2/d**2))/sqrt(d**2), (d**2 > 0) & (e**2 > 0)), (sqrt(-d**2/e**2)*asinh(x*sqrt(-e**2/d**2))/sqrt(d**2), (d**2 > 0) & (e**2 < 0)), (sqrt(d**2/e**2)*acosh(x*sqrt(e**2/d**2))/sqrt(-d**2), (d**2 < 0) & (e**2 < 0))) + 2*d*e*Piecewise((x**2/(2*sqrt(d**2)), Eq(e**2, 0)), (-sqrt(d**2 - e**2*x**2)/e**2, True)) + e**2*Piecewise((-I*d**2*acosh(e*x/d)/(2*e**3) - I*d*x*sqrt(-1 + e**2*x**2/d**2)/(2*e**2), Abs(e**2*x**2/d**2) > 1), (d**2*asin(e*x/d)/(2*e**3) - d*x/(2*e**2*sqrt(1 - e**2*x**2/d**2)) + x**3/(2*d*sqrt(1 - e**2*x**2/d**2)), True))","A",0
38,1,184,0,6.957940," ","integrate((e*x+d)**2/x/(-e**2*x**2+d**2)**(1/2),x)","d^{2} \left(\begin{cases} - \frac{\operatorname{acosh}{\left(\frac{d}{e x} \right)}}{d} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\\frac{i \operatorname{asin}{\left(\frac{d}{e x} \right)}}{d} & \text{otherwise} \end{cases}\right) + 2 d e \left(\begin{cases} \frac{\sqrt{\frac{d^{2}}{e^{2}}} \operatorname{asin}{\left(x \sqrt{\frac{e^{2}}{d^{2}}} \right)}}{\sqrt{d^{2}}} & \text{for}\: d^{2} > 0 \wedge e^{2} > 0 \\\frac{\sqrt{- \frac{d^{2}}{e^{2}}} \operatorname{asinh}{\left(x \sqrt{- \frac{e^{2}}{d^{2}}} \right)}}{\sqrt{d^{2}}} & \text{for}\: d^{2} > 0 \wedge e^{2} < 0 \\\frac{\sqrt{\frac{d^{2}}{e^{2}}} \operatorname{acosh}{\left(x \sqrt{\frac{e^{2}}{d^{2}}} \right)}}{\sqrt{- d^{2}}} & \text{for}\: d^{2} < 0 \wedge e^{2} < 0 \end{cases}\right) + e^{2} \left(\begin{cases} \frac{x^{2}}{2 \sqrt{d^{2}}} & \text{for}\: e^{2} = 0 \\- \frac{\sqrt{d^{2} - e^{2} x^{2}}}{e^{2}} & \text{otherwise} \end{cases}\right)"," ",0,"d**2*Piecewise((-acosh(d/(e*x))/d, Abs(d**2/(e**2*x**2)) > 1), (I*asin(d/(e*x))/d, True)) + 2*d*e*Piecewise((sqrt(d**2/e**2)*asin(x*sqrt(e**2/d**2))/sqrt(d**2), (d**2 > 0) & (e**2 > 0)), (sqrt(-d**2/e**2)*asinh(x*sqrt(-e**2/d**2))/sqrt(d**2), (d**2 > 0) & (e**2 < 0)), (sqrt(d**2/e**2)*acosh(x*sqrt(e**2/d**2))/sqrt(-d**2), (d**2 < 0) & (e**2 < 0))) + e**2*Piecewise((x**2/(2*sqrt(d**2)), Eq(e**2, 0)), (-sqrt(d**2 - e**2*x**2)/e**2, True))","C",0
39,1,207,0,4.295794," ","integrate((e*x+d)**2/x**2/(-e**2*x**2+d**2)**(1/2),x)","d^{2} \left(\begin{cases} - \frac{e \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}}{d^{2}} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\- \frac{i e \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{d^{2}} & \text{otherwise} \end{cases}\right) + 2 d e \left(\begin{cases} - \frac{\operatorname{acosh}{\left(\frac{d}{e x} \right)}}{d} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\\frac{i \operatorname{asin}{\left(\frac{d}{e x} \right)}}{d} & \text{otherwise} \end{cases}\right) + e^{2} \left(\begin{cases} \frac{\sqrt{\frac{d^{2}}{e^{2}}} \operatorname{asin}{\left(x \sqrt{\frac{e^{2}}{d^{2}}} \right)}}{\sqrt{d^{2}}} & \text{for}\: d^{2} > 0 \wedge e^{2} > 0 \\\frac{\sqrt{- \frac{d^{2}}{e^{2}}} \operatorname{asinh}{\left(x \sqrt{- \frac{e^{2}}{d^{2}}} \right)}}{\sqrt{d^{2}}} & \text{for}\: d^{2} > 0 \wedge e^{2} < 0 \\\frac{\sqrt{\frac{d^{2}}{e^{2}}} \operatorname{acosh}{\left(x \sqrt{\frac{e^{2}}{d^{2}}} \right)}}{\sqrt{- d^{2}}} & \text{for}\: d^{2} < 0 \wedge e^{2} < 0 \end{cases}\right)"," ",0,"d**2*Piecewise((-e*sqrt(d**2/(e**2*x**2) - 1)/d**2, Abs(d**2/(e**2*x**2)) > 1), (-I*e*sqrt(-d**2/(e**2*x**2) + 1)/d**2, True)) + 2*d*e*Piecewise((-acosh(d/(e*x))/d, Abs(d**2/(e**2*x**2)) > 1), (I*asin(d/(e*x))/d, True)) + e**2*Piecewise((sqrt(d**2/e**2)*asin(x*sqrt(e**2/d**2))/sqrt(d**2), (d**2 > 0) & (e**2 > 0)), (sqrt(-d**2/e**2)*asinh(x*sqrt(-e**2/d**2))/sqrt(d**2), (d**2 > 0) & (e**2 < 0)), (sqrt(d**2/e**2)*acosh(x*sqrt(e**2/d**2))/sqrt(-d**2), (d**2 < 0) & (e**2 < 0)))","C",0
40,1,214,0,6.721194," ","integrate((e*x+d)**2/x**3/(-e**2*x**2+d**2)**(1/2),x)","d^{2} \left(\begin{cases} - \frac{e \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}}{2 d^{2} x} - \frac{e^{2} \operatorname{acosh}{\left(\frac{d}{e x} \right)}}{2 d^{3}} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\\frac{i}{2 e x^{3} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} - \frac{i e}{2 d^{2} x \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} + \frac{i e^{2} \operatorname{asin}{\left(\frac{d}{e x} \right)}}{2 d^{3}} & \text{otherwise} \end{cases}\right) + 2 d e \left(\begin{cases} - \frac{e \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}}{d^{2}} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\- \frac{i e \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{d^{2}} & \text{otherwise} \end{cases}\right) + e^{2} \left(\begin{cases} - \frac{\operatorname{acosh}{\left(\frac{d}{e x} \right)}}{d} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\\frac{i \operatorname{asin}{\left(\frac{d}{e x} \right)}}{d} & \text{otherwise} \end{cases}\right)"," ",0,"d**2*Piecewise((-e*sqrt(d**2/(e**2*x**2) - 1)/(2*d**2*x) - e**2*acosh(d/(e*x))/(2*d**3), Abs(d**2/(e**2*x**2)) > 1), (I/(2*e*x**3*sqrt(-d**2/(e**2*x**2) + 1)) - I*e/(2*d**2*x*sqrt(-d**2/(e**2*x**2) + 1)) + I*e**2*asin(d/(e*x))/(2*d**3), True)) + 2*d*e*Piecewise((-e*sqrt(d**2/(e**2*x**2) - 1)/d**2, Abs(d**2/(e**2*x**2)) > 1), (-I*e*sqrt(-d**2/(e**2*x**2) + 1)/d**2, True)) + e**2*Piecewise((-acosh(d/(e*x))/d, Abs(d**2/(e**2*x**2)) > 1), (I*asin(d/(e*x))/d, True))","C",0
41,1,303,0,6.089644," ","integrate((e*x+d)**2/x**4/(-e**2*x**2+d**2)**(1/2),x)","d^{2} \left(\begin{cases} - \frac{e \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}}{3 d^{2} x^{2}} - \frac{2 e^{3} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}}{3 d^{4}} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\- \frac{i e \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{3 d^{2} x^{2}} - \frac{2 i e^{3} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{3 d^{4}} & \text{otherwise} \end{cases}\right) + 2 d e \left(\begin{cases} - \frac{e \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}}{2 d^{2} x} - \frac{e^{2} \operatorname{acosh}{\left(\frac{d}{e x} \right)}}{2 d^{3}} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\\frac{i}{2 e x^{3} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} - \frac{i e}{2 d^{2} x \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} + \frac{i e^{2} \operatorname{asin}{\left(\frac{d}{e x} \right)}}{2 d^{3}} & \text{otherwise} \end{cases}\right) + e^{2} \left(\begin{cases} - \frac{e \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}}{d^{2}} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\- \frac{i e \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{d^{2}} & \text{otherwise} \end{cases}\right)"," ",0,"d**2*Piecewise((-e*sqrt(d**2/(e**2*x**2) - 1)/(3*d**2*x**2) - 2*e**3*sqrt(d**2/(e**2*x**2) - 1)/(3*d**4), Abs(d**2/(e**2*x**2)) > 1), (-I*e*sqrt(-d**2/(e**2*x**2) + 1)/(3*d**2*x**2) - 2*I*e**3*sqrt(-d**2/(e**2*x**2) + 1)/(3*d**4), True)) + 2*d*e*Piecewise((-e*sqrt(d**2/(e**2*x**2) - 1)/(2*d**2*x) - e**2*acosh(d/(e*x))/(2*d**3), Abs(d**2/(e**2*x**2)) > 1), (I/(2*e*x**3*sqrt(-d**2/(e**2*x**2) + 1)) - I*e/(2*d**2*x*sqrt(-d**2/(e**2*x**2) + 1)) + I*e**2*asin(d/(e*x))/(2*d**3), True)) + e**2*Piecewise((-e*sqrt(d**2/(e**2*x**2) - 1)/d**2, Abs(d**2/(e**2*x**2)) > 1), (-I*e*sqrt(-d**2/(e**2*x**2) + 1)/d**2, True))","C",0
42,1,449,0,10.315997," ","integrate((e*x+d)**2/x**5/(-e**2*x**2+d**2)**(1/2),x)","d^{2} \left(\begin{cases} - \frac{1}{4 e x^{5} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} - \frac{e}{8 d^{2} x^{3} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{3 e^{3}}{8 d^{4} x \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} - \frac{3 e^{4} \operatorname{acosh}{\left(\frac{d}{e x} \right)}}{8 d^{5}} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\\frac{i}{4 e x^{5} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} + \frac{i e}{8 d^{2} x^{3} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} - \frac{3 i e^{3}}{8 d^{4} x \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} + \frac{3 i e^{4} \operatorname{asin}{\left(\frac{d}{e x} \right)}}{8 d^{5}} & \text{otherwise} \end{cases}\right) + 2 d e \left(\begin{cases} - \frac{e \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}}{3 d^{2} x^{2}} - \frac{2 e^{3} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}}{3 d^{4}} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\- \frac{i e \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{3 d^{2} x^{2}} - \frac{2 i e^{3} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{3 d^{4}} & \text{otherwise} \end{cases}\right) + e^{2} \left(\begin{cases} - \frac{e \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}}{2 d^{2} x} - \frac{e^{2} \operatorname{acosh}{\left(\frac{d}{e x} \right)}}{2 d^{3}} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\\frac{i}{2 e x^{3} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} - \frac{i e}{2 d^{2} x \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} + \frac{i e^{2} \operatorname{asin}{\left(\frac{d}{e x} \right)}}{2 d^{3}} & \text{otherwise} \end{cases}\right)"," ",0,"d**2*Piecewise((-1/(4*e*x**5*sqrt(d**2/(e**2*x**2) - 1)) - e/(8*d**2*x**3*sqrt(d**2/(e**2*x**2) - 1)) + 3*e**3/(8*d**4*x*sqrt(d**2/(e**2*x**2) - 1)) - 3*e**4*acosh(d/(e*x))/(8*d**5), Abs(d**2/(e**2*x**2)) > 1), (I/(4*e*x**5*sqrt(-d**2/(e**2*x**2) + 1)) + I*e/(8*d**2*x**3*sqrt(-d**2/(e**2*x**2) + 1)) - 3*I*e**3/(8*d**4*x*sqrt(-d**2/(e**2*x**2) + 1)) + 3*I*e**4*asin(d/(e*x))/(8*d**5), True)) + 2*d*e*Piecewise((-e*sqrt(d**2/(e**2*x**2) - 1)/(3*d**2*x**2) - 2*e**3*sqrt(d**2/(e**2*x**2) - 1)/(3*d**4), Abs(d**2/(e**2*x**2)) > 1), (-I*e*sqrt(-d**2/(e**2*x**2) + 1)/(3*d**2*x**2) - 2*I*e**3*sqrt(-d**2/(e**2*x**2) + 1)/(3*d**4), True)) + e**2*Piecewise((-e*sqrt(d**2/(e**2*x**2) - 1)/(2*d**2*x) - e**2*acosh(d/(e*x))/(2*d**3), Abs(d**2/(e**2*x**2)) > 1), (I/(2*e*x**3*sqrt(-d**2/(e**2*x**2) + 1)) - I*e/(2*d**2*x*sqrt(-d**2/(e**2*x**2) + 1)) + I*e**2*asin(d/(e*x))/(2*d**3), True))","C",0
43,1,510,0,8.956563," ","integrate((e*x+d)**2/x**6/(-e**2*x**2+d**2)**(1/2),x)","d^{2} \left(\begin{cases} - \frac{e \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}}{5 d^{2} x^{4}} - \frac{4 e^{3} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}}{15 d^{4} x^{2}} - \frac{8 e^{5} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}}{15 d^{6}} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\- \frac{i e \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{5 d^{2} x^{4}} - \frac{4 i e^{3} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{15 d^{4} x^{2}} - \frac{8 i e^{5} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{15 d^{6}} & \text{otherwise} \end{cases}\right) + 2 d e \left(\begin{cases} - \frac{1}{4 e x^{5} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} - \frac{e}{8 d^{2} x^{3} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{3 e^{3}}{8 d^{4} x \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} - \frac{3 e^{4} \operatorname{acosh}{\left(\frac{d}{e x} \right)}}{8 d^{5}} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\\frac{i}{4 e x^{5} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} + \frac{i e}{8 d^{2} x^{3} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} - \frac{3 i e^{3}}{8 d^{4} x \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} + \frac{3 i e^{4} \operatorname{asin}{\left(\frac{d}{e x} \right)}}{8 d^{5}} & \text{otherwise} \end{cases}\right) + e^{2} \left(\begin{cases} - \frac{e \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}}{3 d^{2} x^{2}} - \frac{2 e^{3} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}}{3 d^{4}} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\- \frac{i e \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{3 d^{2} x^{2}} - \frac{2 i e^{3} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{3 d^{4}} & \text{otherwise} \end{cases}\right)"," ",0,"d**2*Piecewise((-e*sqrt(d**2/(e**2*x**2) - 1)/(5*d**2*x**4) - 4*e**3*sqrt(d**2/(e**2*x**2) - 1)/(15*d**4*x**2) - 8*e**5*sqrt(d**2/(e**2*x**2) - 1)/(15*d**6), Abs(d**2/(e**2*x**2)) > 1), (-I*e*sqrt(-d**2/(e**2*x**2) + 1)/(5*d**2*x**4) - 4*I*e**3*sqrt(-d**2/(e**2*x**2) + 1)/(15*d**4*x**2) - 8*I*e**5*sqrt(-d**2/(e**2*x**2) + 1)/(15*d**6), True)) + 2*d*e*Piecewise((-1/(4*e*x**5*sqrt(d**2/(e**2*x**2) - 1)) - e/(8*d**2*x**3*sqrt(d**2/(e**2*x**2) - 1)) + 3*e**3/(8*d**4*x*sqrt(d**2/(e**2*x**2) - 1)) - 3*e**4*acosh(d/(e*x))/(8*d**5), Abs(d**2/(e**2*x**2)) > 1), (I/(4*e*x**5*sqrt(-d**2/(e**2*x**2) + 1)) + I*e/(8*d**2*x**3*sqrt(-d**2/(e**2*x**2) + 1)) - 3*I*e**3/(8*d**4*x*sqrt(-d**2/(e**2*x**2) + 1)) + 3*I*e**4*asin(d/(e*x))/(8*d**5), True)) + e**2*Piecewise((-e*sqrt(d**2/(e**2*x**2) - 1)/(3*d**2*x**2) - 2*e**3*sqrt(d**2/(e**2*x**2) - 1)/(3*d**4), Abs(d**2/(e**2*x**2)) > 1), (-I*e*sqrt(-d**2/(e**2*x**2) + 1)/(3*d**2*x**2) - 2*I*e**3*sqrt(-d**2/(e**2*x**2) + 1)/(3*d**4), True))","C",0
44,0,0,0,0.000000," ","integrate(x**5*(e*x+d)**2/(-e**2*x**2+d**2)**(7/2),x)","\int \frac{x^{5} \left(d + e x\right)^{2}}{\left(- \left(- d + e x\right) \left(d + e x\right)\right)^{\frac{7}{2}}}\, dx"," ",0,"Integral(x**5*(d + e*x)**2/(-(-d + e*x)*(d + e*x))**(7/2), x)","F",0
45,0,0,0,0.000000," ","integrate(x**4*(e*x+d)**2/(-e**2*x**2+d**2)**(7/2),x)","\int \frac{x^{4} \left(d + e x\right)^{2}}{\left(- \left(- d + e x\right) \left(d + e x\right)\right)^{\frac{7}{2}}}\, dx"," ",0,"Integral(x**4*(d + e*x)**2/(-(-d + e*x)*(d + e*x))**(7/2), x)","F",0
46,0,0,0,0.000000," ","integrate(x**3*(e*x+d)**2/(-e**2*x**2+d**2)**(7/2),x)","\int \frac{x^{3} \left(d + e x\right)^{2}}{\left(- \left(- d + e x\right) \left(d + e x\right)\right)^{\frac{7}{2}}}\, dx"," ",0,"Integral(x**3*(d + e*x)**2/(-(-d + e*x)*(d + e*x))**(7/2), x)","F",0
47,0,0,0,0.000000," ","integrate(x**2*(e*x+d)**2/(-e**2*x**2+d**2)**(7/2),x)","\int \frac{x^{2} \left(d + e x\right)^{2}}{\left(- \left(- d + e x\right) \left(d + e x\right)\right)^{\frac{7}{2}}}\, dx"," ",0,"Integral(x**2*(d + e*x)**2/(-(-d + e*x)*(d + e*x))**(7/2), x)","F",0
48,0,0,0,0.000000," ","integrate(x*(e*x+d)**2/(-e**2*x**2+d**2)**(7/2),x)","\int \frac{x \left(d + e x\right)^{2}}{\left(- \left(- d + e x\right) \left(d + e x\right)\right)^{\frac{7}{2}}}\, dx"," ",0,"Integral(x*(d + e*x)**2/(-(-d + e*x)*(d + e*x))**(7/2), x)","F",0
49,0,0,0,0.000000," ","integrate((e*x+d)**2/(-e**2*x**2+d**2)**(7/2),x)","\int \frac{\left(d + e x\right)^{2}}{\left(- \left(- d + e x\right) \left(d + e x\right)\right)^{\frac{7}{2}}}\, dx"," ",0,"Integral((d + e*x)**2/(-(-d + e*x)*(d + e*x))**(7/2), x)","F",0
50,0,0,0,0.000000," ","integrate((e*x+d)**2/x/(-e**2*x**2+d**2)**(7/2),x)","\int \frac{\left(d + e x\right)^{2}}{x \left(- \left(- d + e x\right) \left(d + e x\right)\right)^{\frac{7}{2}}}\, dx"," ",0,"Integral((d + e*x)**2/(x*(-(-d + e*x)*(d + e*x))**(7/2)), x)","F",0
51,0,0,0,0.000000," ","integrate((e*x+d)**2/x**2/(-e**2*x**2+d**2)**(7/2),x)","\int \frac{\left(d + e x\right)^{2}}{x^{2} \left(- \left(- d + e x\right) \left(d + e x\right)\right)^{\frac{7}{2}}}\, dx"," ",0,"Integral((d + e*x)**2/(x**2*(-(-d + e*x)*(d + e*x))**(7/2)), x)","F",0
52,0,0,0,0.000000," ","integrate((e*x+d)**2/x**3/(-e**2*x**2+d**2)**(7/2),x)","\int \frac{\left(d + e x\right)^{2}}{x^{3} \left(- \left(- d + e x\right) \left(d + e x\right)\right)^{\frac{7}{2}}}\, dx"," ",0,"Integral((d + e*x)**2/(x**3*(-(-d + e*x)*(d + e*x))**(7/2)), x)","F",0
53,0,0,0,0.000000," ","integrate((e*x+d)**2/x**4/(-e**2*x**2+d**2)**(7/2),x)","\int \frac{\left(d + e x\right)^{2}}{x^{4} \left(- \left(- d + e x\right) \left(d + e x\right)\right)^{\frac{7}{2}}}\, dx"," ",0,"Integral((d + e*x)**2/(x**4*(-(-d + e*x)*(d + e*x))**(7/2)), x)","F",0
54,1,73,0,1.408550," ","integrate(x**3*(1+x)**2/(-x**2+1)**(1/2),x)","- \frac{x^{4} \sqrt{1 - x^{2}}}{5} - \frac{x^{3} \sqrt{1 - x^{2}}}{2} - \frac{3 x^{2} \sqrt{1 - x^{2}}}{5} - \frac{3 x \sqrt{1 - x^{2}}}{4} - \frac{6 \sqrt{1 - x^{2}}}{5} + \frac{3 \operatorname{asin}{\left(x \right)}}{4}"," ",0,"-x**4*sqrt(1 - x**2)/5 - x**3*sqrt(1 - x**2)/2 - 3*x**2*sqrt(1 - x**2)/5 - 3*x*sqrt(1 - x**2)/4 - 6*sqrt(1 - x**2)/5 + 3*asin(x)/4","A",0
55,1,60,0,0.809685," ","integrate(x**2*(1+x)**2/(-x**2+1)**(1/2),x)","- \frac{x^{3} \sqrt{1 - x^{2}}}{4} - \frac{2 x^{2} \sqrt{1 - x^{2}}}{3} - \frac{7 x \sqrt{1 - x^{2}}}{8} - \frac{4 \sqrt{1 - x^{2}}}{3} + \frac{7 \operatorname{asin}{\left(x \right)}}{8}"," ",0,"-x**3*sqrt(1 - x**2)/4 - 2*x**2*sqrt(1 - x**2)/3 - 7*x*sqrt(1 - x**2)/8 - 4*sqrt(1 - x**2)/3 + 7*asin(x)/8","A",0
56,1,37,0,0.407639," ","integrate(x*(1+x)**2/(-x**2+1)**(1/2),x)","- \frac{x^{2} \sqrt{1 - x^{2}}}{3} - x \sqrt{1 - x^{2}} - \frac{5 \sqrt{1 - x^{2}}}{3} + \operatorname{asin}{\left(x \right)}"," ",0,"-x**2*sqrt(1 - x**2)/3 - x*sqrt(1 - x**2) - 5*sqrt(1 - x**2)/3 + asin(x)","A",0
57,1,27,0,0.242481," ","integrate((1+x)**2/(-x**2+1)**(1/2),x)","- \frac{x \sqrt{1 - x^{2}}}{2} - 2 \sqrt{1 - x^{2}} + \frac{3 \operatorname{asin}{\left(x \right)}}{2}"," ",0,"-x*sqrt(1 - x**2)/2 - 2*sqrt(1 - x**2) + 3*asin(x)/2","A",0
58,1,31,0,6.295214," ","integrate((1+x)**2/x/(-x**2+1)**(1/2),x)","- \sqrt{1 - x^{2}} + \begin{cases} - \operatorname{acosh}{\left(\frac{1}{x} \right)} & \text{for}\: \frac{1}{\left|{x^{2}}\right|} > 1 \\i \operatorname{asin}{\left(\frac{1}{x} \right)} & \text{otherwise} \end{cases} + 2 \operatorname{asin}{\left(x \right)}"," ",0,"-sqrt(1 - x**2) + Piecewise((-acosh(1/x), 1/Abs(x**2) > 1), (I*asin(1/x), True)) + 2*asin(x)","A",0
59,1,51,0,4.684253," ","integrate((1+x)**2/x**2/(-x**2+1)**(1/2),x)","\begin{cases} - \frac{i \sqrt{x^{2} - 1}}{x} & \text{for}\: \left|{x^{2}}\right| > 1 \\- \frac{\sqrt{1 - x^{2}}}{x} & \text{otherwise} \end{cases} + 2 \left(\begin{cases} - \operatorname{acosh}{\left(\frac{1}{x} \right)} & \text{for}\: \frac{1}{\left|{x^{2}}\right|} > 1 \\i \operatorname{asin}{\left(\frac{1}{x} \right)} & \text{otherwise} \end{cases}\right) + \operatorname{asin}{\left(x \right)}"," ",0,"Piecewise((-I*sqrt(x**2 - 1)/x, Abs(x**2) > 1), (-sqrt(1 - x**2)/x, True)) + 2*Piecewise((-acosh(1/x), 1/Abs(x**2) > 1), (I*asin(1/x), True)) + asin(x)","C",0
60,1,116,0,7.033004," ","integrate((1+x)**2/x**3/(-x**2+1)**(1/2),x)","2 \left(\begin{cases} - \frac{i \sqrt{x^{2} - 1}}{x} & \text{for}\: \left|{x^{2}}\right| > 1 \\- \frac{\sqrt{1 - x^{2}}}{x} & \text{otherwise} \end{cases}\right) + \begin{cases} - \frac{\operatorname{acosh}{\left(\frac{1}{x} \right)}}{2} - \frac{\sqrt{-1 + \frac{1}{x^{2}}}}{2 x} & \text{for}\: \frac{1}{\left|{x^{2}}\right|} > 1 \\\frac{i \operatorname{asin}{\left(\frac{1}{x} \right)}}{2} - \frac{i}{2 x \sqrt{1 - \frac{1}{x^{2}}}} + \frac{i}{2 x^{3} \sqrt{1 - \frac{1}{x^{2}}}} & \text{otherwise} \end{cases} + \begin{cases} - \operatorname{acosh}{\left(\frac{1}{x} \right)} & \text{for}\: \frac{1}{\left|{x^{2}}\right|} > 1 \\i \operatorname{asin}{\left(\frac{1}{x} \right)} & \text{otherwise} \end{cases}"," ",0,"2*Piecewise((-I*sqrt(x**2 - 1)/x, Abs(x**2) > 1), (-sqrt(1 - x**2)/x, True)) + Piecewise((-acosh(1/x)/2 - sqrt(-1 + x**(-2))/(2*x), 1/Abs(x**2) > 1), (I*asin(1/x)/2 - I/(2*x*sqrt(1 - 1/x**2)) + I/(2*x**3*sqrt(1 - 1/x**2)), True)) + Piecewise((-acosh(1/x), 1/Abs(x**2) > 1), (I*asin(1/x), True))","C",0
61,1,128,0,8.348494," ","integrate((1+x)**2/x**4/(-x**2+1)**(1/2),x)","\begin{cases} - \frac{\sqrt{1 - x^{2}}}{x} - \frac{\left(1 - x^{2}\right)^{\frac{3}{2}}}{3 x^{3}} & \text{for}\: x > -1 \wedge x < 1 \end{cases} + \begin{cases} - \frac{i \sqrt{x^{2} - 1}}{x} & \text{for}\: \left|{x^{2}}\right| > 1 \\- \frac{\sqrt{1 - x^{2}}}{x} & \text{otherwise} \end{cases} + 2 \left(\begin{cases} - \frac{\operatorname{acosh}{\left(\frac{1}{x} \right)}}{2} - \frac{\sqrt{-1 + \frac{1}{x^{2}}}}{2 x} & \text{for}\: \frac{1}{\left|{x^{2}}\right|} > 1 \\\frac{i \operatorname{asin}{\left(\frac{1}{x} \right)}}{2} - \frac{i}{2 x \sqrt{1 - \frac{1}{x^{2}}}} + \frac{i}{2 x^{3} \sqrt{1 - \frac{1}{x^{2}}}} & \text{otherwise} \end{cases}\right)"," ",0,"Piecewise((-sqrt(1 - x**2)/x - (1 - x**2)**(3/2)/(3*x**3), (x > -1) & (x < 1))) + Piecewise((-I*sqrt(x**2 - 1)/x, Abs(x**2) > 1), (-sqrt(1 - x**2)/x, True)) + 2*Piecewise((-acosh(1/x)/2 - sqrt(-1 + x**(-2))/(2*x), 1/Abs(x**2) > 1), (I*asin(1/x)/2 - I/(2*x*sqrt(1 - 1/x**2)) + I/(2*x**3*sqrt(1 - 1/x**2)), True))","C",0
62,1,223,0,11.058565," ","integrate((1+x)**2/x**5/(-x**2+1)**(1/2),x)","2 \left(\begin{cases} - \frac{\sqrt{1 - x^{2}}}{x} - \frac{\left(1 - x^{2}\right)^{\frac{3}{2}}}{3 x^{3}} & \text{for}\: x > -1 \wedge x < 1 \end{cases}\right) + \begin{cases} - \frac{\operatorname{acosh}{\left(\frac{1}{x} \right)}}{2} - \frac{\sqrt{-1 + \frac{1}{x^{2}}}}{2 x} & \text{for}\: \frac{1}{\left|{x^{2}}\right|} > 1 \\\frac{i \operatorname{asin}{\left(\frac{1}{x} \right)}}{2} - \frac{i}{2 x \sqrt{1 - \frac{1}{x^{2}}}} + \frac{i}{2 x^{3} \sqrt{1 - \frac{1}{x^{2}}}} & \text{otherwise} \end{cases} + \begin{cases} - \frac{3 \operatorname{acosh}{\left(\frac{1}{x} \right)}}{8} + \frac{3}{8 x \sqrt{-1 + \frac{1}{x^{2}}}} - \frac{1}{8 x^{3} \sqrt{-1 + \frac{1}{x^{2}}}} - \frac{1}{4 x^{5} \sqrt{-1 + \frac{1}{x^{2}}}} & \text{for}\: \frac{1}{\left|{x^{2}}\right|} > 1 \\\frac{3 i \operatorname{asin}{\left(\frac{1}{x} \right)}}{8} - \frac{3 i}{8 x \sqrt{1 - \frac{1}{x^{2}}}} + \frac{i}{8 x^{3} \sqrt{1 - \frac{1}{x^{2}}}} + \frac{i}{4 x^{5} \sqrt{1 - \frac{1}{x^{2}}}} & \text{otherwise} \end{cases}"," ",0,"2*Piecewise((-sqrt(1 - x**2)/x - (1 - x**2)**(3/2)/(3*x**3), (x > -1) & (x < 1))) + Piecewise((-acosh(1/x)/2 - sqrt(-1 + x**(-2))/(2*x), 1/Abs(x**2) > 1), (I*asin(1/x)/2 - I/(2*x*sqrt(1 - 1/x**2)) + I/(2*x**3*sqrt(1 - 1/x**2)), True)) + Piecewise((-3*acosh(1/x)/8 + 3/(8*x*sqrt(-1 + x**(-2))) - 1/(8*x**3*sqrt(-1 + x**(-2))) - 1/(4*x**5*sqrt(-1 + x**(-2))), 1/Abs(x**2) > 1), (3*I*asin(1/x)/8 - 3*I/(8*x*sqrt(1 - 1/x**2)) + I/(8*x**3*sqrt(1 - 1/x**2)) + I/(4*x**5*sqrt(1 - 1/x**2)), True))","A",0
63,1,201,0,12.692613," ","integrate((1+x)**2/x**6/(-x**2+1)**(1/2),x)","\begin{cases} - \frac{\sqrt{1 - x^{2}}}{x} - \frac{\left(1 - x^{2}\right)^{\frac{3}{2}}}{3 x^{3}} & \text{for}\: x > -1 \wedge x < 1 \end{cases} + \begin{cases} - \frac{\sqrt{1 - x^{2}}}{x} - \frac{2 \left(1 - x^{2}\right)^{\frac{3}{2}}}{3 x^{3}} - \frac{\left(1 - x^{2}\right)^{\frac{5}{2}}}{5 x^{5}} & \text{for}\: x > -1 \wedge x < 1 \end{cases} + 2 \left(\begin{cases} - \frac{3 \operatorname{acosh}{\left(\frac{1}{x} \right)}}{8} + \frac{3}{8 x \sqrt{-1 + \frac{1}{x^{2}}}} - \frac{1}{8 x^{3} \sqrt{-1 + \frac{1}{x^{2}}}} - \frac{1}{4 x^{5} \sqrt{-1 + \frac{1}{x^{2}}}} & \text{for}\: \frac{1}{\left|{x^{2}}\right|} > 1 \\\frac{3 i \operatorname{asin}{\left(\frac{1}{x} \right)}}{8} - \frac{3 i}{8 x \sqrt{1 - \frac{1}{x^{2}}}} + \frac{i}{8 x^{3} \sqrt{1 - \frac{1}{x^{2}}}} + \frac{i}{4 x^{5} \sqrt{1 - \frac{1}{x^{2}}}} & \text{otherwise} \end{cases}\right)"," ",0,"Piecewise((-sqrt(1 - x**2)/x - (1 - x**2)**(3/2)/(3*x**3), (x > -1) & (x < 1))) + Piecewise((-sqrt(1 - x**2)/x - 2*(1 - x**2)**(3/2)/(3*x**3) - (1 - x**2)**(5/2)/(5*x**5), (x > -1) & (x < 1))) + 2*Piecewise((-3*acosh(1/x)/8 + 3/(8*x*sqrt(-1 + x**(-2))) - 1/(8*x**3*sqrt(-1 + x**(-2))) - 1/(4*x**5*sqrt(-1 + x**(-2))), 1/Abs(x**2) > 1), (3*I*asin(1/x)/8 - 3*I/(8*x*sqrt(1 - 1/x**2)) + I/(8*x**3*sqrt(1 - 1/x**2)) + I/(4*x**5*sqrt(1 - 1/x**2)), True))","C",0
64,1,544,0,10.027081," ","integrate((e*x+d)**3*(-e**2*x**2+d**2)**(1/2)/x**5,x)","d^{3} \left(\begin{cases} - \frac{d^{2}}{4 e x^{5} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{3 e}{8 x^{3} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} - \frac{e^{3}}{8 d^{2} x \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{e^{4} \operatorname{acosh}{\left(\frac{d}{e x} \right)}}{8 d^{3}} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\\frac{i d^{2}}{4 e x^{5} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} - \frac{3 i e}{8 x^{3} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} + \frac{i e^{3}}{8 d^{2} x \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} - \frac{i e^{4} \operatorname{asin}{\left(\frac{d}{e x} \right)}}{8 d^{3}} & \text{otherwise} \end{cases}\right) + 3 d^{2} e \left(\begin{cases} - \frac{e \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}}{3 x^{2}} + \frac{e^{3} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}}{3 d^{2}} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\- \frac{i e \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{3 x^{2}} + \frac{i e^{3} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{3 d^{2}} & \text{otherwise} \end{cases}\right) + 3 d e^{2} \left(\begin{cases} - \frac{d^{2}}{2 e x^{3} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{e}{2 x \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{e^{2} \operatorname{acosh}{\left(\frac{d}{e x} \right)}}{2 d} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\- \frac{i e \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{2 x} - \frac{i e^{2} \operatorname{asin}{\left(\frac{d}{e x} \right)}}{2 d} & \text{otherwise} \end{cases}\right) + e^{3} \left(\begin{cases} \frac{i d}{x \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + i e \operatorname{acosh}{\left(\frac{e x}{d} \right)} - \frac{i e^{2} x}{d \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\- \frac{d}{x \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} - e \operatorname{asin}{\left(\frac{e x}{d} \right)} + \frac{e^{2} x}{d \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} & \text{otherwise} \end{cases}\right)"," ",0,"d**3*Piecewise((-d**2/(4*e*x**5*sqrt(d**2/(e**2*x**2) - 1)) + 3*e/(8*x**3*sqrt(d**2/(e**2*x**2) - 1)) - e**3/(8*d**2*x*sqrt(d**2/(e**2*x**2) - 1)) + e**4*acosh(d/(e*x))/(8*d**3), Abs(d**2/(e**2*x**2)) > 1), (I*d**2/(4*e*x**5*sqrt(-d**2/(e**2*x**2) + 1)) - 3*I*e/(8*x**3*sqrt(-d**2/(e**2*x**2) + 1)) + I*e**3/(8*d**2*x*sqrt(-d**2/(e**2*x**2) + 1)) - I*e**4*asin(d/(e*x))/(8*d**3), True)) + 3*d**2*e*Piecewise((-e*sqrt(d**2/(e**2*x**2) - 1)/(3*x**2) + e**3*sqrt(d**2/(e**2*x**2) - 1)/(3*d**2), Abs(d**2/(e**2*x**2)) > 1), (-I*e*sqrt(-d**2/(e**2*x**2) + 1)/(3*x**2) + I*e**3*sqrt(-d**2/(e**2*x**2) + 1)/(3*d**2), True)) + 3*d*e**2*Piecewise((-d**2/(2*e*x**3*sqrt(d**2/(e**2*x**2) - 1)) + e/(2*x*sqrt(d**2/(e**2*x**2) - 1)) + e**2*acosh(d/(e*x))/(2*d), Abs(d**2/(e**2*x**2)) > 1), (-I*e*sqrt(-d**2/(e**2*x**2) + 1)/(2*x) - I*e**2*asin(d/(e*x))/(2*d), True)) + e**3*Piecewise((I*d/(x*sqrt(-1 + e**2*x**2/d**2)) + I*e*acosh(e*x/d) - I*e**2*x/(d*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (-d/(x*sqrt(1 - e**2*x**2/d**2)) - e*asin(e*x/d) + e**2*x/(d*sqrt(1 - e**2*x**2/d**2)), True))","C",0
65,1,2273,0,101.430866," ","integrate(x**5*(e*x+d)**3*(-e**2*x**2+d**2)**(5/2),x)","d^{7} \left(\begin{cases} - \frac{8 d^{6} \sqrt{d^{2} - e^{2} x^{2}}}{105 e^{6}} - \frac{4 d^{4} x^{2} \sqrt{d^{2} - e^{2} x^{2}}}{105 e^{4}} - \frac{d^{2} x^{4} \sqrt{d^{2} - e^{2} x^{2}}}{35 e^{2}} + \frac{x^{6} \sqrt{d^{2} - e^{2} x^{2}}}{7} & \text{for}\: e \neq 0 \\\frac{x^{6} \sqrt{d^{2}}}{6} & \text{otherwise} \end{cases}\right) + 3 d^{6} e \left(\begin{cases} - \frac{5 i d^{8} \operatorname{acosh}{\left(\frac{e x}{d} \right)}}{128 e^{7}} + \frac{5 i d^{7} x}{128 e^{6} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{5 i d^{5} x^{3}}{384 e^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{i d^{3} x^{5}}{192 e^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{7 i d x^{7}}{48 \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + \frac{i e^{2} x^{9}}{8 d \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{5 d^{8} \operatorname{asin}{\left(\frac{e x}{d} \right)}}{128 e^{7}} - \frac{5 d^{7} x}{128 e^{6} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{5 d^{5} x^{3}}{384 e^{4} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{d^{3} x^{5}}{192 e^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{7 d x^{7}}{48 \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} - \frac{e^{2} x^{9}}{8 d \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} & \text{otherwise} \end{cases}\right) + d^{5} e^{2} \left(\begin{cases} - \frac{16 d^{8} \sqrt{d^{2} - e^{2} x^{2}}}{315 e^{8}} - \frac{8 d^{6} x^{2} \sqrt{d^{2} - e^{2} x^{2}}}{315 e^{6}} - \frac{2 d^{4} x^{4} \sqrt{d^{2} - e^{2} x^{2}}}{105 e^{4}} - \frac{d^{2} x^{6} \sqrt{d^{2} - e^{2} x^{2}}}{63 e^{2}} + \frac{x^{8} \sqrt{d^{2} - e^{2} x^{2}}}{9} & \text{for}\: e \neq 0 \\\frac{x^{8} \sqrt{d^{2}}}{8} & \text{otherwise} \end{cases}\right) - 5 d^{4} e^{3} \left(\begin{cases} - \frac{7 i d^{10} \operatorname{acosh}{\left(\frac{e x}{d} \right)}}{256 e^{9}} + \frac{7 i d^{9} x}{256 e^{8} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{7 i d^{7} x^{3}}{768 e^{6} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{7 i d^{5} x^{5}}{1920 e^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{i d^{3} x^{7}}{480 e^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{9 i d x^{9}}{80 \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + \frac{i e^{2} x^{11}}{10 d \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{7 d^{10} \operatorname{asin}{\left(\frac{e x}{d} \right)}}{256 e^{9}} - \frac{7 d^{9} x}{256 e^{8} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{7 d^{7} x^{3}}{768 e^{6} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{7 d^{5} x^{5}}{1920 e^{4} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{d^{3} x^{7}}{480 e^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{9 d x^{9}}{80 \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} - \frac{e^{2} x^{11}}{10 d \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} & \text{otherwise} \end{cases}\right) - 5 d^{3} e^{4} \left(\begin{cases} - \frac{128 d^{10} \sqrt{d^{2} - e^{2} x^{2}}}{3465 e^{10}} - \frac{64 d^{8} x^{2} \sqrt{d^{2} - e^{2} x^{2}}}{3465 e^{8}} - \frac{16 d^{6} x^{4} \sqrt{d^{2} - e^{2} x^{2}}}{1155 e^{6}} - \frac{8 d^{4} x^{6} \sqrt{d^{2} - e^{2} x^{2}}}{693 e^{4}} - \frac{d^{2} x^{8} \sqrt{d^{2} - e^{2} x^{2}}}{99 e^{2}} + \frac{x^{10} \sqrt{d^{2} - e^{2} x^{2}}}{11} & \text{for}\: e \neq 0 \\\frac{x^{10} \sqrt{d^{2}}}{10} & \text{otherwise} \end{cases}\right) + d^{2} e^{5} \left(\begin{cases} - \frac{21 i d^{12} \operatorname{acosh}{\left(\frac{e x}{d} \right)}}{1024 e^{11}} + \frac{21 i d^{11} x}{1024 e^{10} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{7 i d^{9} x^{3}}{1024 e^{8} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{7 i d^{7} x^{5}}{2560 e^{6} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{i d^{5} x^{7}}{640 e^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{i d^{3} x^{9}}{960 e^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{11 i d x^{11}}{120 \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + \frac{i e^{2} x^{13}}{12 d \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{21 d^{12} \operatorname{asin}{\left(\frac{e x}{d} \right)}}{1024 e^{11}} - \frac{21 d^{11} x}{1024 e^{10} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{7 d^{9} x^{3}}{1024 e^{8} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{7 d^{7} x^{5}}{2560 e^{6} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{d^{5} x^{7}}{640 e^{4} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{d^{3} x^{9}}{960 e^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{11 d x^{11}}{120 \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} - \frac{e^{2} x^{13}}{12 d \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} & \text{otherwise} \end{cases}\right) + 3 d e^{6} \left(\begin{cases} - \frac{256 d^{12} \sqrt{d^{2} - e^{2} x^{2}}}{9009 e^{12}} - \frac{128 d^{10} x^{2} \sqrt{d^{2} - e^{2} x^{2}}}{9009 e^{10}} - \frac{32 d^{8} x^{4} \sqrt{d^{2} - e^{2} x^{2}}}{3003 e^{8}} - \frac{80 d^{6} x^{6} \sqrt{d^{2} - e^{2} x^{2}}}{9009 e^{6}} - \frac{10 d^{4} x^{8} \sqrt{d^{2} - e^{2} x^{2}}}{1287 e^{4}} - \frac{d^{2} x^{10} \sqrt{d^{2} - e^{2} x^{2}}}{143 e^{2}} + \frac{x^{12} \sqrt{d^{2} - e^{2} x^{2}}}{13} & \text{for}\: e \neq 0 \\\frac{x^{12} \sqrt{d^{2}}}{12} & \text{otherwise} \end{cases}\right) + e^{7} \left(\begin{cases} - \frac{33 i d^{14} \operatorname{acosh}{\left(\frac{e x}{d} \right)}}{2048 e^{13}} + \frac{33 i d^{13} x}{2048 e^{12} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{11 i d^{11} x^{3}}{2048 e^{10} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{11 i d^{9} x^{5}}{5120 e^{8} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{11 i d^{7} x^{7}}{8960 e^{6} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{11 i d^{5} x^{9}}{13440 e^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{i d^{3} x^{11}}{1680 e^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{13 i d x^{13}}{168 \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + \frac{i e^{2} x^{15}}{14 d \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{33 d^{14} \operatorname{asin}{\left(\frac{e x}{d} \right)}}{2048 e^{13}} - \frac{33 d^{13} x}{2048 e^{12} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{11 d^{11} x^{3}}{2048 e^{10} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{11 d^{9} x^{5}}{5120 e^{8} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{11 d^{7} x^{7}}{8960 e^{6} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{11 d^{5} x^{9}}{13440 e^{4} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{d^{3} x^{11}}{1680 e^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{13 d x^{13}}{168 \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} - \frac{e^{2} x^{15}}{14 d \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} & \text{otherwise} \end{cases}\right)"," ",0,"d**7*Piecewise((-8*d**6*sqrt(d**2 - e**2*x**2)/(105*e**6) - 4*d**4*x**2*sqrt(d**2 - e**2*x**2)/(105*e**4) - d**2*x**4*sqrt(d**2 - e**2*x**2)/(35*e**2) + x**6*sqrt(d**2 - e**2*x**2)/7, Ne(e, 0)), (x**6*sqrt(d**2)/6, True)) + 3*d**6*e*Piecewise((-5*I*d**8*acosh(e*x/d)/(128*e**7) + 5*I*d**7*x/(128*e**6*sqrt(-1 + e**2*x**2/d**2)) - 5*I*d**5*x**3/(384*e**4*sqrt(-1 + e**2*x**2/d**2)) - I*d**3*x**5/(192*e**2*sqrt(-1 + e**2*x**2/d**2)) - 7*I*d*x**7/(48*sqrt(-1 + e**2*x**2/d**2)) + I*e**2*x**9/(8*d*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (5*d**8*asin(e*x/d)/(128*e**7) - 5*d**7*x/(128*e**6*sqrt(1 - e**2*x**2/d**2)) + 5*d**5*x**3/(384*e**4*sqrt(1 - e**2*x**2/d**2)) + d**3*x**5/(192*e**2*sqrt(1 - e**2*x**2/d**2)) + 7*d*x**7/(48*sqrt(1 - e**2*x**2/d**2)) - e**2*x**9/(8*d*sqrt(1 - e**2*x**2/d**2)), True)) + d**5*e**2*Piecewise((-16*d**8*sqrt(d**2 - e**2*x**2)/(315*e**8) - 8*d**6*x**2*sqrt(d**2 - e**2*x**2)/(315*e**6) - 2*d**4*x**4*sqrt(d**2 - e**2*x**2)/(105*e**4) - d**2*x**6*sqrt(d**2 - e**2*x**2)/(63*e**2) + x**8*sqrt(d**2 - e**2*x**2)/9, Ne(e, 0)), (x**8*sqrt(d**2)/8, True)) - 5*d**4*e**3*Piecewise((-7*I*d**10*acosh(e*x/d)/(256*e**9) + 7*I*d**9*x/(256*e**8*sqrt(-1 + e**2*x**2/d**2)) - 7*I*d**7*x**3/(768*e**6*sqrt(-1 + e**2*x**2/d**2)) - 7*I*d**5*x**5/(1920*e**4*sqrt(-1 + e**2*x**2/d**2)) - I*d**3*x**7/(480*e**2*sqrt(-1 + e**2*x**2/d**2)) - 9*I*d*x**9/(80*sqrt(-1 + e**2*x**2/d**2)) + I*e**2*x**11/(10*d*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (7*d**10*asin(e*x/d)/(256*e**9) - 7*d**9*x/(256*e**8*sqrt(1 - e**2*x**2/d**2)) + 7*d**7*x**3/(768*e**6*sqrt(1 - e**2*x**2/d**2)) + 7*d**5*x**5/(1920*e**4*sqrt(1 - e**2*x**2/d**2)) + d**3*x**7/(480*e**2*sqrt(1 - e**2*x**2/d**2)) + 9*d*x**9/(80*sqrt(1 - e**2*x**2/d**2)) - e**2*x**11/(10*d*sqrt(1 - e**2*x**2/d**2)), True)) - 5*d**3*e**4*Piecewise((-128*d**10*sqrt(d**2 - e**2*x**2)/(3465*e**10) - 64*d**8*x**2*sqrt(d**2 - e**2*x**2)/(3465*e**8) - 16*d**6*x**4*sqrt(d**2 - e**2*x**2)/(1155*e**6) - 8*d**4*x**6*sqrt(d**2 - e**2*x**2)/(693*e**4) - d**2*x**8*sqrt(d**2 - e**2*x**2)/(99*e**2) + x**10*sqrt(d**2 - e**2*x**2)/11, Ne(e, 0)), (x**10*sqrt(d**2)/10, True)) + d**2*e**5*Piecewise((-21*I*d**12*acosh(e*x/d)/(1024*e**11) + 21*I*d**11*x/(1024*e**10*sqrt(-1 + e**2*x**2/d**2)) - 7*I*d**9*x**3/(1024*e**8*sqrt(-1 + e**2*x**2/d**2)) - 7*I*d**7*x**5/(2560*e**6*sqrt(-1 + e**2*x**2/d**2)) - I*d**5*x**7/(640*e**4*sqrt(-1 + e**2*x**2/d**2)) - I*d**3*x**9/(960*e**2*sqrt(-1 + e**2*x**2/d**2)) - 11*I*d*x**11/(120*sqrt(-1 + e**2*x**2/d**2)) + I*e**2*x**13/(12*d*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (21*d**12*asin(e*x/d)/(1024*e**11) - 21*d**11*x/(1024*e**10*sqrt(1 - e**2*x**2/d**2)) + 7*d**9*x**3/(1024*e**8*sqrt(1 - e**2*x**2/d**2)) + 7*d**7*x**5/(2560*e**6*sqrt(1 - e**2*x**2/d**2)) + d**5*x**7/(640*e**4*sqrt(1 - e**2*x**2/d**2)) + d**3*x**9/(960*e**2*sqrt(1 - e**2*x**2/d**2)) + 11*d*x**11/(120*sqrt(1 - e**2*x**2/d**2)) - e**2*x**13/(12*d*sqrt(1 - e**2*x**2/d**2)), True)) + 3*d*e**6*Piecewise((-256*d**12*sqrt(d**2 - e**2*x**2)/(9009*e**12) - 128*d**10*x**2*sqrt(d**2 - e**2*x**2)/(9009*e**10) - 32*d**8*x**4*sqrt(d**2 - e**2*x**2)/(3003*e**8) - 80*d**6*x**6*sqrt(d**2 - e**2*x**2)/(9009*e**6) - 10*d**4*x**8*sqrt(d**2 - e**2*x**2)/(1287*e**4) - d**2*x**10*sqrt(d**2 - e**2*x**2)/(143*e**2) + x**12*sqrt(d**2 - e**2*x**2)/13, Ne(e, 0)), (x**12*sqrt(d**2)/12, True)) + e**7*Piecewise((-33*I*d**14*acosh(e*x/d)/(2048*e**13) + 33*I*d**13*x/(2048*e**12*sqrt(-1 + e**2*x**2/d**2)) - 11*I*d**11*x**3/(2048*e**10*sqrt(-1 + e**2*x**2/d**2)) - 11*I*d**9*x**5/(5120*e**8*sqrt(-1 + e**2*x**2/d**2)) - 11*I*d**7*x**7/(8960*e**6*sqrt(-1 + e**2*x**2/d**2)) - 11*I*d**5*x**9/(13440*e**4*sqrt(-1 + e**2*x**2/d**2)) - I*d**3*x**11/(1680*e**2*sqrt(-1 + e**2*x**2/d**2)) - 13*I*d*x**13/(168*sqrt(-1 + e**2*x**2/d**2)) + I*e**2*x**15/(14*d*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (33*d**14*asin(e*x/d)/(2048*e**13) - 33*d**13*x/(2048*e**12*sqrt(1 - e**2*x**2/d**2)) + 11*d**11*x**3/(2048*e**10*sqrt(1 - e**2*x**2/d**2)) + 11*d**9*x**5/(5120*e**8*sqrt(1 - e**2*x**2/d**2)) + 11*d**7*x**7/(8960*e**6*sqrt(1 - e**2*x**2/d**2)) + 11*d**5*x**9/(13440*e**4*sqrt(1 - e**2*x**2/d**2)) + d**3*x**11/(1680*e**2*sqrt(1 - e**2*x**2/d**2)) + 13*d*x**13/(168*sqrt(1 - e**2*x**2/d**2)) - e**2*x**15/(14*d*sqrt(1 - e**2*x**2/d**2)), True))","A",0
66,1,2028,0,64.638475," ","integrate(x**4*(e*x+d)**3*(-e**2*x**2+d**2)**(5/2),x)","d^{7} \left(\begin{cases} - \frac{i d^{6} \operatorname{acosh}{\left(\frac{e x}{d} \right)}}{16 e^{5}} + \frac{i d^{5} x}{16 e^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{i d^{3} x^{3}}{48 e^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{5 i d x^{5}}{24 \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + \frac{i e^{2} x^{7}}{6 d \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{d^{6} \operatorname{asin}{\left(\frac{e x}{d} \right)}}{16 e^{5}} - \frac{d^{5} x}{16 e^{4} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{d^{3} x^{3}}{48 e^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{5 d x^{5}}{24 \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} - \frac{e^{2} x^{7}}{6 d \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} & \text{otherwise} \end{cases}\right) + 3 d^{6} e \left(\begin{cases} - \frac{8 d^{6} \sqrt{d^{2} - e^{2} x^{2}}}{105 e^{6}} - \frac{4 d^{4} x^{2} \sqrt{d^{2} - e^{2} x^{2}}}{105 e^{4}} - \frac{d^{2} x^{4} \sqrt{d^{2} - e^{2} x^{2}}}{35 e^{2}} + \frac{x^{6} \sqrt{d^{2} - e^{2} x^{2}}}{7} & \text{for}\: e \neq 0 \\\frac{x^{6} \sqrt{d^{2}}}{6} & \text{otherwise} \end{cases}\right) + d^{5} e^{2} \left(\begin{cases} - \frac{5 i d^{8} \operatorname{acosh}{\left(\frac{e x}{d} \right)}}{128 e^{7}} + \frac{5 i d^{7} x}{128 e^{6} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{5 i d^{5} x^{3}}{384 e^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{i d^{3} x^{5}}{192 e^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{7 i d x^{7}}{48 \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + \frac{i e^{2} x^{9}}{8 d \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{5 d^{8} \operatorname{asin}{\left(\frac{e x}{d} \right)}}{128 e^{7}} - \frac{5 d^{7} x}{128 e^{6} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{5 d^{5} x^{3}}{384 e^{4} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{d^{3} x^{5}}{192 e^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{7 d x^{7}}{48 \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} - \frac{e^{2} x^{9}}{8 d \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} & \text{otherwise} \end{cases}\right) - 5 d^{4} e^{3} \left(\begin{cases} - \frac{16 d^{8} \sqrt{d^{2} - e^{2} x^{2}}}{315 e^{8}} - \frac{8 d^{6} x^{2} \sqrt{d^{2} - e^{2} x^{2}}}{315 e^{6}} - \frac{2 d^{4} x^{4} \sqrt{d^{2} - e^{2} x^{2}}}{105 e^{4}} - \frac{d^{2} x^{6} \sqrt{d^{2} - e^{2} x^{2}}}{63 e^{2}} + \frac{x^{8} \sqrt{d^{2} - e^{2} x^{2}}}{9} & \text{for}\: e \neq 0 \\\frac{x^{8} \sqrt{d^{2}}}{8} & \text{otherwise} \end{cases}\right) - 5 d^{3} e^{4} \left(\begin{cases} - \frac{7 i d^{10} \operatorname{acosh}{\left(\frac{e x}{d} \right)}}{256 e^{9}} + \frac{7 i d^{9} x}{256 e^{8} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{7 i d^{7} x^{3}}{768 e^{6} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{7 i d^{5} x^{5}}{1920 e^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{i d^{3} x^{7}}{480 e^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{9 i d x^{9}}{80 \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + \frac{i e^{2} x^{11}}{10 d \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{7 d^{10} \operatorname{asin}{\left(\frac{e x}{d} \right)}}{256 e^{9}} - \frac{7 d^{9} x}{256 e^{8} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{7 d^{7} x^{3}}{768 e^{6} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{7 d^{5} x^{5}}{1920 e^{4} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{d^{3} x^{7}}{480 e^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{9 d x^{9}}{80 \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} - \frac{e^{2} x^{11}}{10 d \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} & \text{otherwise} \end{cases}\right) + d^{2} e^{5} \left(\begin{cases} - \frac{128 d^{10} \sqrt{d^{2} - e^{2} x^{2}}}{3465 e^{10}} - \frac{64 d^{8} x^{2} \sqrt{d^{2} - e^{2} x^{2}}}{3465 e^{8}} - \frac{16 d^{6} x^{4} \sqrt{d^{2} - e^{2} x^{2}}}{1155 e^{6}} - \frac{8 d^{4} x^{6} \sqrt{d^{2} - e^{2} x^{2}}}{693 e^{4}} - \frac{d^{2} x^{8} \sqrt{d^{2} - e^{2} x^{2}}}{99 e^{2}} + \frac{x^{10} \sqrt{d^{2} - e^{2} x^{2}}}{11} & \text{for}\: e \neq 0 \\\frac{x^{10} \sqrt{d^{2}}}{10} & \text{otherwise} \end{cases}\right) + 3 d e^{6} \left(\begin{cases} - \frac{21 i d^{12} \operatorname{acosh}{\left(\frac{e x}{d} \right)}}{1024 e^{11}} + \frac{21 i d^{11} x}{1024 e^{10} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{7 i d^{9} x^{3}}{1024 e^{8} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{7 i d^{7} x^{5}}{2560 e^{6} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{i d^{5} x^{7}}{640 e^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{i d^{3} x^{9}}{960 e^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{11 i d x^{11}}{120 \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + \frac{i e^{2} x^{13}}{12 d \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{21 d^{12} \operatorname{asin}{\left(\frac{e x}{d} \right)}}{1024 e^{11}} - \frac{21 d^{11} x}{1024 e^{10} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{7 d^{9} x^{3}}{1024 e^{8} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{7 d^{7} x^{5}}{2560 e^{6} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{d^{5} x^{7}}{640 e^{4} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{d^{3} x^{9}}{960 e^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{11 d x^{11}}{120 \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} - \frac{e^{2} x^{13}}{12 d \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} & \text{otherwise} \end{cases}\right) + e^{7} \left(\begin{cases} - \frac{256 d^{12} \sqrt{d^{2} - e^{2} x^{2}}}{9009 e^{12}} - \frac{128 d^{10} x^{2} \sqrt{d^{2} - e^{2} x^{2}}}{9009 e^{10}} - \frac{32 d^{8} x^{4} \sqrt{d^{2} - e^{2} x^{2}}}{3003 e^{8}} - \frac{80 d^{6} x^{6} \sqrt{d^{2} - e^{2} x^{2}}}{9009 e^{6}} - \frac{10 d^{4} x^{8} \sqrt{d^{2} - e^{2} x^{2}}}{1287 e^{4}} - \frac{d^{2} x^{10} \sqrt{d^{2} - e^{2} x^{2}}}{143 e^{2}} + \frac{x^{12} \sqrt{d^{2} - e^{2} x^{2}}}{13} & \text{for}\: e \neq 0 \\\frac{x^{12} \sqrt{d^{2}}}{12} & \text{otherwise} \end{cases}\right)"," ",0,"d**7*Piecewise((-I*d**6*acosh(e*x/d)/(16*e**5) + I*d**5*x/(16*e**4*sqrt(-1 + e**2*x**2/d**2)) - I*d**3*x**3/(48*e**2*sqrt(-1 + e**2*x**2/d**2)) - 5*I*d*x**5/(24*sqrt(-1 + e**2*x**2/d**2)) + I*e**2*x**7/(6*d*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (d**6*asin(e*x/d)/(16*e**5) - d**5*x/(16*e**4*sqrt(1 - e**2*x**2/d**2)) + d**3*x**3/(48*e**2*sqrt(1 - e**2*x**2/d**2)) + 5*d*x**5/(24*sqrt(1 - e**2*x**2/d**2)) - e**2*x**7/(6*d*sqrt(1 - e**2*x**2/d**2)), True)) + 3*d**6*e*Piecewise((-8*d**6*sqrt(d**2 - e**2*x**2)/(105*e**6) - 4*d**4*x**2*sqrt(d**2 - e**2*x**2)/(105*e**4) - d**2*x**4*sqrt(d**2 - e**2*x**2)/(35*e**2) + x**6*sqrt(d**2 - e**2*x**2)/7, Ne(e, 0)), (x**6*sqrt(d**2)/6, True)) + d**5*e**2*Piecewise((-5*I*d**8*acosh(e*x/d)/(128*e**7) + 5*I*d**7*x/(128*e**6*sqrt(-1 + e**2*x**2/d**2)) - 5*I*d**5*x**3/(384*e**4*sqrt(-1 + e**2*x**2/d**2)) - I*d**3*x**5/(192*e**2*sqrt(-1 + e**2*x**2/d**2)) - 7*I*d*x**7/(48*sqrt(-1 + e**2*x**2/d**2)) + I*e**2*x**9/(8*d*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (5*d**8*asin(e*x/d)/(128*e**7) - 5*d**7*x/(128*e**6*sqrt(1 - e**2*x**2/d**2)) + 5*d**5*x**3/(384*e**4*sqrt(1 - e**2*x**2/d**2)) + d**3*x**5/(192*e**2*sqrt(1 - e**2*x**2/d**2)) + 7*d*x**7/(48*sqrt(1 - e**2*x**2/d**2)) - e**2*x**9/(8*d*sqrt(1 - e**2*x**2/d**2)), True)) - 5*d**4*e**3*Piecewise((-16*d**8*sqrt(d**2 - e**2*x**2)/(315*e**8) - 8*d**6*x**2*sqrt(d**2 - e**2*x**2)/(315*e**6) - 2*d**4*x**4*sqrt(d**2 - e**2*x**2)/(105*e**4) - d**2*x**6*sqrt(d**2 - e**2*x**2)/(63*e**2) + x**8*sqrt(d**2 - e**2*x**2)/9, Ne(e, 0)), (x**8*sqrt(d**2)/8, True)) - 5*d**3*e**4*Piecewise((-7*I*d**10*acosh(e*x/d)/(256*e**9) + 7*I*d**9*x/(256*e**8*sqrt(-1 + e**2*x**2/d**2)) - 7*I*d**7*x**3/(768*e**6*sqrt(-1 + e**2*x**2/d**2)) - 7*I*d**5*x**5/(1920*e**4*sqrt(-1 + e**2*x**2/d**2)) - I*d**3*x**7/(480*e**2*sqrt(-1 + e**2*x**2/d**2)) - 9*I*d*x**9/(80*sqrt(-1 + e**2*x**2/d**2)) + I*e**2*x**11/(10*d*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (7*d**10*asin(e*x/d)/(256*e**9) - 7*d**9*x/(256*e**8*sqrt(1 - e**2*x**2/d**2)) + 7*d**7*x**3/(768*e**6*sqrt(1 - e**2*x**2/d**2)) + 7*d**5*x**5/(1920*e**4*sqrt(1 - e**2*x**2/d**2)) + d**3*x**7/(480*e**2*sqrt(1 - e**2*x**2/d**2)) + 9*d*x**9/(80*sqrt(1 - e**2*x**2/d**2)) - e**2*x**11/(10*d*sqrt(1 - e**2*x**2/d**2)), True)) + d**2*e**5*Piecewise((-128*d**10*sqrt(d**2 - e**2*x**2)/(3465*e**10) - 64*d**8*x**2*sqrt(d**2 - e**2*x**2)/(3465*e**8) - 16*d**6*x**4*sqrt(d**2 - e**2*x**2)/(1155*e**6) - 8*d**4*x**6*sqrt(d**2 - e**2*x**2)/(693*e**4) - d**2*x**8*sqrt(d**2 - e**2*x**2)/(99*e**2) + x**10*sqrt(d**2 - e**2*x**2)/11, Ne(e, 0)), (x**10*sqrt(d**2)/10, True)) + 3*d*e**6*Piecewise((-21*I*d**12*acosh(e*x/d)/(1024*e**11) + 21*I*d**11*x/(1024*e**10*sqrt(-1 + e**2*x**2/d**2)) - 7*I*d**9*x**3/(1024*e**8*sqrt(-1 + e**2*x**2/d**2)) - 7*I*d**7*x**5/(2560*e**6*sqrt(-1 + e**2*x**2/d**2)) - I*d**5*x**7/(640*e**4*sqrt(-1 + e**2*x**2/d**2)) - I*d**3*x**9/(960*e**2*sqrt(-1 + e**2*x**2/d**2)) - 11*I*d*x**11/(120*sqrt(-1 + e**2*x**2/d**2)) + I*e**2*x**13/(12*d*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (21*d**12*asin(e*x/d)/(1024*e**11) - 21*d**11*x/(1024*e**10*sqrt(1 - e**2*x**2/d**2)) + 7*d**9*x**3/(1024*e**8*sqrt(1 - e**2*x**2/d**2)) + 7*d**7*x**5/(2560*e**6*sqrt(1 - e**2*x**2/d**2)) + d**5*x**7/(640*e**4*sqrt(1 - e**2*x**2/d**2)) + d**3*x**9/(960*e**2*sqrt(1 - e**2*x**2/d**2)) + 11*d*x**11/(120*sqrt(1 - e**2*x**2/d**2)) - e**2*x**13/(12*d*sqrt(1 - e**2*x**2/d**2)), True)) + e**7*Piecewise((-256*d**12*sqrt(d**2 - e**2*x**2)/(9009*e**12) - 128*d**10*x**2*sqrt(d**2 - e**2*x**2)/(9009*e**10) - 32*d**8*x**4*sqrt(d**2 - e**2*x**2)/(3003*e**8) - 80*d**6*x**6*sqrt(d**2 - e**2*x**2)/(9009*e**6) - 10*d**4*x**8*sqrt(d**2 - e**2*x**2)/(1287*e**4) - d**2*x**10*sqrt(d**2 - e**2*x**2)/(143*e**2) + x**12*sqrt(d**2 - e**2*x**2)/13, Ne(e, 0)), (x**12*sqrt(d**2)/12, True))","C",0
67,1,1919,0,59.743729," ","integrate(x**3*(e*x+d)**3*(-e**2*x**2+d**2)**(5/2),x)","d^{7} \left(\begin{cases} - \frac{2 d^{4} \sqrt{d^{2} - e^{2} x^{2}}}{15 e^{4}} - \frac{d^{2} x^{2} \sqrt{d^{2} - e^{2} x^{2}}}{15 e^{2}} + \frac{x^{4} \sqrt{d^{2} - e^{2} x^{2}}}{5} & \text{for}\: e \neq 0 \\\frac{x^{4} \sqrt{d^{2}}}{4} & \text{otherwise} \end{cases}\right) + 3 d^{6} e \left(\begin{cases} - \frac{i d^{6} \operatorname{acosh}{\left(\frac{e x}{d} \right)}}{16 e^{5}} + \frac{i d^{5} x}{16 e^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{i d^{3} x^{3}}{48 e^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{5 i d x^{5}}{24 \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + \frac{i e^{2} x^{7}}{6 d \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{d^{6} \operatorname{asin}{\left(\frac{e x}{d} \right)}}{16 e^{5}} - \frac{d^{5} x}{16 e^{4} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{d^{3} x^{3}}{48 e^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{5 d x^{5}}{24 \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} - \frac{e^{2} x^{7}}{6 d \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} & \text{otherwise} \end{cases}\right) + d^{5} e^{2} \left(\begin{cases} - \frac{8 d^{6} \sqrt{d^{2} - e^{2} x^{2}}}{105 e^{6}} - \frac{4 d^{4} x^{2} \sqrt{d^{2} - e^{2} x^{2}}}{105 e^{4}} - \frac{d^{2} x^{4} \sqrt{d^{2} - e^{2} x^{2}}}{35 e^{2}} + \frac{x^{6} \sqrt{d^{2} - e^{2} x^{2}}}{7} & \text{for}\: e \neq 0 \\\frac{x^{6} \sqrt{d^{2}}}{6} & \text{otherwise} \end{cases}\right) - 5 d^{4} e^{3} \left(\begin{cases} - \frac{5 i d^{8} \operatorname{acosh}{\left(\frac{e x}{d} \right)}}{128 e^{7}} + \frac{5 i d^{7} x}{128 e^{6} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{5 i d^{5} x^{3}}{384 e^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{i d^{3} x^{5}}{192 e^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{7 i d x^{7}}{48 \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + \frac{i e^{2} x^{9}}{8 d \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{5 d^{8} \operatorname{asin}{\left(\frac{e x}{d} \right)}}{128 e^{7}} - \frac{5 d^{7} x}{128 e^{6} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{5 d^{5} x^{3}}{384 e^{4} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{d^{3} x^{5}}{192 e^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{7 d x^{7}}{48 \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} - \frac{e^{2} x^{9}}{8 d \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} & \text{otherwise} \end{cases}\right) - 5 d^{3} e^{4} \left(\begin{cases} - \frac{16 d^{8} \sqrt{d^{2} - e^{2} x^{2}}}{315 e^{8}} - \frac{8 d^{6} x^{2} \sqrt{d^{2} - e^{2} x^{2}}}{315 e^{6}} - \frac{2 d^{4} x^{4} \sqrt{d^{2} - e^{2} x^{2}}}{105 e^{4}} - \frac{d^{2} x^{6} \sqrt{d^{2} - e^{2} x^{2}}}{63 e^{2}} + \frac{x^{8} \sqrt{d^{2} - e^{2} x^{2}}}{9} & \text{for}\: e \neq 0 \\\frac{x^{8} \sqrt{d^{2}}}{8} & \text{otherwise} \end{cases}\right) + d^{2} e^{5} \left(\begin{cases} - \frac{7 i d^{10} \operatorname{acosh}{\left(\frac{e x}{d} \right)}}{256 e^{9}} + \frac{7 i d^{9} x}{256 e^{8} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{7 i d^{7} x^{3}}{768 e^{6} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{7 i d^{5} x^{5}}{1920 e^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{i d^{3} x^{7}}{480 e^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{9 i d x^{9}}{80 \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + \frac{i e^{2} x^{11}}{10 d \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{7 d^{10} \operatorname{asin}{\left(\frac{e x}{d} \right)}}{256 e^{9}} - \frac{7 d^{9} x}{256 e^{8} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{7 d^{7} x^{3}}{768 e^{6} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{7 d^{5} x^{5}}{1920 e^{4} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{d^{3} x^{7}}{480 e^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{9 d x^{9}}{80 \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} - \frac{e^{2} x^{11}}{10 d \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} & \text{otherwise} \end{cases}\right) + 3 d e^{6} \left(\begin{cases} - \frac{128 d^{10} \sqrt{d^{2} - e^{2} x^{2}}}{3465 e^{10}} - \frac{64 d^{8} x^{2} \sqrt{d^{2} - e^{2} x^{2}}}{3465 e^{8}} - \frac{16 d^{6} x^{4} \sqrt{d^{2} - e^{2} x^{2}}}{1155 e^{6}} - \frac{8 d^{4} x^{6} \sqrt{d^{2} - e^{2} x^{2}}}{693 e^{4}} - \frac{d^{2} x^{8} \sqrt{d^{2} - e^{2} x^{2}}}{99 e^{2}} + \frac{x^{10} \sqrt{d^{2} - e^{2} x^{2}}}{11} & \text{for}\: e \neq 0 \\\frac{x^{10} \sqrt{d^{2}}}{10} & \text{otherwise} \end{cases}\right) + e^{7} \left(\begin{cases} - \frac{21 i d^{12} \operatorname{acosh}{\left(\frac{e x}{d} \right)}}{1024 e^{11}} + \frac{21 i d^{11} x}{1024 e^{10} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{7 i d^{9} x^{3}}{1024 e^{8} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{7 i d^{7} x^{5}}{2560 e^{6} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{i d^{5} x^{7}}{640 e^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{i d^{3} x^{9}}{960 e^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{11 i d x^{11}}{120 \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + \frac{i e^{2} x^{13}}{12 d \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{21 d^{12} \operatorname{asin}{\left(\frac{e x}{d} \right)}}{1024 e^{11}} - \frac{21 d^{11} x}{1024 e^{10} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{7 d^{9} x^{3}}{1024 e^{8} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{7 d^{7} x^{5}}{2560 e^{6} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{d^{5} x^{7}}{640 e^{4} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{d^{3} x^{9}}{960 e^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{11 d x^{11}}{120 \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} - \frac{e^{2} x^{13}}{12 d \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} & \text{otherwise} \end{cases}\right)"," ",0,"d**7*Piecewise((-2*d**4*sqrt(d**2 - e**2*x**2)/(15*e**4) - d**2*x**2*sqrt(d**2 - e**2*x**2)/(15*e**2) + x**4*sqrt(d**2 - e**2*x**2)/5, Ne(e, 0)), (x**4*sqrt(d**2)/4, True)) + 3*d**6*e*Piecewise((-I*d**6*acosh(e*x/d)/(16*e**5) + I*d**5*x/(16*e**4*sqrt(-1 + e**2*x**2/d**2)) - I*d**3*x**3/(48*e**2*sqrt(-1 + e**2*x**2/d**2)) - 5*I*d*x**5/(24*sqrt(-1 + e**2*x**2/d**2)) + I*e**2*x**7/(6*d*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (d**6*asin(e*x/d)/(16*e**5) - d**5*x/(16*e**4*sqrt(1 - e**2*x**2/d**2)) + d**3*x**3/(48*e**2*sqrt(1 - e**2*x**2/d**2)) + 5*d*x**5/(24*sqrt(1 - e**2*x**2/d**2)) - e**2*x**7/(6*d*sqrt(1 - e**2*x**2/d**2)), True)) + d**5*e**2*Piecewise((-8*d**6*sqrt(d**2 - e**2*x**2)/(105*e**6) - 4*d**4*x**2*sqrt(d**2 - e**2*x**2)/(105*e**4) - d**2*x**4*sqrt(d**2 - e**2*x**2)/(35*e**2) + x**6*sqrt(d**2 - e**2*x**2)/7, Ne(e, 0)), (x**6*sqrt(d**2)/6, True)) - 5*d**4*e**3*Piecewise((-5*I*d**8*acosh(e*x/d)/(128*e**7) + 5*I*d**7*x/(128*e**6*sqrt(-1 + e**2*x**2/d**2)) - 5*I*d**5*x**3/(384*e**4*sqrt(-1 + e**2*x**2/d**2)) - I*d**3*x**5/(192*e**2*sqrt(-1 + e**2*x**2/d**2)) - 7*I*d*x**7/(48*sqrt(-1 + e**2*x**2/d**2)) + I*e**2*x**9/(8*d*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (5*d**8*asin(e*x/d)/(128*e**7) - 5*d**7*x/(128*e**6*sqrt(1 - e**2*x**2/d**2)) + 5*d**5*x**3/(384*e**4*sqrt(1 - e**2*x**2/d**2)) + d**3*x**5/(192*e**2*sqrt(1 - e**2*x**2/d**2)) + 7*d*x**7/(48*sqrt(1 - e**2*x**2/d**2)) - e**2*x**9/(8*d*sqrt(1 - e**2*x**2/d**2)), True)) - 5*d**3*e**4*Piecewise((-16*d**8*sqrt(d**2 - e**2*x**2)/(315*e**8) - 8*d**6*x**2*sqrt(d**2 - e**2*x**2)/(315*e**6) - 2*d**4*x**4*sqrt(d**2 - e**2*x**2)/(105*e**4) - d**2*x**6*sqrt(d**2 - e**2*x**2)/(63*e**2) + x**8*sqrt(d**2 - e**2*x**2)/9, Ne(e, 0)), (x**8*sqrt(d**2)/8, True)) + d**2*e**5*Piecewise((-7*I*d**10*acosh(e*x/d)/(256*e**9) + 7*I*d**9*x/(256*e**8*sqrt(-1 + e**2*x**2/d**2)) - 7*I*d**7*x**3/(768*e**6*sqrt(-1 + e**2*x**2/d**2)) - 7*I*d**5*x**5/(1920*e**4*sqrt(-1 + e**2*x**2/d**2)) - I*d**3*x**7/(480*e**2*sqrt(-1 + e**2*x**2/d**2)) - 9*I*d*x**9/(80*sqrt(-1 + e**2*x**2/d**2)) + I*e**2*x**11/(10*d*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (7*d**10*asin(e*x/d)/(256*e**9) - 7*d**9*x/(256*e**8*sqrt(1 - e**2*x**2/d**2)) + 7*d**7*x**3/(768*e**6*sqrt(1 - e**2*x**2/d**2)) + 7*d**5*x**5/(1920*e**4*sqrt(1 - e**2*x**2/d**2)) + d**3*x**7/(480*e**2*sqrt(1 - e**2*x**2/d**2)) + 9*d*x**9/(80*sqrt(1 - e**2*x**2/d**2)) - e**2*x**11/(10*d*sqrt(1 - e**2*x**2/d**2)), True)) + 3*d*e**6*Piecewise((-128*d**10*sqrt(d**2 - e**2*x**2)/(3465*e**10) - 64*d**8*x**2*sqrt(d**2 - e**2*x**2)/(3465*e**8) - 16*d**6*x**4*sqrt(d**2 - e**2*x**2)/(1155*e**6) - 8*d**4*x**6*sqrt(d**2 - e**2*x**2)/(693*e**4) - d**2*x**8*sqrt(d**2 - e**2*x**2)/(99*e**2) + x**10*sqrt(d**2 - e**2*x**2)/11, Ne(e, 0)), (x**10*sqrt(d**2)/10, True)) + e**7*Piecewise((-21*I*d**12*acosh(e*x/d)/(1024*e**11) + 21*I*d**11*x/(1024*e**10*sqrt(-1 + e**2*x**2/d**2)) - 7*I*d**9*x**3/(1024*e**8*sqrt(-1 + e**2*x**2/d**2)) - 7*I*d**7*x**5/(2560*e**6*sqrt(-1 + e**2*x**2/d**2)) - I*d**5*x**7/(640*e**4*sqrt(-1 + e**2*x**2/d**2)) - I*d**3*x**9/(960*e**2*sqrt(-1 + e**2*x**2/d**2)) - 11*I*d*x**11/(120*sqrt(-1 + e**2*x**2/d**2)) + I*e**2*x**13/(12*d*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (21*d**12*asin(e*x/d)/(1024*e**11) - 21*d**11*x/(1024*e**10*sqrt(1 - e**2*x**2/d**2)) + 7*d**9*x**3/(1024*e**8*sqrt(1 - e**2*x**2/d**2)) + 7*d**7*x**5/(2560*e**6*sqrt(1 - e**2*x**2/d**2)) + d**5*x**7/(640*e**4*sqrt(1 - e**2*x**2/d**2)) + d**3*x**9/(960*e**2*sqrt(1 - e**2*x**2/d**2)) + 11*d*x**11/(120*sqrt(1 - e**2*x**2/d**2)) - e**2*x**13/(12*d*sqrt(1 - e**2*x**2/d**2)), True))","A",0
68,1,1681,0,40.610123," ","integrate(x**2*(e*x+d)**3*(-e**2*x**2+d**2)**(5/2),x)","d^{7} \left(\begin{cases} - \frac{i d^{4} \operatorname{acosh}{\left(\frac{e x}{d} \right)}}{8 e^{3}} + \frac{i d^{3} x}{8 e^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{3 i d x^{3}}{8 \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + \frac{i e^{2} x^{5}}{4 d \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{d^{4} \operatorname{asin}{\left(\frac{e x}{d} \right)}}{8 e^{3}} - \frac{d^{3} x}{8 e^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{3 d x^{3}}{8 \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} - \frac{e^{2} x^{5}}{4 d \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} & \text{otherwise} \end{cases}\right) + 3 d^{6} e \left(\begin{cases} - \frac{2 d^{4} \sqrt{d^{2} - e^{2} x^{2}}}{15 e^{4}} - \frac{d^{2} x^{2} \sqrt{d^{2} - e^{2} x^{2}}}{15 e^{2}} + \frac{x^{4} \sqrt{d^{2} - e^{2} x^{2}}}{5} & \text{for}\: e \neq 0 \\\frac{x^{4} \sqrt{d^{2}}}{4} & \text{otherwise} \end{cases}\right) + d^{5} e^{2} \left(\begin{cases} - \frac{i d^{6} \operatorname{acosh}{\left(\frac{e x}{d} \right)}}{16 e^{5}} + \frac{i d^{5} x}{16 e^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{i d^{3} x^{3}}{48 e^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{5 i d x^{5}}{24 \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + \frac{i e^{2} x^{7}}{6 d \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{d^{6} \operatorname{asin}{\left(\frac{e x}{d} \right)}}{16 e^{5}} - \frac{d^{5} x}{16 e^{4} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{d^{3} x^{3}}{48 e^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{5 d x^{5}}{24 \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} - \frac{e^{2} x^{7}}{6 d \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} & \text{otherwise} \end{cases}\right) - 5 d^{4} e^{3} \left(\begin{cases} - \frac{8 d^{6} \sqrt{d^{2} - e^{2} x^{2}}}{105 e^{6}} - \frac{4 d^{4} x^{2} \sqrt{d^{2} - e^{2} x^{2}}}{105 e^{4}} - \frac{d^{2} x^{4} \sqrt{d^{2} - e^{2} x^{2}}}{35 e^{2}} + \frac{x^{6} \sqrt{d^{2} - e^{2} x^{2}}}{7} & \text{for}\: e \neq 0 \\\frac{x^{6} \sqrt{d^{2}}}{6} & \text{otherwise} \end{cases}\right) - 5 d^{3} e^{4} \left(\begin{cases} - \frac{5 i d^{8} \operatorname{acosh}{\left(\frac{e x}{d} \right)}}{128 e^{7}} + \frac{5 i d^{7} x}{128 e^{6} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{5 i d^{5} x^{3}}{384 e^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{i d^{3} x^{5}}{192 e^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{7 i d x^{7}}{48 \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + \frac{i e^{2} x^{9}}{8 d \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{5 d^{8} \operatorname{asin}{\left(\frac{e x}{d} \right)}}{128 e^{7}} - \frac{5 d^{7} x}{128 e^{6} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{5 d^{5} x^{3}}{384 e^{4} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{d^{3} x^{5}}{192 e^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{7 d x^{7}}{48 \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} - \frac{e^{2} x^{9}}{8 d \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} & \text{otherwise} \end{cases}\right) + d^{2} e^{5} \left(\begin{cases} - \frac{16 d^{8} \sqrt{d^{2} - e^{2} x^{2}}}{315 e^{8}} - \frac{8 d^{6} x^{2} \sqrt{d^{2} - e^{2} x^{2}}}{315 e^{6}} - \frac{2 d^{4} x^{4} \sqrt{d^{2} - e^{2} x^{2}}}{105 e^{4}} - \frac{d^{2} x^{6} \sqrt{d^{2} - e^{2} x^{2}}}{63 e^{2}} + \frac{x^{8} \sqrt{d^{2} - e^{2} x^{2}}}{9} & \text{for}\: e \neq 0 \\\frac{x^{8} \sqrt{d^{2}}}{8} & \text{otherwise} \end{cases}\right) + 3 d e^{6} \left(\begin{cases} - \frac{7 i d^{10} \operatorname{acosh}{\left(\frac{e x}{d} \right)}}{256 e^{9}} + \frac{7 i d^{9} x}{256 e^{8} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{7 i d^{7} x^{3}}{768 e^{6} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{7 i d^{5} x^{5}}{1920 e^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{i d^{3} x^{7}}{480 e^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{9 i d x^{9}}{80 \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + \frac{i e^{2} x^{11}}{10 d \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{7 d^{10} \operatorname{asin}{\left(\frac{e x}{d} \right)}}{256 e^{9}} - \frac{7 d^{9} x}{256 e^{8} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{7 d^{7} x^{3}}{768 e^{6} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{7 d^{5} x^{5}}{1920 e^{4} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{d^{3} x^{7}}{480 e^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{9 d x^{9}}{80 \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} - \frac{e^{2} x^{11}}{10 d \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} & \text{otherwise} \end{cases}\right) + e^{7} \left(\begin{cases} - \frac{128 d^{10} \sqrt{d^{2} - e^{2} x^{2}}}{3465 e^{10}} - \frac{64 d^{8} x^{2} \sqrt{d^{2} - e^{2} x^{2}}}{3465 e^{8}} - \frac{16 d^{6} x^{4} \sqrt{d^{2} - e^{2} x^{2}}}{1155 e^{6}} - \frac{8 d^{4} x^{6} \sqrt{d^{2} - e^{2} x^{2}}}{693 e^{4}} - \frac{d^{2} x^{8} \sqrt{d^{2} - e^{2} x^{2}}}{99 e^{2}} + \frac{x^{10} \sqrt{d^{2} - e^{2} x^{2}}}{11} & \text{for}\: e \neq 0 \\\frac{x^{10} \sqrt{d^{2}}}{10} & \text{otherwise} \end{cases}\right)"," ",0,"d**7*Piecewise((-I*d**4*acosh(e*x/d)/(8*e**3) + I*d**3*x/(8*e**2*sqrt(-1 + e**2*x**2/d**2)) - 3*I*d*x**3/(8*sqrt(-1 + e**2*x**2/d**2)) + I*e**2*x**5/(4*d*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (d**4*asin(e*x/d)/(8*e**3) - d**3*x/(8*e**2*sqrt(1 - e**2*x**2/d**2)) + 3*d*x**3/(8*sqrt(1 - e**2*x**2/d**2)) - e**2*x**5/(4*d*sqrt(1 - e**2*x**2/d**2)), True)) + 3*d**6*e*Piecewise((-2*d**4*sqrt(d**2 - e**2*x**2)/(15*e**4) - d**2*x**2*sqrt(d**2 - e**2*x**2)/(15*e**2) + x**4*sqrt(d**2 - e**2*x**2)/5, Ne(e, 0)), (x**4*sqrt(d**2)/4, True)) + d**5*e**2*Piecewise((-I*d**6*acosh(e*x/d)/(16*e**5) + I*d**5*x/(16*e**4*sqrt(-1 + e**2*x**2/d**2)) - I*d**3*x**3/(48*e**2*sqrt(-1 + e**2*x**2/d**2)) - 5*I*d*x**5/(24*sqrt(-1 + e**2*x**2/d**2)) + I*e**2*x**7/(6*d*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (d**6*asin(e*x/d)/(16*e**5) - d**5*x/(16*e**4*sqrt(1 - e**2*x**2/d**2)) + d**3*x**3/(48*e**2*sqrt(1 - e**2*x**2/d**2)) + 5*d*x**5/(24*sqrt(1 - e**2*x**2/d**2)) - e**2*x**7/(6*d*sqrt(1 - e**2*x**2/d**2)), True)) - 5*d**4*e**3*Piecewise((-8*d**6*sqrt(d**2 - e**2*x**2)/(105*e**6) - 4*d**4*x**2*sqrt(d**2 - e**2*x**2)/(105*e**4) - d**2*x**4*sqrt(d**2 - e**2*x**2)/(35*e**2) + x**6*sqrt(d**2 - e**2*x**2)/7, Ne(e, 0)), (x**6*sqrt(d**2)/6, True)) - 5*d**3*e**4*Piecewise((-5*I*d**8*acosh(e*x/d)/(128*e**7) + 5*I*d**7*x/(128*e**6*sqrt(-1 + e**2*x**2/d**2)) - 5*I*d**5*x**3/(384*e**4*sqrt(-1 + e**2*x**2/d**2)) - I*d**3*x**5/(192*e**2*sqrt(-1 + e**2*x**2/d**2)) - 7*I*d*x**7/(48*sqrt(-1 + e**2*x**2/d**2)) + I*e**2*x**9/(8*d*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (5*d**8*asin(e*x/d)/(128*e**7) - 5*d**7*x/(128*e**6*sqrt(1 - e**2*x**2/d**2)) + 5*d**5*x**3/(384*e**4*sqrt(1 - e**2*x**2/d**2)) + d**3*x**5/(192*e**2*sqrt(1 - e**2*x**2/d**2)) + 7*d*x**7/(48*sqrt(1 - e**2*x**2/d**2)) - e**2*x**9/(8*d*sqrt(1 - e**2*x**2/d**2)), True)) + d**2*e**5*Piecewise((-16*d**8*sqrt(d**2 - e**2*x**2)/(315*e**8) - 8*d**6*x**2*sqrt(d**2 - e**2*x**2)/(315*e**6) - 2*d**4*x**4*sqrt(d**2 - e**2*x**2)/(105*e**4) - d**2*x**6*sqrt(d**2 - e**2*x**2)/(63*e**2) + x**8*sqrt(d**2 - e**2*x**2)/9, Ne(e, 0)), (x**8*sqrt(d**2)/8, True)) + 3*d*e**6*Piecewise((-7*I*d**10*acosh(e*x/d)/(256*e**9) + 7*I*d**9*x/(256*e**8*sqrt(-1 + e**2*x**2/d**2)) - 7*I*d**7*x**3/(768*e**6*sqrt(-1 + e**2*x**2/d**2)) - 7*I*d**5*x**5/(1920*e**4*sqrt(-1 + e**2*x**2/d**2)) - I*d**3*x**7/(480*e**2*sqrt(-1 + e**2*x**2/d**2)) - 9*I*d*x**9/(80*sqrt(-1 + e**2*x**2/d**2)) + I*e**2*x**11/(10*d*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (7*d**10*asin(e*x/d)/(256*e**9) - 7*d**9*x/(256*e**8*sqrt(1 - e**2*x**2/d**2)) + 7*d**7*x**3/(768*e**6*sqrt(1 - e**2*x**2/d**2)) + 7*d**5*x**5/(1920*e**4*sqrt(1 - e**2*x**2/d**2)) + d**3*x**7/(480*e**2*sqrt(1 - e**2*x**2/d**2)) + 9*d*x**9/(80*sqrt(1 - e**2*x**2/d**2)) - e**2*x**11/(10*d*sqrt(1 - e**2*x**2/d**2)), True)) + e**7*Piecewise((-128*d**10*sqrt(d**2 - e**2*x**2)/(3465*e**10) - 64*d**8*x**2*sqrt(d**2 - e**2*x**2)/(3465*e**8) - 16*d**6*x**4*sqrt(d**2 - e**2*x**2)/(1155*e**6) - 8*d**4*x**6*sqrt(d**2 - e**2*x**2)/(693*e**4) - d**2*x**8*sqrt(d**2 - e**2*x**2)/(99*e**2) + x**10*sqrt(d**2 - e**2*x**2)/11, Ne(e, 0)), (x**10*sqrt(d**2)/10, True))","C",0
69,1,1554,0,40.183193," ","integrate(x*(e*x+d)**3*(-e**2*x**2+d**2)**(5/2),x)","d^{7} \left(\begin{cases} \frac{x^{2} \sqrt{d^{2}}}{2} & \text{for}\: e^{2} = 0 \\- \frac{\left(d^{2} - e^{2} x^{2}\right)^{\frac{3}{2}}}{3 e^{2}} & \text{otherwise} \end{cases}\right) + 3 d^{6} e \left(\begin{cases} - \frac{i d^{4} \operatorname{acosh}{\left(\frac{e x}{d} \right)}}{8 e^{3}} + \frac{i d^{3} x}{8 e^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{3 i d x^{3}}{8 \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + \frac{i e^{2} x^{5}}{4 d \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{d^{4} \operatorname{asin}{\left(\frac{e x}{d} \right)}}{8 e^{3}} - \frac{d^{3} x}{8 e^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{3 d x^{3}}{8 \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} - \frac{e^{2} x^{5}}{4 d \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} & \text{otherwise} \end{cases}\right) + d^{5} e^{2} \left(\begin{cases} - \frac{2 d^{4} \sqrt{d^{2} - e^{2} x^{2}}}{15 e^{4}} - \frac{d^{2} x^{2} \sqrt{d^{2} - e^{2} x^{2}}}{15 e^{2}} + \frac{x^{4} \sqrt{d^{2} - e^{2} x^{2}}}{5} & \text{for}\: e \neq 0 \\\frac{x^{4} \sqrt{d^{2}}}{4} & \text{otherwise} \end{cases}\right) - 5 d^{4} e^{3} \left(\begin{cases} - \frac{i d^{6} \operatorname{acosh}{\left(\frac{e x}{d} \right)}}{16 e^{5}} + \frac{i d^{5} x}{16 e^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{i d^{3} x^{3}}{48 e^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{5 i d x^{5}}{24 \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + \frac{i e^{2} x^{7}}{6 d \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{d^{6} \operatorname{asin}{\left(\frac{e x}{d} \right)}}{16 e^{5}} - \frac{d^{5} x}{16 e^{4} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{d^{3} x^{3}}{48 e^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{5 d x^{5}}{24 \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} - \frac{e^{2} x^{7}}{6 d \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} & \text{otherwise} \end{cases}\right) - 5 d^{3} e^{4} \left(\begin{cases} - \frac{8 d^{6} \sqrt{d^{2} - e^{2} x^{2}}}{105 e^{6}} - \frac{4 d^{4} x^{2} \sqrt{d^{2} - e^{2} x^{2}}}{105 e^{4}} - \frac{d^{2} x^{4} \sqrt{d^{2} - e^{2} x^{2}}}{35 e^{2}} + \frac{x^{6} \sqrt{d^{2} - e^{2} x^{2}}}{7} & \text{for}\: e \neq 0 \\\frac{x^{6} \sqrt{d^{2}}}{6} & \text{otherwise} \end{cases}\right) + d^{2} e^{5} \left(\begin{cases} - \frac{5 i d^{8} \operatorname{acosh}{\left(\frac{e x}{d} \right)}}{128 e^{7}} + \frac{5 i d^{7} x}{128 e^{6} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{5 i d^{5} x^{3}}{384 e^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{i d^{3} x^{5}}{192 e^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{7 i d x^{7}}{48 \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + \frac{i e^{2} x^{9}}{8 d \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{5 d^{8} \operatorname{asin}{\left(\frac{e x}{d} \right)}}{128 e^{7}} - \frac{5 d^{7} x}{128 e^{6} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{5 d^{5} x^{3}}{384 e^{4} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{d^{3} x^{5}}{192 e^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{7 d x^{7}}{48 \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} - \frac{e^{2} x^{9}}{8 d \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} & \text{otherwise} \end{cases}\right) + 3 d e^{6} \left(\begin{cases} - \frac{16 d^{8} \sqrt{d^{2} - e^{2} x^{2}}}{315 e^{8}} - \frac{8 d^{6} x^{2} \sqrt{d^{2} - e^{2} x^{2}}}{315 e^{6}} - \frac{2 d^{4} x^{4} \sqrt{d^{2} - e^{2} x^{2}}}{105 e^{4}} - \frac{d^{2} x^{6} \sqrt{d^{2} - e^{2} x^{2}}}{63 e^{2}} + \frac{x^{8} \sqrt{d^{2} - e^{2} x^{2}}}{9} & \text{for}\: e \neq 0 \\\frac{x^{8} \sqrt{d^{2}}}{8} & \text{otherwise} \end{cases}\right) + e^{7} \left(\begin{cases} - \frac{7 i d^{10} \operatorname{acosh}{\left(\frac{e x}{d} \right)}}{256 e^{9}} + \frac{7 i d^{9} x}{256 e^{8} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{7 i d^{7} x^{3}}{768 e^{6} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{7 i d^{5} x^{5}}{1920 e^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{i d^{3} x^{7}}{480 e^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{9 i d x^{9}}{80 \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + \frac{i e^{2} x^{11}}{10 d \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{7 d^{10} \operatorname{asin}{\left(\frac{e x}{d} \right)}}{256 e^{9}} - \frac{7 d^{9} x}{256 e^{8} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{7 d^{7} x^{3}}{768 e^{6} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{7 d^{5} x^{5}}{1920 e^{4} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{d^{3} x^{7}}{480 e^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{9 d x^{9}}{80 \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} - \frac{e^{2} x^{11}}{10 d \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} & \text{otherwise} \end{cases}\right)"," ",0,"d**7*Piecewise((x**2*sqrt(d**2)/2, Eq(e**2, 0)), (-(d**2 - e**2*x**2)**(3/2)/(3*e**2), True)) + 3*d**6*e*Piecewise((-I*d**4*acosh(e*x/d)/(8*e**3) + I*d**3*x/(8*e**2*sqrt(-1 + e**2*x**2/d**2)) - 3*I*d*x**3/(8*sqrt(-1 + e**2*x**2/d**2)) + I*e**2*x**5/(4*d*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (d**4*asin(e*x/d)/(8*e**3) - d**3*x/(8*e**2*sqrt(1 - e**2*x**2/d**2)) + 3*d*x**3/(8*sqrt(1 - e**2*x**2/d**2)) - e**2*x**5/(4*d*sqrt(1 - e**2*x**2/d**2)), True)) + d**5*e**2*Piecewise((-2*d**4*sqrt(d**2 - e**2*x**2)/(15*e**4) - d**2*x**2*sqrt(d**2 - e**2*x**2)/(15*e**2) + x**4*sqrt(d**2 - e**2*x**2)/5, Ne(e, 0)), (x**4*sqrt(d**2)/4, True)) - 5*d**4*e**3*Piecewise((-I*d**6*acosh(e*x/d)/(16*e**5) + I*d**5*x/(16*e**4*sqrt(-1 + e**2*x**2/d**2)) - I*d**3*x**3/(48*e**2*sqrt(-1 + e**2*x**2/d**2)) - 5*I*d*x**5/(24*sqrt(-1 + e**2*x**2/d**2)) + I*e**2*x**7/(6*d*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (d**6*asin(e*x/d)/(16*e**5) - d**5*x/(16*e**4*sqrt(1 - e**2*x**2/d**2)) + d**3*x**3/(48*e**2*sqrt(1 - e**2*x**2/d**2)) + 5*d*x**5/(24*sqrt(1 - e**2*x**2/d**2)) - e**2*x**7/(6*d*sqrt(1 - e**2*x**2/d**2)), True)) - 5*d**3*e**4*Piecewise((-8*d**6*sqrt(d**2 - e**2*x**2)/(105*e**6) - 4*d**4*x**2*sqrt(d**2 - e**2*x**2)/(105*e**4) - d**2*x**4*sqrt(d**2 - e**2*x**2)/(35*e**2) + x**6*sqrt(d**2 - e**2*x**2)/7, Ne(e, 0)), (x**6*sqrt(d**2)/6, True)) + d**2*e**5*Piecewise((-5*I*d**8*acosh(e*x/d)/(128*e**7) + 5*I*d**7*x/(128*e**6*sqrt(-1 + e**2*x**2/d**2)) - 5*I*d**5*x**3/(384*e**4*sqrt(-1 + e**2*x**2/d**2)) - I*d**3*x**5/(192*e**2*sqrt(-1 + e**2*x**2/d**2)) - 7*I*d*x**7/(48*sqrt(-1 + e**2*x**2/d**2)) + I*e**2*x**9/(8*d*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (5*d**8*asin(e*x/d)/(128*e**7) - 5*d**7*x/(128*e**6*sqrt(1 - e**2*x**2/d**2)) + 5*d**5*x**3/(384*e**4*sqrt(1 - e**2*x**2/d**2)) + d**3*x**5/(192*e**2*sqrt(1 - e**2*x**2/d**2)) + 7*d*x**7/(48*sqrt(1 - e**2*x**2/d**2)) - e**2*x**9/(8*d*sqrt(1 - e**2*x**2/d**2)), True)) + 3*d*e**6*Piecewise((-16*d**8*sqrt(d**2 - e**2*x**2)/(315*e**8) - 8*d**6*x**2*sqrt(d**2 - e**2*x**2)/(315*e**6) - 2*d**4*x**4*sqrt(d**2 - e**2*x**2)/(105*e**4) - d**2*x**6*sqrt(d**2 - e**2*x**2)/(63*e**2) + x**8*sqrt(d**2 - e**2*x**2)/9, Ne(e, 0)), (x**8*sqrt(d**2)/8, True)) + e**7*Piecewise((-7*I*d**10*acosh(e*x/d)/(256*e**9) + 7*I*d**9*x/(256*e**8*sqrt(-1 + e**2*x**2/d**2)) - 7*I*d**7*x**3/(768*e**6*sqrt(-1 + e**2*x**2/d**2)) - 7*I*d**5*x**5/(1920*e**4*sqrt(-1 + e**2*x**2/d**2)) - I*d**3*x**7/(480*e**2*sqrt(-1 + e**2*x**2/d**2)) - 9*I*d*x**9/(80*sqrt(-1 + e**2*x**2/d**2)) + I*e**2*x**11/(10*d*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (7*d**10*asin(e*x/d)/(256*e**9) - 7*d**9*x/(256*e**8*sqrt(1 - e**2*x**2/d**2)) + 7*d**7*x**3/(768*e**6*sqrt(1 - e**2*x**2/d**2)) + 7*d**5*x**5/(1920*e**4*sqrt(1 - e**2*x**2/d**2)) + d**3*x**7/(480*e**2*sqrt(1 - e**2*x**2/d**2)) + 9*d*x**9/(80*sqrt(1 - e**2*x**2/d**2)) - e**2*x**11/(10*d*sqrt(1 - e**2*x**2/d**2)), True))","A",0
70,1,1284,0,25.883613," ","integrate((e*x+d)**3*(-e**2*x**2+d**2)**(5/2),x)","d^{7} \left(\begin{cases} - \frac{i d^{2} \operatorname{acosh}{\left(\frac{e x}{d} \right)}}{2 e} - \frac{i d x}{2 \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + \frac{i e^{2} x^{3}}{2 d \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{d^{2} \operatorname{asin}{\left(\frac{e x}{d} \right)}}{2 e} + \frac{d x \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}}{2} & \text{otherwise} \end{cases}\right) + 3 d^{6} e \left(\begin{cases} \frac{x^{2} \sqrt{d^{2}}}{2} & \text{for}\: e^{2} = 0 \\- \frac{\left(d^{2} - e^{2} x^{2}\right)^{\frac{3}{2}}}{3 e^{2}} & \text{otherwise} \end{cases}\right) + d^{5} e^{2} \left(\begin{cases} - \frac{i d^{4} \operatorname{acosh}{\left(\frac{e x}{d} \right)}}{8 e^{3}} + \frac{i d^{3} x}{8 e^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{3 i d x^{3}}{8 \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + \frac{i e^{2} x^{5}}{4 d \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{d^{4} \operatorname{asin}{\left(\frac{e x}{d} \right)}}{8 e^{3}} - \frac{d^{3} x}{8 e^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{3 d x^{3}}{8 \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} - \frac{e^{2} x^{5}}{4 d \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} & \text{otherwise} \end{cases}\right) - 5 d^{4} e^{3} \left(\begin{cases} - \frac{2 d^{4} \sqrt{d^{2} - e^{2} x^{2}}}{15 e^{4}} - \frac{d^{2} x^{2} \sqrt{d^{2} - e^{2} x^{2}}}{15 e^{2}} + \frac{x^{4} \sqrt{d^{2} - e^{2} x^{2}}}{5} & \text{for}\: e \neq 0 \\\frac{x^{4} \sqrt{d^{2}}}{4} & \text{otherwise} \end{cases}\right) - 5 d^{3} e^{4} \left(\begin{cases} - \frac{i d^{6} \operatorname{acosh}{\left(\frac{e x}{d} \right)}}{16 e^{5}} + \frac{i d^{5} x}{16 e^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{i d^{3} x^{3}}{48 e^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{5 i d x^{5}}{24 \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + \frac{i e^{2} x^{7}}{6 d \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{d^{6} \operatorname{asin}{\left(\frac{e x}{d} \right)}}{16 e^{5}} - \frac{d^{5} x}{16 e^{4} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{d^{3} x^{3}}{48 e^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{5 d x^{5}}{24 \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} - \frac{e^{2} x^{7}}{6 d \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} & \text{otherwise} \end{cases}\right) + d^{2} e^{5} \left(\begin{cases} - \frac{8 d^{6} \sqrt{d^{2} - e^{2} x^{2}}}{105 e^{6}} - \frac{4 d^{4} x^{2} \sqrt{d^{2} - e^{2} x^{2}}}{105 e^{4}} - \frac{d^{2} x^{4} \sqrt{d^{2} - e^{2} x^{2}}}{35 e^{2}} + \frac{x^{6} \sqrt{d^{2} - e^{2} x^{2}}}{7} & \text{for}\: e \neq 0 \\\frac{x^{6} \sqrt{d^{2}}}{6} & \text{otherwise} \end{cases}\right) + 3 d e^{6} \left(\begin{cases} - \frac{5 i d^{8} \operatorname{acosh}{\left(\frac{e x}{d} \right)}}{128 e^{7}} + \frac{5 i d^{7} x}{128 e^{6} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{5 i d^{5} x^{3}}{384 e^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{i d^{3} x^{5}}{192 e^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{7 i d x^{7}}{48 \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + \frac{i e^{2} x^{9}}{8 d \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{5 d^{8} \operatorname{asin}{\left(\frac{e x}{d} \right)}}{128 e^{7}} - \frac{5 d^{7} x}{128 e^{6} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{5 d^{5} x^{3}}{384 e^{4} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{d^{3} x^{5}}{192 e^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{7 d x^{7}}{48 \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} - \frac{e^{2} x^{9}}{8 d \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} & \text{otherwise} \end{cases}\right) + e^{7} \left(\begin{cases} - \frac{16 d^{8} \sqrt{d^{2} - e^{2} x^{2}}}{315 e^{8}} - \frac{8 d^{6} x^{2} \sqrt{d^{2} - e^{2} x^{2}}}{315 e^{6}} - \frac{2 d^{4} x^{4} \sqrt{d^{2} - e^{2} x^{2}}}{105 e^{4}} - \frac{d^{2} x^{6} \sqrt{d^{2} - e^{2} x^{2}}}{63 e^{2}} + \frac{x^{8} \sqrt{d^{2} - e^{2} x^{2}}}{9} & \text{for}\: e \neq 0 \\\frac{x^{8} \sqrt{d^{2}}}{8} & \text{otherwise} \end{cases}\right)"," ",0,"d**7*Piecewise((-I*d**2*acosh(e*x/d)/(2*e) - I*d*x/(2*sqrt(-1 + e**2*x**2/d**2)) + I*e**2*x**3/(2*d*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (d**2*asin(e*x/d)/(2*e) + d*x*sqrt(1 - e**2*x**2/d**2)/2, True)) + 3*d**6*e*Piecewise((x**2*sqrt(d**2)/2, Eq(e**2, 0)), (-(d**2 - e**2*x**2)**(3/2)/(3*e**2), True)) + d**5*e**2*Piecewise((-I*d**4*acosh(e*x/d)/(8*e**3) + I*d**3*x/(8*e**2*sqrt(-1 + e**2*x**2/d**2)) - 3*I*d*x**3/(8*sqrt(-1 + e**2*x**2/d**2)) + I*e**2*x**5/(4*d*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (d**4*asin(e*x/d)/(8*e**3) - d**3*x/(8*e**2*sqrt(1 - e**2*x**2/d**2)) + 3*d*x**3/(8*sqrt(1 - e**2*x**2/d**2)) - e**2*x**5/(4*d*sqrt(1 - e**2*x**2/d**2)), True)) - 5*d**4*e**3*Piecewise((-2*d**4*sqrt(d**2 - e**2*x**2)/(15*e**4) - d**2*x**2*sqrt(d**2 - e**2*x**2)/(15*e**2) + x**4*sqrt(d**2 - e**2*x**2)/5, Ne(e, 0)), (x**4*sqrt(d**2)/4, True)) - 5*d**3*e**4*Piecewise((-I*d**6*acosh(e*x/d)/(16*e**5) + I*d**5*x/(16*e**4*sqrt(-1 + e**2*x**2/d**2)) - I*d**3*x**3/(48*e**2*sqrt(-1 + e**2*x**2/d**2)) - 5*I*d*x**5/(24*sqrt(-1 + e**2*x**2/d**2)) + I*e**2*x**7/(6*d*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (d**6*asin(e*x/d)/(16*e**5) - d**5*x/(16*e**4*sqrt(1 - e**2*x**2/d**2)) + d**3*x**3/(48*e**2*sqrt(1 - e**2*x**2/d**2)) + 5*d*x**5/(24*sqrt(1 - e**2*x**2/d**2)) - e**2*x**7/(6*d*sqrt(1 - e**2*x**2/d**2)), True)) + d**2*e**5*Piecewise((-8*d**6*sqrt(d**2 - e**2*x**2)/(105*e**6) - 4*d**4*x**2*sqrt(d**2 - e**2*x**2)/(105*e**4) - d**2*x**4*sqrt(d**2 - e**2*x**2)/(35*e**2) + x**6*sqrt(d**2 - e**2*x**2)/7, Ne(e, 0)), (x**6*sqrt(d**2)/6, True)) + 3*d*e**6*Piecewise((-5*I*d**8*acosh(e*x/d)/(128*e**7) + 5*I*d**7*x/(128*e**6*sqrt(-1 + e**2*x**2/d**2)) - 5*I*d**5*x**3/(384*e**4*sqrt(-1 + e**2*x**2/d**2)) - I*d**3*x**5/(192*e**2*sqrt(-1 + e**2*x**2/d**2)) - 7*I*d*x**7/(48*sqrt(-1 + e**2*x**2/d**2)) + I*e**2*x**9/(8*d*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (5*d**8*asin(e*x/d)/(128*e**7) - 5*d**7*x/(128*e**6*sqrt(1 - e**2*x**2/d**2)) + 5*d**5*x**3/(384*e**4*sqrt(1 - e**2*x**2/d**2)) + d**3*x**5/(192*e**2*sqrt(1 - e**2*x**2/d**2)) + 7*d*x**7/(48*sqrt(1 - e**2*x**2/d**2)) - e**2*x**9/(8*d*sqrt(1 - e**2*x**2/d**2)), True)) + e**7*Piecewise((-16*d**8*sqrt(d**2 - e**2*x**2)/(315*e**8) - 8*d**6*x**2*sqrt(d**2 - e**2*x**2)/(315*e**6) - 2*d**4*x**4*sqrt(d**2 - e**2*x**2)/(105*e**4) - d**2*x**6*sqrt(d**2 - e**2*x**2)/(63*e**2) + x**8*sqrt(d**2 - e**2*x**2)/9, Ne(e, 0)), (x**8*sqrt(d**2)/8, True))","C",0
71,1,1263,0,47.722248," ","integrate((e*x+d)**3*(-e**2*x**2+d**2)**(5/2)/x,x)","d^{7} \left(\begin{cases} \frac{d^{2}}{e x \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} - d \operatorname{acosh}{\left(\frac{d}{e x} \right)} - \frac{e x}{\sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\- \frac{i d^{2}}{e x \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} + i d \operatorname{asin}{\left(\frac{d}{e x} \right)} + \frac{i e x}{\sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} & \text{otherwise} \end{cases}\right) + 3 d^{6} e \left(\begin{cases} - \frac{i d^{2} \operatorname{acosh}{\left(\frac{e x}{d} \right)}}{2 e} - \frac{i d x}{2 \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + \frac{i e^{2} x^{3}}{2 d \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{d^{2} \operatorname{asin}{\left(\frac{e x}{d} \right)}}{2 e} + \frac{d x \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}}{2} & \text{otherwise} \end{cases}\right) + d^{5} e^{2} \left(\begin{cases} \frac{x^{2} \sqrt{d^{2}}}{2} & \text{for}\: e^{2} = 0 \\- \frac{\left(d^{2} - e^{2} x^{2}\right)^{\frac{3}{2}}}{3 e^{2}} & \text{otherwise} \end{cases}\right) - 5 d^{4} e^{3} \left(\begin{cases} - \frac{i d^{4} \operatorname{acosh}{\left(\frac{e x}{d} \right)}}{8 e^{3}} + \frac{i d^{3} x}{8 e^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{3 i d x^{3}}{8 \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + \frac{i e^{2} x^{5}}{4 d \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{d^{4} \operatorname{asin}{\left(\frac{e x}{d} \right)}}{8 e^{3}} - \frac{d^{3} x}{8 e^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{3 d x^{3}}{8 \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} - \frac{e^{2} x^{5}}{4 d \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} & \text{otherwise} \end{cases}\right) - 5 d^{3} e^{4} \left(\begin{cases} - \frac{2 d^{4} \sqrt{d^{2} - e^{2} x^{2}}}{15 e^{4}} - \frac{d^{2} x^{2} \sqrt{d^{2} - e^{2} x^{2}}}{15 e^{2}} + \frac{x^{4} \sqrt{d^{2} - e^{2} x^{2}}}{5} & \text{for}\: e \neq 0 \\\frac{x^{4} \sqrt{d^{2}}}{4} & \text{otherwise} \end{cases}\right) + d^{2} e^{5} \left(\begin{cases} - \frac{i d^{6} \operatorname{acosh}{\left(\frac{e x}{d} \right)}}{16 e^{5}} + \frac{i d^{5} x}{16 e^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{i d^{3} x^{3}}{48 e^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{5 i d x^{5}}{24 \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + \frac{i e^{2} x^{7}}{6 d \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{d^{6} \operatorname{asin}{\left(\frac{e x}{d} \right)}}{16 e^{5}} - \frac{d^{5} x}{16 e^{4} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{d^{3} x^{3}}{48 e^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{5 d x^{5}}{24 \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} - \frac{e^{2} x^{7}}{6 d \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} & \text{otherwise} \end{cases}\right) + 3 d e^{6} \left(\begin{cases} - \frac{8 d^{6} \sqrt{d^{2} - e^{2} x^{2}}}{105 e^{6}} - \frac{4 d^{4} x^{2} \sqrt{d^{2} - e^{2} x^{2}}}{105 e^{4}} - \frac{d^{2} x^{4} \sqrt{d^{2} - e^{2} x^{2}}}{35 e^{2}} + \frac{x^{6} \sqrt{d^{2} - e^{2} x^{2}}}{7} & \text{for}\: e \neq 0 \\\frac{x^{6} \sqrt{d^{2}}}{6} & \text{otherwise} \end{cases}\right) + e^{7} \left(\begin{cases} - \frac{5 i d^{8} \operatorname{acosh}{\left(\frac{e x}{d} \right)}}{128 e^{7}} + \frac{5 i d^{7} x}{128 e^{6} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{5 i d^{5} x^{3}}{384 e^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{i d^{3} x^{5}}{192 e^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{7 i d x^{7}}{48 \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + \frac{i e^{2} x^{9}}{8 d \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{5 d^{8} \operatorname{asin}{\left(\frac{e x}{d} \right)}}{128 e^{7}} - \frac{5 d^{7} x}{128 e^{6} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{5 d^{5} x^{3}}{384 e^{4} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{d^{3} x^{5}}{192 e^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{7 d x^{7}}{48 \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} - \frac{e^{2} x^{9}}{8 d \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} & \text{otherwise} \end{cases}\right)"," ",0,"d**7*Piecewise((d**2/(e*x*sqrt(d**2/(e**2*x**2) - 1)) - d*acosh(d/(e*x)) - e*x/sqrt(d**2/(e**2*x**2) - 1), Abs(d**2/(e**2*x**2)) > 1), (-I*d**2/(e*x*sqrt(-d**2/(e**2*x**2) + 1)) + I*d*asin(d/(e*x)) + I*e*x/sqrt(-d**2/(e**2*x**2) + 1), True)) + 3*d**6*e*Piecewise((-I*d**2*acosh(e*x/d)/(2*e) - I*d*x/(2*sqrt(-1 + e**2*x**2/d**2)) + I*e**2*x**3/(2*d*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (d**2*asin(e*x/d)/(2*e) + d*x*sqrt(1 - e**2*x**2/d**2)/2, True)) + d**5*e**2*Piecewise((x**2*sqrt(d**2)/2, Eq(e**2, 0)), (-(d**2 - e**2*x**2)**(3/2)/(3*e**2), True)) - 5*d**4*e**3*Piecewise((-I*d**4*acosh(e*x/d)/(8*e**3) + I*d**3*x/(8*e**2*sqrt(-1 + e**2*x**2/d**2)) - 3*I*d*x**3/(8*sqrt(-1 + e**2*x**2/d**2)) + I*e**2*x**5/(4*d*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (d**4*asin(e*x/d)/(8*e**3) - d**3*x/(8*e**2*sqrt(1 - e**2*x**2/d**2)) + 3*d*x**3/(8*sqrt(1 - e**2*x**2/d**2)) - e**2*x**5/(4*d*sqrt(1 - e**2*x**2/d**2)), True)) - 5*d**3*e**4*Piecewise((-2*d**4*sqrt(d**2 - e**2*x**2)/(15*e**4) - d**2*x**2*sqrt(d**2 - e**2*x**2)/(15*e**2) + x**4*sqrt(d**2 - e**2*x**2)/5, Ne(e, 0)), (x**4*sqrt(d**2)/4, True)) + d**2*e**5*Piecewise((-I*d**6*acosh(e*x/d)/(16*e**5) + I*d**5*x/(16*e**4*sqrt(-1 + e**2*x**2/d**2)) - I*d**3*x**3/(48*e**2*sqrt(-1 + e**2*x**2/d**2)) - 5*I*d*x**5/(24*sqrt(-1 + e**2*x**2/d**2)) + I*e**2*x**7/(6*d*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (d**6*asin(e*x/d)/(16*e**5) - d**5*x/(16*e**4*sqrt(1 - e**2*x**2/d**2)) + d**3*x**3/(48*e**2*sqrt(1 - e**2*x**2/d**2)) + 5*d*x**5/(24*sqrt(1 - e**2*x**2/d**2)) - e**2*x**7/(6*d*sqrt(1 - e**2*x**2/d**2)), True)) + 3*d*e**6*Piecewise((-8*d**6*sqrt(d**2 - e**2*x**2)/(105*e**6) - 4*d**4*x**2*sqrt(d**2 - e**2*x**2)/(105*e**4) - d**2*x**4*sqrt(d**2 - e**2*x**2)/(35*e**2) + x**6*sqrt(d**2 - e**2*x**2)/7, Ne(e, 0)), (x**6*sqrt(d**2)/6, True)) + e**7*Piecewise((-5*I*d**8*acosh(e*x/d)/(128*e**7) + 5*I*d**7*x/(128*e**6*sqrt(-1 + e**2*x**2/d**2)) - 5*I*d**5*x**3/(384*e**4*sqrt(-1 + e**2*x**2/d**2)) - I*d**3*x**5/(192*e**2*sqrt(-1 + e**2*x**2/d**2)) - 7*I*d*x**7/(48*sqrt(-1 + e**2*x**2/d**2)) + I*e**2*x**9/(8*d*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (5*d**8*asin(e*x/d)/(128*e**7) - 5*d**7*x/(128*e**6*sqrt(1 - e**2*x**2/d**2)) + 5*d**5*x**3/(384*e**4*sqrt(1 - e**2*x**2/d**2)) + d**3*x**5/(192*e**2*sqrt(1 - e**2*x**2/d**2)) + 7*d*x**7/(48*sqrt(1 - e**2*x**2/d**2)) - e**2*x**9/(8*d*sqrt(1 - e**2*x**2/d**2)), True))","C",0
72,1,1057,0,19.884185," ","integrate((e*x+d)**3*(-e**2*x**2+d**2)**(5/2)/x**2,x)","d^{7} \left(\begin{cases} \frac{i d}{x \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + i e \operatorname{acosh}{\left(\frac{e x}{d} \right)} - \frac{i e^{2} x}{d \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\- \frac{d}{x \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} - e \operatorname{asin}{\left(\frac{e x}{d} \right)} + \frac{e^{2} x}{d \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} & \text{otherwise} \end{cases}\right) + 3 d^{6} e \left(\begin{cases} \frac{d^{2}}{e x \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} - d \operatorname{acosh}{\left(\frac{d}{e x} \right)} - \frac{e x}{\sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\- \frac{i d^{2}}{e x \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} + i d \operatorname{asin}{\left(\frac{d}{e x} \right)} + \frac{i e x}{\sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} & \text{otherwise} \end{cases}\right) + d^{5} e^{2} \left(\begin{cases} - \frac{i d^{2} \operatorname{acosh}{\left(\frac{e x}{d} \right)}}{2 e} - \frac{i d x}{2 \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + \frac{i e^{2} x^{3}}{2 d \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{d^{2} \operatorname{asin}{\left(\frac{e x}{d} \right)}}{2 e} + \frac{d x \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}}{2} & \text{otherwise} \end{cases}\right) - 5 d^{4} e^{3} \left(\begin{cases} \frac{x^{2} \sqrt{d^{2}}}{2} & \text{for}\: e^{2} = 0 \\- \frac{\left(d^{2} - e^{2} x^{2}\right)^{\frac{3}{2}}}{3 e^{2}} & \text{otherwise} \end{cases}\right) - 5 d^{3} e^{4} \left(\begin{cases} - \frac{i d^{4} \operatorname{acosh}{\left(\frac{e x}{d} \right)}}{8 e^{3}} + \frac{i d^{3} x}{8 e^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{3 i d x^{3}}{8 \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + \frac{i e^{2} x^{5}}{4 d \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{d^{4} \operatorname{asin}{\left(\frac{e x}{d} \right)}}{8 e^{3}} - \frac{d^{3} x}{8 e^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{3 d x^{3}}{8 \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} - \frac{e^{2} x^{5}}{4 d \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} & \text{otherwise} \end{cases}\right) + d^{2} e^{5} \left(\begin{cases} - \frac{2 d^{4} \sqrt{d^{2} - e^{2} x^{2}}}{15 e^{4}} - \frac{d^{2} x^{2} \sqrt{d^{2} - e^{2} x^{2}}}{15 e^{2}} + \frac{x^{4} \sqrt{d^{2} - e^{2} x^{2}}}{5} & \text{for}\: e \neq 0 \\\frac{x^{4} \sqrt{d^{2}}}{4} & \text{otherwise} \end{cases}\right) + 3 d e^{6} \left(\begin{cases} - \frac{i d^{6} \operatorname{acosh}{\left(\frac{e x}{d} \right)}}{16 e^{5}} + \frac{i d^{5} x}{16 e^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{i d^{3} x^{3}}{48 e^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{5 i d x^{5}}{24 \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + \frac{i e^{2} x^{7}}{6 d \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{d^{6} \operatorname{asin}{\left(\frac{e x}{d} \right)}}{16 e^{5}} - \frac{d^{5} x}{16 e^{4} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{d^{3} x^{3}}{48 e^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{5 d x^{5}}{24 \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} - \frac{e^{2} x^{7}}{6 d \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} & \text{otherwise} \end{cases}\right) + e^{7} \left(\begin{cases} - \frac{8 d^{6} \sqrt{d^{2} - e^{2} x^{2}}}{105 e^{6}} - \frac{4 d^{4} x^{2} \sqrt{d^{2} - e^{2} x^{2}}}{105 e^{4}} - \frac{d^{2} x^{4} \sqrt{d^{2} - e^{2} x^{2}}}{35 e^{2}} + \frac{x^{6} \sqrt{d^{2} - e^{2} x^{2}}}{7} & \text{for}\: e \neq 0 \\\frac{x^{6} \sqrt{d^{2}}}{6} & \text{otherwise} \end{cases}\right)"," ",0,"d**7*Piecewise((I*d/(x*sqrt(-1 + e**2*x**2/d**2)) + I*e*acosh(e*x/d) - I*e**2*x/(d*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (-d/(x*sqrt(1 - e**2*x**2/d**2)) - e*asin(e*x/d) + e**2*x/(d*sqrt(1 - e**2*x**2/d**2)), True)) + 3*d**6*e*Piecewise((d**2/(e*x*sqrt(d**2/(e**2*x**2) - 1)) - d*acosh(d/(e*x)) - e*x/sqrt(d**2/(e**2*x**2) - 1), Abs(d**2/(e**2*x**2)) > 1), (-I*d**2/(e*x*sqrt(-d**2/(e**2*x**2) + 1)) + I*d*asin(d/(e*x)) + I*e*x/sqrt(-d**2/(e**2*x**2) + 1), True)) + d**5*e**2*Piecewise((-I*d**2*acosh(e*x/d)/(2*e) - I*d*x/(2*sqrt(-1 + e**2*x**2/d**2)) + I*e**2*x**3/(2*d*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (d**2*asin(e*x/d)/(2*e) + d*x*sqrt(1 - e**2*x**2/d**2)/2, True)) - 5*d**4*e**3*Piecewise((x**2*sqrt(d**2)/2, Eq(e**2, 0)), (-(d**2 - e**2*x**2)**(3/2)/(3*e**2), True)) - 5*d**3*e**4*Piecewise((-I*d**4*acosh(e*x/d)/(8*e**3) + I*d**3*x/(8*e**2*sqrt(-1 + e**2*x**2/d**2)) - 3*I*d*x**3/(8*sqrt(-1 + e**2*x**2/d**2)) + I*e**2*x**5/(4*d*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (d**4*asin(e*x/d)/(8*e**3) - d**3*x/(8*e**2*sqrt(1 - e**2*x**2/d**2)) + 3*d*x**3/(8*sqrt(1 - e**2*x**2/d**2)) - e**2*x**5/(4*d*sqrt(1 - e**2*x**2/d**2)), True)) + d**2*e**5*Piecewise((-2*d**4*sqrt(d**2 - e**2*x**2)/(15*e**4) - d**2*x**2*sqrt(d**2 - e**2*x**2)/(15*e**2) + x**4*sqrt(d**2 - e**2*x**2)/5, Ne(e, 0)), (x**4*sqrt(d**2)/4, True)) + 3*d*e**6*Piecewise((-I*d**6*acosh(e*x/d)/(16*e**5) + I*d**5*x/(16*e**4*sqrt(-1 + e**2*x**2/d**2)) - I*d**3*x**3/(48*e**2*sqrt(-1 + e**2*x**2/d**2)) - 5*I*d*x**5/(24*sqrt(-1 + e**2*x**2/d**2)) + I*e**2*x**7/(6*d*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (d**6*asin(e*x/d)/(16*e**5) - d**5*x/(16*e**4*sqrt(1 - e**2*x**2/d**2)) + d**3*x**3/(48*e**2*sqrt(1 - e**2*x**2/d**2)) + 5*d*x**5/(24*sqrt(1 - e**2*x**2/d**2)) - e**2*x**7/(6*d*sqrt(1 - e**2*x**2/d**2)), True)) + e**7*Piecewise((-8*d**6*sqrt(d**2 - e**2*x**2)/(105*e**6) - 4*d**4*x**2*sqrt(d**2 - e**2*x**2)/(105*e**4) - d**2*x**4*sqrt(d**2 - e**2*x**2)/(35*e**2) + x**6*sqrt(d**2 - e**2*x**2)/7, Ne(e, 0)), (x**6*sqrt(d**2)/6, True))","C",0
73,1,1059,0,22.216799," ","integrate((e*x+d)**3*(-e**2*x**2+d**2)**(5/2)/x**3,x)","d^{7} \left(\begin{cases} - \frac{d^{2}}{2 e x^{3} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{e}{2 x \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{e^{2} \operatorname{acosh}{\left(\frac{d}{e x} \right)}}{2 d} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\- \frac{i e \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{2 x} - \frac{i e^{2} \operatorname{asin}{\left(\frac{d}{e x} \right)}}{2 d} & \text{otherwise} \end{cases}\right) + 3 d^{6} e \left(\begin{cases} \frac{i d}{x \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + i e \operatorname{acosh}{\left(\frac{e x}{d} \right)} - \frac{i e^{2} x}{d \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\- \frac{d}{x \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} - e \operatorname{asin}{\left(\frac{e x}{d} \right)} + \frac{e^{2} x}{d \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} & \text{otherwise} \end{cases}\right) + d^{5} e^{2} \left(\begin{cases} \frac{d^{2}}{e x \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} - d \operatorname{acosh}{\left(\frac{d}{e x} \right)} - \frac{e x}{\sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\- \frac{i d^{2}}{e x \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} + i d \operatorname{asin}{\left(\frac{d}{e x} \right)} + \frac{i e x}{\sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} & \text{otherwise} \end{cases}\right) - 5 d^{4} e^{3} \left(\begin{cases} - \frac{i d^{2} \operatorname{acosh}{\left(\frac{e x}{d} \right)}}{2 e} - \frac{i d x}{2 \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + \frac{i e^{2} x^{3}}{2 d \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{d^{2} \operatorname{asin}{\left(\frac{e x}{d} \right)}}{2 e} + \frac{d x \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}}{2} & \text{otherwise} \end{cases}\right) - 5 d^{3} e^{4} \left(\begin{cases} \frac{x^{2} \sqrt{d^{2}}}{2} & \text{for}\: e^{2} = 0 \\- \frac{\left(d^{2} - e^{2} x^{2}\right)^{\frac{3}{2}}}{3 e^{2}} & \text{otherwise} \end{cases}\right) + d^{2} e^{5} \left(\begin{cases} - \frac{i d^{4} \operatorname{acosh}{\left(\frac{e x}{d} \right)}}{8 e^{3}} + \frac{i d^{3} x}{8 e^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{3 i d x^{3}}{8 \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + \frac{i e^{2} x^{5}}{4 d \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{d^{4} \operatorname{asin}{\left(\frac{e x}{d} \right)}}{8 e^{3}} - \frac{d^{3} x}{8 e^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{3 d x^{3}}{8 \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} - \frac{e^{2} x^{5}}{4 d \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} & \text{otherwise} \end{cases}\right) + 3 d e^{6} \left(\begin{cases} - \frac{2 d^{4} \sqrt{d^{2} - e^{2} x^{2}}}{15 e^{4}} - \frac{d^{2} x^{2} \sqrt{d^{2} - e^{2} x^{2}}}{15 e^{2}} + \frac{x^{4} \sqrt{d^{2} - e^{2} x^{2}}}{5} & \text{for}\: e \neq 0 \\\frac{x^{4} \sqrt{d^{2}}}{4} & \text{otherwise} \end{cases}\right) + e^{7} \left(\begin{cases} - \frac{i d^{6} \operatorname{acosh}{\left(\frac{e x}{d} \right)}}{16 e^{5}} + \frac{i d^{5} x}{16 e^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{i d^{3} x^{3}}{48 e^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{5 i d x^{5}}{24 \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + \frac{i e^{2} x^{7}}{6 d \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{d^{6} \operatorname{asin}{\left(\frac{e x}{d} \right)}}{16 e^{5}} - \frac{d^{5} x}{16 e^{4} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{d^{3} x^{3}}{48 e^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{5 d x^{5}}{24 \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} - \frac{e^{2} x^{7}}{6 d \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} & \text{otherwise} \end{cases}\right)"," ",0,"d**7*Piecewise((-d**2/(2*e*x**3*sqrt(d**2/(e**2*x**2) - 1)) + e/(2*x*sqrt(d**2/(e**2*x**2) - 1)) + e**2*acosh(d/(e*x))/(2*d), Abs(d**2/(e**2*x**2)) > 1), (-I*e*sqrt(-d**2/(e**2*x**2) + 1)/(2*x) - I*e**2*asin(d/(e*x))/(2*d), True)) + 3*d**6*e*Piecewise((I*d/(x*sqrt(-1 + e**2*x**2/d**2)) + I*e*acosh(e*x/d) - I*e**2*x/(d*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (-d/(x*sqrt(1 - e**2*x**2/d**2)) - e*asin(e*x/d) + e**2*x/(d*sqrt(1 - e**2*x**2/d**2)), True)) + d**5*e**2*Piecewise((d**2/(e*x*sqrt(d**2/(e**2*x**2) - 1)) - d*acosh(d/(e*x)) - e*x/sqrt(d**2/(e**2*x**2) - 1), Abs(d**2/(e**2*x**2)) > 1), (-I*d**2/(e*x*sqrt(-d**2/(e**2*x**2) + 1)) + I*d*asin(d/(e*x)) + I*e*x/sqrt(-d**2/(e**2*x**2) + 1), True)) - 5*d**4*e**3*Piecewise((-I*d**2*acosh(e*x/d)/(2*e) - I*d*x/(2*sqrt(-1 + e**2*x**2/d**2)) + I*e**2*x**3/(2*d*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (d**2*asin(e*x/d)/(2*e) + d*x*sqrt(1 - e**2*x**2/d**2)/2, True)) - 5*d**3*e**4*Piecewise((x**2*sqrt(d**2)/2, Eq(e**2, 0)), (-(d**2 - e**2*x**2)**(3/2)/(3*e**2), True)) + d**2*e**5*Piecewise((-I*d**4*acosh(e*x/d)/(8*e**3) + I*d**3*x/(8*e**2*sqrt(-1 + e**2*x**2/d**2)) - 3*I*d*x**3/(8*sqrt(-1 + e**2*x**2/d**2)) + I*e**2*x**5/(4*d*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (d**4*asin(e*x/d)/(8*e**3) - d**3*x/(8*e**2*sqrt(1 - e**2*x**2/d**2)) + 3*d*x**3/(8*sqrt(1 - e**2*x**2/d**2)) - e**2*x**5/(4*d*sqrt(1 - e**2*x**2/d**2)), True)) + 3*d*e**6*Piecewise((-2*d**4*sqrt(d**2 - e**2*x**2)/(15*e**4) - d**2*x**2*sqrt(d**2 - e**2*x**2)/(15*e**2) + x**4*sqrt(d**2 - e**2*x**2)/5, Ne(e, 0)), (x**4*sqrt(d**2)/4, True)) + e**7*Piecewise((-I*d**6*acosh(e*x/d)/(16*e**5) + I*d**5*x/(16*e**4*sqrt(-1 + e**2*x**2/d**2)) - I*d**3*x**3/(48*e**2*sqrt(-1 + e**2*x**2/d**2)) - 5*I*d*x**5/(24*sqrt(-1 + e**2*x**2/d**2)) + I*e**2*x**7/(6*d*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (d**6*asin(e*x/d)/(16*e**5) - d**5*x/(16*e**4*sqrt(1 - e**2*x**2/d**2)) + d**3*x**3/(48*e**2*sqrt(1 - e**2*x**2/d**2)) + 5*d*x**5/(24*sqrt(1 - e**2*x**2/d**2)) - e**2*x**7/(6*d*sqrt(1 - e**2*x**2/d**2)), True))","C",0
74,1,911,0,15.742374," ","integrate((e*x+d)**3*(-e**2*x**2+d**2)**(5/2)/x**4,x)","d^{7} \left(\begin{cases} - \frac{e \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}}{3 x^{2}} + \frac{e^{3} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}}{3 d^{2}} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\- \frac{i e \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{3 x^{2}} + \frac{i e^{3} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{3 d^{2}} & \text{otherwise} \end{cases}\right) + 3 d^{6} e \left(\begin{cases} - \frac{d^{2}}{2 e x^{3} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{e}{2 x \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{e^{2} \operatorname{acosh}{\left(\frac{d}{e x} \right)}}{2 d} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\- \frac{i e \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{2 x} - \frac{i e^{2} \operatorname{asin}{\left(\frac{d}{e x} \right)}}{2 d} & \text{otherwise} \end{cases}\right) + d^{5} e^{2} \left(\begin{cases} \frac{i d}{x \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + i e \operatorname{acosh}{\left(\frac{e x}{d} \right)} - \frac{i e^{2} x}{d \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\- \frac{d}{x \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} - e \operatorname{asin}{\left(\frac{e x}{d} \right)} + \frac{e^{2} x}{d \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} & \text{otherwise} \end{cases}\right) - 5 d^{4} e^{3} \left(\begin{cases} \frac{d^{2}}{e x \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} - d \operatorname{acosh}{\left(\frac{d}{e x} \right)} - \frac{e x}{\sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\- \frac{i d^{2}}{e x \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} + i d \operatorname{asin}{\left(\frac{d}{e x} \right)} + \frac{i e x}{\sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} & \text{otherwise} \end{cases}\right) - 5 d^{3} e^{4} \left(\begin{cases} - \frac{i d^{2} \operatorname{acosh}{\left(\frac{e x}{d} \right)}}{2 e} - \frac{i d x}{2 \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + \frac{i e^{2} x^{3}}{2 d \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{d^{2} \operatorname{asin}{\left(\frac{e x}{d} \right)}}{2 e} + \frac{d x \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}}{2} & \text{otherwise} \end{cases}\right) + d^{2} e^{5} \left(\begin{cases} \frac{x^{2} \sqrt{d^{2}}}{2} & \text{for}\: e^{2} = 0 \\- \frac{\left(d^{2} - e^{2} x^{2}\right)^{\frac{3}{2}}}{3 e^{2}} & \text{otherwise} \end{cases}\right) + 3 d e^{6} \left(\begin{cases} - \frac{i d^{4} \operatorname{acosh}{\left(\frac{e x}{d} \right)}}{8 e^{3}} + \frac{i d^{3} x}{8 e^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{3 i d x^{3}}{8 \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + \frac{i e^{2} x^{5}}{4 d \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{d^{4} \operatorname{asin}{\left(\frac{e x}{d} \right)}}{8 e^{3}} - \frac{d^{3} x}{8 e^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{3 d x^{3}}{8 \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} - \frac{e^{2} x^{5}}{4 d \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} & \text{otherwise} \end{cases}\right) + e^{7} \left(\begin{cases} - \frac{2 d^{4} \sqrt{d^{2} - e^{2} x^{2}}}{15 e^{4}} - \frac{d^{2} x^{2} \sqrt{d^{2} - e^{2} x^{2}}}{15 e^{2}} + \frac{x^{4} \sqrt{d^{2} - e^{2} x^{2}}}{5} & \text{for}\: e \neq 0 \\\frac{x^{4} \sqrt{d^{2}}}{4} & \text{otherwise} \end{cases}\right)"," ",0,"d**7*Piecewise((-e*sqrt(d**2/(e**2*x**2) - 1)/(3*x**2) + e**3*sqrt(d**2/(e**2*x**2) - 1)/(3*d**2), Abs(d**2/(e**2*x**2)) > 1), (-I*e*sqrt(-d**2/(e**2*x**2) + 1)/(3*x**2) + I*e**3*sqrt(-d**2/(e**2*x**2) + 1)/(3*d**2), True)) + 3*d**6*e*Piecewise((-d**2/(2*e*x**3*sqrt(d**2/(e**2*x**2) - 1)) + e/(2*x*sqrt(d**2/(e**2*x**2) - 1)) + e**2*acosh(d/(e*x))/(2*d), Abs(d**2/(e**2*x**2)) > 1), (-I*e*sqrt(-d**2/(e**2*x**2) + 1)/(2*x) - I*e**2*asin(d/(e*x))/(2*d), True)) + d**5*e**2*Piecewise((I*d/(x*sqrt(-1 + e**2*x**2/d**2)) + I*e*acosh(e*x/d) - I*e**2*x/(d*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (-d/(x*sqrt(1 - e**2*x**2/d**2)) - e*asin(e*x/d) + e**2*x/(d*sqrt(1 - e**2*x**2/d**2)), True)) - 5*d**4*e**3*Piecewise((d**2/(e*x*sqrt(d**2/(e**2*x**2) - 1)) - d*acosh(d/(e*x)) - e*x/sqrt(d**2/(e**2*x**2) - 1), Abs(d**2/(e**2*x**2)) > 1), (-I*d**2/(e*x*sqrt(-d**2/(e**2*x**2) + 1)) + I*d*asin(d/(e*x)) + I*e*x/sqrt(-d**2/(e**2*x**2) + 1), True)) - 5*d**3*e**4*Piecewise((-I*d**2*acosh(e*x/d)/(2*e) - I*d*x/(2*sqrt(-1 + e**2*x**2/d**2)) + I*e**2*x**3/(2*d*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (d**2*asin(e*x/d)/(2*e) + d*x*sqrt(1 - e**2*x**2/d**2)/2, True)) + d**2*e**5*Piecewise((x**2*sqrt(d**2)/2, Eq(e**2, 0)), (-(d**2 - e**2*x**2)**(3/2)/(3*e**2), True)) + 3*d*e**6*Piecewise((-I*d**4*acosh(e*x/d)/(8*e**3) + I*d**3*x/(8*e**2*sqrt(-1 + e**2*x**2/d**2)) - 3*I*d*x**3/(8*sqrt(-1 + e**2*x**2/d**2)) + I*e**2*x**5/(4*d*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (d**4*asin(e*x/d)/(8*e**3) - d**3*x/(8*e**2*sqrt(1 - e**2*x**2/d**2)) + 3*d*x**3/(8*sqrt(1 - e**2*x**2/d**2)) - e**2*x**5/(4*d*sqrt(1 - e**2*x**2/d**2)), True)) + e**7*Piecewise((-2*d**4*sqrt(d**2 - e**2*x**2)/(15*e**4) - d**2*x**2*sqrt(d**2 - e**2*x**2)/(15*e**2) + x**4*sqrt(d**2 - e**2*x**2)/5, Ne(e, 0)), (x**4*sqrt(d**2)/4, True))","C",0
75,1,1028,0,20.103139," ","integrate((e*x+d)**3*(-e**2*x**2+d**2)**(5/2)/x**5,x)","d^{7} \left(\begin{cases} - \frac{d^{2}}{4 e x^{5} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{3 e}{8 x^{3} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} - \frac{e^{3}}{8 d^{2} x \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{e^{4} \operatorname{acosh}{\left(\frac{d}{e x} \right)}}{8 d^{3}} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\\frac{i d^{2}}{4 e x^{5} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} - \frac{3 i e}{8 x^{3} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} + \frac{i e^{3}}{8 d^{2} x \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} - \frac{i e^{4} \operatorname{asin}{\left(\frac{d}{e x} \right)}}{8 d^{3}} & \text{otherwise} \end{cases}\right) + 3 d^{6} e \left(\begin{cases} - \frac{e \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}}{3 x^{2}} + \frac{e^{3} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}}{3 d^{2}} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\- \frac{i e \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{3 x^{2}} + \frac{i e^{3} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{3 d^{2}} & \text{otherwise} \end{cases}\right) + d^{5} e^{2} \left(\begin{cases} - \frac{d^{2}}{2 e x^{3} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{e}{2 x \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{e^{2} \operatorname{acosh}{\left(\frac{d}{e x} \right)}}{2 d} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\- \frac{i e \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{2 x} - \frac{i e^{2} \operatorname{asin}{\left(\frac{d}{e x} \right)}}{2 d} & \text{otherwise} \end{cases}\right) - 5 d^{4} e^{3} \left(\begin{cases} \frac{i d}{x \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + i e \operatorname{acosh}{\left(\frac{e x}{d} \right)} - \frac{i e^{2} x}{d \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\- \frac{d}{x \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} - e \operatorname{asin}{\left(\frac{e x}{d} \right)} + \frac{e^{2} x}{d \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} & \text{otherwise} \end{cases}\right) - 5 d^{3} e^{4} \left(\begin{cases} \frac{d^{2}}{e x \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} - d \operatorname{acosh}{\left(\frac{d}{e x} \right)} - \frac{e x}{\sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\- \frac{i d^{2}}{e x \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} + i d \operatorname{asin}{\left(\frac{d}{e x} \right)} + \frac{i e x}{\sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} & \text{otherwise} \end{cases}\right) + d^{2} e^{5} \left(\begin{cases} - \frac{i d^{2} \operatorname{acosh}{\left(\frac{e x}{d} \right)}}{2 e} - \frac{i d x}{2 \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + \frac{i e^{2} x^{3}}{2 d \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{d^{2} \operatorname{asin}{\left(\frac{e x}{d} \right)}}{2 e} + \frac{d x \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}}{2} & \text{otherwise} \end{cases}\right) + 3 d e^{6} \left(\begin{cases} \frac{x^{2} \sqrt{d^{2}}}{2} & \text{for}\: e^{2} = 0 \\- \frac{\left(d^{2} - e^{2} x^{2}\right)^{\frac{3}{2}}}{3 e^{2}} & \text{otherwise} \end{cases}\right) + e^{7} \left(\begin{cases} - \frac{i d^{4} \operatorname{acosh}{\left(\frac{e x}{d} \right)}}{8 e^{3}} + \frac{i d^{3} x}{8 e^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{3 i d x^{3}}{8 \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + \frac{i e^{2} x^{5}}{4 d \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{d^{4} \operatorname{asin}{\left(\frac{e x}{d} \right)}}{8 e^{3}} - \frac{d^{3} x}{8 e^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{3 d x^{3}}{8 \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} - \frac{e^{2} x^{5}}{4 d \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} & \text{otherwise} \end{cases}\right)"," ",0,"d**7*Piecewise((-d**2/(4*e*x**5*sqrt(d**2/(e**2*x**2) - 1)) + 3*e/(8*x**3*sqrt(d**2/(e**2*x**2) - 1)) - e**3/(8*d**2*x*sqrt(d**2/(e**2*x**2) - 1)) + e**4*acosh(d/(e*x))/(8*d**3), Abs(d**2/(e**2*x**2)) > 1), (I*d**2/(4*e*x**5*sqrt(-d**2/(e**2*x**2) + 1)) - 3*I*e/(8*x**3*sqrt(-d**2/(e**2*x**2) + 1)) + I*e**3/(8*d**2*x*sqrt(-d**2/(e**2*x**2) + 1)) - I*e**4*asin(d/(e*x))/(8*d**3), True)) + 3*d**6*e*Piecewise((-e*sqrt(d**2/(e**2*x**2) - 1)/(3*x**2) + e**3*sqrt(d**2/(e**2*x**2) - 1)/(3*d**2), Abs(d**2/(e**2*x**2)) > 1), (-I*e*sqrt(-d**2/(e**2*x**2) + 1)/(3*x**2) + I*e**3*sqrt(-d**2/(e**2*x**2) + 1)/(3*d**2), True)) + d**5*e**2*Piecewise((-d**2/(2*e*x**3*sqrt(d**2/(e**2*x**2) - 1)) + e/(2*x*sqrt(d**2/(e**2*x**2) - 1)) + e**2*acosh(d/(e*x))/(2*d), Abs(d**2/(e**2*x**2)) > 1), (-I*e*sqrt(-d**2/(e**2*x**2) + 1)/(2*x) - I*e**2*asin(d/(e*x))/(2*d), True)) - 5*d**4*e**3*Piecewise((I*d/(x*sqrt(-1 + e**2*x**2/d**2)) + I*e*acosh(e*x/d) - I*e**2*x/(d*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (-d/(x*sqrt(1 - e**2*x**2/d**2)) - e*asin(e*x/d) + e**2*x/(d*sqrt(1 - e**2*x**2/d**2)), True)) - 5*d**3*e**4*Piecewise((d**2/(e*x*sqrt(d**2/(e**2*x**2) - 1)) - d*acosh(d/(e*x)) - e*x/sqrt(d**2/(e**2*x**2) - 1), Abs(d**2/(e**2*x**2)) > 1), (-I*d**2/(e*x*sqrt(-d**2/(e**2*x**2) + 1)) + I*d*asin(d/(e*x)) + I*e*x/sqrt(-d**2/(e**2*x**2) + 1), True)) + d**2*e**5*Piecewise((-I*d**2*acosh(e*x/d)/(2*e) - I*d*x/(2*sqrt(-1 + e**2*x**2/d**2)) + I*e**2*x**3/(2*d*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (d**2*asin(e*x/d)/(2*e) + d*x*sqrt(1 - e**2*x**2/d**2)/2, True)) + 3*d*e**6*Piecewise((x**2*sqrt(d**2)/2, Eq(e**2, 0)), (-(d**2 - e**2*x**2)**(3/2)/(3*e**2), True)) + e**7*Piecewise((-I*d**4*acosh(e*x/d)/(8*e**3) + I*d**3*x/(8*e**2*sqrt(-1 + e**2*x**2/d**2)) - 3*I*d*x**3/(8*sqrt(-1 + e**2*x**2/d**2)) + I*e**2*x**5/(4*d*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (d**4*asin(e*x/d)/(8*e**3) - d**3*x/(8*e**2*sqrt(1 - e**2*x**2/d**2)) + 3*d*x**3/(8*sqrt(1 - e**2*x**2/d**2)) - e**2*x**5/(4*d*sqrt(1 - e**2*x**2/d**2)), True))","C",0
76,1,1178,0,20.702396," ","integrate((e*x+d)**3*(-e**2*x**2+d**2)**(5/2)/x**6,x)","d^{7} \left(\begin{cases} \frac{3 i d^{3} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{2} x^{5} + 15 e^{2} x^{7}} - \frac{4 i d e^{2} x^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{2} x^{5} + 15 e^{2} x^{7}} + \frac{2 i e^{6} x^{6} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{5} x^{5} + 15 d^{3} e^{2} x^{7}} - \frac{i e^{4} x^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{3} x^{5} + 15 d e^{2} x^{7}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{3 d^{3} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{2} x^{5} + 15 e^{2} x^{7}} - \frac{4 d e^{2} x^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{2} x^{5} + 15 e^{2} x^{7}} + \frac{2 e^{6} x^{6} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{5} x^{5} + 15 d^{3} e^{2} x^{7}} - \frac{e^{4} x^{4} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{3} x^{5} + 15 d e^{2} x^{7}} & \text{otherwise} \end{cases}\right) + 3 d^{6} e \left(\begin{cases} - \frac{d^{2}}{4 e x^{5} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{3 e}{8 x^{3} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} - \frac{e^{3}}{8 d^{2} x \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{e^{4} \operatorname{acosh}{\left(\frac{d}{e x} \right)}}{8 d^{3}} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\\frac{i d^{2}}{4 e x^{5} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} - \frac{3 i e}{8 x^{3} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} + \frac{i e^{3}}{8 d^{2} x \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} - \frac{i e^{4} \operatorname{asin}{\left(\frac{d}{e x} \right)}}{8 d^{3}} & \text{otherwise} \end{cases}\right) + d^{5} e^{2} \left(\begin{cases} - \frac{e \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}}{3 x^{2}} + \frac{e^{3} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}}{3 d^{2}} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\- \frac{i e \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{3 x^{2}} + \frac{i e^{3} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{3 d^{2}} & \text{otherwise} \end{cases}\right) - 5 d^{4} e^{3} \left(\begin{cases} - \frac{d^{2}}{2 e x^{3} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{e}{2 x \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{e^{2} \operatorname{acosh}{\left(\frac{d}{e x} \right)}}{2 d} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\- \frac{i e \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{2 x} - \frac{i e^{2} \operatorname{asin}{\left(\frac{d}{e x} \right)}}{2 d} & \text{otherwise} \end{cases}\right) - 5 d^{3} e^{4} \left(\begin{cases} \frac{i d}{x \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + i e \operatorname{acosh}{\left(\frac{e x}{d} \right)} - \frac{i e^{2} x}{d \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\- \frac{d}{x \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} - e \operatorname{asin}{\left(\frac{e x}{d} \right)} + \frac{e^{2} x}{d \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} & \text{otherwise} \end{cases}\right) + d^{2} e^{5} \left(\begin{cases} \frac{d^{2}}{e x \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} - d \operatorname{acosh}{\left(\frac{d}{e x} \right)} - \frac{e x}{\sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\- \frac{i d^{2}}{e x \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} + i d \operatorname{asin}{\left(\frac{d}{e x} \right)} + \frac{i e x}{\sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} & \text{otherwise} \end{cases}\right) + 3 d e^{6} \left(\begin{cases} - \frac{i d^{2} \operatorname{acosh}{\left(\frac{e x}{d} \right)}}{2 e} - \frac{i d x}{2 \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + \frac{i e^{2} x^{3}}{2 d \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{d^{2} \operatorname{asin}{\left(\frac{e x}{d} \right)}}{2 e} + \frac{d x \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}}{2} & \text{otherwise} \end{cases}\right) + e^{7} \left(\begin{cases} \frac{x^{2} \sqrt{d^{2}}}{2} & \text{for}\: e^{2} = 0 \\- \frac{\left(d^{2} - e^{2} x^{2}\right)^{\frac{3}{2}}}{3 e^{2}} & \text{otherwise} \end{cases}\right)"," ",0,"d**7*Piecewise((3*I*d**3*sqrt(-1 + e**2*x**2/d**2)/(-15*d**2*x**5 + 15*e**2*x**7) - 4*I*d*e**2*x**2*sqrt(-1 + e**2*x**2/d**2)/(-15*d**2*x**5 + 15*e**2*x**7) + 2*I*e**6*x**6*sqrt(-1 + e**2*x**2/d**2)/(-15*d**5*x**5 + 15*d**3*e**2*x**7) - I*e**4*x**4*sqrt(-1 + e**2*x**2/d**2)/(-15*d**3*x**5 + 15*d*e**2*x**7), Abs(e**2*x**2/d**2) > 1), (3*d**3*sqrt(1 - e**2*x**2/d**2)/(-15*d**2*x**5 + 15*e**2*x**7) - 4*d*e**2*x**2*sqrt(1 - e**2*x**2/d**2)/(-15*d**2*x**5 + 15*e**2*x**7) + 2*e**6*x**6*sqrt(1 - e**2*x**2/d**2)/(-15*d**5*x**5 + 15*d**3*e**2*x**7) - e**4*x**4*sqrt(1 - e**2*x**2/d**2)/(-15*d**3*x**5 + 15*d*e**2*x**7), True)) + 3*d**6*e*Piecewise((-d**2/(4*e*x**5*sqrt(d**2/(e**2*x**2) - 1)) + 3*e/(8*x**3*sqrt(d**2/(e**2*x**2) - 1)) - e**3/(8*d**2*x*sqrt(d**2/(e**2*x**2) - 1)) + e**4*acosh(d/(e*x))/(8*d**3), Abs(d**2/(e**2*x**2)) > 1), (I*d**2/(4*e*x**5*sqrt(-d**2/(e**2*x**2) + 1)) - 3*I*e/(8*x**3*sqrt(-d**2/(e**2*x**2) + 1)) + I*e**3/(8*d**2*x*sqrt(-d**2/(e**2*x**2) + 1)) - I*e**4*asin(d/(e*x))/(8*d**3), True)) + d**5*e**2*Piecewise((-e*sqrt(d**2/(e**2*x**2) - 1)/(3*x**2) + e**3*sqrt(d**2/(e**2*x**2) - 1)/(3*d**2), Abs(d**2/(e**2*x**2)) > 1), (-I*e*sqrt(-d**2/(e**2*x**2) + 1)/(3*x**2) + I*e**3*sqrt(-d**2/(e**2*x**2) + 1)/(3*d**2), True)) - 5*d**4*e**3*Piecewise((-d**2/(2*e*x**3*sqrt(d**2/(e**2*x**2) - 1)) + e/(2*x*sqrt(d**2/(e**2*x**2) - 1)) + e**2*acosh(d/(e*x))/(2*d), Abs(d**2/(e**2*x**2)) > 1), (-I*e*sqrt(-d**2/(e**2*x**2) + 1)/(2*x) - I*e**2*asin(d/(e*x))/(2*d), True)) - 5*d**3*e**4*Piecewise((I*d/(x*sqrt(-1 + e**2*x**2/d**2)) + I*e*acosh(e*x/d) - I*e**2*x/(d*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (-d/(x*sqrt(1 - e**2*x**2/d**2)) - e*asin(e*x/d) + e**2*x/(d*sqrt(1 - e**2*x**2/d**2)), True)) + d**2*e**5*Piecewise((d**2/(e*x*sqrt(d**2/(e**2*x**2) - 1)) - d*acosh(d/(e*x)) - e*x/sqrt(d**2/(e**2*x**2) - 1), Abs(d**2/(e**2*x**2)) > 1), (-I*d**2/(e*x*sqrt(-d**2/(e**2*x**2) + 1)) + I*d*asin(d/(e*x)) + I*e*x/sqrt(-d**2/(e**2*x**2) + 1), True)) + 3*d*e**6*Piecewise((-I*d**2*acosh(e*x/d)/(2*e) - I*d*x/(2*sqrt(-1 + e**2*x**2/d**2)) + I*e**2*x**3/(2*d*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (d**2*asin(e*x/d)/(2*e) + d*x*sqrt(1 - e**2*x**2/d**2)/2, True)) + e**7*Piecewise((x**2*sqrt(d**2)/2, Eq(e**2, 0)), (-(d**2 - e**2*x**2)**(3/2)/(3*e**2), True))","C",0
77,1,1397,0,21.705706," ","integrate((e*x+d)**3*(-e**2*x**2+d**2)**(5/2)/x**7,x)","d^{7} \left(\begin{cases} - \frac{d^{2}}{6 e x^{7} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{5 e}{24 x^{5} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{e^{3}}{48 d^{2} x^{3} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} - \frac{e^{5}}{16 d^{4} x \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{e^{6} \operatorname{acosh}{\left(\frac{d}{e x} \right)}}{16 d^{5}} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\\frac{i d^{2}}{6 e x^{7} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} - \frac{5 i e}{24 x^{5} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} - \frac{i e^{3}}{48 d^{2} x^{3} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} + \frac{i e^{5}}{16 d^{4} x \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} - \frac{i e^{6} \operatorname{asin}{\left(\frac{d}{e x} \right)}}{16 d^{5}} & \text{otherwise} \end{cases}\right) + 3 d^{6} e \left(\begin{cases} \frac{3 i d^{3} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{2} x^{5} + 15 e^{2} x^{7}} - \frac{4 i d e^{2} x^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{2} x^{5} + 15 e^{2} x^{7}} + \frac{2 i e^{6} x^{6} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{5} x^{5} + 15 d^{3} e^{2} x^{7}} - \frac{i e^{4} x^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{3} x^{5} + 15 d e^{2} x^{7}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{3 d^{3} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{2} x^{5} + 15 e^{2} x^{7}} - \frac{4 d e^{2} x^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{2} x^{5} + 15 e^{2} x^{7}} + \frac{2 e^{6} x^{6} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{5} x^{5} + 15 d^{3} e^{2} x^{7}} - \frac{e^{4} x^{4} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{3} x^{5} + 15 d e^{2} x^{7}} & \text{otherwise} \end{cases}\right) + d^{5} e^{2} \left(\begin{cases} - \frac{d^{2}}{4 e x^{5} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{3 e}{8 x^{3} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} - \frac{e^{3}}{8 d^{2} x \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{e^{4} \operatorname{acosh}{\left(\frac{d}{e x} \right)}}{8 d^{3}} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\\frac{i d^{2}}{4 e x^{5} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} - \frac{3 i e}{8 x^{3} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} + \frac{i e^{3}}{8 d^{2} x \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} - \frac{i e^{4} \operatorname{asin}{\left(\frac{d}{e x} \right)}}{8 d^{3}} & \text{otherwise} \end{cases}\right) - 5 d^{4} e^{3} \left(\begin{cases} - \frac{e \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}}{3 x^{2}} + \frac{e^{3} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}}{3 d^{2}} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\- \frac{i e \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{3 x^{2}} + \frac{i e^{3} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{3 d^{2}} & \text{otherwise} \end{cases}\right) - 5 d^{3} e^{4} \left(\begin{cases} - \frac{d^{2}}{2 e x^{3} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{e}{2 x \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{e^{2} \operatorname{acosh}{\left(\frac{d}{e x} \right)}}{2 d} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\- \frac{i e \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{2 x} - \frac{i e^{2} \operatorname{asin}{\left(\frac{d}{e x} \right)}}{2 d} & \text{otherwise} \end{cases}\right) + d^{2} e^{5} \left(\begin{cases} \frac{i d}{x \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + i e \operatorname{acosh}{\left(\frac{e x}{d} \right)} - \frac{i e^{2} x}{d \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\- \frac{d}{x \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} - e \operatorname{asin}{\left(\frac{e x}{d} \right)} + \frac{e^{2} x}{d \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} & \text{otherwise} \end{cases}\right) + 3 d e^{6} \left(\begin{cases} \frac{d^{2}}{e x \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} - d \operatorname{acosh}{\left(\frac{d}{e x} \right)} - \frac{e x}{\sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\- \frac{i d^{2}}{e x \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} + i d \operatorname{asin}{\left(\frac{d}{e x} \right)} + \frac{i e x}{\sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} & \text{otherwise} \end{cases}\right) + e^{7} \left(\begin{cases} - \frac{i d^{2} \operatorname{acosh}{\left(\frac{e x}{d} \right)}}{2 e} - \frac{i d x}{2 \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + \frac{i e^{2} x^{3}}{2 d \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{d^{2} \operatorname{asin}{\left(\frac{e x}{d} \right)}}{2 e} + \frac{d x \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}}{2} & \text{otherwise} \end{cases}\right)"," ",0,"d**7*Piecewise((-d**2/(6*e*x**7*sqrt(d**2/(e**2*x**2) - 1)) + 5*e/(24*x**5*sqrt(d**2/(e**2*x**2) - 1)) + e**3/(48*d**2*x**3*sqrt(d**2/(e**2*x**2) - 1)) - e**5/(16*d**4*x*sqrt(d**2/(e**2*x**2) - 1)) + e**6*acosh(d/(e*x))/(16*d**5), Abs(d**2/(e**2*x**2)) > 1), (I*d**2/(6*e*x**7*sqrt(-d**2/(e**2*x**2) + 1)) - 5*I*e/(24*x**5*sqrt(-d**2/(e**2*x**2) + 1)) - I*e**3/(48*d**2*x**3*sqrt(-d**2/(e**2*x**2) + 1)) + I*e**5/(16*d**4*x*sqrt(-d**2/(e**2*x**2) + 1)) - I*e**6*asin(d/(e*x))/(16*d**5), True)) + 3*d**6*e*Piecewise((3*I*d**3*sqrt(-1 + e**2*x**2/d**2)/(-15*d**2*x**5 + 15*e**2*x**7) - 4*I*d*e**2*x**2*sqrt(-1 + e**2*x**2/d**2)/(-15*d**2*x**5 + 15*e**2*x**7) + 2*I*e**6*x**6*sqrt(-1 + e**2*x**2/d**2)/(-15*d**5*x**5 + 15*d**3*e**2*x**7) - I*e**4*x**4*sqrt(-1 + e**2*x**2/d**2)/(-15*d**3*x**5 + 15*d*e**2*x**7), Abs(e**2*x**2/d**2) > 1), (3*d**3*sqrt(1 - e**2*x**2/d**2)/(-15*d**2*x**5 + 15*e**2*x**7) - 4*d*e**2*x**2*sqrt(1 - e**2*x**2/d**2)/(-15*d**2*x**5 + 15*e**2*x**7) + 2*e**6*x**6*sqrt(1 - e**2*x**2/d**2)/(-15*d**5*x**5 + 15*d**3*e**2*x**7) - e**4*x**4*sqrt(1 - e**2*x**2/d**2)/(-15*d**3*x**5 + 15*d*e**2*x**7), True)) + d**5*e**2*Piecewise((-d**2/(4*e*x**5*sqrt(d**2/(e**2*x**2) - 1)) + 3*e/(8*x**3*sqrt(d**2/(e**2*x**2) - 1)) - e**3/(8*d**2*x*sqrt(d**2/(e**2*x**2) - 1)) + e**4*acosh(d/(e*x))/(8*d**3), Abs(d**2/(e**2*x**2)) > 1), (I*d**2/(4*e*x**5*sqrt(-d**2/(e**2*x**2) + 1)) - 3*I*e/(8*x**3*sqrt(-d**2/(e**2*x**2) + 1)) + I*e**3/(8*d**2*x*sqrt(-d**2/(e**2*x**2) + 1)) - I*e**4*asin(d/(e*x))/(8*d**3), True)) - 5*d**4*e**3*Piecewise((-e*sqrt(d**2/(e**2*x**2) - 1)/(3*x**2) + e**3*sqrt(d**2/(e**2*x**2) - 1)/(3*d**2), Abs(d**2/(e**2*x**2)) > 1), (-I*e*sqrt(-d**2/(e**2*x**2) + 1)/(3*x**2) + I*e**3*sqrt(-d**2/(e**2*x**2) + 1)/(3*d**2), True)) - 5*d**3*e**4*Piecewise((-d**2/(2*e*x**3*sqrt(d**2/(e**2*x**2) - 1)) + e/(2*x*sqrt(d**2/(e**2*x**2) - 1)) + e**2*acosh(d/(e*x))/(2*d), Abs(d**2/(e**2*x**2)) > 1), (-I*e*sqrt(-d**2/(e**2*x**2) + 1)/(2*x) - I*e**2*asin(d/(e*x))/(2*d), True)) + d**2*e**5*Piecewise((I*d/(x*sqrt(-1 + e**2*x**2/d**2)) + I*e*acosh(e*x/d) - I*e**2*x/(d*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (-d/(x*sqrt(1 - e**2*x**2/d**2)) - e*asin(e*x/d) + e**2*x/(d*sqrt(1 - e**2*x**2/d**2)), True)) + 3*d*e**6*Piecewise((d**2/(e*x*sqrt(d**2/(e**2*x**2) - 1)) - d*acosh(d/(e*x)) - e*x/sqrt(d**2/(e**2*x**2) - 1), Abs(d**2/(e**2*x**2)) > 1), (-I*d**2/(e*x*sqrt(-d**2/(e**2*x**2) + 1)) + I*d*asin(d/(e*x)) + I*e*x/sqrt(-d**2/(e**2*x**2) + 1), True)) + e**7*Piecewise((-I*d**2*acosh(e*x/d)/(2*e) - I*d*x/(2*sqrt(-1 + e**2*x**2/d**2)) + I*e**2*x**3/(2*d*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (d**2*asin(e*x/d)/(2*e) + d*x*sqrt(1 - e**2*x**2/d**2)/2, True))","C",0
78,1,1513,0,22.292764," ","integrate((e*x+d)**3*(-e**2*x**2+d**2)**(5/2)/x**8,x)","d^{7} \left(\begin{cases} - \frac{e \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}}{7 x^{6}} + \frac{e^{3} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}}{35 d^{2} x^{4}} + \frac{4 e^{5} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}}{105 d^{4} x^{2}} + \frac{8 e^{7} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}}{105 d^{6}} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\- \frac{i e \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{7 x^{6}} + \frac{i e^{3} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{35 d^{2} x^{4}} + \frac{4 i e^{5} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{105 d^{4} x^{2}} + \frac{8 i e^{7} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{105 d^{6}} & \text{otherwise} \end{cases}\right) + 3 d^{6} e \left(\begin{cases} - \frac{d^{2}}{6 e x^{7} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{5 e}{24 x^{5} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{e^{3}}{48 d^{2} x^{3} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} - \frac{e^{5}}{16 d^{4} x \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{e^{6} \operatorname{acosh}{\left(\frac{d}{e x} \right)}}{16 d^{5}} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\\frac{i d^{2}}{6 e x^{7} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} - \frac{5 i e}{24 x^{5} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} - \frac{i e^{3}}{48 d^{2} x^{3} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} + \frac{i e^{5}}{16 d^{4} x \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} - \frac{i e^{6} \operatorname{asin}{\left(\frac{d}{e x} \right)}}{16 d^{5}} & \text{otherwise} \end{cases}\right) + d^{5} e^{2} \left(\begin{cases} \frac{3 i d^{3} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{2} x^{5} + 15 e^{2} x^{7}} - \frac{4 i d e^{2} x^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{2} x^{5} + 15 e^{2} x^{7}} + \frac{2 i e^{6} x^{6} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{5} x^{5} + 15 d^{3} e^{2} x^{7}} - \frac{i e^{4} x^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{3} x^{5} + 15 d e^{2} x^{7}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{3 d^{3} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{2} x^{5} + 15 e^{2} x^{7}} - \frac{4 d e^{2} x^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{2} x^{5} + 15 e^{2} x^{7}} + \frac{2 e^{6} x^{6} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{5} x^{5} + 15 d^{3} e^{2} x^{7}} - \frac{e^{4} x^{4} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{3} x^{5} + 15 d e^{2} x^{7}} & \text{otherwise} \end{cases}\right) - 5 d^{4} e^{3} \left(\begin{cases} - \frac{d^{2}}{4 e x^{5} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{3 e}{8 x^{3} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} - \frac{e^{3}}{8 d^{2} x \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{e^{4} \operatorname{acosh}{\left(\frac{d}{e x} \right)}}{8 d^{3}} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\\frac{i d^{2}}{4 e x^{5} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} - \frac{3 i e}{8 x^{3} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} + \frac{i e^{3}}{8 d^{2} x \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} - \frac{i e^{4} \operatorname{asin}{\left(\frac{d}{e x} \right)}}{8 d^{3}} & \text{otherwise} \end{cases}\right) - 5 d^{3} e^{4} \left(\begin{cases} - \frac{e \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}}{3 x^{2}} + \frac{e^{3} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}}{3 d^{2}} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\- \frac{i e \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{3 x^{2}} + \frac{i e^{3} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{3 d^{2}} & \text{otherwise} \end{cases}\right) + d^{2} e^{5} \left(\begin{cases} - \frac{d^{2}}{2 e x^{3} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{e}{2 x \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{e^{2} \operatorname{acosh}{\left(\frac{d}{e x} \right)}}{2 d} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\- \frac{i e \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{2 x} - \frac{i e^{2} \operatorname{asin}{\left(\frac{d}{e x} \right)}}{2 d} & \text{otherwise} \end{cases}\right) + 3 d e^{6} \left(\begin{cases} \frac{i d}{x \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + i e \operatorname{acosh}{\left(\frac{e x}{d} \right)} - \frac{i e^{2} x}{d \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\- \frac{d}{x \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} - e \operatorname{asin}{\left(\frac{e x}{d} \right)} + \frac{e^{2} x}{d \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} & \text{otherwise} \end{cases}\right) + e^{7} \left(\begin{cases} \frac{d^{2}}{e x \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} - d \operatorname{acosh}{\left(\frac{d}{e x} \right)} - \frac{e x}{\sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\- \frac{i d^{2}}{e x \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} + i d \operatorname{asin}{\left(\frac{d}{e x} \right)} + \frac{i e x}{\sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} & \text{otherwise} \end{cases}\right)"," ",0,"d**7*Piecewise((-e*sqrt(d**2/(e**2*x**2) - 1)/(7*x**6) + e**3*sqrt(d**2/(e**2*x**2) - 1)/(35*d**2*x**4) + 4*e**5*sqrt(d**2/(e**2*x**2) - 1)/(105*d**4*x**2) + 8*e**7*sqrt(d**2/(e**2*x**2) - 1)/(105*d**6), Abs(d**2/(e**2*x**2)) > 1), (-I*e*sqrt(-d**2/(e**2*x**2) + 1)/(7*x**6) + I*e**3*sqrt(-d**2/(e**2*x**2) + 1)/(35*d**2*x**4) + 4*I*e**5*sqrt(-d**2/(e**2*x**2) + 1)/(105*d**4*x**2) + 8*I*e**7*sqrt(-d**2/(e**2*x**2) + 1)/(105*d**6), True)) + 3*d**6*e*Piecewise((-d**2/(6*e*x**7*sqrt(d**2/(e**2*x**2) - 1)) + 5*e/(24*x**5*sqrt(d**2/(e**2*x**2) - 1)) + e**3/(48*d**2*x**3*sqrt(d**2/(e**2*x**2) - 1)) - e**5/(16*d**4*x*sqrt(d**2/(e**2*x**2) - 1)) + e**6*acosh(d/(e*x))/(16*d**5), Abs(d**2/(e**2*x**2)) > 1), (I*d**2/(6*e*x**7*sqrt(-d**2/(e**2*x**2) + 1)) - 5*I*e/(24*x**5*sqrt(-d**2/(e**2*x**2) + 1)) - I*e**3/(48*d**2*x**3*sqrt(-d**2/(e**2*x**2) + 1)) + I*e**5/(16*d**4*x*sqrt(-d**2/(e**2*x**2) + 1)) - I*e**6*asin(d/(e*x))/(16*d**5), True)) + d**5*e**2*Piecewise((3*I*d**3*sqrt(-1 + e**2*x**2/d**2)/(-15*d**2*x**5 + 15*e**2*x**7) - 4*I*d*e**2*x**2*sqrt(-1 + e**2*x**2/d**2)/(-15*d**2*x**5 + 15*e**2*x**7) + 2*I*e**6*x**6*sqrt(-1 + e**2*x**2/d**2)/(-15*d**5*x**5 + 15*d**3*e**2*x**7) - I*e**4*x**4*sqrt(-1 + e**2*x**2/d**2)/(-15*d**3*x**5 + 15*d*e**2*x**7), Abs(e**2*x**2/d**2) > 1), (3*d**3*sqrt(1 - e**2*x**2/d**2)/(-15*d**2*x**5 + 15*e**2*x**7) - 4*d*e**2*x**2*sqrt(1 - e**2*x**2/d**2)/(-15*d**2*x**5 + 15*e**2*x**7) + 2*e**6*x**6*sqrt(1 - e**2*x**2/d**2)/(-15*d**5*x**5 + 15*d**3*e**2*x**7) - e**4*x**4*sqrt(1 - e**2*x**2/d**2)/(-15*d**3*x**5 + 15*d*e**2*x**7), True)) - 5*d**4*e**3*Piecewise((-d**2/(4*e*x**5*sqrt(d**2/(e**2*x**2) - 1)) + 3*e/(8*x**3*sqrt(d**2/(e**2*x**2) - 1)) - e**3/(8*d**2*x*sqrt(d**2/(e**2*x**2) - 1)) + e**4*acosh(d/(e*x))/(8*d**3), Abs(d**2/(e**2*x**2)) > 1), (I*d**2/(4*e*x**5*sqrt(-d**2/(e**2*x**2) + 1)) - 3*I*e/(8*x**3*sqrt(-d**2/(e**2*x**2) + 1)) + I*e**3/(8*d**2*x*sqrt(-d**2/(e**2*x**2) + 1)) - I*e**4*asin(d/(e*x))/(8*d**3), True)) - 5*d**3*e**4*Piecewise((-e*sqrt(d**2/(e**2*x**2) - 1)/(3*x**2) + e**3*sqrt(d**2/(e**2*x**2) - 1)/(3*d**2), Abs(d**2/(e**2*x**2)) > 1), (-I*e*sqrt(-d**2/(e**2*x**2) + 1)/(3*x**2) + I*e**3*sqrt(-d**2/(e**2*x**2) + 1)/(3*d**2), True)) + d**2*e**5*Piecewise((-d**2/(2*e*x**3*sqrt(d**2/(e**2*x**2) - 1)) + e/(2*x*sqrt(d**2/(e**2*x**2) - 1)) + e**2*acosh(d/(e*x))/(2*d), Abs(d**2/(e**2*x**2)) > 1), (-I*e*sqrt(-d**2/(e**2*x**2) + 1)/(2*x) - I*e**2*asin(d/(e*x))/(2*d), True)) + 3*d*e**6*Piecewise((I*d/(x*sqrt(-1 + e**2*x**2/d**2)) + I*e*acosh(e*x/d) - I*e**2*x/(d*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (-d/(x*sqrt(1 - e**2*x**2/d**2)) - e*asin(e*x/d) + e**2*x/(d*sqrt(1 - e**2*x**2/d**2)), True)) + e**7*Piecewise((d**2/(e*x*sqrt(d**2/(e**2*x**2) - 1)) - d*acosh(d/(e*x)) - e*x/sqrt(d**2/(e**2*x**2) - 1), Abs(d**2/(e**2*x**2)) > 1), (-I*d**2/(e*x*sqrt(-d**2/(e**2*x**2) + 1)) + I*d*asin(d/(e*x)) + I*e*x/sqrt(-d**2/(e**2*x**2) + 1), True))","C",0
79,1,1719,0,31.403314," ","integrate((e*x+d)**3*(-e**2*x**2+d**2)**(5/2)/x**9,x)","d^{7} \left(\begin{cases} - \frac{d^{2}}{8 e x^{9} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{7 e}{48 x^{7} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{e^{3}}{192 d^{2} x^{5} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{5 e^{5}}{384 d^{4} x^{3} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} - \frac{5 e^{7}}{128 d^{6} x \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{5 e^{8} \operatorname{acosh}{\left(\frac{d}{e x} \right)}}{128 d^{7}} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\\frac{i d^{2}}{8 e x^{9} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} - \frac{7 i e}{48 x^{7} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} - \frac{i e^{3}}{192 d^{2} x^{5} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} - \frac{5 i e^{5}}{384 d^{4} x^{3} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} + \frac{5 i e^{7}}{128 d^{6} x \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} - \frac{5 i e^{8} \operatorname{asin}{\left(\frac{d}{e x} \right)}}{128 d^{7}} & \text{otherwise} \end{cases}\right) + 3 d^{6} e \left(\begin{cases} - \frac{e \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}}{7 x^{6}} + \frac{e^{3} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}}{35 d^{2} x^{4}} + \frac{4 e^{5} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}}{105 d^{4} x^{2}} + \frac{8 e^{7} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}}{105 d^{6}} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\- \frac{i e \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{7 x^{6}} + \frac{i e^{3} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{35 d^{2} x^{4}} + \frac{4 i e^{5} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{105 d^{4} x^{2}} + \frac{8 i e^{7} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{105 d^{6}} & \text{otherwise} \end{cases}\right) + d^{5} e^{2} \left(\begin{cases} - \frac{d^{2}}{6 e x^{7} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{5 e}{24 x^{5} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{e^{3}}{48 d^{2} x^{3} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} - \frac{e^{5}}{16 d^{4} x \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{e^{6} \operatorname{acosh}{\left(\frac{d}{e x} \right)}}{16 d^{5}} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\\frac{i d^{2}}{6 e x^{7} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} - \frac{5 i e}{24 x^{5} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} - \frac{i e^{3}}{48 d^{2} x^{3} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} + \frac{i e^{5}}{16 d^{4} x \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} - \frac{i e^{6} \operatorname{asin}{\left(\frac{d}{e x} \right)}}{16 d^{5}} & \text{otherwise} \end{cases}\right) - 5 d^{4} e^{3} \left(\begin{cases} \frac{3 i d^{3} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{2} x^{5} + 15 e^{2} x^{7}} - \frac{4 i d e^{2} x^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{2} x^{5} + 15 e^{2} x^{7}} + \frac{2 i e^{6} x^{6} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{5} x^{5} + 15 d^{3} e^{2} x^{7}} - \frac{i e^{4} x^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{3} x^{5} + 15 d e^{2} x^{7}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{3 d^{3} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{2} x^{5} + 15 e^{2} x^{7}} - \frac{4 d e^{2} x^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{2} x^{5} + 15 e^{2} x^{7}} + \frac{2 e^{6} x^{6} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{5} x^{5} + 15 d^{3} e^{2} x^{7}} - \frac{e^{4} x^{4} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{3} x^{5} + 15 d e^{2} x^{7}} & \text{otherwise} \end{cases}\right) - 5 d^{3} e^{4} \left(\begin{cases} - \frac{d^{2}}{4 e x^{5} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{3 e}{8 x^{3} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} - \frac{e^{3}}{8 d^{2} x \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{e^{4} \operatorname{acosh}{\left(\frac{d}{e x} \right)}}{8 d^{3}} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\\frac{i d^{2}}{4 e x^{5} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} - \frac{3 i e}{8 x^{3} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} + \frac{i e^{3}}{8 d^{2} x \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} - \frac{i e^{4} \operatorname{asin}{\left(\frac{d}{e x} \right)}}{8 d^{3}} & \text{otherwise} \end{cases}\right) + d^{2} e^{5} \left(\begin{cases} - \frac{e \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}}{3 x^{2}} + \frac{e^{3} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}}{3 d^{2}} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\- \frac{i e \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{3 x^{2}} + \frac{i e^{3} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{3 d^{2}} & \text{otherwise} \end{cases}\right) + 3 d e^{6} \left(\begin{cases} - \frac{d^{2}}{2 e x^{3} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{e}{2 x \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{e^{2} \operatorname{acosh}{\left(\frac{d}{e x} \right)}}{2 d} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\- \frac{i e \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{2 x} - \frac{i e^{2} \operatorname{asin}{\left(\frac{d}{e x} \right)}}{2 d} & \text{otherwise} \end{cases}\right) + e^{7} \left(\begin{cases} \frac{i d}{x \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + i e \operatorname{acosh}{\left(\frac{e x}{d} \right)} - \frac{i e^{2} x}{d \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\- \frac{d}{x \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} - e \operatorname{asin}{\left(\frac{e x}{d} \right)} + \frac{e^{2} x}{d \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} & \text{otherwise} \end{cases}\right)"," ",0,"d**7*Piecewise((-d**2/(8*e*x**9*sqrt(d**2/(e**2*x**2) - 1)) + 7*e/(48*x**7*sqrt(d**2/(e**2*x**2) - 1)) + e**3/(192*d**2*x**5*sqrt(d**2/(e**2*x**2) - 1)) + 5*e**5/(384*d**4*x**3*sqrt(d**2/(e**2*x**2) - 1)) - 5*e**7/(128*d**6*x*sqrt(d**2/(e**2*x**2) - 1)) + 5*e**8*acosh(d/(e*x))/(128*d**7), Abs(d**2/(e**2*x**2)) > 1), (I*d**2/(8*e*x**9*sqrt(-d**2/(e**2*x**2) + 1)) - 7*I*e/(48*x**7*sqrt(-d**2/(e**2*x**2) + 1)) - I*e**3/(192*d**2*x**5*sqrt(-d**2/(e**2*x**2) + 1)) - 5*I*e**5/(384*d**4*x**3*sqrt(-d**2/(e**2*x**2) + 1)) + 5*I*e**7/(128*d**6*x*sqrt(-d**2/(e**2*x**2) + 1)) - 5*I*e**8*asin(d/(e*x))/(128*d**7), True)) + 3*d**6*e*Piecewise((-e*sqrt(d**2/(e**2*x**2) - 1)/(7*x**6) + e**3*sqrt(d**2/(e**2*x**2) - 1)/(35*d**2*x**4) + 4*e**5*sqrt(d**2/(e**2*x**2) - 1)/(105*d**4*x**2) + 8*e**7*sqrt(d**2/(e**2*x**2) - 1)/(105*d**6), Abs(d**2/(e**2*x**2)) > 1), (-I*e*sqrt(-d**2/(e**2*x**2) + 1)/(7*x**6) + I*e**3*sqrt(-d**2/(e**2*x**2) + 1)/(35*d**2*x**4) + 4*I*e**5*sqrt(-d**2/(e**2*x**2) + 1)/(105*d**4*x**2) + 8*I*e**7*sqrt(-d**2/(e**2*x**2) + 1)/(105*d**6), True)) + d**5*e**2*Piecewise((-d**2/(6*e*x**7*sqrt(d**2/(e**2*x**2) - 1)) + 5*e/(24*x**5*sqrt(d**2/(e**2*x**2) - 1)) + e**3/(48*d**2*x**3*sqrt(d**2/(e**2*x**2) - 1)) - e**5/(16*d**4*x*sqrt(d**2/(e**2*x**2) - 1)) + e**6*acosh(d/(e*x))/(16*d**5), Abs(d**2/(e**2*x**2)) > 1), (I*d**2/(6*e*x**7*sqrt(-d**2/(e**2*x**2) + 1)) - 5*I*e/(24*x**5*sqrt(-d**2/(e**2*x**2) + 1)) - I*e**3/(48*d**2*x**3*sqrt(-d**2/(e**2*x**2) + 1)) + I*e**5/(16*d**4*x*sqrt(-d**2/(e**2*x**2) + 1)) - I*e**6*asin(d/(e*x))/(16*d**5), True)) - 5*d**4*e**3*Piecewise((3*I*d**3*sqrt(-1 + e**2*x**2/d**2)/(-15*d**2*x**5 + 15*e**2*x**7) - 4*I*d*e**2*x**2*sqrt(-1 + e**2*x**2/d**2)/(-15*d**2*x**5 + 15*e**2*x**7) + 2*I*e**6*x**6*sqrt(-1 + e**2*x**2/d**2)/(-15*d**5*x**5 + 15*d**3*e**2*x**7) - I*e**4*x**4*sqrt(-1 + e**2*x**2/d**2)/(-15*d**3*x**5 + 15*d*e**2*x**7), Abs(e**2*x**2/d**2) > 1), (3*d**3*sqrt(1 - e**2*x**2/d**2)/(-15*d**2*x**5 + 15*e**2*x**7) - 4*d*e**2*x**2*sqrt(1 - e**2*x**2/d**2)/(-15*d**2*x**5 + 15*e**2*x**7) + 2*e**6*x**6*sqrt(1 - e**2*x**2/d**2)/(-15*d**5*x**5 + 15*d**3*e**2*x**7) - e**4*x**4*sqrt(1 - e**2*x**2/d**2)/(-15*d**3*x**5 + 15*d*e**2*x**7), True)) - 5*d**3*e**4*Piecewise((-d**2/(4*e*x**5*sqrt(d**2/(e**2*x**2) - 1)) + 3*e/(8*x**3*sqrt(d**2/(e**2*x**2) - 1)) - e**3/(8*d**2*x*sqrt(d**2/(e**2*x**2) - 1)) + e**4*acosh(d/(e*x))/(8*d**3), Abs(d**2/(e**2*x**2)) > 1), (I*d**2/(4*e*x**5*sqrt(-d**2/(e**2*x**2) + 1)) - 3*I*e/(8*x**3*sqrt(-d**2/(e**2*x**2) + 1)) + I*e**3/(8*d**2*x*sqrt(-d**2/(e**2*x**2) + 1)) - I*e**4*asin(d/(e*x))/(8*d**3), True)) + d**2*e**5*Piecewise((-e*sqrt(d**2/(e**2*x**2) - 1)/(3*x**2) + e**3*sqrt(d**2/(e**2*x**2) - 1)/(3*d**2), Abs(d**2/(e**2*x**2)) > 1), (-I*e*sqrt(-d**2/(e**2*x**2) + 1)/(3*x**2) + I*e**3*sqrt(-d**2/(e**2*x**2) + 1)/(3*d**2), True)) + 3*d*e**6*Piecewise((-d**2/(2*e*x**3*sqrt(d**2/(e**2*x**2) - 1)) + e/(2*x*sqrt(d**2/(e**2*x**2) - 1)) + e**2*acosh(d/(e*x))/(2*d), Abs(d**2/(e**2*x**2)) > 1), (-I*e*sqrt(-d**2/(e**2*x**2) + 1)/(2*x) - I*e**2*asin(d/(e*x))/(2*d), True)) + e**7*Piecewise((I*d/(x*sqrt(-1 + e**2*x**2/d**2)) + I*e*acosh(e*x/d) - I*e**2*x/(d*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (-d/(x*sqrt(1 - e**2*x**2/d**2)) - e*asin(e*x/d) + e**2*x/(d*sqrt(1 - e**2*x**2/d**2)), True))","C",0
80,1,1889,0,36.711798," ","integrate((e*x+d)**3*(-e**2*x**2+d**2)**(5/2)/x**10,x)","d^{7} \left(\begin{cases} - \frac{e \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}}{9 x^{8}} + \frac{e^{3} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}}{63 d^{2} x^{6}} + \frac{2 e^{5} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}}{105 d^{4} x^{4}} + \frac{8 e^{7} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}}{315 d^{6} x^{2}} + \frac{16 e^{9} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}}{315 d^{8}} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\- \frac{i e \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{9 x^{8}} + \frac{i e^{3} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{63 d^{2} x^{6}} + \frac{2 i e^{5} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{105 d^{4} x^{4}} + \frac{8 i e^{7} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{315 d^{6} x^{2}} + \frac{16 i e^{9} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{315 d^{8}} & \text{otherwise} \end{cases}\right) + 3 d^{6} e \left(\begin{cases} - \frac{d^{2}}{8 e x^{9} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{7 e}{48 x^{7} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{e^{3}}{192 d^{2} x^{5} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{5 e^{5}}{384 d^{4} x^{3} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} - \frac{5 e^{7}}{128 d^{6} x \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{5 e^{8} \operatorname{acosh}{\left(\frac{d}{e x} \right)}}{128 d^{7}} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\\frac{i d^{2}}{8 e x^{9} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} - \frac{7 i e}{48 x^{7} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} - \frac{i e^{3}}{192 d^{2} x^{5} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} - \frac{5 i e^{5}}{384 d^{4} x^{3} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} + \frac{5 i e^{7}}{128 d^{6} x \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} - \frac{5 i e^{8} \operatorname{asin}{\left(\frac{d}{e x} \right)}}{128 d^{7}} & \text{otherwise} \end{cases}\right) + d^{5} e^{2} \left(\begin{cases} - \frac{e \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}}{7 x^{6}} + \frac{e^{3} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}}{35 d^{2} x^{4}} + \frac{4 e^{5} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}}{105 d^{4} x^{2}} + \frac{8 e^{7} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}}{105 d^{6}} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\- \frac{i e \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{7 x^{6}} + \frac{i e^{3} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{35 d^{2} x^{4}} + \frac{4 i e^{5} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{105 d^{4} x^{2}} + \frac{8 i e^{7} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{105 d^{6}} & \text{otherwise} \end{cases}\right) - 5 d^{4} e^{3} \left(\begin{cases} - \frac{d^{2}}{6 e x^{7} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{5 e}{24 x^{5} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{e^{3}}{48 d^{2} x^{3} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} - \frac{e^{5}}{16 d^{4} x \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{e^{6} \operatorname{acosh}{\left(\frac{d}{e x} \right)}}{16 d^{5}} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\\frac{i d^{2}}{6 e x^{7} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} - \frac{5 i e}{24 x^{5} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} - \frac{i e^{3}}{48 d^{2} x^{3} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} + \frac{i e^{5}}{16 d^{4} x \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} - \frac{i e^{6} \operatorname{asin}{\left(\frac{d}{e x} \right)}}{16 d^{5}} & \text{otherwise} \end{cases}\right) - 5 d^{3} e^{4} \left(\begin{cases} \frac{3 i d^{3} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{2} x^{5} + 15 e^{2} x^{7}} - \frac{4 i d e^{2} x^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{2} x^{5} + 15 e^{2} x^{7}} + \frac{2 i e^{6} x^{6} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{5} x^{5} + 15 d^{3} e^{2} x^{7}} - \frac{i e^{4} x^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{3} x^{5} + 15 d e^{2} x^{7}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{3 d^{3} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{2} x^{5} + 15 e^{2} x^{7}} - \frac{4 d e^{2} x^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{2} x^{5} + 15 e^{2} x^{7}} + \frac{2 e^{6} x^{6} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{5} x^{5} + 15 d^{3} e^{2} x^{7}} - \frac{e^{4} x^{4} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{3} x^{5} + 15 d e^{2} x^{7}} & \text{otherwise} \end{cases}\right) + d^{2} e^{5} \left(\begin{cases} - \frac{d^{2}}{4 e x^{5} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{3 e}{8 x^{3} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} - \frac{e^{3}}{8 d^{2} x \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{e^{4} \operatorname{acosh}{\left(\frac{d}{e x} \right)}}{8 d^{3}} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\\frac{i d^{2}}{4 e x^{5} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} - \frac{3 i e}{8 x^{3} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} + \frac{i e^{3}}{8 d^{2} x \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} - \frac{i e^{4} \operatorname{asin}{\left(\frac{d}{e x} \right)}}{8 d^{3}} & \text{otherwise} \end{cases}\right) + 3 d e^{6} \left(\begin{cases} - \frac{e \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}}{3 x^{2}} + \frac{e^{3} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}}{3 d^{2}} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\- \frac{i e \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{3 x^{2}} + \frac{i e^{3} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{3 d^{2}} & \text{otherwise} \end{cases}\right) + e^{7} \left(\begin{cases} - \frac{d^{2}}{2 e x^{3} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{e}{2 x \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{e^{2} \operatorname{acosh}{\left(\frac{d}{e x} \right)}}{2 d} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\- \frac{i e \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{2 x} - \frac{i e^{2} \operatorname{asin}{\left(\frac{d}{e x} \right)}}{2 d} & \text{otherwise} \end{cases}\right)"," ",0,"d**7*Piecewise((-e*sqrt(d**2/(e**2*x**2) - 1)/(9*x**8) + e**3*sqrt(d**2/(e**2*x**2) - 1)/(63*d**2*x**6) + 2*e**5*sqrt(d**2/(e**2*x**2) - 1)/(105*d**4*x**4) + 8*e**7*sqrt(d**2/(e**2*x**2) - 1)/(315*d**6*x**2) + 16*e**9*sqrt(d**2/(e**2*x**2) - 1)/(315*d**8), Abs(d**2/(e**2*x**2)) > 1), (-I*e*sqrt(-d**2/(e**2*x**2) + 1)/(9*x**8) + I*e**3*sqrt(-d**2/(e**2*x**2) + 1)/(63*d**2*x**6) + 2*I*e**5*sqrt(-d**2/(e**2*x**2) + 1)/(105*d**4*x**4) + 8*I*e**7*sqrt(-d**2/(e**2*x**2) + 1)/(315*d**6*x**2) + 16*I*e**9*sqrt(-d**2/(e**2*x**2) + 1)/(315*d**8), True)) + 3*d**6*e*Piecewise((-d**2/(8*e*x**9*sqrt(d**2/(e**2*x**2) - 1)) + 7*e/(48*x**7*sqrt(d**2/(e**2*x**2) - 1)) + e**3/(192*d**2*x**5*sqrt(d**2/(e**2*x**2) - 1)) + 5*e**5/(384*d**4*x**3*sqrt(d**2/(e**2*x**2) - 1)) - 5*e**7/(128*d**6*x*sqrt(d**2/(e**2*x**2) - 1)) + 5*e**8*acosh(d/(e*x))/(128*d**7), Abs(d**2/(e**2*x**2)) > 1), (I*d**2/(8*e*x**9*sqrt(-d**2/(e**2*x**2) + 1)) - 7*I*e/(48*x**7*sqrt(-d**2/(e**2*x**2) + 1)) - I*e**3/(192*d**2*x**5*sqrt(-d**2/(e**2*x**2) + 1)) - 5*I*e**5/(384*d**4*x**3*sqrt(-d**2/(e**2*x**2) + 1)) + 5*I*e**7/(128*d**6*x*sqrt(-d**2/(e**2*x**2) + 1)) - 5*I*e**8*asin(d/(e*x))/(128*d**7), True)) + d**5*e**2*Piecewise((-e*sqrt(d**2/(e**2*x**2) - 1)/(7*x**6) + e**3*sqrt(d**2/(e**2*x**2) - 1)/(35*d**2*x**4) + 4*e**5*sqrt(d**2/(e**2*x**2) - 1)/(105*d**4*x**2) + 8*e**7*sqrt(d**2/(e**2*x**2) - 1)/(105*d**6), Abs(d**2/(e**2*x**2)) > 1), (-I*e*sqrt(-d**2/(e**2*x**2) + 1)/(7*x**6) + I*e**3*sqrt(-d**2/(e**2*x**2) + 1)/(35*d**2*x**4) + 4*I*e**5*sqrt(-d**2/(e**2*x**2) + 1)/(105*d**4*x**2) + 8*I*e**7*sqrt(-d**2/(e**2*x**2) + 1)/(105*d**6), True)) - 5*d**4*e**3*Piecewise((-d**2/(6*e*x**7*sqrt(d**2/(e**2*x**2) - 1)) + 5*e/(24*x**5*sqrt(d**2/(e**2*x**2) - 1)) + e**3/(48*d**2*x**3*sqrt(d**2/(e**2*x**2) - 1)) - e**5/(16*d**4*x*sqrt(d**2/(e**2*x**2) - 1)) + e**6*acosh(d/(e*x))/(16*d**5), Abs(d**2/(e**2*x**2)) > 1), (I*d**2/(6*e*x**7*sqrt(-d**2/(e**2*x**2) + 1)) - 5*I*e/(24*x**5*sqrt(-d**2/(e**2*x**2) + 1)) - I*e**3/(48*d**2*x**3*sqrt(-d**2/(e**2*x**2) + 1)) + I*e**5/(16*d**4*x*sqrt(-d**2/(e**2*x**2) + 1)) - I*e**6*asin(d/(e*x))/(16*d**5), True)) - 5*d**3*e**4*Piecewise((3*I*d**3*sqrt(-1 + e**2*x**2/d**2)/(-15*d**2*x**5 + 15*e**2*x**7) - 4*I*d*e**2*x**2*sqrt(-1 + e**2*x**2/d**2)/(-15*d**2*x**5 + 15*e**2*x**7) + 2*I*e**6*x**6*sqrt(-1 + e**2*x**2/d**2)/(-15*d**5*x**5 + 15*d**3*e**2*x**7) - I*e**4*x**4*sqrt(-1 + e**2*x**2/d**2)/(-15*d**3*x**5 + 15*d*e**2*x**7), Abs(e**2*x**2/d**2) > 1), (3*d**3*sqrt(1 - e**2*x**2/d**2)/(-15*d**2*x**5 + 15*e**2*x**7) - 4*d*e**2*x**2*sqrt(1 - e**2*x**2/d**2)/(-15*d**2*x**5 + 15*e**2*x**7) + 2*e**6*x**6*sqrt(1 - e**2*x**2/d**2)/(-15*d**5*x**5 + 15*d**3*e**2*x**7) - e**4*x**4*sqrt(1 - e**2*x**2/d**2)/(-15*d**3*x**5 + 15*d*e**2*x**7), True)) + d**2*e**5*Piecewise((-d**2/(4*e*x**5*sqrt(d**2/(e**2*x**2) - 1)) + 3*e/(8*x**3*sqrt(d**2/(e**2*x**2) - 1)) - e**3/(8*d**2*x*sqrt(d**2/(e**2*x**2) - 1)) + e**4*acosh(d/(e*x))/(8*d**3), Abs(d**2/(e**2*x**2)) > 1), (I*d**2/(4*e*x**5*sqrt(-d**2/(e**2*x**2) + 1)) - 3*I*e/(8*x**3*sqrt(-d**2/(e**2*x**2) + 1)) + I*e**3/(8*d**2*x*sqrt(-d**2/(e**2*x**2) + 1)) - I*e**4*asin(d/(e*x))/(8*d**3), True)) + 3*d*e**6*Piecewise((-e*sqrt(d**2/(e**2*x**2) - 1)/(3*x**2) + e**3*sqrt(d**2/(e**2*x**2) - 1)/(3*d**2), Abs(d**2/(e**2*x**2)) > 1), (-I*e*sqrt(-d**2/(e**2*x**2) + 1)/(3*x**2) + I*e**3*sqrt(-d**2/(e**2*x**2) + 1)/(3*d**2), True)) + e**7*Piecewise((-d**2/(2*e*x**3*sqrt(d**2/(e**2*x**2) - 1)) + e/(2*x*sqrt(d**2/(e**2*x**2) - 1)) + e**2*acosh(d/(e*x))/(2*d), Abs(d**2/(e**2*x**2)) > 1), (-I*e*sqrt(-d**2/(e**2*x**2) + 1)/(2*x) - I*e**2*asin(d/(e*x))/(2*d), True))","C",0
81,1,2159,0,49.867117," ","integrate((e*x+d)**3*(-e**2*x**2+d**2)**(5/2)/x**11,x)","d^{7} \left(\begin{cases} - \frac{d^{2}}{10 e x^{11} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{9 e}{80 x^{9} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{e^{3}}{480 d^{2} x^{7} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{7 e^{5}}{1920 d^{4} x^{5} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{7 e^{7}}{768 d^{6} x^{3} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} - \frac{7 e^{9}}{256 d^{8} x \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{7 e^{10} \operatorname{acosh}{\left(\frac{d}{e x} \right)}}{256 d^{9}} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\\frac{i d^{2}}{10 e x^{11} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} - \frac{9 i e}{80 x^{9} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} - \frac{i e^{3}}{480 d^{2} x^{7} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} - \frac{7 i e^{5}}{1920 d^{4} x^{5} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} - \frac{7 i e^{7}}{768 d^{6} x^{3} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} + \frac{7 i e^{9}}{256 d^{8} x \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} - \frac{7 i e^{10} \operatorname{asin}{\left(\frac{d}{e x} \right)}}{256 d^{9}} & \text{otherwise} \end{cases}\right) + 3 d^{6} e \left(\begin{cases} - \frac{e \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}}{9 x^{8}} + \frac{e^{3} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}}{63 d^{2} x^{6}} + \frac{2 e^{5} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}}{105 d^{4} x^{4}} + \frac{8 e^{7} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}}{315 d^{6} x^{2}} + \frac{16 e^{9} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}}{315 d^{8}} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\- \frac{i e \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{9 x^{8}} + \frac{i e^{3} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{63 d^{2} x^{6}} + \frac{2 i e^{5} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{105 d^{4} x^{4}} + \frac{8 i e^{7} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{315 d^{6} x^{2}} + \frac{16 i e^{9} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{315 d^{8}} & \text{otherwise} \end{cases}\right) + d^{5} e^{2} \left(\begin{cases} - \frac{d^{2}}{8 e x^{9} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{7 e}{48 x^{7} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{e^{3}}{192 d^{2} x^{5} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{5 e^{5}}{384 d^{4} x^{3} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} - \frac{5 e^{7}}{128 d^{6} x \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{5 e^{8} \operatorname{acosh}{\left(\frac{d}{e x} \right)}}{128 d^{7}} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\\frac{i d^{2}}{8 e x^{9} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} - \frac{7 i e}{48 x^{7} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} - \frac{i e^{3}}{192 d^{2} x^{5} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} - \frac{5 i e^{5}}{384 d^{4} x^{3} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} + \frac{5 i e^{7}}{128 d^{6} x \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} - \frac{5 i e^{8} \operatorname{asin}{\left(\frac{d}{e x} \right)}}{128 d^{7}} & \text{otherwise} \end{cases}\right) - 5 d^{4} e^{3} \left(\begin{cases} - \frac{e \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}}{7 x^{6}} + \frac{e^{3} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}}{35 d^{2} x^{4}} + \frac{4 e^{5} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}}{105 d^{4} x^{2}} + \frac{8 e^{7} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}}{105 d^{6}} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\- \frac{i e \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{7 x^{6}} + \frac{i e^{3} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{35 d^{2} x^{4}} + \frac{4 i e^{5} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{105 d^{4} x^{2}} + \frac{8 i e^{7} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{105 d^{6}} & \text{otherwise} \end{cases}\right) - 5 d^{3} e^{4} \left(\begin{cases} - \frac{d^{2}}{6 e x^{7} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{5 e}{24 x^{5} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{e^{3}}{48 d^{2} x^{3} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} - \frac{e^{5}}{16 d^{4} x \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{e^{6} \operatorname{acosh}{\left(\frac{d}{e x} \right)}}{16 d^{5}} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\\frac{i d^{2}}{6 e x^{7} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} - \frac{5 i e}{24 x^{5} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} - \frac{i e^{3}}{48 d^{2} x^{3} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} + \frac{i e^{5}}{16 d^{4} x \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} - \frac{i e^{6} \operatorname{asin}{\left(\frac{d}{e x} \right)}}{16 d^{5}} & \text{otherwise} \end{cases}\right) + d^{2} e^{5} \left(\begin{cases} \frac{3 i d^{3} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{2} x^{5} + 15 e^{2} x^{7}} - \frac{4 i d e^{2} x^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{2} x^{5} + 15 e^{2} x^{7}} + \frac{2 i e^{6} x^{6} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{5} x^{5} + 15 d^{3} e^{2} x^{7}} - \frac{i e^{4} x^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{3} x^{5} + 15 d e^{2} x^{7}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{3 d^{3} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{2} x^{5} + 15 e^{2} x^{7}} - \frac{4 d e^{2} x^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{2} x^{5} + 15 e^{2} x^{7}} + \frac{2 e^{6} x^{6} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{5} x^{5} + 15 d^{3} e^{2} x^{7}} - \frac{e^{4} x^{4} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{3} x^{5} + 15 d e^{2} x^{7}} & \text{otherwise} \end{cases}\right) + 3 d e^{6} \left(\begin{cases} - \frac{d^{2}}{4 e x^{5} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{3 e}{8 x^{3} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} - \frac{e^{3}}{8 d^{2} x \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{e^{4} \operatorname{acosh}{\left(\frac{d}{e x} \right)}}{8 d^{3}} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\\frac{i d^{2}}{4 e x^{5} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} - \frac{3 i e}{8 x^{3} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} + \frac{i e^{3}}{8 d^{2} x \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} - \frac{i e^{4} \operatorname{asin}{\left(\frac{d}{e x} \right)}}{8 d^{3}} & \text{otherwise} \end{cases}\right) + e^{7} \left(\begin{cases} - \frac{e \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}}{3 x^{2}} + \frac{e^{3} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}}{3 d^{2}} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\- \frac{i e \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{3 x^{2}} + \frac{i e^{3} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{3 d^{2}} & \text{otherwise} \end{cases}\right)"," ",0,"d**7*Piecewise((-d**2/(10*e*x**11*sqrt(d**2/(e**2*x**2) - 1)) + 9*e/(80*x**9*sqrt(d**2/(e**2*x**2) - 1)) + e**3/(480*d**2*x**7*sqrt(d**2/(e**2*x**2) - 1)) + 7*e**5/(1920*d**4*x**5*sqrt(d**2/(e**2*x**2) - 1)) + 7*e**7/(768*d**6*x**3*sqrt(d**2/(e**2*x**2) - 1)) - 7*e**9/(256*d**8*x*sqrt(d**2/(e**2*x**2) - 1)) + 7*e**10*acosh(d/(e*x))/(256*d**9), Abs(d**2/(e**2*x**2)) > 1), (I*d**2/(10*e*x**11*sqrt(-d**2/(e**2*x**2) + 1)) - 9*I*e/(80*x**9*sqrt(-d**2/(e**2*x**2) + 1)) - I*e**3/(480*d**2*x**7*sqrt(-d**2/(e**2*x**2) + 1)) - 7*I*e**5/(1920*d**4*x**5*sqrt(-d**2/(e**2*x**2) + 1)) - 7*I*e**7/(768*d**6*x**3*sqrt(-d**2/(e**2*x**2) + 1)) + 7*I*e**9/(256*d**8*x*sqrt(-d**2/(e**2*x**2) + 1)) - 7*I*e**10*asin(d/(e*x))/(256*d**9), True)) + 3*d**6*e*Piecewise((-e*sqrt(d**2/(e**2*x**2) - 1)/(9*x**8) + e**3*sqrt(d**2/(e**2*x**2) - 1)/(63*d**2*x**6) + 2*e**5*sqrt(d**2/(e**2*x**2) - 1)/(105*d**4*x**4) + 8*e**7*sqrt(d**2/(e**2*x**2) - 1)/(315*d**6*x**2) + 16*e**9*sqrt(d**2/(e**2*x**2) - 1)/(315*d**8), Abs(d**2/(e**2*x**2)) > 1), (-I*e*sqrt(-d**2/(e**2*x**2) + 1)/(9*x**8) + I*e**3*sqrt(-d**2/(e**2*x**2) + 1)/(63*d**2*x**6) + 2*I*e**5*sqrt(-d**2/(e**2*x**2) + 1)/(105*d**4*x**4) + 8*I*e**7*sqrt(-d**2/(e**2*x**2) + 1)/(315*d**6*x**2) + 16*I*e**9*sqrt(-d**2/(e**2*x**2) + 1)/(315*d**8), True)) + d**5*e**2*Piecewise((-d**2/(8*e*x**9*sqrt(d**2/(e**2*x**2) - 1)) + 7*e/(48*x**7*sqrt(d**2/(e**2*x**2) - 1)) + e**3/(192*d**2*x**5*sqrt(d**2/(e**2*x**2) - 1)) + 5*e**5/(384*d**4*x**3*sqrt(d**2/(e**2*x**2) - 1)) - 5*e**7/(128*d**6*x*sqrt(d**2/(e**2*x**2) - 1)) + 5*e**8*acosh(d/(e*x))/(128*d**7), Abs(d**2/(e**2*x**2)) > 1), (I*d**2/(8*e*x**9*sqrt(-d**2/(e**2*x**2) + 1)) - 7*I*e/(48*x**7*sqrt(-d**2/(e**2*x**2) + 1)) - I*e**3/(192*d**2*x**5*sqrt(-d**2/(e**2*x**2) + 1)) - 5*I*e**5/(384*d**4*x**3*sqrt(-d**2/(e**2*x**2) + 1)) + 5*I*e**7/(128*d**6*x*sqrt(-d**2/(e**2*x**2) + 1)) - 5*I*e**8*asin(d/(e*x))/(128*d**7), True)) - 5*d**4*e**3*Piecewise((-e*sqrt(d**2/(e**2*x**2) - 1)/(7*x**6) + e**3*sqrt(d**2/(e**2*x**2) - 1)/(35*d**2*x**4) + 4*e**5*sqrt(d**2/(e**2*x**2) - 1)/(105*d**4*x**2) + 8*e**7*sqrt(d**2/(e**2*x**2) - 1)/(105*d**6), Abs(d**2/(e**2*x**2)) > 1), (-I*e*sqrt(-d**2/(e**2*x**2) + 1)/(7*x**6) + I*e**3*sqrt(-d**2/(e**2*x**2) + 1)/(35*d**2*x**4) + 4*I*e**5*sqrt(-d**2/(e**2*x**2) + 1)/(105*d**4*x**2) + 8*I*e**7*sqrt(-d**2/(e**2*x**2) + 1)/(105*d**6), True)) - 5*d**3*e**4*Piecewise((-d**2/(6*e*x**7*sqrt(d**2/(e**2*x**2) - 1)) + 5*e/(24*x**5*sqrt(d**2/(e**2*x**2) - 1)) + e**3/(48*d**2*x**3*sqrt(d**2/(e**2*x**2) - 1)) - e**5/(16*d**4*x*sqrt(d**2/(e**2*x**2) - 1)) + e**6*acosh(d/(e*x))/(16*d**5), Abs(d**2/(e**2*x**2)) > 1), (I*d**2/(6*e*x**7*sqrt(-d**2/(e**2*x**2) + 1)) - 5*I*e/(24*x**5*sqrt(-d**2/(e**2*x**2) + 1)) - I*e**3/(48*d**2*x**3*sqrt(-d**2/(e**2*x**2) + 1)) + I*e**5/(16*d**4*x*sqrt(-d**2/(e**2*x**2) + 1)) - I*e**6*asin(d/(e*x))/(16*d**5), True)) + d**2*e**5*Piecewise((3*I*d**3*sqrt(-1 + e**2*x**2/d**2)/(-15*d**2*x**5 + 15*e**2*x**7) - 4*I*d*e**2*x**2*sqrt(-1 + e**2*x**2/d**2)/(-15*d**2*x**5 + 15*e**2*x**7) + 2*I*e**6*x**6*sqrt(-1 + e**2*x**2/d**2)/(-15*d**5*x**5 + 15*d**3*e**2*x**7) - I*e**4*x**4*sqrt(-1 + e**2*x**2/d**2)/(-15*d**3*x**5 + 15*d*e**2*x**7), Abs(e**2*x**2/d**2) > 1), (3*d**3*sqrt(1 - e**2*x**2/d**2)/(-15*d**2*x**5 + 15*e**2*x**7) - 4*d*e**2*x**2*sqrt(1 - e**2*x**2/d**2)/(-15*d**2*x**5 + 15*e**2*x**7) + 2*e**6*x**6*sqrt(1 - e**2*x**2/d**2)/(-15*d**5*x**5 + 15*d**3*e**2*x**7) - e**4*x**4*sqrt(1 - e**2*x**2/d**2)/(-15*d**3*x**5 + 15*d*e**2*x**7), True)) + 3*d*e**6*Piecewise((-d**2/(4*e*x**5*sqrt(d**2/(e**2*x**2) - 1)) + 3*e/(8*x**3*sqrt(d**2/(e**2*x**2) - 1)) - e**3/(8*d**2*x*sqrt(d**2/(e**2*x**2) - 1)) + e**4*acosh(d/(e*x))/(8*d**3), Abs(d**2/(e**2*x**2)) > 1), (I*d**2/(4*e*x**5*sqrt(-d**2/(e**2*x**2) + 1)) - 3*I*e/(8*x**3*sqrt(-d**2/(e**2*x**2) + 1)) + I*e**3/(8*d**2*x*sqrt(-d**2/(e**2*x**2) + 1)) - I*e**4*asin(d/(e*x))/(8*d**3), True)) + e**7*Piecewise((-e*sqrt(d**2/(e**2*x**2) - 1)/(3*x**2) + e**3*sqrt(d**2/(e**2*x**2) - 1)/(3*d**2), Abs(d**2/(e**2*x**2)) > 1), (-I*e*sqrt(-d**2/(e**2*x**2) + 1)/(3*x**2) + I*e**3*sqrt(-d**2/(e**2*x**2) + 1)/(3*d**2), True))","C",0
82,1,2397,0,74.515530," ","integrate((e*x+d)**3*(-e**2*x**2+d**2)**(5/2)/x**12,x)","d^{7} \left(\begin{cases} - \frac{e \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}}{11 x^{10}} + \frac{e^{3} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}}{99 d^{2} x^{8}} + \frac{8 e^{5} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}}{693 d^{4} x^{6}} + \frac{16 e^{7} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}}{1155 d^{6} x^{4}} + \frac{64 e^{9} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}}{3465 d^{8} x^{2}} + \frac{128 e^{11} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}}{3465 d^{10}} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\- \frac{i e \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{11 x^{10}} + \frac{i e^{3} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{99 d^{2} x^{8}} + \frac{8 i e^{5} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{693 d^{4} x^{6}} + \frac{16 i e^{7} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{1155 d^{6} x^{4}} + \frac{64 i e^{9} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{3465 d^{8} x^{2}} + \frac{128 i e^{11} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{3465 d^{10}} & \text{otherwise} \end{cases}\right) + 3 d^{6} e \left(\begin{cases} - \frac{d^{2}}{10 e x^{11} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{9 e}{80 x^{9} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{e^{3}}{480 d^{2} x^{7} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{7 e^{5}}{1920 d^{4} x^{5} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{7 e^{7}}{768 d^{6} x^{3} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} - \frac{7 e^{9}}{256 d^{8} x \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{7 e^{10} \operatorname{acosh}{\left(\frac{d}{e x} \right)}}{256 d^{9}} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\\frac{i d^{2}}{10 e x^{11} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} - \frac{9 i e}{80 x^{9} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} - \frac{i e^{3}}{480 d^{2} x^{7} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} - \frac{7 i e^{5}}{1920 d^{4} x^{5} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} - \frac{7 i e^{7}}{768 d^{6} x^{3} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} + \frac{7 i e^{9}}{256 d^{8} x \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} - \frac{7 i e^{10} \operatorname{asin}{\left(\frac{d}{e x} \right)}}{256 d^{9}} & \text{otherwise} \end{cases}\right) + d^{5} e^{2} \left(\begin{cases} - \frac{e \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}}{9 x^{8}} + \frac{e^{3} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}}{63 d^{2} x^{6}} + \frac{2 e^{5} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}}{105 d^{4} x^{4}} + \frac{8 e^{7} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}}{315 d^{6} x^{2}} + \frac{16 e^{9} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}}{315 d^{8}} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\- \frac{i e \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{9 x^{8}} + \frac{i e^{3} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{63 d^{2} x^{6}} + \frac{2 i e^{5} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{105 d^{4} x^{4}} + \frac{8 i e^{7} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{315 d^{6} x^{2}} + \frac{16 i e^{9} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{315 d^{8}} & \text{otherwise} \end{cases}\right) - 5 d^{4} e^{3} \left(\begin{cases} - \frac{d^{2}}{8 e x^{9} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{7 e}{48 x^{7} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{e^{3}}{192 d^{2} x^{5} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{5 e^{5}}{384 d^{4} x^{3} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} - \frac{5 e^{7}}{128 d^{6} x \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{5 e^{8} \operatorname{acosh}{\left(\frac{d}{e x} \right)}}{128 d^{7}} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\\frac{i d^{2}}{8 e x^{9} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} - \frac{7 i e}{48 x^{7} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} - \frac{i e^{3}}{192 d^{2} x^{5} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} - \frac{5 i e^{5}}{384 d^{4} x^{3} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} + \frac{5 i e^{7}}{128 d^{6} x \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} - \frac{5 i e^{8} \operatorname{asin}{\left(\frac{d}{e x} \right)}}{128 d^{7}} & \text{otherwise} \end{cases}\right) - 5 d^{3} e^{4} \left(\begin{cases} - \frac{e \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}}{7 x^{6}} + \frac{e^{3} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}}{35 d^{2} x^{4}} + \frac{4 e^{5} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}}{105 d^{4} x^{2}} + \frac{8 e^{7} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}}{105 d^{6}} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\- \frac{i e \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{7 x^{6}} + \frac{i e^{3} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{35 d^{2} x^{4}} + \frac{4 i e^{5} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{105 d^{4} x^{2}} + \frac{8 i e^{7} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{105 d^{6}} & \text{otherwise} \end{cases}\right) + d^{2} e^{5} \left(\begin{cases} - \frac{d^{2}}{6 e x^{7} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{5 e}{24 x^{5} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{e^{3}}{48 d^{2} x^{3} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} - \frac{e^{5}}{16 d^{4} x \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{e^{6} \operatorname{acosh}{\left(\frac{d}{e x} \right)}}{16 d^{5}} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\\frac{i d^{2}}{6 e x^{7} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} - \frac{5 i e}{24 x^{5} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} - \frac{i e^{3}}{48 d^{2} x^{3} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} + \frac{i e^{5}}{16 d^{4} x \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} - \frac{i e^{6} \operatorname{asin}{\left(\frac{d}{e x} \right)}}{16 d^{5}} & \text{otherwise} \end{cases}\right) + 3 d e^{6} \left(\begin{cases} \frac{3 i d^{3} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{2} x^{5} + 15 e^{2} x^{7}} - \frac{4 i d e^{2} x^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{2} x^{5} + 15 e^{2} x^{7}} + \frac{2 i e^{6} x^{6} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{5} x^{5} + 15 d^{3} e^{2} x^{7}} - \frac{i e^{4} x^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{3} x^{5} + 15 d e^{2} x^{7}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{3 d^{3} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{2} x^{5} + 15 e^{2} x^{7}} - \frac{4 d e^{2} x^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{2} x^{5} + 15 e^{2} x^{7}} + \frac{2 e^{6} x^{6} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{5} x^{5} + 15 d^{3} e^{2} x^{7}} - \frac{e^{4} x^{4} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{3} x^{5} + 15 d e^{2} x^{7}} & \text{otherwise} \end{cases}\right) + e^{7} \left(\begin{cases} - \frac{d^{2}}{4 e x^{5} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{3 e}{8 x^{3} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} - \frac{e^{3}}{8 d^{2} x \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{e^{4} \operatorname{acosh}{\left(\frac{d}{e x} \right)}}{8 d^{3}} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\\frac{i d^{2}}{4 e x^{5} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} - \frac{3 i e}{8 x^{3} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} + \frac{i e^{3}}{8 d^{2} x \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} - \frac{i e^{4} \operatorname{asin}{\left(\frac{d}{e x} \right)}}{8 d^{3}} & \text{otherwise} \end{cases}\right)"," ",0,"d**7*Piecewise((-e*sqrt(d**2/(e**2*x**2) - 1)/(11*x**10) + e**3*sqrt(d**2/(e**2*x**2) - 1)/(99*d**2*x**8) + 8*e**5*sqrt(d**2/(e**2*x**2) - 1)/(693*d**4*x**6) + 16*e**7*sqrt(d**2/(e**2*x**2) - 1)/(1155*d**6*x**4) + 64*e**9*sqrt(d**2/(e**2*x**2) - 1)/(3465*d**8*x**2) + 128*e**11*sqrt(d**2/(e**2*x**2) - 1)/(3465*d**10), Abs(d**2/(e**2*x**2)) > 1), (-I*e*sqrt(-d**2/(e**2*x**2) + 1)/(11*x**10) + I*e**3*sqrt(-d**2/(e**2*x**2) + 1)/(99*d**2*x**8) + 8*I*e**5*sqrt(-d**2/(e**2*x**2) + 1)/(693*d**4*x**6) + 16*I*e**7*sqrt(-d**2/(e**2*x**2) + 1)/(1155*d**6*x**4) + 64*I*e**9*sqrt(-d**2/(e**2*x**2) + 1)/(3465*d**8*x**2) + 128*I*e**11*sqrt(-d**2/(e**2*x**2) + 1)/(3465*d**10), True)) + 3*d**6*e*Piecewise((-d**2/(10*e*x**11*sqrt(d**2/(e**2*x**2) - 1)) + 9*e/(80*x**9*sqrt(d**2/(e**2*x**2) - 1)) + e**3/(480*d**2*x**7*sqrt(d**2/(e**2*x**2) - 1)) + 7*e**5/(1920*d**4*x**5*sqrt(d**2/(e**2*x**2) - 1)) + 7*e**7/(768*d**6*x**3*sqrt(d**2/(e**2*x**2) - 1)) - 7*e**9/(256*d**8*x*sqrt(d**2/(e**2*x**2) - 1)) + 7*e**10*acosh(d/(e*x))/(256*d**9), Abs(d**2/(e**2*x**2)) > 1), (I*d**2/(10*e*x**11*sqrt(-d**2/(e**2*x**2) + 1)) - 9*I*e/(80*x**9*sqrt(-d**2/(e**2*x**2) + 1)) - I*e**3/(480*d**2*x**7*sqrt(-d**2/(e**2*x**2) + 1)) - 7*I*e**5/(1920*d**4*x**5*sqrt(-d**2/(e**2*x**2) + 1)) - 7*I*e**7/(768*d**6*x**3*sqrt(-d**2/(e**2*x**2) + 1)) + 7*I*e**9/(256*d**8*x*sqrt(-d**2/(e**2*x**2) + 1)) - 7*I*e**10*asin(d/(e*x))/(256*d**9), True)) + d**5*e**2*Piecewise((-e*sqrt(d**2/(e**2*x**2) - 1)/(9*x**8) + e**3*sqrt(d**2/(e**2*x**2) - 1)/(63*d**2*x**6) + 2*e**5*sqrt(d**2/(e**2*x**2) - 1)/(105*d**4*x**4) + 8*e**7*sqrt(d**2/(e**2*x**2) - 1)/(315*d**6*x**2) + 16*e**9*sqrt(d**2/(e**2*x**2) - 1)/(315*d**8), Abs(d**2/(e**2*x**2)) > 1), (-I*e*sqrt(-d**2/(e**2*x**2) + 1)/(9*x**8) + I*e**3*sqrt(-d**2/(e**2*x**2) + 1)/(63*d**2*x**6) + 2*I*e**5*sqrt(-d**2/(e**2*x**2) + 1)/(105*d**4*x**4) + 8*I*e**7*sqrt(-d**2/(e**2*x**2) + 1)/(315*d**6*x**2) + 16*I*e**9*sqrt(-d**2/(e**2*x**2) + 1)/(315*d**8), True)) - 5*d**4*e**3*Piecewise((-d**2/(8*e*x**9*sqrt(d**2/(e**2*x**2) - 1)) + 7*e/(48*x**7*sqrt(d**2/(e**2*x**2) - 1)) + e**3/(192*d**2*x**5*sqrt(d**2/(e**2*x**2) - 1)) + 5*e**5/(384*d**4*x**3*sqrt(d**2/(e**2*x**2) - 1)) - 5*e**7/(128*d**6*x*sqrt(d**2/(e**2*x**2) - 1)) + 5*e**8*acosh(d/(e*x))/(128*d**7), Abs(d**2/(e**2*x**2)) > 1), (I*d**2/(8*e*x**9*sqrt(-d**2/(e**2*x**2) + 1)) - 7*I*e/(48*x**7*sqrt(-d**2/(e**2*x**2) + 1)) - I*e**3/(192*d**2*x**5*sqrt(-d**2/(e**2*x**2) + 1)) - 5*I*e**5/(384*d**4*x**3*sqrt(-d**2/(e**2*x**2) + 1)) + 5*I*e**7/(128*d**6*x*sqrt(-d**2/(e**2*x**2) + 1)) - 5*I*e**8*asin(d/(e*x))/(128*d**7), True)) - 5*d**3*e**4*Piecewise((-e*sqrt(d**2/(e**2*x**2) - 1)/(7*x**6) + e**3*sqrt(d**2/(e**2*x**2) - 1)/(35*d**2*x**4) + 4*e**5*sqrt(d**2/(e**2*x**2) - 1)/(105*d**4*x**2) + 8*e**7*sqrt(d**2/(e**2*x**2) - 1)/(105*d**6), Abs(d**2/(e**2*x**2)) > 1), (-I*e*sqrt(-d**2/(e**2*x**2) + 1)/(7*x**6) + I*e**3*sqrt(-d**2/(e**2*x**2) + 1)/(35*d**2*x**4) + 4*I*e**5*sqrt(-d**2/(e**2*x**2) + 1)/(105*d**4*x**2) + 8*I*e**7*sqrt(-d**2/(e**2*x**2) + 1)/(105*d**6), True)) + d**2*e**5*Piecewise((-d**2/(6*e*x**7*sqrt(d**2/(e**2*x**2) - 1)) + 5*e/(24*x**5*sqrt(d**2/(e**2*x**2) - 1)) + e**3/(48*d**2*x**3*sqrt(d**2/(e**2*x**2) - 1)) - e**5/(16*d**4*x*sqrt(d**2/(e**2*x**2) - 1)) + e**6*acosh(d/(e*x))/(16*d**5), Abs(d**2/(e**2*x**2)) > 1), (I*d**2/(6*e*x**7*sqrt(-d**2/(e**2*x**2) + 1)) - 5*I*e/(24*x**5*sqrt(-d**2/(e**2*x**2) + 1)) - I*e**3/(48*d**2*x**3*sqrt(-d**2/(e**2*x**2) + 1)) + I*e**5/(16*d**4*x*sqrt(-d**2/(e**2*x**2) + 1)) - I*e**6*asin(d/(e*x))/(16*d**5), True)) + 3*d*e**6*Piecewise((3*I*d**3*sqrt(-1 + e**2*x**2/d**2)/(-15*d**2*x**5 + 15*e**2*x**7) - 4*I*d*e**2*x**2*sqrt(-1 + e**2*x**2/d**2)/(-15*d**2*x**5 + 15*e**2*x**7) + 2*I*e**6*x**6*sqrt(-1 + e**2*x**2/d**2)/(-15*d**5*x**5 + 15*d**3*e**2*x**7) - I*e**4*x**4*sqrt(-1 + e**2*x**2/d**2)/(-15*d**3*x**5 + 15*d*e**2*x**7), Abs(e**2*x**2/d**2) > 1), (3*d**3*sqrt(1 - e**2*x**2/d**2)/(-15*d**2*x**5 + 15*e**2*x**7) - 4*d*e**2*x**2*sqrt(1 - e**2*x**2/d**2)/(-15*d**2*x**5 + 15*e**2*x**7) + 2*e**6*x**6*sqrt(1 - e**2*x**2/d**2)/(-15*d**5*x**5 + 15*d**3*e**2*x**7) - e**4*x**4*sqrt(1 - e**2*x**2/d**2)/(-15*d**3*x**5 + 15*d*e**2*x**7), True)) + e**7*Piecewise((-d**2/(4*e*x**5*sqrt(d**2/(e**2*x**2) - 1)) + 3*e/(8*x**3*sqrt(d**2/(e**2*x**2) - 1)) - e**3/(8*d**2*x*sqrt(d**2/(e**2*x**2) - 1)) + e**4*acosh(d/(e*x))/(8*d**3), Abs(d**2/(e**2*x**2)) > 1), (I*d**2/(4*e*x**5*sqrt(-d**2/(e**2*x**2) + 1)) - 3*I*e/(8*x**3*sqrt(-d**2/(e**2*x**2) + 1)) + I*e**3/(8*d**2*x*sqrt(-d**2/(e**2*x**2) + 1)) - I*e**4*asin(d/(e*x))/(8*d**3), True))","C",0
83,0,0,0,0.000000," ","integrate(x**5*(e*x+d)**3/(-e**2*x**2+d**2)**(7/2),x)","\int \frac{x^{5} \left(d + e x\right)^{3}}{\left(- \left(- d + e x\right) \left(d + e x\right)\right)^{\frac{7}{2}}}\, dx"," ",0,"Integral(x**5*(d + e*x)**3/(-(-d + e*x)*(d + e*x))**(7/2), x)","F",0
84,0,0,0,0.000000," ","integrate(x**4*(e*x+d)**3/(-e**2*x**2+d**2)**(7/2),x)","\int \frac{x^{4} \left(d + e x\right)^{3}}{\left(- \left(- d + e x\right) \left(d + e x\right)\right)^{\frac{7}{2}}}\, dx"," ",0,"Integral(x**4*(d + e*x)**3/(-(-d + e*x)*(d + e*x))**(7/2), x)","F",0
85,0,0,0,0.000000," ","integrate(x**3*(e*x+d)**3/(-e**2*x**2+d**2)**(7/2),x)","\int \frac{x^{3} \left(d + e x\right)^{3}}{\left(- \left(- d + e x\right) \left(d + e x\right)\right)^{\frac{7}{2}}}\, dx"," ",0,"Integral(x**3*(d + e*x)**3/(-(-d + e*x)*(d + e*x))**(7/2), x)","F",0
86,0,0,0,0.000000," ","integrate(x**2*(e*x+d)**3/(-e**2*x**2+d**2)**(7/2),x)","\int \frac{x^{2} \left(d + e x\right)^{3}}{\left(- \left(- d + e x\right) \left(d + e x\right)\right)^{\frac{7}{2}}}\, dx"," ",0,"Integral(x**2*(d + e*x)**3/(-(-d + e*x)*(d + e*x))**(7/2), x)","F",0
87,0,0,0,0.000000," ","integrate(x*(e*x+d)**3/(-e**2*x**2+d**2)**(7/2),x)","\int \frac{x \left(d + e x\right)^{3}}{\left(- \left(- d + e x\right) \left(d + e x\right)\right)^{\frac{7}{2}}}\, dx"," ",0,"Integral(x*(d + e*x)**3/(-(-d + e*x)*(d + e*x))**(7/2), x)","F",0
88,0,0,0,0.000000," ","integrate((e*x+d)**3/(-e**2*x**2+d**2)**(7/2),x)","\int \frac{\left(d + e x\right)^{3}}{\left(- \left(- d + e x\right) \left(d + e x\right)\right)^{\frac{7}{2}}}\, dx"," ",0,"Integral((d + e*x)**3/(-(-d + e*x)*(d + e*x))**(7/2), x)","F",0
89,0,0,0,0.000000," ","integrate((e*x+d)**3/x/(-e**2*x**2+d**2)**(7/2),x)","\int \frac{\left(d + e x\right)^{3}}{x \left(- \left(- d + e x\right) \left(d + e x\right)\right)^{\frac{7}{2}}}\, dx"," ",0,"Integral((d + e*x)**3/(x*(-(-d + e*x)*(d + e*x))**(7/2)), x)","F",0
90,0,0,0,0.000000," ","integrate((e*x+d)**3/x**2/(-e**2*x**2+d**2)**(7/2),x)","\int \frac{\left(d + e x\right)^{3}}{x^{2} \left(- \left(- d + e x\right) \left(d + e x\right)\right)^{\frac{7}{2}}}\, dx"," ",0,"Integral((d + e*x)**3/(x**2*(-(-d + e*x)*(d + e*x))**(7/2)), x)","F",0
91,0,0,0,0.000000," ","integrate((e*x+d)**3/x**3/(-e**2*x**2+d**2)**(7/2),x)","\int \frac{\left(d + e x\right)^{3}}{x^{3} \left(- \left(- d + e x\right) \left(d + e x\right)\right)^{\frac{7}{2}}}\, dx"," ",0,"Integral((d + e*x)**3/(x**3*(-(-d + e*x)*(d + e*x))**(7/2)), x)","F",0
92,0,0,0,0.000000," ","integrate(x**4*(-e**2*x**2+d**2)**(1/2)/(e*x+d),x)","\int \frac{x^{4} \sqrt{- \left(- d + e x\right) \left(d + e x\right)}}{d + e x}\, dx"," ",0,"Integral(x**4*sqrt(-(-d + e*x)*(d + e*x))/(d + e*x), x)","F",0
93,0,0,0,0.000000," ","integrate(x**3*(-e**2*x**2+d**2)**(1/2)/(e*x+d),x)","\int \frac{x^{3} \sqrt{- \left(- d + e x\right) \left(d + e x\right)}}{d + e x}\, dx"," ",0,"Integral(x**3*sqrt(-(-d + e*x)*(d + e*x))/(d + e*x), x)","F",0
94,0,0,0,0.000000," ","integrate(x**2*(-e**2*x**2+d**2)**(1/2)/(e*x+d),x)","\int \frac{x^{2} \sqrt{- \left(- d + e x\right) \left(d + e x\right)}}{d + e x}\, dx"," ",0,"Integral(x**2*sqrt(-(-d + e*x)*(d + e*x))/(d + e*x), x)","F",0
95,0,0,0,0.000000," ","integrate(x*(-e**2*x**2+d**2)**(1/2)/(e*x+d),x)","\int \frac{x \sqrt{- \left(- d + e x\right) \left(d + e x\right)}}{d + e x}\, dx"," ",0,"Integral(x*sqrt(-(-d + e*x)*(d + e*x))/(d + e*x), x)","F",0
96,0,0,0,0.000000," ","integrate((-e**2*x**2+d**2)**(1/2)/(e*x+d),x)","\int \frac{\sqrt{- \left(- d + e x\right) \left(d + e x\right)}}{d + e x}\, dx"," ",0,"Integral(sqrt(-(-d + e*x)*(d + e*x))/(d + e*x), x)","F",0
97,0,0,0,0.000000," ","integrate((-e**2*x**2+d**2)**(1/2)/x/(e*x+d),x)","\int \frac{\sqrt{- \left(- d + e x\right) \left(d + e x\right)}}{x \left(d + e x\right)}\, dx"," ",0,"Integral(sqrt(-(-d + e*x)*(d + e*x))/(x*(d + e*x)), x)","F",0
98,0,0,0,0.000000," ","integrate((-e**2*x**2+d**2)**(1/2)/x**2/(e*x+d),x)","\int \frac{\sqrt{- \left(- d + e x\right) \left(d + e x\right)}}{x^{2} \left(d + e x\right)}\, dx"," ",0,"Integral(sqrt(-(-d + e*x)*(d + e*x))/(x**2*(d + e*x)), x)","F",0
99,0,0,0,0.000000," ","integrate((-e**2*x**2+d**2)**(1/2)/x**3/(e*x+d),x)","\int \frac{\sqrt{- \left(- d + e x\right) \left(d + e x\right)}}{x^{3} \left(d + e x\right)}\, dx"," ",0,"Integral(sqrt(-(-d + e*x)*(d + e*x))/(x**3*(d + e*x)), x)","F",0
100,0,0,0,0.000000," ","integrate((-e**2*x**2+d**2)**(1/2)/x**4/(e*x+d),x)","\int \frac{\sqrt{- \left(- d + e x\right) \left(d + e x\right)}}{x^{4} \left(d + e x\right)}\, dx"," ",0,"Integral(sqrt(-(-d + e*x)*(d + e*x))/(x**4*(d + e*x)), x)","F",0
101,0,0,0,0.000000," ","integrate((-e**2*x**2+d**2)**(1/2)/x**5/(e*x+d),x)","\int \frac{\sqrt{- \left(- d + e x\right) \left(d + e x\right)}}{x^{5} \left(d + e x\right)}\, dx"," ",0,"Integral(sqrt(-(-d + e*x)*(d + e*x))/(x**5*(d + e*x)), x)","F",0
102,1,279,0,7.847912," ","integrate(x**2*(-e**2*x**2+d**2)**(3/2)/(e*x+d),x)","d \left(\begin{cases} - \frac{i d^{4} \operatorname{acosh}{\left(\frac{e x}{d} \right)}}{8 e^{3}} + \frac{i d^{3} x}{8 e^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{3 i d x^{3}}{8 \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + \frac{i e^{2} x^{5}}{4 d \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{d^{4} \operatorname{asin}{\left(\frac{e x}{d} \right)}}{8 e^{3}} - \frac{d^{3} x}{8 e^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{3 d x^{3}}{8 \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} - \frac{e^{2} x^{5}}{4 d \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} & \text{otherwise} \end{cases}\right) - e \left(\begin{cases} - \frac{2 d^{4} \sqrt{d^{2} - e^{2} x^{2}}}{15 e^{4}} - \frac{d^{2} x^{2} \sqrt{d^{2} - e^{2} x^{2}}}{15 e^{2}} + \frac{x^{4} \sqrt{d^{2} - e^{2} x^{2}}}{5} & \text{for}\: e \neq 0 \\\frac{x^{4} \sqrt{d^{2}}}{4} & \text{otherwise} \end{cases}\right)"," ",0,"d*Piecewise((-I*d**4*acosh(e*x/d)/(8*e**3) + I*d**3*x/(8*e**2*sqrt(-1 + e**2*x**2/d**2)) - 3*I*d*x**3/(8*sqrt(-1 + e**2*x**2/d**2)) + I*e**2*x**5/(4*d*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (d**4*asin(e*x/d)/(8*e**3) - d**3*x/(8*e**2*sqrt(1 - e**2*x**2/d**2)) + 3*d*x**3/(8*sqrt(1 - e**2*x**2/d**2)) - e**2*x**5/(4*d*sqrt(1 - e**2*x**2/d**2)), True)) - e*Piecewise((-2*d**4*sqrt(d**2 - e**2*x**2)/(15*e**4) - d**2*x**2*sqrt(d**2 - e**2*x**2)/(15*e**2) + x**4*sqrt(d**2 - e**2*x**2)/5, Ne(e, 0)), (x**4*sqrt(d**2)/4, True))","C",0
103,1,830,0,25.151048," ","integrate(x**4*(-e**2*x**2+d**2)**(5/2)/(e*x+d),x)","d^{3} \left(\begin{cases} - \frac{i d^{6} \operatorname{acosh}{\left(\frac{e x}{d} \right)}}{16 e^{5}} + \frac{i d^{5} x}{16 e^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{i d^{3} x^{3}}{48 e^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{5 i d x^{5}}{24 \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + \frac{i e^{2} x^{7}}{6 d \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{d^{6} \operatorname{asin}{\left(\frac{e x}{d} \right)}}{16 e^{5}} - \frac{d^{5} x}{16 e^{4} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{d^{3} x^{3}}{48 e^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{5 d x^{5}}{24 \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} - \frac{e^{2} x^{7}}{6 d \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} & \text{otherwise} \end{cases}\right) - d^{2} e \left(\begin{cases} - \frac{8 d^{6} \sqrt{d^{2} - e^{2} x^{2}}}{105 e^{6}} - \frac{4 d^{4} x^{2} \sqrt{d^{2} - e^{2} x^{2}}}{105 e^{4}} - \frac{d^{2} x^{4} \sqrt{d^{2} - e^{2} x^{2}}}{35 e^{2}} + \frac{x^{6} \sqrt{d^{2} - e^{2} x^{2}}}{7} & \text{for}\: e \neq 0 \\\frac{x^{6} \sqrt{d^{2}}}{6} & \text{otherwise} \end{cases}\right) - d e^{2} \left(\begin{cases} - \frac{5 i d^{8} \operatorname{acosh}{\left(\frac{e x}{d} \right)}}{128 e^{7}} + \frac{5 i d^{7} x}{128 e^{6} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{5 i d^{5} x^{3}}{384 e^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{i d^{3} x^{5}}{192 e^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{7 i d x^{7}}{48 \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + \frac{i e^{2} x^{9}}{8 d \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{5 d^{8} \operatorname{asin}{\left(\frac{e x}{d} \right)}}{128 e^{7}} - \frac{5 d^{7} x}{128 e^{6} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{5 d^{5} x^{3}}{384 e^{4} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{d^{3} x^{5}}{192 e^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{7 d x^{7}}{48 \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} - \frac{e^{2} x^{9}}{8 d \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} & \text{otherwise} \end{cases}\right) + e^{3} \left(\begin{cases} - \frac{16 d^{8} \sqrt{d^{2} - e^{2} x^{2}}}{315 e^{8}} - \frac{8 d^{6} x^{2} \sqrt{d^{2} - e^{2} x^{2}}}{315 e^{6}} - \frac{2 d^{4} x^{4} \sqrt{d^{2} - e^{2} x^{2}}}{105 e^{4}} - \frac{d^{2} x^{6} \sqrt{d^{2} - e^{2} x^{2}}}{63 e^{2}} + \frac{x^{8} \sqrt{d^{2} - e^{2} x^{2}}}{9} & \text{for}\: e \neq 0 \\\frac{x^{8} \sqrt{d^{2}}}{8} & \text{otherwise} \end{cases}\right)"," ",0,"d**3*Piecewise((-I*d**6*acosh(e*x/d)/(16*e**5) + I*d**5*x/(16*e**4*sqrt(-1 + e**2*x**2/d**2)) - I*d**3*x**3/(48*e**2*sqrt(-1 + e**2*x**2/d**2)) - 5*I*d*x**5/(24*sqrt(-1 + e**2*x**2/d**2)) + I*e**2*x**7/(6*d*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (d**6*asin(e*x/d)/(16*e**5) - d**5*x/(16*e**4*sqrt(1 - e**2*x**2/d**2)) + d**3*x**3/(48*e**2*sqrt(1 - e**2*x**2/d**2)) + 5*d*x**5/(24*sqrt(1 - e**2*x**2/d**2)) - e**2*x**7/(6*d*sqrt(1 - e**2*x**2/d**2)), True)) - d**2*e*Piecewise((-8*d**6*sqrt(d**2 - e**2*x**2)/(105*e**6) - 4*d**4*x**2*sqrt(d**2 - e**2*x**2)/(105*e**4) - d**2*x**4*sqrt(d**2 - e**2*x**2)/(35*e**2) + x**6*sqrt(d**2 - e**2*x**2)/7, Ne(e, 0)), (x**6*sqrt(d**2)/6, True)) - d*e**2*Piecewise((-5*I*d**8*acosh(e*x/d)/(128*e**7) + 5*I*d**7*x/(128*e**6*sqrt(-1 + e**2*x**2/d**2)) - 5*I*d**5*x**3/(384*e**4*sqrt(-1 + e**2*x**2/d**2)) - I*d**3*x**5/(192*e**2*sqrt(-1 + e**2*x**2/d**2)) - 7*I*d*x**7/(48*sqrt(-1 + e**2*x**2/d**2)) + I*e**2*x**9/(8*d*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (5*d**8*asin(e*x/d)/(128*e**7) - 5*d**7*x/(128*e**6*sqrt(1 - e**2*x**2/d**2)) + 5*d**5*x**3/(384*e**4*sqrt(1 - e**2*x**2/d**2)) + d**3*x**5/(192*e**2*sqrt(1 - e**2*x**2/d**2)) + 7*d*x**7/(48*sqrt(1 - e**2*x**2/d**2)) - e**2*x**9/(8*d*sqrt(1 - e**2*x**2/d**2)), True)) + e**3*Piecewise((-16*d**8*sqrt(d**2 - e**2*x**2)/(315*e**8) - 8*d**6*x**2*sqrt(d**2 - e**2*x**2)/(315*e**6) - 2*d**4*x**4*sqrt(d**2 - e**2*x**2)/(105*e**4) - d**2*x**6*sqrt(d**2 - e**2*x**2)/(63*e**2) + x**8*sqrt(d**2 - e**2*x**2)/9, Ne(e, 0)), (x**8*sqrt(d**2)/8, True))","C",0
104,1,775,0,23.006344," ","integrate(x**3*(-e**2*x**2+d**2)**(5/2)/(e*x+d),x)","d^{3} \left(\begin{cases} - \frac{2 d^{4} \sqrt{d^{2} - e^{2} x^{2}}}{15 e^{4}} - \frac{d^{2} x^{2} \sqrt{d^{2} - e^{2} x^{2}}}{15 e^{2}} + \frac{x^{4} \sqrt{d^{2} - e^{2} x^{2}}}{5} & \text{for}\: e \neq 0 \\\frac{x^{4} \sqrt{d^{2}}}{4} & \text{otherwise} \end{cases}\right) - d^{2} e \left(\begin{cases} - \frac{i d^{6} \operatorname{acosh}{\left(\frac{e x}{d} \right)}}{16 e^{5}} + \frac{i d^{5} x}{16 e^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{i d^{3} x^{3}}{48 e^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{5 i d x^{5}}{24 \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + \frac{i e^{2} x^{7}}{6 d \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{d^{6} \operatorname{asin}{\left(\frac{e x}{d} \right)}}{16 e^{5}} - \frac{d^{5} x}{16 e^{4} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{d^{3} x^{3}}{48 e^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{5 d x^{5}}{24 \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} - \frac{e^{2} x^{7}}{6 d \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} & \text{otherwise} \end{cases}\right) - d e^{2} \left(\begin{cases} - \frac{8 d^{6} \sqrt{d^{2} - e^{2} x^{2}}}{105 e^{6}} - \frac{4 d^{4} x^{2} \sqrt{d^{2} - e^{2} x^{2}}}{105 e^{4}} - \frac{d^{2} x^{4} \sqrt{d^{2} - e^{2} x^{2}}}{35 e^{2}} + \frac{x^{6} \sqrt{d^{2} - e^{2} x^{2}}}{7} & \text{for}\: e \neq 0 \\\frac{x^{6} \sqrt{d^{2}}}{6} & \text{otherwise} \end{cases}\right) + e^{3} \left(\begin{cases} - \frac{5 i d^{8} \operatorname{acosh}{\left(\frac{e x}{d} \right)}}{128 e^{7}} + \frac{5 i d^{7} x}{128 e^{6} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{5 i d^{5} x^{3}}{384 e^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{i d^{3} x^{5}}{192 e^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{7 i d x^{7}}{48 \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + \frac{i e^{2} x^{9}}{8 d \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{5 d^{8} \operatorname{asin}{\left(\frac{e x}{d} \right)}}{128 e^{7}} - \frac{5 d^{7} x}{128 e^{6} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{5 d^{5} x^{3}}{384 e^{4} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{d^{3} x^{5}}{192 e^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{7 d x^{7}}{48 \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} - \frac{e^{2} x^{9}}{8 d \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} & \text{otherwise} \end{cases}\right)"," ",0,"d**3*Piecewise((-2*d**4*sqrt(d**2 - e**2*x**2)/(15*e**4) - d**2*x**2*sqrt(d**2 - e**2*x**2)/(15*e**2) + x**4*sqrt(d**2 - e**2*x**2)/5, Ne(e, 0)), (x**4*sqrt(d**2)/4, True)) - d**2*e*Piecewise((-I*d**6*acosh(e*x/d)/(16*e**5) + I*d**5*x/(16*e**4*sqrt(-1 + e**2*x**2/d**2)) - I*d**3*x**3/(48*e**2*sqrt(-1 + e**2*x**2/d**2)) - 5*I*d*x**5/(24*sqrt(-1 + e**2*x**2/d**2)) + I*e**2*x**7/(6*d*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (d**6*asin(e*x/d)/(16*e**5) - d**5*x/(16*e**4*sqrt(1 - e**2*x**2/d**2)) + d**3*x**3/(48*e**2*sqrt(1 - e**2*x**2/d**2)) + 5*d*x**5/(24*sqrt(1 - e**2*x**2/d**2)) - e**2*x**7/(6*d*sqrt(1 - e**2*x**2/d**2)), True)) - d*e**2*Piecewise((-8*d**6*sqrt(d**2 - e**2*x**2)/(105*e**6) - 4*d**4*x**2*sqrt(d**2 - e**2*x**2)/(105*e**4) - d**2*x**4*sqrt(d**2 - e**2*x**2)/(35*e**2) + x**6*sqrt(d**2 - e**2*x**2)/7, Ne(e, 0)), (x**6*sqrt(d**2)/6, True)) + e**3*Piecewise((-5*I*d**8*acosh(e*x/d)/(128*e**7) + 5*I*d**7*x/(128*e**6*sqrt(-1 + e**2*x**2/d**2)) - 5*I*d**5*x**3/(384*e**4*sqrt(-1 + e**2*x**2/d**2)) - I*d**3*x**5/(192*e**2*sqrt(-1 + e**2*x**2/d**2)) - 7*I*d*x**7/(48*sqrt(-1 + e**2*x**2/d**2)) + I*e**2*x**9/(8*d*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (5*d**8*asin(e*x/d)/(128*e**7) - 5*d**7*x/(128*e**6*sqrt(1 - e**2*x**2/d**2)) + 5*d**5*x**3/(384*e**4*sqrt(1 - e**2*x**2/d**2)) + d**3*x**5/(192*e**2*sqrt(1 - e**2*x**2/d**2)) + 7*d*x**7/(48*sqrt(1 - e**2*x**2/d**2)) - e**2*x**9/(8*d*sqrt(1 - e**2*x**2/d**2)), True))","A",0
105,1,653,0,16.656710," ","integrate(x**2*(-e**2*x**2+d**2)**(5/2)/(e*x+d),x)","d^{3} \left(\begin{cases} - \frac{i d^{4} \operatorname{acosh}{\left(\frac{e x}{d} \right)}}{8 e^{3}} + \frac{i d^{3} x}{8 e^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{3 i d x^{3}}{8 \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + \frac{i e^{2} x^{5}}{4 d \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{d^{4} \operatorname{asin}{\left(\frac{e x}{d} \right)}}{8 e^{3}} - \frac{d^{3} x}{8 e^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{3 d x^{3}}{8 \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} - \frac{e^{2} x^{5}}{4 d \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} & \text{otherwise} \end{cases}\right) - d^{2} e \left(\begin{cases} - \frac{2 d^{4} \sqrt{d^{2} - e^{2} x^{2}}}{15 e^{4}} - \frac{d^{2} x^{2} \sqrt{d^{2} - e^{2} x^{2}}}{15 e^{2}} + \frac{x^{4} \sqrt{d^{2} - e^{2} x^{2}}}{5} & \text{for}\: e \neq 0 \\\frac{x^{4} \sqrt{d^{2}}}{4} & \text{otherwise} \end{cases}\right) - d e^{2} \left(\begin{cases} - \frac{i d^{6} \operatorname{acosh}{\left(\frac{e x}{d} \right)}}{16 e^{5}} + \frac{i d^{5} x}{16 e^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{i d^{3} x^{3}}{48 e^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{5 i d x^{5}}{24 \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + \frac{i e^{2} x^{7}}{6 d \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{d^{6} \operatorname{asin}{\left(\frac{e x}{d} \right)}}{16 e^{5}} - \frac{d^{5} x}{16 e^{4} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{d^{3} x^{3}}{48 e^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{5 d x^{5}}{24 \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} - \frac{e^{2} x^{7}}{6 d \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} & \text{otherwise} \end{cases}\right) + e^{3} \left(\begin{cases} - \frac{8 d^{6} \sqrt{d^{2} - e^{2} x^{2}}}{105 e^{6}} - \frac{4 d^{4} x^{2} \sqrt{d^{2} - e^{2} x^{2}}}{105 e^{4}} - \frac{d^{2} x^{4} \sqrt{d^{2} - e^{2} x^{2}}}{35 e^{2}} + \frac{x^{6} \sqrt{d^{2} - e^{2} x^{2}}}{7} & \text{for}\: e \neq 0 \\\frac{x^{6} \sqrt{d^{2}}}{6} & \text{otherwise} \end{cases}\right)"," ",0,"d**3*Piecewise((-I*d**4*acosh(e*x/d)/(8*e**3) + I*d**3*x/(8*e**2*sqrt(-1 + e**2*x**2/d**2)) - 3*I*d*x**3/(8*sqrt(-1 + e**2*x**2/d**2)) + I*e**2*x**5/(4*d*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (d**4*asin(e*x/d)/(8*e**3) - d**3*x/(8*e**2*sqrt(1 - e**2*x**2/d**2)) + 3*d*x**3/(8*sqrt(1 - e**2*x**2/d**2)) - e**2*x**5/(4*d*sqrt(1 - e**2*x**2/d**2)), True)) - d**2*e*Piecewise((-2*d**4*sqrt(d**2 - e**2*x**2)/(15*e**4) - d**2*x**2*sqrt(d**2 - e**2*x**2)/(15*e**2) + x**4*sqrt(d**2 - e**2*x**2)/5, Ne(e, 0)), (x**4*sqrt(d**2)/4, True)) - d*e**2*Piecewise((-I*d**6*acosh(e*x/d)/(16*e**5) + I*d**5*x/(16*e**4*sqrt(-1 + e**2*x**2/d**2)) - I*d**3*x**3/(48*e**2*sqrt(-1 + e**2*x**2/d**2)) - 5*I*d*x**5/(24*sqrt(-1 + e**2*x**2/d**2)) + I*e**2*x**7/(6*d*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (d**6*asin(e*x/d)/(16*e**5) - d**5*x/(16*e**4*sqrt(1 - e**2*x**2/d**2)) + d**3*x**3/(48*e**2*sqrt(1 - e**2*x**2/d**2)) + 5*d*x**5/(24*sqrt(1 - e**2*x**2/d**2)) - e**2*x**7/(6*d*sqrt(1 - e**2*x**2/d**2)), True)) + e**3*Piecewise((-8*d**6*sqrt(d**2 - e**2*x**2)/(105*e**6) - 4*d**4*x**2*sqrt(d**2 - e**2*x**2)/(105*e**4) - d**2*x**4*sqrt(d**2 - e**2*x**2)/(35*e**2) + x**6*sqrt(d**2 - e**2*x**2)/7, Ne(e, 0)), (x**6*sqrt(d**2)/6, True))","C",0
106,1,580,0,16.117444," ","integrate(x*(-e**2*x**2+d**2)**(5/2)/(e*x+d),x)","d^{3} \left(\begin{cases} \frac{x^{2} \sqrt{d^{2}}}{2} & \text{for}\: e^{2} = 0 \\- \frac{\left(d^{2} - e^{2} x^{2}\right)^{\frac{3}{2}}}{3 e^{2}} & \text{otherwise} \end{cases}\right) - d^{2} e \left(\begin{cases} - \frac{i d^{4} \operatorname{acosh}{\left(\frac{e x}{d} \right)}}{8 e^{3}} + \frac{i d^{3} x}{8 e^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{3 i d x^{3}}{8 \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + \frac{i e^{2} x^{5}}{4 d \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{d^{4} \operatorname{asin}{\left(\frac{e x}{d} \right)}}{8 e^{3}} - \frac{d^{3} x}{8 e^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{3 d x^{3}}{8 \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} - \frac{e^{2} x^{5}}{4 d \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} & \text{otherwise} \end{cases}\right) - d e^{2} \left(\begin{cases} - \frac{2 d^{4} \sqrt{d^{2} - e^{2} x^{2}}}{15 e^{4}} - \frac{d^{2} x^{2} \sqrt{d^{2} - e^{2} x^{2}}}{15 e^{2}} + \frac{x^{4} \sqrt{d^{2} - e^{2} x^{2}}}{5} & \text{for}\: e \neq 0 \\\frac{x^{4} \sqrt{d^{2}}}{4} & \text{otherwise} \end{cases}\right) + e^{3} \left(\begin{cases} - \frac{i d^{6} \operatorname{acosh}{\left(\frac{e x}{d} \right)}}{16 e^{5}} + \frac{i d^{5} x}{16 e^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{i d^{3} x^{3}}{48 e^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{5 i d x^{5}}{24 \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + \frac{i e^{2} x^{7}}{6 d \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{d^{6} \operatorname{asin}{\left(\frac{e x}{d} \right)}}{16 e^{5}} - \frac{d^{5} x}{16 e^{4} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{d^{3} x^{3}}{48 e^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{5 d x^{5}}{24 \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} - \frac{e^{2} x^{7}}{6 d \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} & \text{otherwise} \end{cases}\right)"," ",0,"d**3*Piecewise((x**2*sqrt(d**2)/2, Eq(e**2, 0)), (-(d**2 - e**2*x**2)**(3/2)/(3*e**2), True)) - d**2*e*Piecewise((-I*d**4*acosh(e*x/d)/(8*e**3) + I*d**3*x/(8*e**2*sqrt(-1 + e**2*x**2/d**2)) - 3*I*d*x**3/(8*sqrt(-1 + e**2*x**2/d**2)) + I*e**2*x**5/(4*d*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (d**4*asin(e*x/d)/(8*e**3) - d**3*x/(8*e**2*sqrt(1 - e**2*x**2/d**2)) + 3*d*x**3/(8*sqrt(1 - e**2*x**2/d**2)) - e**2*x**5/(4*d*sqrt(1 - e**2*x**2/d**2)), True)) - d*e**2*Piecewise((-2*d**4*sqrt(d**2 - e**2*x**2)/(15*e**4) - d**2*x**2*sqrt(d**2 - e**2*x**2)/(15*e**2) + x**4*sqrt(d**2 - e**2*x**2)/5, Ne(e, 0)), (x**4*sqrt(d**2)/4, True)) + e**3*Piecewise((-I*d**6*acosh(e*x/d)/(16*e**5) + I*d**5*x/(16*e**4*sqrt(-1 + e**2*x**2/d**2)) - I*d**3*x**3/(48*e**2*sqrt(-1 + e**2*x**2/d**2)) - 5*I*d*x**5/(24*sqrt(-1 + e**2*x**2/d**2)) + I*e**2*x**7/(6*d*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (d**6*asin(e*x/d)/(16*e**5) - d**5*x/(16*e**4*sqrt(1 - e**2*x**2/d**2)) + d**3*x**3/(48*e**2*sqrt(1 - e**2*x**2/d**2)) + 5*d*x**5/(24*sqrt(1 - e**2*x**2/d**2)) - e**2*x**7/(6*d*sqrt(1 - e**2*x**2/d**2)), True))","A",0
107,1,435,0,10.461224," ","integrate((-e**2*x**2+d**2)**(5/2)/(e*x+d),x)","d^{3} \left(\begin{cases} - \frac{i d^{2} \operatorname{acosh}{\left(\frac{e x}{d} \right)}}{2 e} - \frac{i d x}{2 \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + \frac{i e^{2} x^{3}}{2 d \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{d^{2} \operatorname{asin}{\left(\frac{e x}{d} \right)}}{2 e} + \frac{d x \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}}{2} & \text{otherwise} \end{cases}\right) - d^{2} e \left(\begin{cases} \frac{x^{2} \sqrt{d^{2}}}{2} & \text{for}\: e^{2} = 0 \\- \frac{\left(d^{2} - e^{2} x^{2}\right)^{\frac{3}{2}}}{3 e^{2}} & \text{otherwise} \end{cases}\right) - d e^{2} \left(\begin{cases} - \frac{i d^{4} \operatorname{acosh}{\left(\frac{e x}{d} \right)}}{8 e^{3}} + \frac{i d^{3} x}{8 e^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{3 i d x^{3}}{8 \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + \frac{i e^{2} x^{5}}{4 d \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{d^{4} \operatorname{asin}{\left(\frac{e x}{d} \right)}}{8 e^{3}} - \frac{d^{3} x}{8 e^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{3 d x^{3}}{8 \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} - \frac{e^{2} x^{5}}{4 d \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} & \text{otherwise} \end{cases}\right) + e^{3} \left(\begin{cases} - \frac{2 d^{4} \sqrt{d^{2} - e^{2} x^{2}}}{15 e^{4}} - \frac{d^{2} x^{2} \sqrt{d^{2} - e^{2} x^{2}}}{15 e^{2}} + \frac{x^{4} \sqrt{d^{2} - e^{2} x^{2}}}{5} & \text{for}\: e \neq 0 \\\frac{x^{4} \sqrt{d^{2}}}{4} & \text{otherwise} \end{cases}\right)"," ",0,"d**3*Piecewise((-I*d**2*acosh(e*x/d)/(2*e) - I*d*x/(2*sqrt(-1 + e**2*x**2/d**2)) + I*e**2*x**3/(2*d*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (d**2*asin(e*x/d)/(2*e) + d*x*sqrt(1 - e**2*x**2/d**2)/2, True)) - d**2*e*Piecewise((x**2*sqrt(d**2)/2, Eq(e**2, 0)), (-(d**2 - e**2*x**2)**(3/2)/(3*e**2), True)) - d*e**2*Piecewise((-I*d**4*acosh(e*x/d)/(8*e**3) + I*d**3*x/(8*e**2*sqrt(-1 + e**2*x**2/d**2)) - 3*I*d*x**3/(8*sqrt(-1 + e**2*x**2/d**2)) + I*e**2*x**5/(4*d*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (d**4*asin(e*x/d)/(8*e**3) - d**3*x/(8*e**2*sqrt(1 - e**2*x**2/d**2)) + 3*d*x**3/(8*sqrt(1 - e**2*x**2/d**2)) - e**2*x**5/(4*d*sqrt(1 - e**2*x**2/d**2)), True)) + e**3*Piecewise((-2*d**4*sqrt(d**2 - e**2*x**2)/(15*e**4) - d**2*x**2*sqrt(d**2 - e**2*x**2)/(15*e**2) + x**4*sqrt(d**2 - e**2*x**2)/5, Ne(e, 0)), (x**4*sqrt(d**2)/4, True))","C",0
108,1,469,0,25.648862," ","integrate((-e**2*x**2+d**2)**(5/2)/x/(e*x+d),x)","d^{3} \left(\begin{cases} \frac{d^{2}}{e x \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} - d \operatorname{acosh}{\left(\frac{d}{e x} \right)} - \frac{e x}{\sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\- \frac{i d^{2}}{e x \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} + i d \operatorname{asin}{\left(\frac{d}{e x} \right)} + \frac{i e x}{\sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} & \text{otherwise} \end{cases}\right) - d^{2} e \left(\begin{cases} - \frac{i d^{2} \operatorname{acosh}{\left(\frac{e x}{d} \right)}}{2 e} - \frac{i d x}{2 \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + \frac{i e^{2} x^{3}}{2 d \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{d^{2} \operatorname{asin}{\left(\frac{e x}{d} \right)}}{2 e} + \frac{d x \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}}{2} & \text{otherwise} \end{cases}\right) - d e^{2} \left(\begin{cases} \frac{x^{2} \sqrt{d^{2}}}{2} & \text{for}\: e^{2} = 0 \\- \frac{\left(d^{2} - e^{2} x^{2}\right)^{\frac{3}{2}}}{3 e^{2}} & \text{otherwise} \end{cases}\right) + e^{3} \left(\begin{cases} - \frac{i d^{4} \operatorname{acosh}{\left(\frac{e x}{d} \right)}}{8 e^{3}} + \frac{i d^{3} x}{8 e^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{3 i d x^{3}}{8 \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + \frac{i e^{2} x^{5}}{4 d \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{d^{4} \operatorname{asin}{\left(\frac{e x}{d} \right)}}{8 e^{3}} - \frac{d^{3} x}{8 e^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{3 d x^{3}}{8 \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} - \frac{e^{2} x^{5}}{4 d \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} & \text{otherwise} \end{cases}\right)"," ",0,"d**3*Piecewise((d**2/(e*x*sqrt(d**2/(e**2*x**2) - 1)) - d*acosh(d/(e*x)) - e*x/sqrt(d**2/(e**2*x**2) - 1), Abs(d**2/(e**2*x**2)) > 1), (-I*d**2/(e*x*sqrt(-d**2/(e**2*x**2) + 1)) + I*d*asin(d/(e*x)) + I*e*x/sqrt(-d**2/(e**2*x**2) + 1), True)) - d**2*e*Piecewise((-I*d**2*acosh(e*x/d)/(2*e) - I*d*x/(2*sqrt(-1 + e**2*x**2/d**2)) + I*e**2*x**3/(2*d*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (d**2*asin(e*x/d)/(2*e) + d*x*sqrt(1 - e**2*x**2/d**2)/2, True)) - d*e**2*Piecewise((x**2*sqrt(d**2)/2, Eq(e**2, 0)), (-(d**2 - e**2*x**2)**(3/2)/(3*e**2), True)) + e**3*Piecewise((-I*d**4*acosh(e*x/d)/(8*e**3) + I*d**3*x/(8*e**2*sqrt(-1 + e**2*x**2/d**2)) - 3*I*d*x**3/(8*sqrt(-1 + e**2*x**2/d**2)) + I*e**2*x**5/(4*d*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (d**4*asin(e*x/d)/(8*e**3) - d**3*x/(8*e**2*sqrt(1 - e**2*x**2/d**2)) + 3*d*x**3/(8*sqrt(1 - e**2*x**2/d**2)) - e**2*x**5/(4*d*sqrt(1 - e**2*x**2/d**2)), True))","C",0
109,1,386,0,10.204939," ","integrate((-e**2*x**2+d**2)**(5/2)/x**2/(e*x+d),x)","d^{3} \left(\begin{cases} \frac{i d}{x \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + i e \operatorname{acosh}{\left(\frac{e x}{d} \right)} - \frac{i e^{2} x}{d \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\- \frac{d}{x \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} - e \operatorname{asin}{\left(\frac{e x}{d} \right)} + \frac{e^{2} x}{d \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} & \text{otherwise} \end{cases}\right) - d^{2} e \left(\begin{cases} \frac{d^{2}}{e x \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} - d \operatorname{acosh}{\left(\frac{d}{e x} \right)} - \frac{e x}{\sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\- \frac{i d^{2}}{e x \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} + i d \operatorname{asin}{\left(\frac{d}{e x} \right)} + \frac{i e x}{\sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} & \text{otherwise} \end{cases}\right) - d e^{2} \left(\begin{cases} - \frac{i d^{2} \operatorname{acosh}{\left(\frac{e x}{d} \right)}}{2 e} - \frac{i d x}{2 \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + \frac{i e^{2} x^{3}}{2 d \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{d^{2} \operatorname{asin}{\left(\frac{e x}{d} \right)}}{2 e} + \frac{d x \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}}{2} & \text{otherwise} \end{cases}\right) + e^{3} \left(\begin{cases} \frac{x^{2} \sqrt{d^{2}}}{2} & \text{for}\: e^{2} = 0 \\- \frac{\left(d^{2} - e^{2} x^{2}\right)^{\frac{3}{2}}}{3 e^{2}} & \text{otherwise} \end{cases}\right)"," ",0,"d**3*Piecewise((I*d/(x*sqrt(-1 + e**2*x**2/d**2)) + I*e*acosh(e*x/d) - I*e**2*x/(d*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (-d/(x*sqrt(1 - e**2*x**2/d**2)) - e*asin(e*x/d) + e**2*x/(d*sqrt(1 - e**2*x**2/d**2)), True)) - d**2*e*Piecewise((d**2/(e*x*sqrt(d**2/(e**2*x**2) - 1)) - d*acosh(d/(e*x)) - e*x/sqrt(d**2/(e**2*x**2) - 1), Abs(d**2/(e**2*x**2)) > 1), (-I*d**2/(e*x*sqrt(-d**2/(e**2*x**2) + 1)) + I*d*asin(d/(e*x)) + I*e*x/sqrt(-d**2/(e**2*x**2) + 1), True)) - d*e**2*Piecewise((-I*d**2*acosh(e*x/d)/(2*e) - I*d*x/(2*sqrt(-1 + e**2*x**2/d**2)) + I*e**2*x**3/(2*d*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (d**2*asin(e*x/d)/(2*e) + d*x*sqrt(1 - e**2*x**2/d**2)/2, True)) + e**3*Piecewise((x**2*sqrt(d**2)/2, Eq(e**2, 0)), (-(d**2 - e**2*x**2)**(3/2)/(3*e**2), True))","C",0
110,1,461,0,13.347085," ","integrate((-e**2*x**2+d**2)**(5/2)/x**3/(e*x+d),x)","d^{3} \left(\begin{cases} - \frac{d^{2}}{2 e x^{3} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{e}{2 x \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{e^{2} \operatorname{acosh}{\left(\frac{d}{e x} \right)}}{2 d} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\- \frac{i e \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{2 x} - \frac{i e^{2} \operatorname{asin}{\left(\frac{d}{e x} \right)}}{2 d} & \text{otherwise} \end{cases}\right) - d^{2} e \left(\begin{cases} \frac{i d}{x \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + i e \operatorname{acosh}{\left(\frac{e x}{d} \right)} - \frac{i e^{2} x}{d \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\- \frac{d}{x \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} - e \operatorname{asin}{\left(\frac{e x}{d} \right)} + \frac{e^{2} x}{d \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} & \text{otherwise} \end{cases}\right) - d e^{2} \left(\begin{cases} \frac{d^{2}}{e x \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} - d \operatorname{acosh}{\left(\frac{d}{e x} \right)} - \frac{e x}{\sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\- \frac{i d^{2}}{e x \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} + i d \operatorname{asin}{\left(\frac{d}{e x} \right)} + \frac{i e x}{\sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} & \text{otherwise} \end{cases}\right) + e^{3} \left(\begin{cases} - \frac{i d^{2} \operatorname{acosh}{\left(\frac{e x}{d} \right)}}{2 e} - \frac{i d x}{2 \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + \frac{i e^{2} x^{3}}{2 d \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{d^{2} \operatorname{asin}{\left(\frac{e x}{d} \right)}}{2 e} + \frac{d x \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}}{2} & \text{otherwise} \end{cases}\right)"," ",0,"d**3*Piecewise((-d**2/(2*e*x**3*sqrt(d**2/(e**2*x**2) - 1)) + e/(2*x*sqrt(d**2/(e**2*x**2) - 1)) + e**2*acosh(d/(e*x))/(2*d), Abs(d**2/(e**2*x**2)) > 1), (-I*e*sqrt(-d**2/(e**2*x**2) + 1)/(2*x) - I*e**2*asin(d/(e*x))/(2*d), True)) - d**2*e*Piecewise((I*d/(x*sqrt(-1 + e**2*x**2/d**2)) + I*e*acosh(e*x/d) - I*e**2*x/(d*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (-d/(x*sqrt(1 - e**2*x**2/d**2)) - e*asin(e*x/d) + e**2*x/(d*sqrt(1 - e**2*x**2/d**2)), True)) - d*e**2*Piecewise((d**2/(e*x*sqrt(d**2/(e**2*x**2) - 1)) - d*acosh(d/(e*x)) - e*x/sqrt(d**2/(e**2*x**2) - 1), Abs(d**2/(e**2*x**2)) > 1), (-I*d**2/(e*x*sqrt(-d**2/(e**2*x**2) + 1)) + I*d*asin(d/(e*x)) + I*e*x/sqrt(-d**2/(e**2*x**2) + 1), True)) + e**3*Piecewise((-I*d**2*acosh(e*x/d)/(2*e) - I*d*x/(2*sqrt(-1 + e**2*x**2/d**2)) + I*e**2*x**3/(2*d*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (d**2*asin(e*x/d)/(2*e) + d*x*sqrt(1 - e**2*x**2/d**2)/2, True))","C",0
111,1,457,0,11.684167," ","integrate((-e**2*x**2+d**2)**(5/2)/x**4/(e*x+d),x)","d^{3} \left(\begin{cases} - \frac{e \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}}{3 x^{2}} + \frac{e^{3} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}}{3 d^{2}} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\- \frac{i e \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{3 x^{2}} + \frac{i e^{3} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{3 d^{2}} & \text{otherwise} \end{cases}\right) - d^{2} e \left(\begin{cases} - \frac{d^{2}}{2 e x^{3} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{e}{2 x \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{e^{2} \operatorname{acosh}{\left(\frac{d}{e x} \right)}}{2 d} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\- \frac{i e \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{2 x} - \frac{i e^{2} \operatorname{asin}{\left(\frac{d}{e x} \right)}}{2 d} & \text{otherwise} \end{cases}\right) - d e^{2} \left(\begin{cases} \frac{i d}{x \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + i e \operatorname{acosh}{\left(\frac{e x}{d} \right)} - \frac{i e^{2} x}{d \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\- \frac{d}{x \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} - e \operatorname{asin}{\left(\frac{e x}{d} \right)} + \frac{e^{2} x}{d \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} & \text{otherwise} \end{cases}\right) + e^{3} \left(\begin{cases} \frac{d^{2}}{e x \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} - d \operatorname{acosh}{\left(\frac{d}{e x} \right)} - \frac{e x}{\sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\- \frac{i d^{2}}{e x \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} + i d \operatorname{asin}{\left(\frac{d}{e x} \right)} + \frac{i e x}{\sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} & \text{otherwise} \end{cases}\right)"," ",0,"d**3*Piecewise((-e*sqrt(d**2/(e**2*x**2) - 1)/(3*x**2) + e**3*sqrt(d**2/(e**2*x**2) - 1)/(3*d**2), Abs(d**2/(e**2*x**2)) > 1), (-I*e*sqrt(-d**2/(e**2*x**2) + 1)/(3*x**2) + I*e**3*sqrt(-d**2/(e**2*x**2) + 1)/(3*d**2), True)) - d**2*e*Piecewise((-d**2/(2*e*x**3*sqrt(d**2/(e**2*x**2) - 1)) + e/(2*x*sqrt(d**2/(e**2*x**2) - 1)) + e**2*acosh(d/(e*x))/(2*d), Abs(d**2/(e**2*x**2)) > 1), (-I*e*sqrt(-d**2/(e**2*x**2) + 1)/(2*x) - I*e**2*asin(d/(e*x))/(2*d), True)) - d*e**2*Piecewise((I*d/(x*sqrt(-1 + e**2*x**2/d**2)) + I*e*acosh(e*x/d) - I*e**2*x/(d*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (-d/(x*sqrt(1 - e**2*x**2/d**2)) - e*asin(e*x/d) + e**2*x/(d*sqrt(1 - e**2*x**2/d**2)), True)) + e**3*Piecewise((d**2/(e*x*sqrt(d**2/(e**2*x**2) - 1)) - d*acosh(d/(e*x)) - e*x/sqrt(d**2/(e**2*x**2) - 1), Abs(d**2/(e**2*x**2)) > 1), (-I*d**2/(e*x*sqrt(-d**2/(e**2*x**2) + 1)) + I*d*asin(d/(e*x)) + I*e*x/sqrt(-d**2/(e**2*x**2) + 1), True))","C",0
112,1,541,0,14.371476," ","integrate((-e**2*x**2+d**2)**(5/2)/x**5/(e*x+d),x)","d^{3} \left(\begin{cases} - \frac{d^{2}}{4 e x^{5} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{3 e}{8 x^{3} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} - \frac{e^{3}}{8 d^{2} x \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{e^{4} \operatorname{acosh}{\left(\frac{d}{e x} \right)}}{8 d^{3}} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\\frac{i d^{2}}{4 e x^{5} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} - \frac{3 i e}{8 x^{3} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} + \frac{i e^{3}}{8 d^{2} x \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} - \frac{i e^{4} \operatorname{asin}{\left(\frac{d}{e x} \right)}}{8 d^{3}} & \text{otherwise} \end{cases}\right) - d^{2} e \left(\begin{cases} - \frac{e \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}}{3 x^{2}} + \frac{e^{3} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}}{3 d^{2}} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\- \frac{i e \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{3 x^{2}} + \frac{i e^{3} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{3 d^{2}} & \text{otherwise} \end{cases}\right) - d e^{2} \left(\begin{cases} - \frac{d^{2}}{2 e x^{3} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{e}{2 x \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{e^{2} \operatorname{acosh}{\left(\frac{d}{e x} \right)}}{2 d} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\- \frac{i e \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{2 x} - \frac{i e^{2} \operatorname{asin}{\left(\frac{d}{e x} \right)}}{2 d} & \text{otherwise} \end{cases}\right) + e^{3} \left(\begin{cases} \frac{i d}{x \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + i e \operatorname{acosh}{\left(\frac{e x}{d} \right)} - \frac{i e^{2} x}{d \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\- \frac{d}{x \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} - e \operatorname{asin}{\left(\frac{e x}{d} \right)} + \frac{e^{2} x}{d \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} & \text{otherwise} \end{cases}\right)"," ",0,"d**3*Piecewise((-d**2/(4*e*x**5*sqrt(d**2/(e**2*x**2) - 1)) + 3*e/(8*x**3*sqrt(d**2/(e**2*x**2) - 1)) - e**3/(8*d**2*x*sqrt(d**2/(e**2*x**2) - 1)) + e**4*acosh(d/(e*x))/(8*d**3), Abs(d**2/(e**2*x**2)) > 1), (I*d**2/(4*e*x**5*sqrt(-d**2/(e**2*x**2) + 1)) - 3*I*e/(8*x**3*sqrt(-d**2/(e**2*x**2) + 1)) + I*e**3/(8*d**2*x*sqrt(-d**2/(e**2*x**2) + 1)) - I*e**4*asin(d/(e*x))/(8*d**3), True)) - d**2*e*Piecewise((-e*sqrt(d**2/(e**2*x**2) - 1)/(3*x**2) + e**3*sqrt(d**2/(e**2*x**2) - 1)/(3*d**2), Abs(d**2/(e**2*x**2)) > 1), (-I*e*sqrt(-d**2/(e**2*x**2) + 1)/(3*x**2) + I*e**3*sqrt(-d**2/(e**2*x**2) + 1)/(3*d**2), True)) - d*e**2*Piecewise((-d**2/(2*e*x**3*sqrt(d**2/(e**2*x**2) - 1)) + e/(2*x*sqrt(d**2/(e**2*x**2) - 1)) + e**2*acosh(d/(e*x))/(2*d), Abs(d**2/(e**2*x**2)) > 1), (-I*e*sqrt(-d**2/(e**2*x**2) + 1)/(2*x) - I*e**2*asin(d/(e*x))/(2*d), True)) + e**3*Piecewise((I*d/(x*sqrt(-1 + e**2*x**2/d**2)) + I*e*acosh(e*x/d) - I*e**2*x/(d*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (-d/(x*sqrt(1 - e**2*x**2/d**2)) - e*asin(e*x/d) + e**2*x/(d*sqrt(1 - e**2*x**2/d**2)), True))","C",0
113,1,774,0,13.938643," ","integrate((-e**2*x**2+d**2)**(5/2)/x**6/(e*x+d),x)","d^{3} \left(\begin{cases} \frac{3 i d^{3} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{2} x^{5} + 15 e^{2} x^{7}} - \frac{4 i d e^{2} x^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{2} x^{5} + 15 e^{2} x^{7}} + \frac{2 i e^{6} x^{6} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{5} x^{5} + 15 d^{3} e^{2} x^{7}} - \frac{i e^{4} x^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{3} x^{5} + 15 d e^{2} x^{7}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{3 d^{3} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{2} x^{5} + 15 e^{2} x^{7}} - \frac{4 d e^{2} x^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{2} x^{5} + 15 e^{2} x^{7}} + \frac{2 e^{6} x^{6} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{5} x^{5} + 15 d^{3} e^{2} x^{7}} - \frac{e^{4} x^{4} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{3} x^{5} + 15 d e^{2} x^{7}} & \text{otherwise} \end{cases}\right) - d^{2} e \left(\begin{cases} - \frac{d^{2}}{4 e x^{5} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{3 e}{8 x^{3} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} - \frac{e^{3}}{8 d^{2} x \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{e^{4} \operatorname{acosh}{\left(\frac{d}{e x} \right)}}{8 d^{3}} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\\frac{i d^{2}}{4 e x^{5} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} - \frac{3 i e}{8 x^{3} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} + \frac{i e^{3}}{8 d^{2} x \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} - \frac{i e^{4} \operatorname{asin}{\left(\frac{d}{e x} \right)}}{8 d^{3}} & \text{otherwise} \end{cases}\right) - d e^{2} \left(\begin{cases} - \frac{e \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}}{3 x^{2}} + \frac{e^{3} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}}{3 d^{2}} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\- \frac{i e \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{3 x^{2}} + \frac{i e^{3} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{3 d^{2}} & \text{otherwise} \end{cases}\right) + e^{3} \left(\begin{cases} - \frac{d^{2}}{2 e x^{3} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{e}{2 x \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{e^{2} \operatorname{acosh}{\left(\frac{d}{e x} \right)}}{2 d} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\- \frac{i e \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{2 x} - \frac{i e^{2} \operatorname{asin}{\left(\frac{d}{e x} \right)}}{2 d} & \text{otherwise} \end{cases}\right)"," ",0,"d**3*Piecewise((3*I*d**3*sqrt(-1 + e**2*x**2/d**2)/(-15*d**2*x**5 + 15*e**2*x**7) - 4*I*d*e**2*x**2*sqrt(-1 + e**2*x**2/d**2)/(-15*d**2*x**5 + 15*e**2*x**7) + 2*I*e**6*x**6*sqrt(-1 + e**2*x**2/d**2)/(-15*d**5*x**5 + 15*d**3*e**2*x**7) - I*e**4*x**4*sqrt(-1 + e**2*x**2/d**2)/(-15*d**3*x**5 + 15*d*e**2*x**7), Abs(e**2*x**2/d**2) > 1), (3*d**3*sqrt(1 - e**2*x**2/d**2)/(-15*d**2*x**5 + 15*e**2*x**7) - 4*d*e**2*x**2*sqrt(1 - e**2*x**2/d**2)/(-15*d**2*x**5 + 15*e**2*x**7) + 2*e**6*x**6*sqrt(1 - e**2*x**2/d**2)/(-15*d**5*x**5 + 15*d**3*e**2*x**7) - e**4*x**4*sqrt(1 - e**2*x**2/d**2)/(-15*d**3*x**5 + 15*d*e**2*x**7), True)) - d**2*e*Piecewise((-d**2/(4*e*x**5*sqrt(d**2/(e**2*x**2) - 1)) + 3*e/(8*x**3*sqrt(d**2/(e**2*x**2) - 1)) - e**3/(8*d**2*x*sqrt(d**2/(e**2*x**2) - 1)) + e**4*acosh(d/(e*x))/(8*d**3), Abs(d**2/(e**2*x**2)) > 1), (I*d**2/(4*e*x**5*sqrt(-d**2/(e**2*x**2) + 1)) - 3*I*e/(8*x**3*sqrt(-d**2/(e**2*x**2) + 1)) + I*e**3/(8*d**2*x*sqrt(-d**2/(e**2*x**2) + 1)) - I*e**4*asin(d/(e*x))/(8*d**3), True)) - d*e**2*Piecewise((-e*sqrt(d**2/(e**2*x**2) - 1)/(3*x**2) + e**3*sqrt(d**2/(e**2*x**2) - 1)/(3*d**2), Abs(d**2/(e**2*x**2)) > 1), (-I*e*sqrt(-d**2/(e**2*x**2) + 1)/(3*x**2) + I*e**3*sqrt(-d**2/(e**2*x**2) + 1)/(3*d**2), True)) + e**3*Piecewise((-d**2/(2*e*x**3*sqrt(d**2/(e**2*x**2) - 1)) + e/(2*x*sqrt(d**2/(e**2*x**2) - 1)) + e**2*acosh(d/(e*x))/(2*d), Abs(d**2/(e**2*x**2)) > 1), (-I*e*sqrt(-d**2/(e**2*x**2) + 1)/(2*x) - I*e**2*asin(d/(e*x))/(2*d), True))","C",0
114,1,918,0,18.691279," ","integrate((-e**2*x**2+d**2)**(5/2)/x**7/(e*x+d),x)","d^{3} \left(\begin{cases} - \frac{d^{2}}{6 e x^{7} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{5 e}{24 x^{5} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{e^{3}}{48 d^{2} x^{3} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} - \frac{e^{5}}{16 d^{4} x \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{e^{6} \operatorname{acosh}{\left(\frac{d}{e x} \right)}}{16 d^{5}} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\\frac{i d^{2}}{6 e x^{7} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} - \frac{5 i e}{24 x^{5} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} - \frac{i e^{3}}{48 d^{2} x^{3} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} + \frac{i e^{5}}{16 d^{4} x \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} - \frac{i e^{6} \operatorname{asin}{\left(\frac{d}{e x} \right)}}{16 d^{5}} & \text{otherwise} \end{cases}\right) - d^{2} e \left(\begin{cases} \frac{3 i d^{3} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{2} x^{5} + 15 e^{2} x^{7}} - \frac{4 i d e^{2} x^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{2} x^{5} + 15 e^{2} x^{7}} + \frac{2 i e^{6} x^{6} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{5} x^{5} + 15 d^{3} e^{2} x^{7}} - \frac{i e^{4} x^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{3} x^{5} + 15 d e^{2} x^{7}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{3 d^{3} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{2} x^{5} + 15 e^{2} x^{7}} - \frac{4 d e^{2} x^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{2} x^{5} + 15 e^{2} x^{7}} + \frac{2 e^{6} x^{6} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{5} x^{5} + 15 d^{3} e^{2} x^{7}} - \frac{e^{4} x^{4} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{3} x^{5} + 15 d e^{2} x^{7}} & \text{otherwise} \end{cases}\right) - d e^{2} \left(\begin{cases} - \frac{d^{2}}{4 e x^{5} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{3 e}{8 x^{3} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} - \frac{e^{3}}{8 d^{2} x \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{e^{4} \operatorname{acosh}{\left(\frac{d}{e x} \right)}}{8 d^{3}} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\\frac{i d^{2}}{4 e x^{5} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} - \frac{3 i e}{8 x^{3} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} + \frac{i e^{3}}{8 d^{2} x \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} - \frac{i e^{4} \operatorname{asin}{\left(\frac{d}{e x} \right)}}{8 d^{3}} & \text{otherwise} \end{cases}\right) + e^{3} \left(\begin{cases} - \frac{e \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}}{3 x^{2}} + \frac{e^{3} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}}{3 d^{2}} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\- \frac{i e \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{3 x^{2}} + \frac{i e^{3} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{3 d^{2}} & \text{otherwise} \end{cases}\right)"," ",0,"d**3*Piecewise((-d**2/(6*e*x**7*sqrt(d**2/(e**2*x**2) - 1)) + 5*e/(24*x**5*sqrt(d**2/(e**2*x**2) - 1)) + e**3/(48*d**2*x**3*sqrt(d**2/(e**2*x**2) - 1)) - e**5/(16*d**4*x*sqrt(d**2/(e**2*x**2) - 1)) + e**6*acosh(d/(e*x))/(16*d**5), Abs(d**2/(e**2*x**2)) > 1), (I*d**2/(6*e*x**7*sqrt(-d**2/(e**2*x**2) + 1)) - 5*I*e/(24*x**5*sqrt(-d**2/(e**2*x**2) + 1)) - I*e**3/(48*d**2*x**3*sqrt(-d**2/(e**2*x**2) + 1)) + I*e**5/(16*d**4*x*sqrt(-d**2/(e**2*x**2) + 1)) - I*e**6*asin(d/(e*x))/(16*d**5), True)) - d**2*e*Piecewise((3*I*d**3*sqrt(-1 + e**2*x**2/d**2)/(-15*d**2*x**5 + 15*e**2*x**7) - 4*I*d*e**2*x**2*sqrt(-1 + e**2*x**2/d**2)/(-15*d**2*x**5 + 15*e**2*x**7) + 2*I*e**6*x**6*sqrt(-1 + e**2*x**2/d**2)/(-15*d**5*x**5 + 15*d**3*e**2*x**7) - I*e**4*x**4*sqrt(-1 + e**2*x**2/d**2)/(-15*d**3*x**5 + 15*d*e**2*x**7), Abs(e**2*x**2/d**2) > 1), (3*d**3*sqrt(1 - e**2*x**2/d**2)/(-15*d**2*x**5 + 15*e**2*x**7) - 4*d*e**2*x**2*sqrt(1 - e**2*x**2/d**2)/(-15*d**2*x**5 + 15*e**2*x**7) + 2*e**6*x**6*sqrt(1 - e**2*x**2/d**2)/(-15*d**5*x**5 + 15*d**3*e**2*x**7) - e**4*x**4*sqrt(1 - e**2*x**2/d**2)/(-15*d**3*x**5 + 15*d*e**2*x**7), True)) - d*e**2*Piecewise((-d**2/(4*e*x**5*sqrt(d**2/(e**2*x**2) - 1)) + 3*e/(8*x**3*sqrt(d**2/(e**2*x**2) - 1)) - e**3/(8*d**2*x*sqrt(d**2/(e**2*x**2) - 1)) + e**4*acosh(d/(e*x))/(8*d**3), Abs(d**2/(e**2*x**2)) > 1), (I*d**2/(4*e*x**5*sqrt(-d**2/(e**2*x**2) + 1)) - 3*I*e/(8*x**3*sqrt(-d**2/(e**2*x**2) + 1)) + I*e**3/(8*d**2*x*sqrt(-d**2/(e**2*x**2) + 1)) - I*e**4*asin(d/(e*x))/(8*d**3), True)) + e**3*Piecewise((-e*sqrt(d**2/(e**2*x**2) - 1)/(3*x**2) + e**3*sqrt(d**2/(e**2*x**2) - 1)/(3*d**2), Abs(d**2/(e**2*x**2)) > 1), (-I*e*sqrt(-d**2/(e**2*x**2) + 1)/(3*x**2) + I*e**3*sqrt(-d**2/(e**2*x**2) + 1)/(3*d**2), True))","C",0
115,1,1037,0,18.790294," ","integrate((-e**2*x**2+d**2)**(5/2)/x**8/(e*x+d),x)","d^{3} \left(\begin{cases} - \frac{e \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}}{7 x^{6}} + \frac{e^{3} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}}{35 d^{2} x^{4}} + \frac{4 e^{5} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}}{105 d^{4} x^{2}} + \frac{8 e^{7} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}}{105 d^{6}} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\- \frac{i e \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{7 x^{6}} + \frac{i e^{3} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{35 d^{2} x^{4}} + \frac{4 i e^{5} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{105 d^{4} x^{2}} + \frac{8 i e^{7} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{105 d^{6}} & \text{otherwise} \end{cases}\right) - d^{2} e \left(\begin{cases} - \frac{d^{2}}{6 e x^{7} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{5 e}{24 x^{5} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{e^{3}}{48 d^{2} x^{3} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} - \frac{e^{5}}{16 d^{4} x \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{e^{6} \operatorname{acosh}{\left(\frac{d}{e x} \right)}}{16 d^{5}} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\\frac{i d^{2}}{6 e x^{7} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} - \frac{5 i e}{24 x^{5} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} - \frac{i e^{3}}{48 d^{2} x^{3} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} + \frac{i e^{5}}{16 d^{4} x \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} - \frac{i e^{6} \operatorname{asin}{\left(\frac{d}{e x} \right)}}{16 d^{5}} & \text{otherwise} \end{cases}\right) - d e^{2} \left(\begin{cases} \frac{3 i d^{3} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{2} x^{5} + 15 e^{2} x^{7}} - \frac{4 i d e^{2} x^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{2} x^{5} + 15 e^{2} x^{7}} + \frac{2 i e^{6} x^{6} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{5} x^{5} + 15 d^{3} e^{2} x^{7}} - \frac{i e^{4} x^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{3} x^{5} + 15 d e^{2} x^{7}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{3 d^{3} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{2} x^{5} + 15 e^{2} x^{7}} - \frac{4 d e^{2} x^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{2} x^{5} + 15 e^{2} x^{7}} + \frac{2 e^{6} x^{6} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{5} x^{5} + 15 d^{3} e^{2} x^{7}} - \frac{e^{4} x^{4} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{3} x^{5} + 15 d e^{2} x^{7}} & \text{otherwise} \end{cases}\right) + e^{3} \left(\begin{cases} - \frac{d^{2}}{4 e x^{5} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{3 e}{8 x^{3} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} - \frac{e^{3}}{8 d^{2} x \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{e^{4} \operatorname{acosh}{\left(\frac{d}{e x} \right)}}{8 d^{3}} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\\frac{i d^{2}}{4 e x^{5} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} - \frac{3 i e}{8 x^{3} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} + \frac{i e^{3}}{8 d^{2} x \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} - \frac{i e^{4} \operatorname{asin}{\left(\frac{d}{e x} \right)}}{8 d^{3}} & \text{otherwise} \end{cases}\right)"," ",0,"d**3*Piecewise((-e*sqrt(d**2/(e**2*x**2) - 1)/(7*x**6) + e**3*sqrt(d**2/(e**2*x**2) - 1)/(35*d**2*x**4) + 4*e**5*sqrt(d**2/(e**2*x**2) - 1)/(105*d**4*x**2) + 8*e**7*sqrt(d**2/(e**2*x**2) - 1)/(105*d**6), Abs(d**2/(e**2*x**2)) > 1), (-I*e*sqrt(-d**2/(e**2*x**2) + 1)/(7*x**6) + I*e**3*sqrt(-d**2/(e**2*x**2) + 1)/(35*d**2*x**4) + 4*I*e**5*sqrt(-d**2/(e**2*x**2) + 1)/(105*d**4*x**2) + 8*I*e**7*sqrt(-d**2/(e**2*x**2) + 1)/(105*d**6), True)) - d**2*e*Piecewise((-d**2/(6*e*x**7*sqrt(d**2/(e**2*x**2) - 1)) + 5*e/(24*x**5*sqrt(d**2/(e**2*x**2) - 1)) + e**3/(48*d**2*x**3*sqrt(d**2/(e**2*x**2) - 1)) - e**5/(16*d**4*x*sqrt(d**2/(e**2*x**2) - 1)) + e**6*acosh(d/(e*x))/(16*d**5), Abs(d**2/(e**2*x**2)) > 1), (I*d**2/(6*e*x**7*sqrt(-d**2/(e**2*x**2) + 1)) - 5*I*e/(24*x**5*sqrt(-d**2/(e**2*x**2) + 1)) - I*e**3/(48*d**2*x**3*sqrt(-d**2/(e**2*x**2) + 1)) + I*e**5/(16*d**4*x*sqrt(-d**2/(e**2*x**2) + 1)) - I*e**6*asin(d/(e*x))/(16*d**5), True)) - d*e**2*Piecewise((3*I*d**3*sqrt(-1 + e**2*x**2/d**2)/(-15*d**2*x**5 + 15*e**2*x**7) - 4*I*d*e**2*x**2*sqrt(-1 + e**2*x**2/d**2)/(-15*d**2*x**5 + 15*e**2*x**7) + 2*I*e**6*x**6*sqrt(-1 + e**2*x**2/d**2)/(-15*d**5*x**5 + 15*d**3*e**2*x**7) - I*e**4*x**4*sqrt(-1 + e**2*x**2/d**2)/(-15*d**3*x**5 + 15*d*e**2*x**7), Abs(e**2*x**2/d**2) > 1), (3*d**3*sqrt(1 - e**2*x**2/d**2)/(-15*d**2*x**5 + 15*e**2*x**7) - 4*d*e**2*x**2*sqrt(1 - e**2*x**2/d**2)/(-15*d**2*x**5 + 15*e**2*x**7) + 2*e**6*x**6*sqrt(1 - e**2*x**2/d**2)/(-15*d**5*x**5 + 15*d**3*e**2*x**7) - e**4*x**4*sqrt(1 - e**2*x**2/d**2)/(-15*d**3*x**5 + 15*d*e**2*x**7), True)) + e**3*Piecewise((-d**2/(4*e*x**5*sqrt(d**2/(e**2*x**2) - 1)) + 3*e/(8*x**3*sqrt(d**2/(e**2*x**2) - 1)) - e**3/(8*d**2*x*sqrt(d**2/(e**2*x**2) - 1)) + e**4*acosh(d/(e*x))/(8*d**3), Abs(d**2/(e**2*x**2)) > 1), (I*d**2/(4*e*x**5*sqrt(-d**2/(e**2*x**2) + 1)) - 3*I*e/(8*x**3*sqrt(-d**2/(e**2*x**2) + 1)) + I*e**3/(8*d**2*x*sqrt(-d**2/(e**2*x**2) + 1)) - I*e**4*asin(d/(e*x))/(8*d**3), True))","C",0
116,1,1159,0,27.711627," ","integrate((-e**2*x**2+d**2)**(5/2)/x**9/(e*x+d),x)","d^{3} \left(\begin{cases} - \frac{d^{2}}{8 e x^{9} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{7 e}{48 x^{7} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{e^{3}}{192 d^{2} x^{5} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{5 e^{5}}{384 d^{4} x^{3} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} - \frac{5 e^{7}}{128 d^{6} x \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{5 e^{8} \operatorname{acosh}{\left(\frac{d}{e x} \right)}}{128 d^{7}} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\\frac{i d^{2}}{8 e x^{9} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} - \frac{7 i e}{48 x^{7} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} - \frac{i e^{3}}{192 d^{2} x^{5} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} - \frac{5 i e^{5}}{384 d^{4} x^{3} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} + \frac{5 i e^{7}}{128 d^{6} x \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} - \frac{5 i e^{8} \operatorname{asin}{\left(\frac{d}{e x} \right)}}{128 d^{7}} & \text{otherwise} \end{cases}\right) - d^{2} e \left(\begin{cases} - \frac{e \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}}{7 x^{6}} + \frac{e^{3} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}}{35 d^{2} x^{4}} + \frac{4 e^{5} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}}{105 d^{4} x^{2}} + \frac{8 e^{7} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}}{105 d^{6}} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\- \frac{i e \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{7 x^{6}} + \frac{i e^{3} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{35 d^{2} x^{4}} + \frac{4 i e^{5} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{105 d^{4} x^{2}} + \frac{8 i e^{7} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{105 d^{6}} & \text{otherwise} \end{cases}\right) - d e^{2} \left(\begin{cases} - \frac{d^{2}}{6 e x^{7} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{5 e}{24 x^{5} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{e^{3}}{48 d^{2} x^{3} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} - \frac{e^{5}}{16 d^{4} x \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{e^{6} \operatorname{acosh}{\left(\frac{d}{e x} \right)}}{16 d^{5}} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\\frac{i d^{2}}{6 e x^{7} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} - \frac{5 i e}{24 x^{5} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} - \frac{i e^{3}}{48 d^{2} x^{3} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} + \frac{i e^{5}}{16 d^{4} x \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} - \frac{i e^{6} \operatorname{asin}{\left(\frac{d}{e x} \right)}}{16 d^{5}} & \text{otherwise} \end{cases}\right) + e^{3} \left(\begin{cases} \frac{3 i d^{3} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{2} x^{5} + 15 e^{2} x^{7}} - \frac{4 i d e^{2} x^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{2} x^{5} + 15 e^{2} x^{7}} + \frac{2 i e^{6} x^{6} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{5} x^{5} + 15 d^{3} e^{2} x^{7}} - \frac{i e^{4} x^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{3} x^{5} + 15 d e^{2} x^{7}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{3 d^{3} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{2} x^{5} + 15 e^{2} x^{7}} - \frac{4 d e^{2} x^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{2} x^{5} + 15 e^{2} x^{7}} + \frac{2 e^{6} x^{6} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{5} x^{5} + 15 d^{3} e^{2} x^{7}} - \frac{e^{4} x^{4} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{3} x^{5} + 15 d e^{2} x^{7}} & \text{otherwise} \end{cases}\right)"," ",0,"d**3*Piecewise((-d**2/(8*e*x**9*sqrt(d**2/(e**2*x**2) - 1)) + 7*e/(48*x**7*sqrt(d**2/(e**2*x**2) - 1)) + e**3/(192*d**2*x**5*sqrt(d**2/(e**2*x**2) - 1)) + 5*e**5/(384*d**4*x**3*sqrt(d**2/(e**2*x**2) - 1)) - 5*e**7/(128*d**6*x*sqrt(d**2/(e**2*x**2) - 1)) + 5*e**8*acosh(d/(e*x))/(128*d**7), Abs(d**2/(e**2*x**2)) > 1), (I*d**2/(8*e*x**9*sqrt(-d**2/(e**2*x**2) + 1)) - 7*I*e/(48*x**7*sqrt(-d**2/(e**2*x**2) + 1)) - I*e**3/(192*d**2*x**5*sqrt(-d**2/(e**2*x**2) + 1)) - 5*I*e**5/(384*d**4*x**3*sqrt(-d**2/(e**2*x**2) + 1)) + 5*I*e**7/(128*d**6*x*sqrt(-d**2/(e**2*x**2) + 1)) - 5*I*e**8*asin(d/(e*x))/(128*d**7), True)) - d**2*e*Piecewise((-e*sqrt(d**2/(e**2*x**2) - 1)/(7*x**6) + e**3*sqrt(d**2/(e**2*x**2) - 1)/(35*d**2*x**4) + 4*e**5*sqrt(d**2/(e**2*x**2) - 1)/(105*d**4*x**2) + 8*e**7*sqrt(d**2/(e**2*x**2) - 1)/(105*d**6), Abs(d**2/(e**2*x**2)) > 1), (-I*e*sqrt(-d**2/(e**2*x**2) + 1)/(7*x**6) + I*e**3*sqrt(-d**2/(e**2*x**2) + 1)/(35*d**2*x**4) + 4*I*e**5*sqrt(-d**2/(e**2*x**2) + 1)/(105*d**4*x**2) + 8*I*e**7*sqrt(-d**2/(e**2*x**2) + 1)/(105*d**6), True)) - d*e**2*Piecewise((-d**2/(6*e*x**7*sqrt(d**2/(e**2*x**2) - 1)) + 5*e/(24*x**5*sqrt(d**2/(e**2*x**2) - 1)) + e**3/(48*d**2*x**3*sqrt(d**2/(e**2*x**2) - 1)) - e**5/(16*d**4*x*sqrt(d**2/(e**2*x**2) - 1)) + e**6*acosh(d/(e*x))/(16*d**5), Abs(d**2/(e**2*x**2)) > 1), (I*d**2/(6*e*x**7*sqrt(-d**2/(e**2*x**2) + 1)) - 5*I*e/(24*x**5*sqrt(-d**2/(e**2*x**2) + 1)) - I*e**3/(48*d**2*x**3*sqrt(-d**2/(e**2*x**2) + 1)) + I*e**5/(16*d**4*x*sqrt(-d**2/(e**2*x**2) + 1)) - I*e**6*asin(d/(e*x))/(16*d**5), True)) + e**3*Piecewise((3*I*d**3*sqrt(-1 + e**2*x**2/d**2)/(-15*d**2*x**5 + 15*e**2*x**7) - 4*I*d*e**2*x**2*sqrt(-1 + e**2*x**2/d**2)/(-15*d**2*x**5 + 15*e**2*x**7) + 2*I*e**6*x**6*sqrt(-1 + e**2*x**2/d**2)/(-15*d**5*x**5 + 15*d**3*e**2*x**7) - I*e**4*x**4*sqrt(-1 + e**2*x**2/d**2)/(-15*d**3*x**5 + 15*d*e**2*x**7), Abs(e**2*x**2/d**2) > 1), (3*d**3*sqrt(1 - e**2*x**2/d**2)/(-15*d**2*x**5 + 15*e**2*x**7) - 4*d*e**2*x**2*sqrt(1 - e**2*x**2/d**2)/(-15*d**2*x**5 + 15*e**2*x**7) + 2*e**6*x**6*sqrt(1 - e**2*x**2/d**2)/(-15*d**5*x**5 + 15*d**3*e**2*x**7) - e**4*x**4*sqrt(1 - e**2*x**2/d**2)/(-15*d**3*x**5 + 15*d*e**2*x**7), True))","C",0
117,1,29,0,3.350411," ","integrate(x*(-x**2+1)**(1/2)/(1+x),x)","\begin{cases} \frac{x \sqrt{1 - x^{2}}}{2} - \sqrt{1 - x^{2}} - \frac{\operatorname{asin}{\left(x \right)}}{2} & \text{for}\: x > -1 \wedge x < 1 \end{cases}"," ",0,"Piecewise((x*sqrt(1 - x**2)/2 - sqrt(1 - x**2) - asin(x)/2, (x > -1) & (x < 1)))","A",0
118,1,170,0,6.532725," ","integrate((-a**2*x**2+1)**(3/2)/x**2/(-a*x+1),x)","a \left(\begin{cases} i \sqrt{a^{2} x^{2} - 1} - \log{\left(a x \right)} + \frac{\log{\left(a^{2} x^{2} \right)}}{2} + i \operatorname{asin}{\left(\frac{1}{a x} \right)} & \text{for}\: \left|{a^{2} x^{2}}\right| > 1 \\\sqrt{- a^{2} x^{2} + 1} + \frac{\log{\left(a^{2} x^{2} \right)}}{2} - \log{\left(\sqrt{- a^{2} x^{2} + 1} + 1 \right)} & \text{otherwise} \end{cases}\right) + \begin{cases} - \frac{i a^{2} x}{\sqrt{a^{2} x^{2} - 1}} + i a \operatorname{acosh}{\left(a x \right)} + \frac{i}{x \sqrt{a^{2} x^{2} - 1}} & \text{for}\: \left|{a^{2} x^{2}}\right| > 1 \\\frac{a^{2} x}{\sqrt{- a^{2} x^{2} + 1}} - a \operatorname{asin}{\left(a x \right)} - \frac{1}{x \sqrt{- a^{2} x^{2} + 1}} & \text{otherwise} \end{cases}"," ",0,"a*Piecewise((I*sqrt(a**2*x**2 - 1) - log(a*x) + log(a**2*x**2)/2 + I*asin(1/(a*x)), Abs(a**2*x**2) > 1), (sqrt(-a**2*x**2 + 1) + log(a**2*x**2)/2 - log(sqrt(-a**2*x**2 + 1) + 1), True)) + Piecewise((-I*a**2*x/sqrt(a**2*x**2 - 1) + I*a*acosh(a*x) + I/(x*sqrt(a**2*x**2 - 1)), Abs(a**2*x**2) > 1), (a**2*x/sqrt(-a**2*x**2 + 1) - a*asin(a*x) - 1/(x*sqrt(-a**2*x**2 + 1)), True))","C",0
119,0,0,0,0.000000," ","integrate(x**4/(e*x+d)/(-e**2*x**2+d**2)**(1/2),x)","\int \frac{x^{4}}{\sqrt{- \left(- d + e x\right) \left(d + e x\right)} \left(d + e x\right)}\, dx"," ",0,"Integral(x**4/(sqrt(-(-d + e*x)*(d + e*x))*(d + e*x)), x)","F",0
120,0,0,0,0.000000," ","integrate(x**3/(e*x+d)/(-e**2*x**2+d**2)**(1/2),x)","\int \frac{x^{3}}{\sqrt{- \left(- d + e x\right) \left(d + e x\right)} \left(d + e x\right)}\, dx"," ",0,"Integral(x**3/(sqrt(-(-d + e*x)*(d + e*x))*(d + e*x)), x)","F",0
121,0,0,0,0.000000," ","integrate(x**2/(e*x+d)/(-e**2*x**2+d**2)**(1/2),x)","\int \frac{x^{2}}{\sqrt{- \left(- d + e x\right) \left(d + e x\right)} \left(d + e x\right)}\, dx"," ",0,"Integral(x**2/(sqrt(-(-d + e*x)*(d + e*x))*(d + e*x)), x)","F",0
122,0,0,0,0.000000," ","integrate(x/(e*x+d)/(-e**2*x**2+d**2)**(1/2),x)","\int \frac{x}{\sqrt{- \left(- d + e x\right) \left(d + e x\right)} \left(d + e x\right)}\, dx"," ",0,"Integral(x/(sqrt(-(-d + e*x)*(d + e*x))*(d + e*x)), x)","F",0
123,0,0,0,0.000000," ","integrate(1/(e*x+d)/(-e**2*x**2+d**2)**(1/2),x)","\int \frac{1}{\sqrt{- \left(- d + e x\right) \left(d + e x\right)} \left(d + e x\right)}\, dx"," ",0,"Integral(1/(sqrt(-(-d + e*x)*(d + e*x))*(d + e*x)), x)","F",0
124,0,0,0,0.000000," ","integrate(1/x/(e*x+d)/(-e**2*x**2+d**2)**(1/2),x)","\int \frac{1}{x \sqrt{- \left(- d + e x\right) \left(d + e x\right)} \left(d + e x\right)}\, dx"," ",0,"Integral(1/(x*sqrt(-(-d + e*x)*(d + e*x))*(d + e*x)), x)","F",0
125,0,0,0,0.000000," ","integrate(1/x**2/(e*x+d)/(-e**2*x**2+d**2)**(1/2),x)","\int \frac{1}{x^{2} \sqrt{- \left(- d + e x\right) \left(d + e x\right)} \left(d + e x\right)}\, dx"," ",0,"Integral(1/(x**2*sqrt(-(-d + e*x)*(d + e*x))*(d + e*x)), x)","F",0
126,0,0,0,0.000000," ","integrate(1/x**3/(e*x+d)/(-e**2*x**2+d**2)**(1/2),x)","\int \frac{1}{x^{3} \sqrt{- \left(- d + e x\right) \left(d + e x\right)} \left(d + e x\right)}\, dx"," ",0,"Integral(1/(x**3*sqrt(-(-d + e*x)*(d + e*x))*(d + e*x)), x)","F",0
127,0,0,0,0.000000," ","integrate(x**5/(e*x+d)/(-e**2*x**2+d**2)**(3/2),x)","\int \frac{x^{5}}{\left(- \left(- d + e x\right) \left(d + e x\right)\right)^{\frac{3}{2}} \left(d + e x\right)}\, dx"," ",0,"Integral(x**5/((-(-d + e*x)*(d + e*x))**(3/2)*(d + e*x)), x)","F",0
128,0,0,0,0.000000," ","integrate(x**4/(e*x+d)/(-e**2*x**2+d**2)**(3/2),x)","\int \frac{x^{4}}{\left(- \left(- d + e x\right) \left(d + e x\right)\right)^{\frac{3}{2}} \left(d + e x\right)}\, dx"," ",0,"Integral(x**4/((-(-d + e*x)*(d + e*x))**(3/2)*(d + e*x)), x)","F",0
129,0,0,0,0.000000," ","integrate(x**3/(e*x+d)/(-e**2*x**2+d**2)**(3/2),x)","\int \frac{x^{3}}{\left(- \left(- d + e x\right) \left(d + e x\right)\right)^{\frac{3}{2}} \left(d + e x\right)}\, dx"," ",0,"Integral(x**3/((-(-d + e*x)*(d + e*x))**(3/2)*(d + e*x)), x)","F",0
130,0,0,0,0.000000," ","integrate(x**2/(e*x+d)/(-e**2*x**2+d**2)**(3/2),x)","\int \frac{x^{2}}{\left(- \left(- d + e x\right) \left(d + e x\right)\right)^{\frac{3}{2}} \left(d + e x\right)}\, dx"," ",0,"Integral(x**2/((-(-d + e*x)*(d + e*x))**(3/2)*(d + e*x)), x)","F",0
131,0,0,0,0.000000," ","integrate(x/(e*x+d)/(-e**2*x**2+d**2)**(3/2),x)","\int \frac{x}{\left(- \left(- d + e x\right) \left(d + e x\right)\right)^{\frac{3}{2}} \left(d + e x\right)}\, dx"," ",0,"Integral(x/((-(-d + e*x)*(d + e*x))**(3/2)*(d + e*x)), x)","F",0
132,0,0,0,0.000000," ","integrate(1/(e*x+d)/(-e**2*x**2+d**2)**(3/2),x)","\int \frac{1}{\left(- \left(- d + e x\right) \left(d + e x\right)\right)^{\frac{3}{2}} \left(d + e x\right)}\, dx"," ",0,"Integral(1/((-(-d + e*x)*(d + e*x))**(3/2)*(d + e*x)), x)","F",0
133,0,0,0,0.000000," ","integrate(1/x/(e*x+d)/(-e**2*x**2+d**2)**(3/2),x)","\int \frac{1}{x \left(- \left(- d + e x\right) \left(d + e x\right)\right)^{\frac{3}{2}} \left(d + e x\right)}\, dx"," ",0,"Integral(1/(x*(-(-d + e*x)*(d + e*x))**(3/2)*(d + e*x)), x)","F",0
134,0,0,0,0.000000," ","integrate(1/x**2/(e*x+d)/(-e**2*x**2+d**2)**(3/2),x)","\int \frac{1}{x^{2} \left(- \left(- d + e x\right) \left(d + e x\right)\right)^{\frac{3}{2}} \left(d + e x\right)}\, dx"," ",0,"Integral(1/(x**2*(-(-d + e*x)*(d + e*x))**(3/2)*(d + e*x)), x)","F",0
135,0,0,0,0.000000," ","integrate(1/x**3/(e*x+d)/(-e**2*x**2+d**2)**(3/2),x)","\int \frac{1}{x^{3} \left(- \left(- d + e x\right) \left(d + e x\right)\right)^{\frac{3}{2}} \left(d + e x\right)}\, dx"," ",0,"Integral(1/(x**3*(-(-d + e*x)*(d + e*x))**(3/2)*(d + e*x)), x)","F",0
136,0,0,0,0.000000," ","integrate(x**7/(e*x+d)/(-e**2*x**2+d**2)**(5/2),x)","\int \frac{x^{7}}{\left(- \left(- d + e x\right) \left(d + e x\right)\right)^{\frac{5}{2}} \left(d + e x\right)}\, dx"," ",0,"Integral(x**7/((-(-d + e*x)*(d + e*x))**(5/2)*(d + e*x)), x)","F",0
137,0,0,0,0.000000," ","integrate(x**6/(e*x+d)/(-e**2*x**2+d**2)**(5/2),x)","\int \frac{x^{6}}{\left(- \left(- d + e x\right) \left(d + e x\right)\right)^{\frac{5}{2}} \left(d + e x\right)}\, dx"," ",0,"Integral(x**6/((-(-d + e*x)*(d + e*x))**(5/2)*(d + e*x)), x)","F",0
138,0,0,0,0.000000," ","integrate(x**5/(e*x+d)/(-e**2*x**2+d**2)**(5/2),x)","\int \frac{x^{5}}{\left(- \left(- d + e x\right) \left(d + e x\right)\right)^{\frac{5}{2}} \left(d + e x\right)}\, dx"," ",0,"Integral(x**5/((-(-d + e*x)*(d + e*x))**(5/2)*(d + e*x)), x)","F",0
139,0,0,0,0.000000," ","integrate(x**4/(e*x+d)/(-e**2*x**2+d**2)**(5/2),x)","\int \frac{x^{4}}{\left(- \left(- d + e x\right) \left(d + e x\right)\right)^{\frac{5}{2}} \left(d + e x\right)}\, dx"," ",0,"Integral(x**4/((-(-d + e*x)*(d + e*x))**(5/2)*(d + e*x)), x)","F",0
140,0,0,0,0.000000," ","integrate(x**3/(e*x+d)/(-e**2*x**2+d**2)**(5/2),x)","\int \frac{x^{3}}{\left(- \left(- d + e x\right) \left(d + e x\right)\right)^{\frac{5}{2}} \left(d + e x\right)}\, dx"," ",0,"Integral(x**3/((-(-d + e*x)*(d + e*x))**(5/2)*(d + e*x)), x)","F",0
141,0,0,0,0.000000," ","integrate(x**2/(e*x+d)/(-e**2*x**2+d**2)**(5/2),x)","\int \frac{x^{2}}{\left(- \left(- d + e x\right) \left(d + e x\right)\right)^{\frac{5}{2}} \left(d + e x\right)}\, dx"," ",0,"Integral(x**2/((-(-d + e*x)*(d + e*x))**(5/2)*(d + e*x)), x)","F",0
142,0,0,0,0.000000," ","integrate(x/(e*x+d)/(-e**2*x**2+d**2)**(5/2),x)","\int \frac{x}{\left(- \left(- d + e x\right) \left(d + e x\right)\right)^{\frac{5}{2}} \left(d + e x\right)}\, dx"," ",0,"Integral(x/((-(-d + e*x)*(d + e*x))**(5/2)*(d + e*x)), x)","F",0
143,0,0,0,0.000000," ","integrate(1/(e*x+d)/(-e**2*x**2+d**2)**(5/2),x)","\int \frac{1}{\left(- \left(- d + e x\right) \left(d + e x\right)\right)^{\frac{5}{2}} \left(d + e x\right)}\, dx"," ",0,"Integral(1/((-(-d + e*x)*(d + e*x))**(5/2)*(d + e*x)), x)","F",0
144,0,0,0,0.000000," ","integrate(1/x/(e*x+d)/(-e**2*x**2+d**2)**(5/2),x)","\int \frac{1}{x \left(- \left(- d + e x\right) \left(d + e x\right)\right)^{\frac{5}{2}} \left(d + e x\right)}\, dx"," ",0,"Integral(1/(x*(-(-d + e*x)*(d + e*x))**(5/2)*(d + e*x)), x)","F",0
145,0,0,0,0.000000," ","integrate(1/x**2/(e*x+d)/(-e**2*x**2+d**2)**(5/2),x)","\int \frac{1}{x^{2} \left(- \left(- d + e x\right) \left(d + e x\right)\right)^{\frac{5}{2}} \left(d + e x\right)}\, dx"," ",0,"Integral(1/(x**2*(-(-d + e*x)*(d + e*x))**(5/2)*(d + e*x)), x)","F",0
146,0,0,0,0.000000," ","integrate(1/x**3/(e*x+d)/(-e**2*x**2+d**2)**(5/2),x)","\int \frac{1}{x^{3} \left(- \left(- d + e x\right) \left(d + e x\right)\right)^{\frac{5}{2}} \left(d + e x\right)}\, dx"," ",0,"Integral(1/(x**3*(-(-d + e*x)*(d + e*x))**(5/2)*(d + e*x)), x)","F",0
147,0,0,0,0.000000," ","integrate(1/x**4/(e*x+d)/(-e**2*x**2+d**2)**(5/2),x)","\int \frac{1}{x^{4} \left(- \left(- d + e x\right) \left(d + e x\right)\right)^{\frac{5}{2}} \left(d + e x\right)}\, dx"," ",0,"Integral(1/(x**4*(-(-d + e*x)*(d + e*x))**(5/2)*(d + e*x)), x)","F",0
148,0,0,0,0.000000," ","integrate(x**3/(e*x+d)/(-e**2*x**2+d**2)**(7/2),x)","\int \frac{x^{3}}{\left(- \left(- d + e x\right) \left(d + e x\right)\right)^{\frac{7}{2}} \left(d + e x\right)}\, dx"," ",0,"Integral(x**3/((-(-d + e*x)*(d + e*x))**(7/2)*(d + e*x)), x)","F",0
149,0,0,0,0.000000," ","integrate(x**2/(e*x+d)/(-e**2*x**2+d**2)**(7/2),x)","\int \frac{x^{2}}{\left(- \left(- d + e x\right) \left(d + e x\right)\right)^{\frac{7}{2}} \left(d + e x\right)}\, dx"," ",0,"Integral(x**2/((-(-d + e*x)*(d + e*x))**(7/2)*(d + e*x)), x)","F",0
150,0,0,0,0.000000," ","integrate(x**3/(a*x+1)/(-a**2*x**2+1)**(1/2),x)","\int \frac{x^{3}}{\sqrt{- \left(a x - 1\right) \left(a x + 1\right)} \left(a x + 1\right)}\, dx"," ",0,"Integral(x**3/(sqrt(-(a*x - 1)*(a*x + 1))*(a*x + 1)), x)","F",0
151,0,0,0,0.000000," ","integrate(x**2/(a*x+1)/(-a**2*x**2+1)**(1/2),x)","\int \frac{x^{2}}{\sqrt{- \left(a x - 1\right) \left(a x + 1\right)} \left(a x + 1\right)}\, dx"," ",0,"Integral(x**2/(sqrt(-(a*x - 1)*(a*x + 1))*(a*x + 1)), x)","F",0
152,0,0,0,0.000000," ","integrate(x/(a*x+1)/(-a**2*x**2+1)**(1/2),x)","\int \frac{x}{\sqrt{- \left(a x - 1\right) \left(a x + 1\right)} \left(a x + 1\right)}\, dx"," ",0,"Integral(x/(sqrt(-(a*x - 1)*(a*x + 1))*(a*x + 1)), x)","F",0
153,0,0,0,0.000000," ","integrate(1/(a*x+1)/(-a**2*x**2+1)**(1/2),x)","\int \frac{1}{\sqrt{- \left(a x - 1\right) \left(a x + 1\right)} \left(a x + 1\right)}\, dx"," ",0,"Integral(1/(sqrt(-(a*x - 1)*(a*x + 1))*(a*x + 1)), x)","F",0
154,0,0,0,0.000000," ","integrate(1/x/(-a*x+1)/(-a**2*x**2+1)**(1/2),x)","- \int \frac{1}{a x^{2} \sqrt{- a^{2} x^{2} + 1} - x \sqrt{- a^{2} x^{2} + 1}}\, dx"," ",0,"-Integral(1/(a*x**2*sqrt(-a**2*x**2 + 1) - x*sqrt(-a**2*x**2 + 1)), x)","F",0
155,0,0,0,0.000000," ","integrate(1/x**2/(-a*x+1)/(-a**2*x**2+1)**(1/2),x)","- \int \frac{1}{a x^{3} \sqrt{- a^{2} x^{2} + 1} - x^{2} \sqrt{- a^{2} x^{2} + 1}}\, dx"," ",0,"-Integral(1/(a*x**3*sqrt(-a**2*x**2 + 1) - x**2*sqrt(-a**2*x**2 + 1)), x)","F",0
156,0,0,0,0.000000," ","integrate(1/x**3/(-a*x+1)/(-a**2*x**2+1)**(1/2),x)","- \int \frac{1}{a x^{4} \sqrt{- a^{2} x^{2} + 1} - x^{3} \sqrt{- a^{2} x^{2} + 1}}\, dx"," ",0,"-Integral(1/(a*x**4*sqrt(-a**2*x**2 + 1) - x**3*sqrt(-a**2*x**2 + 1)), x)","F",0
157,1,571,0,17.476324," ","integrate(x**5*(-e**2*x**2+d**2)**(5/2)/(e*x+d)**2,x)","d^{2} \left(\begin{cases} - \frac{8 d^{6} \sqrt{d^{2} - e^{2} x^{2}}}{105 e^{6}} - \frac{4 d^{4} x^{2} \sqrt{d^{2} - e^{2} x^{2}}}{105 e^{4}} - \frac{d^{2} x^{4} \sqrt{d^{2} - e^{2} x^{2}}}{35 e^{2}} + \frac{x^{6} \sqrt{d^{2} - e^{2} x^{2}}}{7} & \text{for}\: e \neq 0 \\\frac{x^{6} \sqrt{d^{2}}}{6} & \text{otherwise} \end{cases}\right) - 2 d e \left(\begin{cases} - \frac{5 i d^{8} \operatorname{acosh}{\left(\frac{e x}{d} \right)}}{128 e^{7}} + \frac{5 i d^{7} x}{128 e^{6} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{5 i d^{5} x^{3}}{384 e^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{i d^{3} x^{5}}{192 e^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{7 i d x^{7}}{48 \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + \frac{i e^{2} x^{9}}{8 d \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{5 d^{8} \operatorname{asin}{\left(\frac{e x}{d} \right)}}{128 e^{7}} - \frac{5 d^{7} x}{128 e^{6} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{5 d^{5} x^{3}}{384 e^{4} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{d^{3} x^{5}}{192 e^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{7 d x^{7}}{48 \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} - \frac{e^{2} x^{9}}{8 d \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} & \text{otherwise} \end{cases}\right) + e^{2} \left(\begin{cases} - \frac{16 d^{8} \sqrt{d^{2} - e^{2} x^{2}}}{315 e^{8}} - \frac{8 d^{6} x^{2} \sqrt{d^{2} - e^{2} x^{2}}}{315 e^{6}} - \frac{2 d^{4} x^{4} \sqrt{d^{2} - e^{2} x^{2}}}{105 e^{4}} - \frac{d^{2} x^{6} \sqrt{d^{2} - e^{2} x^{2}}}{63 e^{2}} + \frac{x^{8} \sqrt{d^{2} - e^{2} x^{2}}}{9} & \text{for}\: e \neq 0 \\\frac{x^{8} \sqrt{d^{2}}}{8} & \text{otherwise} \end{cases}\right)"," ",0,"d**2*Piecewise((-8*d**6*sqrt(d**2 - e**2*x**2)/(105*e**6) - 4*d**4*x**2*sqrt(d**2 - e**2*x**2)/(105*e**4) - d**2*x**4*sqrt(d**2 - e**2*x**2)/(35*e**2) + x**6*sqrt(d**2 - e**2*x**2)/7, Ne(e, 0)), (x**6*sqrt(d**2)/6, True)) - 2*d*e*Piecewise((-5*I*d**8*acosh(e*x/d)/(128*e**7) + 5*I*d**7*x/(128*e**6*sqrt(-1 + e**2*x**2/d**2)) - 5*I*d**5*x**3/(384*e**4*sqrt(-1 + e**2*x**2/d**2)) - I*d**3*x**5/(192*e**2*sqrt(-1 + e**2*x**2/d**2)) - 7*I*d*x**7/(48*sqrt(-1 + e**2*x**2/d**2)) + I*e**2*x**9/(8*d*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (5*d**8*asin(e*x/d)/(128*e**7) - 5*d**7*x/(128*e**6*sqrt(1 - e**2*x**2/d**2)) + 5*d**5*x**3/(384*e**4*sqrt(1 - e**2*x**2/d**2)) + d**3*x**5/(192*e**2*sqrt(1 - e**2*x**2/d**2)) + 7*d*x**7/(48*sqrt(1 - e**2*x**2/d**2)) - e**2*x**9/(8*d*sqrt(1 - e**2*x**2/d**2)), True)) + e**2*Piecewise((-16*d**8*sqrt(d**2 - e**2*x**2)/(315*e**8) - 8*d**6*x**2*sqrt(d**2 - e**2*x**2)/(315*e**6) - 2*d**4*x**4*sqrt(d**2 - e**2*x**2)/(105*e**4) - d**2*x**6*sqrt(d**2 - e**2*x**2)/(63*e**2) + x**8*sqrt(d**2 - e**2*x**2)/9, Ne(e, 0)), (x**8*sqrt(d**2)/8, True))","A",0
158,1,690,0,21.396012," ","integrate(x**4*(-e**2*x**2+d**2)**(5/2)/(e*x+d)**2,x)","d^{2} \left(\begin{cases} - \frac{i d^{6} \operatorname{acosh}{\left(\frac{e x}{d} \right)}}{16 e^{5}} + \frac{i d^{5} x}{16 e^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{i d^{3} x^{3}}{48 e^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{5 i d x^{5}}{24 \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + \frac{i e^{2} x^{7}}{6 d \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{d^{6} \operatorname{asin}{\left(\frac{e x}{d} \right)}}{16 e^{5}} - \frac{d^{5} x}{16 e^{4} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{d^{3} x^{3}}{48 e^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{5 d x^{5}}{24 \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} - \frac{e^{2} x^{7}}{6 d \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} & \text{otherwise} \end{cases}\right) - 2 d e \left(\begin{cases} - \frac{8 d^{6} \sqrt{d^{2} - e^{2} x^{2}}}{105 e^{6}} - \frac{4 d^{4} x^{2} \sqrt{d^{2} - e^{2} x^{2}}}{105 e^{4}} - \frac{d^{2} x^{4} \sqrt{d^{2} - e^{2} x^{2}}}{35 e^{2}} + \frac{x^{6} \sqrt{d^{2} - e^{2} x^{2}}}{7} & \text{for}\: e \neq 0 \\\frac{x^{6} \sqrt{d^{2}}}{6} & \text{otherwise} \end{cases}\right) + e^{2} \left(\begin{cases} - \frac{5 i d^{8} \operatorname{acosh}{\left(\frac{e x}{d} \right)}}{128 e^{7}} + \frac{5 i d^{7} x}{128 e^{6} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{5 i d^{5} x^{3}}{384 e^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{i d^{3} x^{5}}{192 e^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{7 i d x^{7}}{48 \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + \frac{i e^{2} x^{9}}{8 d \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{5 d^{8} \operatorname{asin}{\left(\frac{e x}{d} \right)}}{128 e^{7}} - \frac{5 d^{7} x}{128 e^{6} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{5 d^{5} x^{3}}{384 e^{4} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{d^{3} x^{5}}{192 e^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{7 d x^{7}}{48 \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} - \frac{e^{2} x^{9}}{8 d \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} & \text{otherwise} \end{cases}\right)"," ",0,"d**2*Piecewise((-I*d**6*acosh(e*x/d)/(16*e**5) + I*d**5*x/(16*e**4*sqrt(-1 + e**2*x**2/d**2)) - I*d**3*x**3/(48*e**2*sqrt(-1 + e**2*x**2/d**2)) - 5*I*d*x**5/(24*sqrt(-1 + e**2*x**2/d**2)) + I*e**2*x**7/(6*d*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (d**6*asin(e*x/d)/(16*e**5) - d**5*x/(16*e**4*sqrt(1 - e**2*x**2/d**2)) + d**3*x**3/(48*e**2*sqrt(1 - e**2*x**2/d**2)) + 5*d*x**5/(24*sqrt(1 - e**2*x**2/d**2)) - e**2*x**7/(6*d*sqrt(1 - e**2*x**2/d**2)), True)) - 2*d*e*Piecewise((-8*d**6*sqrt(d**2 - e**2*x**2)/(105*e**6) - 4*d**4*x**2*sqrt(d**2 - e**2*x**2)/(105*e**4) - d**2*x**4*sqrt(d**2 - e**2*x**2)/(35*e**2) + x**6*sqrt(d**2 - e**2*x**2)/7, Ne(e, 0)), (x**6*sqrt(d**2)/6, True)) + e**2*Piecewise((-5*I*d**8*acosh(e*x/d)/(128*e**7) + 5*I*d**7*x/(128*e**6*sqrt(-1 + e**2*x**2/d**2)) - 5*I*d**5*x**3/(384*e**4*sqrt(-1 + e**2*x**2/d**2)) - I*d**3*x**5/(192*e**2*sqrt(-1 + e**2*x**2/d**2)) - 7*I*d*x**7/(48*sqrt(-1 + e**2*x**2/d**2)) + I*e**2*x**9/(8*d*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (5*d**8*asin(e*x/d)/(128*e**7) - 5*d**7*x/(128*e**6*sqrt(1 - e**2*x**2/d**2)) + 5*d**5*x**3/(384*e**4*sqrt(1 - e**2*x**2/d**2)) + d**3*x**5/(192*e**2*sqrt(1 - e**2*x**2/d**2)) + 7*d*x**7/(48*sqrt(1 - e**2*x**2/d**2)) - e**2*x**9/(8*d*sqrt(1 - e**2*x**2/d**2)), True))","C",0
159,1,450,0,12.029498," ","integrate(x**3*(-e**2*x**2+d**2)**(5/2)/(e*x+d)**2,x)","d^{2} \left(\begin{cases} - \frac{2 d^{4} \sqrt{d^{2} - e^{2} x^{2}}}{15 e^{4}} - \frac{d^{2} x^{2} \sqrt{d^{2} - e^{2} x^{2}}}{15 e^{2}} + \frac{x^{4} \sqrt{d^{2} - e^{2} x^{2}}}{5} & \text{for}\: e \neq 0 \\\frac{x^{4} \sqrt{d^{2}}}{4} & \text{otherwise} \end{cases}\right) - 2 d e \left(\begin{cases} - \frac{i d^{6} \operatorname{acosh}{\left(\frac{e x}{d} \right)}}{16 e^{5}} + \frac{i d^{5} x}{16 e^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{i d^{3} x^{3}}{48 e^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{5 i d x^{5}}{24 \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + \frac{i e^{2} x^{7}}{6 d \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{d^{6} \operatorname{asin}{\left(\frac{e x}{d} \right)}}{16 e^{5}} - \frac{d^{5} x}{16 e^{4} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{d^{3} x^{3}}{48 e^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{5 d x^{5}}{24 \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} - \frac{e^{2} x^{7}}{6 d \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} & \text{otherwise} \end{cases}\right) + e^{2} \left(\begin{cases} - \frac{8 d^{6} \sqrt{d^{2} - e^{2} x^{2}}}{105 e^{6}} - \frac{4 d^{4} x^{2} \sqrt{d^{2} - e^{2} x^{2}}}{105 e^{4}} - \frac{d^{2} x^{4} \sqrt{d^{2} - e^{2} x^{2}}}{35 e^{2}} + \frac{x^{6} \sqrt{d^{2} - e^{2} x^{2}}}{7} & \text{for}\: e \neq 0 \\\frac{x^{6} \sqrt{d^{2}}}{6} & \text{otherwise} \end{cases}\right)"," ",0,"d**2*Piecewise((-2*d**4*sqrt(d**2 - e**2*x**2)/(15*e**4) - d**2*x**2*sqrt(d**2 - e**2*x**2)/(15*e**2) + x**4*sqrt(d**2 - e**2*x**2)/5, Ne(e, 0)), (x**4*sqrt(d**2)/4, True)) - 2*d*e*Piecewise((-I*d**6*acosh(e*x/d)/(16*e**5) + I*d**5*x/(16*e**4*sqrt(-1 + e**2*x**2/d**2)) - I*d**3*x**3/(48*e**2*sqrt(-1 + e**2*x**2/d**2)) - 5*I*d*x**5/(24*sqrt(-1 + e**2*x**2/d**2)) + I*e**2*x**7/(6*d*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (d**6*asin(e*x/d)/(16*e**5) - d**5*x/(16*e**4*sqrt(1 - e**2*x**2/d**2)) + d**3*x**3/(48*e**2*sqrt(1 - e**2*x**2/d**2)) + 5*d*x**5/(24*sqrt(1 - e**2*x**2/d**2)) - e**2*x**7/(6*d*sqrt(1 - e**2*x**2/d**2)), True)) + e**2*Piecewise((-8*d**6*sqrt(d**2 - e**2*x**2)/(105*e**6) - 4*d**4*x**2*sqrt(d**2 - e**2*x**2)/(105*e**4) - d**2*x**4*sqrt(d**2 - e**2*x**2)/(35*e**2) + x**6*sqrt(d**2 - e**2*x**2)/7, Ne(e, 0)), (x**6*sqrt(d**2)/6, True))","A",0
160,1,541,0,14.452585," ","integrate(x**2*(-e**2*x**2+d**2)**(5/2)/(e*x+d)**2,x)","d^{2} \left(\begin{cases} - \frac{i d^{4} \operatorname{acosh}{\left(\frac{e x}{d} \right)}}{8 e^{3}} + \frac{i d^{3} x}{8 e^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{3 i d x^{3}}{8 \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + \frac{i e^{2} x^{5}}{4 d \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{d^{4} \operatorname{asin}{\left(\frac{e x}{d} \right)}}{8 e^{3}} - \frac{d^{3} x}{8 e^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{3 d x^{3}}{8 \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} - \frac{e^{2} x^{5}}{4 d \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} & \text{otherwise} \end{cases}\right) - 2 d e \left(\begin{cases} - \frac{2 d^{4} \sqrt{d^{2} - e^{2} x^{2}}}{15 e^{4}} - \frac{d^{2} x^{2} \sqrt{d^{2} - e^{2} x^{2}}}{15 e^{2}} + \frac{x^{4} \sqrt{d^{2} - e^{2} x^{2}}}{5} & \text{for}\: e \neq 0 \\\frac{x^{4} \sqrt{d^{2}}}{4} & \text{otherwise} \end{cases}\right) + e^{2} \left(\begin{cases} - \frac{i d^{6} \operatorname{acosh}{\left(\frac{e x}{d} \right)}}{16 e^{5}} + \frac{i d^{5} x}{16 e^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{i d^{3} x^{3}}{48 e^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{5 i d x^{5}}{24 \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + \frac{i e^{2} x^{7}}{6 d \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{d^{6} \operatorname{asin}{\left(\frac{e x}{d} \right)}}{16 e^{5}} - \frac{d^{5} x}{16 e^{4} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{d^{3} x^{3}}{48 e^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{5 d x^{5}}{24 \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} - \frac{e^{2} x^{7}}{6 d \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} & \text{otherwise} \end{cases}\right)"," ",0,"d**2*Piecewise((-I*d**4*acosh(e*x/d)/(8*e**3) + I*d**3*x/(8*e**2*sqrt(-1 + e**2*x**2/d**2)) - 3*I*d*x**3/(8*sqrt(-1 + e**2*x**2/d**2)) + I*e**2*x**5/(4*d*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (d**4*asin(e*x/d)/(8*e**3) - d**3*x/(8*e**2*sqrt(1 - e**2*x**2/d**2)) + 3*d*x**3/(8*sqrt(1 - e**2*x**2/d**2)) - e**2*x**5/(4*d*sqrt(1 - e**2*x**2/d**2)), True)) - 2*d*e*Piecewise((-2*d**4*sqrt(d**2 - e**2*x**2)/(15*e**4) - d**2*x**2*sqrt(d**2 - e**2*x**2)/(15*e**2) + x**4*sqrt(d**2 - e**2*x**2)/5, Ne(e, 0)), (x**4*sqrt(d**2)/4, True)) + e**2*Piecewise((-I*d**6*acosh(e*x/d)/(16*e**5) + I*d**5*x/(16*e**4*sqrt(-1 + e**2*x**2/d**2)) - I*d**3*x**3/(48*e**2*sqrt(-1 + e**2*x**2/d**2)) - 5*I*d*x**5/(24*sqrt(-1 + e**2*x**2/d**2)) + I*e**2*x**7/(6*d*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (d**6*asin(e*x/d)/(16*e**5) - d**5*x/(16*e**4*sqrt(1 - e**2*x**2/d**2)) + d**3*x**3/(48*e**2*sqrt(1 - e**2*x**2/d**2)) + 5*d*x**5/(24*sqrt(1 - e**2*x**2/d**2)) - e**2*x**7/(6*d*sqrt(1 - e**2*x**2/d**2)), True))","C",0
161,1,321,0,8.566213," ","integrate(x*(-e**2*x**2+d**2)**(5/2)/(e*x+d)**2,x)","d^{2} \left(\begin{cases} \frac{x^{2} \sqrt{d^{2}}}{2} & \text{for}\: e^{2} = 0 \\- \frac{\left(d^{2} - e^{2} x^{2}\right)^{\frac{3}{2}}}{3 e^{2}} & \text{otherwise} \end{cases}\right) - 2 d e \left(\begin{cases} - \frac{i d^{4} \operatorname{acosh}{\left(\frac{e x}{d} \right)}}{8 e^{3}} + \frac{i d^{3} x}{8 e^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{3 i d x^{3}}{8 \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + \frac{i e^{2} x^{5}}{4 d \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{d^{4} \operatorname{asin}{\left(\frac{e x}{d} \right)}}{8 e^{3}} - \frac{d^{3} x}{8 e^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{3 d x^{3}}{8 \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} - \frac{e^{2} x^{5}}{4 d \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} & \text{otherwise} \end{cases}\right) + e^{2} \left(\begin{cases} - \frac{2 d^{4} \sqrt{d^{2} - e^{2} x^{2}}}{15 e^{4}} - \frac{d^{2} x^{2} \sqrt{d^{2} - e^{2} x^{2}}}{15 e^{2}} + \frac{x^{4} \sqrt{d^{2} - e^{2} x^{2}}}{5} & \text{for}\: e \neq 0 \\\frac{x^{4} \sqrt{d^{2}}}{4} & \text{otherwise} \end{cases}\right)"," ",0,"d**2*Piecewise((x**2*sqrt(d**2)/2, Eq(e**2, 0)), (-(d**2 - e**2*x**2)**(3/2)/(3*e**2), True)) - 2*d*e*Piecewise((-I*d**4*acosh(e*x/d)/(8*e**3) + I*d**3*x/(8*e**2*sqrt(-1 + e**2*x**2/d**2)) - 3*I*d*x**3/(8*sqrt(-1 + e**2*x**2/d**2)) + I*e**2*x**5/(4*d*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (d**4*asin(e*x/d)/(8*e**3) - d**3*x/(8*e**2*sqrt(1 - e**2*x**2/d**2)) + 3*d*x**3/(8*sqrt(1 - e**2*x**2/d**2)) - e**2*x**5/(4*d*sqrt(1 - e**2*x**2/d**2)), True)) + e**2*Piecewise((-2*d**4*sqrt(d**2 - e**2*x**2)/(15*e**4) - d**2*x**2*sqrt(d**2 - e**2*x**2)/(15*e**2) + x**4*sqrt(d**2 - e**2*x**2)/5, Ne(e, 0)), (x**4*sqrt(d**2)/4, True))","A",0
162,1,350,0,9.348927," ","integrate((-e**2*x**2+d**2)**(5/2)/(e*x+d)**2,x)","d^{2} \left(\begin{cases} - \frac{i d^{2} \operatorname{acosh}{\left(\frac{e x}{d} \right)}}{2 e} - \frac{i d x}{2 \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + \frac{i e^{2} x^{3}}{2 d \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{d^{2} \operatorname{asin}{\left(\frac{e x}{d} \right)}}{2 e} + \frac{d x \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}}{2} & \text{otherwise} \end{cases}\right) - 2 d e \left(\begin{cases} \frac{x^{2} \sqrt{d^{2}}}{2} & \text{for}\: e^{2} = 0 \\- \frac{\left(d^{2} - e^{2} x^{2}\right)^{\frac{3}{2}}}{3 e^{2}} & \text{otherwise} \end{cases}\right) + e^{2} \left(\begin{cases} - \frac{i d^{4} \operatorname{acosh}{\left(\frac{e x}{d} \right)}}{8 e^{3}} + \frac{i d^{3} x}{8 e^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} - \frac{3 i d x^{3}}{8 \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + \frac{i e^{2} x^{5}}{4 d \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{d^{4} \operatorname{asin}{\left(\frac{e x}{d} \right)}}{8 e^{3}} - \frac{d^{3} x}{8 e^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} + \frac{3 d x^{3}}{8 \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} - \frac{e^{2} x^{5}}{4 d \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} & \text{otherwise} \end{cases}\right)"," ",0,"d**2*Piecewise((-I*d**2*acosh(e*x/d)/(2*e) - I*d*x/(2*sqrt(-1 + e**2*x**2/d**2)) + I*e**2*x**3/(2*d*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (d**2*asin(e*x/d)/(2*e) + d*x*sqrt(1 - e**2*x**2/d**2)/2, True)) - 2*d*e*Piecewise((x**2*sqrt(d**2)/2, Eq(e**2, 0)), (-(d**2 - e**2*x**2)**(3/2)/(3*e**2), True)) + e**2*Piecewise((-I*d**4*acosh(e*x/d)/(8*e**3) + I*d**3*x/(8*e**2*sqrt(-1 + e**2*x**2/d**2)) - 3*I*d*x**3/(8*sqrt(-1 + e**2*x**2/d**2)) + I*e**2*x**5/(4*d*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (d**4*asin(e*x/d)/(8*e**3) - d**3*x/(8*e**2*sqrt(1 - e**2*x**2/d**2)) + 3*d*x**3/(8*sqrt(1 - e**2*x**2/d**2)) - e**2*x**5/(4*d*sqrt(1 - e**2*x**2/d**2)), True))","C",0
163,1,267,0,14.832920," ","integrate((-e**2*x**2+d**2)**(5/2)/x/(e*x+d)**2,x)","d^{2} \left(\begin{cases} \frac{d^{2}}{e x \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} - d \operatorname{acosh}{\left(\frac{d}{e x} \right)} - \frac{e x}{\sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\- \frac{i d^{2}}{e x \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} + i d \operatorname{asin}{\left(\frac{d}{e x} \right)} + \frac{i e x}{\sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} & \text{otherwise} \end{cases}\right) - 2 d e \left(\begin{cases} - \frac{i d^{2} \operatorname{acosh}{\left(\frac{e x}{d} \right)}}{2 e} - \frac{i d x}{2 \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + \frac{i e^{2} x^{3}}{2 d \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{d^{2} \operatorname{asin}{\left(\frac{e x}{d} \right)}}{2 e} + \frac{d x \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}}{2} & \text{otherwise} \end{cases}\right) + e^{2} \left(\begin{cases} \frac{x^{2} \sqrt{d^{2}}}{2} & \text{for}\: e^{2} = 0 \\- \frac{\left(d^{2} - e^{2} x^{2}\right)^{\frac{3}{2}}}{3 e^{2}} & \text{otherwise} \end{cases}\right)"," ",0,"d**2*Piecewise((d**2/(e*x*sqrt(d**2/(e**2*x**2) - 1)) - d*acosh(d/(e*x)) - e*x/sqrt(d**2/(e**2*x**2) - 1), Abs(d**2/(e**2*x**2)) > 1), (-I*d**2/(e*x*sqrt(-d**2/(e**2*x**2) + 1)) + I*d*asin(d/(e*x)) + I*e*x/sqrt(-d**2/(e**2*x**2) + 1), True)) - 2*d*e*Piecewise((-I*d**2*acosh(e*x/d)/(2*e) - I*d*x/(2*sqrt(-1 + e**2*x**2/d**2)) + I*e**2*x**3/(2*d*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (d**2*asin(e*x/d)/(2*e) + d*x*sqrt(1 - e**2*x**2/d**2)/2, True)) + e**2*Piecewise((x**2*sqrt(d**2)/2, Eq(e**2, 0)), (-(d**2 - e**2*x**2)**(3/2)/(3*e**2), True))","C",0
164,1,347,0,9.854329," ","integrate((-e**2*x**2+d**2)**(5/2)/x**2/(e*x+d)**2,x)","d^{2} \left(\begin{cases} \frac{i d}{x \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + i e \operatorname{acosh}{\left(\frac{e x}{d} \right)} - \frac{i e^{2} x}{d \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\- \frac{d}{x \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} - e \operatorname{asin}{\left(\frac{e x}{d} \right)} + \frac{e^{2} x}{d \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} & \text{otherwise} \end{cases}\right) - 2 d e \left(\begin{cases} \frac{d^{2}}{e x \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} - d \operatorname{acosh}{\left(\frac{d}{e x} \right)} - \frac{e x}{\sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\- \frac{i d^{2}}{e x \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} + i d \operatorname{asin}{\left(\frac{d}{e x} \right)} + \frac{i e x}{\sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} & \text{otherwise} \end{cases}\right) + e^{2} \left(\begin{cases} - \frac{i d^{2} \operatorname{acosh}{\left(\frac{e x}{d} \right)}}{2 e} - \frac{i d x}{2 \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + \frac{i e^{2} x^{3}}{2 d \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{d^{2} \operatorname{asin}{\left(\frac{e x}{d} \right)}}{2 e} + \frac{d x \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}}{2} & \text{otherwise} \end{cases}\right)"," ",0,"d**2*Piecewise((I*d/(x*sqrt(-1 + e**2*x**2/d**2)) + I*e*acosh(e*x/d) - I*e**2*x/(d*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (-d/(x*sqrt(1 - e**2*x**2/d**2)) - e*asin(e*x/d) + e**2*x/(d*sqrt(1 - e**2*x**2/d**2)), True)) - 2*d*e*Piecewise((d**2/(e*x*sqrt(d**2/(e**2*x**2) - 1)) - d*acosh(d/(e*x)) - e*x/sqrt(d**2/(e**2*x**2) - 1), Abs(d**2/(e**2*x**2)) > 1), (-I*d**2/(e*x*sqrt(-d**2/(e**2*x**2) + 1)) + I*d*asin(d/(e*x)) + I*e*x/sqrt(-d**2/(e**2*x**2) + 1), True)) + e**2*Piecewise((-I*d**2*acosh(e*x/d)/(2*e) - I*d*x/(2*sqrt(-1 + e**2*x**2/d**2)) + I*e**2*x**3/(2*d*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (d**2*asin(e*x/d)/(2*e) + d*x*sqrt(1 - e**2*x**2/d**2)/2, True))","C",0
165,1,347,0,10.174607," ","integrate((-e**2*x**2+d**2)**(5/2)/x**3/(e*x+d)**2,x)","d^{2} \left(\begin{cases} - \frac{d^{2}}{2 e x^{3} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{e}{2 x \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{e^{2} \operatorname{acosh}{\left(\frac{d}{e x} \right)}}{2 d} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\- \frac{i e \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{2 x} - \frac{i e^{2} \operatorname{asin}{\left(\frac{d}{e x} \right)}}{2 d} & \text{otherwise} \end{cases}\right) - 2 d e \left(\begin{cases} \frac{i d}{x \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + i e \operatorname{acosh}{\left(\frac{e x}{d} \right)} - \frac{i e^{2} x}{d \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\- \frac{d}{x \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} - e \operatorname{asin}{\left(\frac{e x}{d} \right)} + \frac{e^{2} x}{d \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} & \text{otherwise} \end{cases}\right) + e^{2} \left(\begin{cases} \frac{d^{2}}{e x \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} - d \operatorname{acosh}{\left(\frac{d}{e x} \right)} - \frac{e x}{\sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\- \frac{i d^{2}}{e x \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} + i d \operatorname{asin}{\left(\frac{d}{e x} \right)} + \frac{i e x}{\sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} & \text{otherwise} \end{cases}\right)"," ",0,"d**2*Piecewise((-d**2/(2*e*x**3*sqrt(d**2/(e**2*x**2) - 1)) + e/(2*x*sqrt(d**2/(e**2*x**2) - 1)) + e**2*acosh(d/(e*x))/(2*d), Abs(d**2/(e**2*x**2)) > 1), (-I*e*sqrt(-d**2/(e**2*x**2) + 1)/(2*x) - I*e**2*asin(d/(e*x))/(2*d), True)) - 2*d*e*Piecewise((I*d/(x*sqrt(-1 + e**2*x**2/d**2)) + I*e*acosh(e*x/d) - I*e**2*x/(d*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (-d/(x*sqrt(1 - e**2*x**2/d**2)) - e*asin(e*x/d) + e**2*x/(d*sqrt(1 - e**2*x**2/d**2)), True)) + e**2*Piecewise((d**2/(e*x*sqrt(d**2/(e**2*x**2) - 1)) - d*acosh(d/(e*x)) - e*x/sqrt(d**2/(e**2*x**2) - 1), Abs(d**2/(e**2*x**2)) > 1), (-I*d**2/(e*x*sqrt(-d**2/(e**2*x**2) + 1)) + I*d*asin(d/(e*x)) + I*e*x/sqrt(-d**2/(e**2*x**2) + 1), True))","C",0
166,1,338,0,9.734604," ","integrate((-e**2*x**2+d**2)**(5/2)/x**4/(e*x+d)**2,x)","d^{2} \left(\begin{cases} - \frac{e \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}}{3 x^{2}} + \frac{e^{3} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}}{3 d^{2}} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\- \frac{i e \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{3 x^{2}} + \frac{i e^{3} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{3 d^{2}} & \text{otherwise} \end{cases}\right) - 2 d e \left(\begin{cases} - \frac{d^{2}}{2 e x^{3} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{e}{2 x \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{e^{2} \operatorname{acosh}{\left(\frac{d}{e x} \right)}}{2 d} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\- \frac{i e \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{2 x} - \frac{i e^{2} \operatorname{asin}{\left(\frac{d}{e x} \right)}}{2 d} & \text{otherwise} \end{cases}\right) + e^{2} \left(\begin{cases} \frac{i d}{x \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} + i e \operatorname{acosh}{\left(\frac{e x}{d} \right)} - \frac{i e^{2} x}{d \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\- \frac{d}{x \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} - e \operatorname{asin}{\left(\frac{e x}{d} \right)} + \frac{e^{2} x}{d \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}} & \text{otherwise} \end{cases}\right)"," ",0,"d**2*Piecewise((-e*sqrt(d**2/(e**2*x**2) - 1)/(3*x**2) + e**3*sqrt(d**2/(e**2*x**2) - 1)/(3*d**2), Abs(d**2/(e**2*x**2)) > 1), (-I*e*sqrt(-d**2/(e**2*x**2) + 1)/(3*x**2) + I*e**3*sqrt(-d**2/(e**2*x**2) + 1)/(3*d**2), True)) - 2*d*e*Piecewise((-d**2/(2*e*x**3*sqrt(d**2/(e**2*x**2) - 1)) + e/(2*x*sqrt(d**2/(e**2*x**2) - 1)) + e**2*acosh(d/(e*x))/(2*d), Abs(d**2/(e**2*x**2)) > 1), (-I*e*sqrt(-d**2/(e**2*x**2) + 1)/(2*x) - I*e**2*asin(d/(e*x))/(2*d), True)) + e**2*Piecewise((I*d/(x*sqrt(-1 + e**2*x**2/d**2)) + I*e*acosh(e*x/d) - I*e**2*x/(d*sqrt(-1 + e**2*x**2/d**2)), Abs(e**2*x**2/d**2) > 1), (-d/(x*sqrt(1 - e**2*x**2/d**2)) - e*asin(e*x/d) + e**2*x/(d*sqrt(1 - e**2*x**2/d**2)), True))","C",0
167,1,422,0,12.355484," ","integrate((-e**2*x**2+d**2)**(5/2)/x**5/(e*x+d)**2,x)","d^{2} \left(\begin{cases} - \frac{d^{2}}{4 e x^{5} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{3 e}{8 x^{3} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} - \frac{e^{3}}{8 d^{2} x \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{e^{4} \operatorname{acosh}{\left(\frac{d}{e x} \right)}}{8 d^{3}} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\\frac{i d^{2}}{4 e x^{5} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} - \frac{3 i e}{8 x^{3} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} + \frac{i e^{3}}{8 d^{2} x \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} - \frac{i e^{4} \operatorname{asin}{\left(\frac{d}{e x} \right)}}{8 d^{3}} & \text{otherwise} \end{cases}\right) - 2 d e \left(\begin{cases} - \frac{e \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}}{3 x^{2}} + \frac{e^{3} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}}{3 d^{2}} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\- \frac{i e \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{3 x^{2}} + \frac{i e^{3} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{3 d^{2}} & \text{otherwise} \end{cases}\right) + e^{2} \left(\begin{cases} - \frac{d^{2}}{2 e x^{3} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{e}{2 x \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{e^{2} \operatorname{acosh}{\left(\frac{d}{e x} \right)}}{2 d} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\- \frac{i e \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{2 x} - \frac{i e^{2} \operatorname{asin}{\left(\frac{d}{e x} \right)}}{2 d} & \text{otherwise} \end{cases}\right)"," ",0,"d**2*Piecewise((-d**2/(4*e*x**5*sqrt(d**2/(e**2*x**2) - 1)) + 3*e/(8*x**3*sqrt(d**2/(e**2*x**2) - 1)) - e**3/(8*d**2*x*sqrt(d**2/(e**2*x**2) - 1)) + e**4*acosh(d/(e*x))/(8*d**3), Abs(d**2/(e**2*x**2)) > 1), (I*d**2/(4*e*x**5*sqrt(-d**2/(e**2*x**2) + 1)) - 3*I*e/(8*x**3*sqrt(-d**2/(e**2*x**2) + 1)) + I*e**3/(8*d**2*x*sqrt(-d**2/(e**2*x**2) + 1)) - I*e**4*asin(d/(e*x))/(8*d**3), True)) - 2*d*e*Piecewise((-e*sqrt(d**2/(e**2*x**2) - 1)/(3*x**2) + e**3*sqrt(d**2/(e**2*x**2) - 1)/(3*d**2), Abs(d**2/(e**2*x**2)) > 1), (-I*e*sqrt(-d**2/(e**2*x**2) + 1)/(3*x**2) + I*e**3*sqrt(-d**2/(e**2*x**2) + 1)/(3*d**2), True)) + e**2*Piecewise((-d**2/(2*e*x**3*sqrt(d**2/(e**2*x**2) - 1)) + e/(2*x*sqrt(d**2/(e**2*x**2) - 1)) + e**2*acosh(d/(e*x))/(2*d), Abs(d**2/(e**2*x**2)) > 1), (-I*e*sqrt(-d**2/(e**2*x**2) + 1)/(2*x) - I*e**2*asin(d/(e*x))/(2*d), True))","C",0
168,1,660,0,13.421559," ","integrate((-e**2*x**2+d**2)**(5/2)/x**6/(e*x+d)**2,x)","d^{2} \left(\begin{cases} \frac{3 i d^{3} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{2} x^{5} + 15 e^{2} x^{7}} - \frac{4 i d e^{2} x^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{2} x^{5} + 15 e^{2} x^{7}} + \frac{2 i e^{6} x^{6} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{5} x^{5} + 15 d^{3} e^{2} x^{7}} - \frac{i e^{4} x^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{3} x^{5} + 15 d e^{2} x^{7}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{3 d^{3} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{2} x^{5} + 15 e^{2} x^{7}} - \frac{4 d e^{2} x^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{2} x^{5} + 15 e^{2} x^{7}} + \frac{2 e^{6} x^{6} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{5} x^{5} + 15 d^{3} e^{2} x^{7}} - \frac{e^{4} x^{4} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{3} x^{5} + 15 d e^{2} x^{7}} & \text{otherwise} \end{cases}\right) - 2 d e \left(\begin{cases} - \frac{d^{2}}{4 e x^{5} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{3 e}{8 x^{3} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} - \frac{e^{3}}{8 d^{2} x \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{e^{4} \operatorname{acosh}{\left(\frac{d}{e x} \right)}}{8 d^{3}} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\\frac{i d^{2}}{4 e x^{5} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} - \frac{3 i e}{8 x^{3} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} + \frac{i e^{3}}{8 d^{2} x \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} - \frac{i e^{4} \operatorname{asin}{\left(\frac{d}{e x} \right)}}{8 d^{3}} & \text{otherwise} \end{cases}\right) + e^{2} \left(\begin{cases} - \frac{e \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}}{3 x^{2}} + \frac{e^{3} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}}{3 d^{2}} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\- \frac{i e \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{3 x^{2}} + \frac{i e^{3} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{3 d^{2}} & \text{otherwise} \end{cases}\right)"," ",0,"d**2*Piecewise((3*I*d**3*sqrt(-1 + e**2*x**2/d**2)/(-15*d**2*x**5 + 15*e**2*x**7) - 4*I*d*e**2*x**2*sqrt(-1 + e**2*x**2/d**2)/(-15*d**2*x**5 + 15*e**2*x**7) + 2*I*e**6*x**6*sqrt(-1 + e**2*x**2/d**2)/(-15*d**5*x**5 + 15*d**3*e**2*x**7) - I*e**4*x**4*sqrt(-1 + e**2*x**2/d**2)/(-15*d**3*x**5 + 15*d*e**2*x**7), Abs(e**2*x**2/d**2) > 1), (3*d**3*sqrt(1 - e**2*x**2/d**2)/(-15*d**2*x**5 + 15*e**2*x**7) - 4*d*e**2*x**2*sqrt(1 - e**2*x**2/d**2)/(-15*d**2*x**5 + 15*e**2*x**7) + 2*e**6*x**6*sqrt(1 - e**2*x**2/d**2)/(-15*d**5*x**5 + 15*d**3*e**2*x**7) - e**4*x**4*sqrt(1 - e**2*x**2/d**2)/(-15*d**3*x**5 + 15*d*e**2*x**7), True)) - 2*d*e*Piecewise((-d**2/(4*e*x**5*sqrt(d**2/(e**2*x**2) - 1)) + 3*e/(8*x**3*sqrt(d**2/(e**2*x**2) - 1)) - e**3/(8*d**2*x*sqrt(d**2/(e**2*x**2) - 1)) + e**4*acosh(d/(e*x))/(8*d**3), Abs(d**2/(e**2*x**2)) > 1), (I*d**2/(4*e*x**5*sqrt(-d**2/(e**2*x**2) + 1)) - 3*I*e/(8*x**3*sqrt(-d**2/(e**2*x**2) + 1)) + I*e**3/(8*d**2*x*sqrt(-d**2/(e**2*x**2) + 1)) - I*e**4*asin(d/(e*x))/(8*d**3), True)) + e**2*Piecewise((-e*sqrt(d**2/(e**2*x**2) - 1)/(3*x**2) + e**3*sqrt(d**2/(e**2*x**2) - 1)/(3*d**2), Abs(d**2/(e**2*x**2)) > 1), (-I*e*sqrt(-d**2/(e**2*x**2) + 1)/(3*x**2) + I*e**3*sqrt(-d**2/(e**2*x**2) + 1)/(3*d**2), True))","C",0
169,1,808,0,19.721317," ","integrate((-e**2*x**2+d**2)**(5/2)/x**7/(e*x+d)**2,x)","d^{2} \left(\begin{cases} - \frac{d^{2}}{6 e x^{7} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{5 e}{24 x^{5} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{e^{3}}{48 d^{2} x^{3} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} - \frac{e^{5}}{16 d^{4} x \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{e^{6} \operatorname{acosh}{\left(\frac{d}{e x} \right)}}{16 d^{5}} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\\frac{i d^{2}}{6 e x^{7} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} - \frac{5 i e}{24 x^{5} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} - \frac{i e^{3}}{48 d^{2} x^{3} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} + \frac{i e^{5}}{16 d^{4} x \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} - \frac{i e^{6} \operatorname{asin}{\left(\frac{d}{e x} \right)}}{16 d^{5}} & \text{otherwise} \end{cases}\right) - 2 d e \left(\begin{cases} \frac{3 i d^{3} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{2} x^{5} + 15 e^{2} x^{7}} - \frac{4 i d e^{2} x^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{2} x^{5} + 15 e^{2} x^{7}} + \frac{2 i e^{6} x^{6} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{5} x^{5} + 15 d^{3} e^{2} x^{7}} - \frac{i e^{4} x^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{3} x^{5} + 15 d e^{2} x^{7}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{3 d^{3} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{2} x^{5} + 15 e^{2} x^{7}} - \frac{4 d e^{2} x^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{2} x^{5} + 15 e^{2} x^{7}} + \frac{2 e^{6} x^{6} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{5} x^{5} + 15 d^{3} e^{2} x^{7}} - \frac{e^{4} x^{4} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{3} x^{5} + 15 d e^{2} x^{7}} & \text{otherwise} \end{cases}\right) + e^{2} \left(\begin{cases} - \frac{d^{2}}{4 e x^{5} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{3 e}{8 x^{3} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} - \frac{e^{3}}{8 d^{2} x \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{e^{4} \operatorname{acosh}{\left(\frac{d}{e x} \right)}}{8 d^{3}} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\\frac{i d^{2}}{4 e x^{5} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} - \frac{3 i e}{8 x^{3} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} + \frac{i e^{3}}{8 d^{2} x \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} - \frac{i e^{4} \operatorname{asin}{\left(\frac{d}{e x} \right)}}{8 d^{3}} & \text{otherwise} \end{cases}\right)"," ",0,"d**2*Piecewise((-d**2/(6*e*x**7*sqrt(d**2/(e**2*x**2) - 1)) + 5*e/(24*x**5*sqrt(d**2/(e**2*x**2) - 1)) + e**3/(48*d**2*x**3*sqrt(d**2/(e**2*x**2) - 1)) - e**5/(16*d**4*x*sqrt(d**2/(e**2*x**2) - 1)) + e**6*acosh(d/(e*x))/(16*d**5), Abs(d**2/(e**2*x**2)) > 1), (I*d**2/(6*e*x**7*sqrt(-d**2/(e**2*x**2) + 1)) - 5*I*e/(24*x**5*sqrt(-d**2/(e**2*x**2) + 1)) - I*e**3/(48*d**2*x**3*sqrt(-d**2/(e**2*x**2) + 1)) + I*e**5/(16*d**4*x*sqrt(-d**2/(e**2*x**2) + 1)) - I*e**6*asin(d/(e*x))/(16*d**5), True)) - 2*d*e*Piecewise((3*I*d**3*sqrt(-1 + e**2*x**2/d**2)/(-15*d**2*x**5 + 15*e**2*x**7) - 4*I*d*e**2*x**2*sqrt(-1 + e**2*x**2/d**2)/(-15*d**2*x**5 + 15*e**2*x**7) + 2*I*e**6*x**6*sqrt(-1 + e**2*x**2/d**2)/(-15*d**5*x**5 + 15*d**3*e**2*x**7) - I*e**4*x**4*sqrt(-1 + e**2*x**2/d**2)/(-15*d**3*x**5 + 15*d*e**2*x**7), Abs(e**2*x**2/d**2) > 1), (3*d**3*sqrt(1 - e**2*x**2/d**2)/(-15*d**2*x**5 + 15*e**2*x**7) - 4*d*e**2*x**2*sqrt(1 - e**2*x**2/d**2)/(-15*d**2*x**5 + 15*e**2*x**7) + 2*e**6*x**6*sqrt(1 - e**2*x**2/d**2)/(-15*d**5*x**5 + 15*d**3*e**2*x**7) - e**4*x**4*sqrt(1 - e**2*x**2/d**2)/(-15*d**3*x**5 + 15*d*e**2*x**7), True)) + e**2*Piecewise((-d**2/(4*e*x**5*sqrt(d**2/(e**2*x**2) - 1)) + 3*e/(8*x**3*sqrt(d**2/(e**2*x**2) - 1)) - e**3/(8*d**2*x*sqrt(d**2/(e**2*x**2) - 1)) + e**4*acosh(d/(e*x))/(8*d**3), Abs(d**2/(e**2*x**2)) > 1), (I*d**2/(4*e*x**5*sqrt(-d**2/(e**2*x**2) + 1)) - 3*I*e/(8*x**3*sqrt(-d**2/(e**2*x**2) + 1)) + I*e**3/(8*d**2*x*sqrt(-d**2/(e**2*x**2) + 1)) - I*e**4*asin(d/(e*x))/(8*d**3), True))","C",0
170,1,835,0,18.182779," ","integrate((-e**2*x**2+d**2)**(5/2)/x**8/(e*x+d)**2,x)","d^{2} \left(\begin{cases} - \frac{e \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}}{7 x^{6}} + \frac{e^{3} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}}{35 d^{2} x^{4}} + \frac{4 e^{5} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}}{105 d^{4} x^{2}} + \frac{8 e^{7} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}}{105 d^{6}} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\- \frac{i e \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{7 x^{6}} + \frac{i e^{3} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{35 d^{2} x^{4}} + \frac{4 i e^{5} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{105 d^{4} x^{2}} + \frac{8 i e^{7} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}}{105 d^{6}} & \text{otherwise} \end{cases}\right) - 2 d e \left(\begin{cases} - \frac{d^{2}}{6 e x^{7} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{5 e}{24 x^{5} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{e^{3}}{48 d^{2} x^{3} \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} - \frac{e^{5}}{16 d^{4} x \sqrt{\frac{d^{2}}{e^{2} x^{2}} - 1}} + \frac{e^{6} \operatorname{acosh}{\left(\frac{d}{e x} \right)}}{16 d^{5}} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\\frac{i d^{2}}{6 e x^{7} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} - \frac{5 i e}{24 x^{5} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} - \frac{i e^{3}}{48 d^{2} x^{3} \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} + \frac{i e^{5}}{16 d^{4} x \sqrt{- \frac{d^{2}}{e^{2} x^{2}} + 1}} - \frac{i e^{6} \operatorname{asin}{\left(\frac{d}{e x} \right)}}{16 d^{5}} & \text{otherwise} \end{cases}\right) + e^{2} \left(\begin{cases} \frac{3 i d^{3} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{2} x^{5} + 15 e^{2} x^{7}} - \frac{4 i d e^{2} x^{2} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{2} x^{5} + 15 e^{2} x^{7}} + \frac{2 i e^{6} x^{6} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{5} x^{5} + 15 d^{3} e^{2} x^{7}} - \frac{i e^{4} x^{4} \sqrt{-1 + \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{3} x^{5} + 15 d e^{2} x^{7}} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{3 d^{3} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{2} x^{5} + 15 e^{2} x^{7}} - \frac{4 d e^{2} x^{2} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{2} x^{5} + 15 e^{2} x^{7}} + \frac{2 e^{6} x^{6} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{5} x^{5} + 15 d^{3} e^{2} x^{7}} - \frac{e^{4} x^{4} \sqrt{1 - \frac{e^{2} x^{2}}{d^{2}}}}{- 15 d^{3} x^{5} + 15 d e^{2} x^{7}} & \text{otherwise} \end{cases}\right)"," ",0,"d**2*Piecewise((-e*sqrt(d**2/(e**2*x**2) - 1)/(7*x**6) + e**3*sqrt(d**2/(e**2*x**2) - 1)/(35*d**2*x**4) + 4*e**5*sqrt(d**2/(e**2*x**2) - 1)/(105*d**4*x**2) + 8*e**7*sqrt(d**2/(e**2*x**2) - 1)/(105*d**6), Abs(d**2/(e**2*x**2)) > 1), (-I*e*sqrt(-d**2/(e**2*x**2) + 1)/(7*x**6) + I*e**3*sqrt(-d**2/(e**2*x**2) + 1)/(35*d**2*x**4) + 4*I*e**5*sqrt(-d**2/(e**2*x**2) + 1)/(105*d**4*x**2) + 8*I*e**7*sqrt(-d**2/(e**2*x**2) + 1)/(105*d**6), True)) - 2*d*e*Piecewise((-d**2/(6*e*x**7*sqrt(d**2/(e**2*x**2) - 1)) + 5*e/(24*x**5*sqrt(d**2/(e**2*x**2) - 1)) + e**3/(48*d**2*x**3*sqrt(d**2/(e**2*x**2) - 1)) - e**5/(16*d**4*x*sqrt(d**2/(e**2*x**2) - 1)) + e**6*acosh(d/(e*x))/(16*d**5), Abs(d**2/(e**2*x**2)) > 1), (I*d**2/(6*e*x**7*sqrt(-d**2/(e**2*x**2) + 1)) - 5*I*e/(24*x**5*sqrt(-d**2/(e**2*x**2) + 1)) - I*e**3/(48*d**2*x**3*sqrt(-d**2/(e**2*x**2) + 1)) + I*e**5/(16*d**4*x*sqrt(-d**2/(e**2*x**2) + 1)) - I*e**6*asin(d/(e*x))/(16*d**5), True)) + e**2*Piecewise((3*I*d**3*sqrt(-1 + e**2*x**2/d**2)/(-15*d**2*x**5 + 15*e**2*x**7) - 4*I*d*e**2*x**2*sqrt(-1 + e**2*x**2/d**2)/(-15*d**2*x**5 + 15*e**2*x**7) + 2*I*e**6*x**6*sqrt(-1 + e**2*x**2/d**2)/(-15*d**5*x**5 + 15*d**3*e**2*x**7) - I*e**4*x**4*sqrt(-1 + e**2*x**2/d**2)/(-15*d**3*x**5 + 15*d*e**2*x**7), Abs(e**2*x**2/d**2) > 1), (3*d**3*sqrt(1 - e**2*x**2/d**2)/(-15*d**2*x**5 + 15*e**2*x**7) - 4*d*e**2*x**2*sqrt(1 - e**2*x**2/d**2)/(-15*d**2*x**5 + 15*e**2*x**7) + 2*e**6*x**6*sqrt(1 - e**2*x**2/d**2)/(-15*d**5*x**5 + 15*d**3*e**2*x**7) - e**4*x**4*sqrt(1 - e**2*x**2/d**2)/(-15*d**3*x**5 + 15*d*e**2*x**7), True))","C",0
171,0,0,0,0.000000," ","integrate(x**4/(e*x+d)**2/(-e**2*x**2+d**2)**(3/2),x)","\int \frac{x^{4}}{\left(- \left(- d + e x\right) \left(d + e x\right)\right)^{\frac{3}{2}} \left(d + e x\right)^{2}}\, dx"," ",0,"Integral(x**4/((-(-d + e*x)*(d + e*x))**(3/2)*(d + e*x)**2), x)","F",0
172,0,0,0,0.000000," ","integrate(x**3/(e*x+d)**2/(-e**2*x**2+d**2)**(3/2),x)","\int \frac{x^{3}}{\left(- \left(- d + e x\right) \left(d + e x\right)\right)^{\frac{3}{2}} \left(d + e x\right)^{2}}\, dx"," ",0,"Integral(x**3/((-(-d + e*x)*(d + e*x))**(3/2)*(d + e*x)**2), x)","F",0
173,0,0,0,0.000000," ","integrate(x**2/(e*x+d)**2/(-e**2*x**2+d**2)**(3/2),x)","\int \frac{x^{2}}{\left(- \left(- d + e x\right) \left(d + e x\right)\right)^{\frac{3}{2}} \left(d + e x\right)^{2}}\, dx"," ",0,"Integral(x**2/((-(-d + e*x)*(d + e*x))**(3/2)*(d + e*x)**2), x)","F",0
174,0,0,0,0.000000," ","integrate(x/(e*x+d)**2/(-e**2*x**2+d**2)**(3/2),x)","\int \frac{x}{\left(- \left(- d + e x\right) \left(d + e x\right)\right)^{\frac{3}{2}} \left(d + e x\right)^{2}}\, dx"," ",0,"Integral(x/((-(-d + e*x)*(d + e*x))**(3/2)*(d + e*x)**2), x)","F",0
175,0,0,0,0.000000," ","integrate(1/(e*x+d)**2/(-e**2*x**2+d**2)**(3/2),x)","\int \frac{1}{\left(- \left(- d + e x\right) \left(d + e x\right)\right)^{\frac{3}{2}} \left(d + e x\right)^{2}}\, dx"," ",0,"Integral(1/((-(-d + e*x)*(d + e*x))**(3/2)*(d + e*x)**2), x)","F",0
176,0,0,0,0.000000," ","integrate(1/x/(e*x+d)**2/(-e**2*x**2+d**2)**(3/2),x)","\int \frac{1}{x \left(- \left(- d + e x\right) \left(d + e x\right)\right)^{\frac{3}{2}} \left(d + e x\right)^{2}}\, dx"," ",0,"Integral(1/(x*(-(-d + e*x)*(d + e*x))**(3/2)*(d + e*x)**2), x)","F",0
177,0,0,0,0.000000," ","integrate(1/x**2/(e*x+d)**2/(-e**2*x**2+d**2)**(3/2),x)","\int \frac{1}{x^{2} \left(- \left(- d + e x\right) \left(d + e x\right)\right)^{\frac{3}{2}} \left(d + e x\right)^{2}}\, dx"," ",0,"Integral(1/(x**2*(-(-d + e*x)*(d + e*x))**(3/2)*(d + e*x)**2), x)","F",0
178,0,0,0,0.000000," ","integrate(1/x**3/(e*x+d)**2/(-e**2*x**2+d**2)**(3/2),x)","\int \frac{1}{x^{3} \left(- \left(- d + e x\right) \left(d + e x\right)\right)^{\frac{3}{2}} \left(d + e x\right)^{2}}\, dx"," ",0,"Integral(1/(x**3*(-(-d + e*x)*(d + e*x))**(3/2)*(d + e*x)**2), x)","F",0
179,0,0,0,0.000000," ","integrate(x**5/(e*x+d)**3/(-e**2*x**2+d**2)**(1/2),x)","\int \frac{x^{5}}{\sqrt{- \left(- d + e x\right) \left(d + e x\right)} \left(d + e x\right)^{3}}\, dx"," ",0,"Integral(x**5/(sqrt(-(-d + e*x)*(d + e*x))*(d + e*x)**3), x)","F",0
180,0,0,0,0.000000," ","integrate(x**4/(e*x+d)**3/(-e**2*x**2+d**2)**(1/2),x)","\int \frac{x^{4}}{\sqrt{- \left(- d + e x\right) \left(d + e x\right)} \left(d + e x\right)^{3}}\, dx"," ",0,"Integral(x**4/(sqrt(-(-d + e*x)*(d + e*x))*(d + e*x)**3), x)","F",0
181,0,0,0,0.000000," ","integrate(x**3/(e*x+d)**3/(-e**2*x**2+d**2)**(1/2),x)","\int \frac{x^{3}}{\sqrt{- \left(- d + e x\right) \left(d + e x\right)} \left(d + e x\right)^{3}}\, dx"," ",0,"Integral(x**3/(sqrt(-(-d + e*x)*(d + e*x))*(d + e*x)**3), x)","F",0
182,0,0,0,0.000000," ","integrate(x**2/(e*x+d)**3/(-e**2*x**2+d**2)**(1/2),x)","\int \frac{x^{2}}{\sqrt{- \left(- d + e x\right) \left(d + e x\right)} \left(d + e x\right)^{3}}\, dx"," ",0,"Integral(x**2/(sqrt(-(-d + e*x)*(d + e*x))*(d + e*x)**3), x)","F",0
183,0,0,0,0.000000," ","integrate(x/(e*x+d)**3/(-e**2*x**2+d**2)**(1/2),x)","\int \frac{x}{\sqrt{- \left(- d + e x\right) \left(d + e x\right)} \left(d + e x\right)^{3}}\, dx"," ",0,"Integral(x/(sqrt(-(-d + e*x)*(d + e*x))*(d + e*x)**3), x)","F",0
184,0,0,0,0.000000," ","integrate(1/(e*x+d)**3/(-e**2*x**2+d**2)**(1/2),x)","\int \frac{1}{\sqrt{- \left(- d + e x\right) \left(d + e x\right)} \left(d + e x\right)^{3}}\, dx"," ",0,"Integral(1/(sqrt(-(-d + e*x)*(d + e*x))*(d + e*x)**3), x)","F",0
185,0,0,0,0.000000," ","integrate(1/x/(e*x+d)**3/(-e**2*x**2+d**2)**(1/2),x)","\int \frac{1}{x \sqrt{- \left(- d + e x\right) \left(d + e x\right)} \left(d + e x\right)^{3}}\, dx"," ",0,"Integral(1/(x*sqrt(-(-d + e*x)*(d + e*x))*(d + e*x)**3), x)","F",0
186,0,0,0,0.000000," ","integrate(1/x**2/(e*x+d)**3/(-e**2*x**2+d**2)**(1/2),x)","\int \frac{1}{x^{2} \sqrt{- \left(- d + e x\right) \left(d + e x\right)} \left(d + e x\right)^{3}}\, dx"," ",0,"Integral(1/(x**2*sqrt(-(-d + e*x)*(d + e*x))*(d + e*x)**3), x)","F",0
187,0,0,0,0.000000," ","integrate(1/x**3/(e*x+d)**3/(-e**2*x**2+d**2)**(1/2),x)","\int \frac{1}{x^{3} \sqrt{- \left(- d + e x\right) \left(d + e x\right)} \left(d + e x\right)^{3}}\, dx"," ",0,"Integral(1/(x**3*sqrt(-(-d + e*x)*(d + e*x))*(d + e*x)**3), x)","F",0
188,0,0,0,0.000000," ","integrate(x**5*(-e**2*x**2+d**2)**(1/2)/(e*x+d)**4,x)","\int \frac{x^{5} \sqrt{- \left(- d + e x\right) \left(d + e x\right)}}{\left(d + e x\right)^{4}}\, dx"," ",0,"Integral(x**5*sqrt(-(-d + e*x)*(d + e*x))/(d + e*x)**4, x)","F",0
189,0,0,0,0.000000," ","integrate(x**4*(-e**2*x**2+d**2)**(1/2)/(e*x+d)**4,x)","\int \frac{x^{4} \sqrt{- \left(- d + e x\right) \left(d + e x\right)}}{\left(d + e x\right)^{4}}\, dx"," ",0,"Integral(x**4*sqrt(-(-d + e*x)*(d + e*x))/(d + e*x)**4, x)","F",0
190,0,0,0,0.000000," ","integrate(x**3*(-e**2*x**2+d**2)**(1/2)/(e*x+d)**4,x)","\int \frac{x^{3} \sqrt{- \left(- d + e x\right) \left(d + e x\right)}}{\left(d + e x\right)^{4}}\, dx"," ",0,"Integral(x**3*sqrt(-(-d + e*x)*(d + e*x))/(d + e*x)**4, x)","F",0
191,0,0,0,0.000000," ","integrate(x**2*(-e**2*x**2+d**2)**(1/2)/(e*x+d)**4,x)","\int \frac{x^{2} \sqrt{- \left(- d + e x\right) \left(d + e x\right)}}{\left(d + e x\right)^{4}}\, dx"," ",0,"Integral(x**2*sqrt(-(-d + e*x)*(d + e*x))/(d + e*x)**4, x)","F",0
192,0,0,0,0.000000," ","integrate(x*(-e**2*x**2+d**2)**(1/2)/(e*x+d)**4,x)","\int \frac{x \sqrt{- \left(- d + e x\right) \left(d + e x\right)}}{\left(d + e x\right)^{4}}\, dx"," ",0,"Integral(x*sqrt(-(-d + e*x)*(d + e*x))/(d + e*x)**4, x)","F",0
193,0,0,0,0.000000," ","integrate((-e**2*x**2+d**2)**(1/2)/(e*x+d)**4,x)","\int \frac{\sqrt{- \left(- d + e x\right) \left(d + e x\right)}}{\left(d + e x\right)^{4}}\, dx"," ",0,"Integral(sqrt(-(-d + e*x)*(d + e*x))/(d + e*x)**4, x)","F",0
194,0,0,0,0.000000," ","integrate((-e**2*x**2+d**2)**(1/2)/x/(e*x+d)**4,x)","\int \frac{\sqrt{- \left(- d + e x\right) \left(d + e x\right)}}{x \left(d + e x\right)^{4}}\, dx"," ",0,"Integral(sqrt(-(-d + e*x)*(d + e*x))/(x*(d + e*x)**4), x)","F",0
195,0,0,0,0.000000," ","integrate((-e**2*x**2+d**2)**(1/2)/x**2/(e*x+d)**4,x)","\int \frac{\sqrt{- \left(- d + e x\right) \left(d + e x\right)}}{x^{2} \left(d + e x\right)^{4}}\, dx"," ",0,"Integral(sqrt(-(-d + e*x)*(d + e*x))/(x**2*(d + e*x)**4), x)","F",0
196,0,0,0,0.000000," ","integrate((-e**2*x**2+d**2)**(1/2)/x**3/(e*x+d)**4,x)","\int \frac{\sqrt{- \left(- d + e x\right) \left(d + e x\right)}}{x^{3} \left(d + e x\right)^{4}}\, dx"," ",0,"Integral(sqrt(-(-d + e*x)*(d + e*x))/(x**3*(d + e*x)**4), x)","F",0
197,0,0,0,0.000000," ","integrate((-e**2*x**2+d**2)**(1/2)/x**4/(e*x+d)**4,x)","\int \frac{\sqrt{- \left(- d + e x\right) \left(d + e x\right)}}{x^{4} \left(d + e x\right)^{4}}\, dx"," ",0,"Integral(sqrt(-(-d + e*x)*(d + e*x))/(x**4*(d + e*x)**4), x)","F",0
198,0,0,0,0.000000," ","integrate(x**5*(-e**2*x**2+d**2)**(5/2)/(e*x+d)**4,x)","\int \frac{x^{5} \left(- \left(- d + e x\right) \left(d + e x\right)\right)^{\frac{5}{2}}}{\left(d + e x\right)^{4}}\, dx"," ",0,"Integral(x**5*(-(-d + e*x)*(d + e*x))**(5/2)/(d + e*x)**4, x)","F",0
199,0,0,0,0.000000," ","integrate(x**4*(-e**2*x**2+d**2)**(5/2)/(e*x+d)**4,x)","\int \frac{x^{4} \left(- \left(- d + e x\right) \left(d + e x\right)\right)^{\frac{5}{2}}}{\left(d + e x\right)^{4}}\, dx"," ",0,"Integral(x**4*(-(-d + e*x)*(d + e*x))**(5/2)/(d + e*x)**4, x)","F",0
200,0,0,0,0.000000," ","integrate(x**3*(-e**2*x**2+d**2)**(5/2)/(e*x+d)**4,x)","\int \frac{x^{3} \left(- \left(- d + e x\right) \left(d + e x\right)\right)^{\frac{5}{2}}}{\left(d + e x\right)^{4}}\, dx"," ",0,"Integral(x**3*(-(-d + e*x)*(d + e*x))**(5/2)/(d + e*x)**4, x)","F",0
201,0,0,0,0.000000," ","integrate(x**2*(-e**2*x**2+d**2)**(5/2)/(e*x+d)**4,x)","\int \frac{x^{2} \left(- \left(- d + e x\right) \left(d + e x\right)\right)^{\frac{5}{2}}}{\left(d + e x\right)^{4}}\, dx"," ",0,"Integral(x**2*(-(-d + e*x)*(d + e*x))**(5/2)/(d + e*x)**4, x)","F",0
202,0,0,0,0.000000," ","integrate(x*(-e**2*x**2+d**2)**(5/2)/(e*x+d)**4,x)","\int \frac{x \left(- \left(- d + e x\right) \left(d + e x\right)\right)^{\frac{5}{2}}}{\left(d + e x\right)^{4}}\, dx"," ",0,"Integral(x*(-(-d + e*x)*(d + e*x))**(5/2)/(d + e*x)**4, x)","F",0
203,0,0,0,0.000000," ","integrate((-e**2*x**2+d**2)**(5/2)/(e*x+d)**4,x)","\int \frac{\left(- \left(- d + e x\right) \left(d + e x\right)\right)^{\frac{5}{2}}}{\left(d + e x\right)^{4}}\, dx"," ",0,"Integral((-(-d + e*x)*(d + e*x))**(5/2)/(d + e*x)**4, x)","F",0
204,0,0,0,0.000000," ","integrate((-e**2*x**2+d**2)**(5/2)/x/(e*x+d)**4,x)","\int \frac{\left(- \left(- d + e x\right) \left(d + e x\right)\right)^{\frac{5}{2}}}{x \left(d + e x\right)^{4}}\, dx"," ",0,"Integral((-(-d + e*x)*(d + e*x))**(5/2)/(x*(d + e*x)**4), x)","F",0
205,0,0,0,0.000000," ","integrate((-e**2*x**2+d**2)**(5/2)/x**2/(e*x+d)**4,x)","\int \frac{\left(- \left(- d + e x\right) \left(d + e x\right)\right)^{\frac{5}{2}}}{x^{2} \left(d + e x\right)^{4}}\, dx"," ",0,"Integral((-(-d + e*x)*(d + e*x))**(5/2)/(x**2*(d + e*x)**4), x)","F",0
206,0,0,0,0.000000," ","integrate((-e**2*x**2+d**2)**(5/2)/x**3/(e*x+d)**4,x)","\int \frac{\left(- \left(- d + e x\right) \left(d + e x\right)\right)^{\frac{5}{2}}}{x^{3} \left(d + e x\right)^{4}}\, dx"," ",0,"Integral((-(-d + e*x)*(d + e*x))**(5/2)/(x**3*(d + e*x)**4), x)","F",0
207,0,0,0,0.000000," ","integrate((-e**2*x**2+d**2)**(5/2)/x**4/(e*x+d)**4,x)","\int \frac{\left(- \left(- d + e x\right) \left(d + e x\right)\right)^{\frac{5}{2}}}{x^{4} \left(d + e x\right)^{4}}\, dx"," ",0,"Integral((-(-d + e*x)*(d + e*x))**(5/2)/(x**4*(d + e*x)**4), x)","F",0
208,0,0,0,0.000000," ","integrate((-e**2*x**2+d**2)**(5/2)/x**5/(e*x+d)**4,x)","\int \frac{\left(- \left(- d + e x\right) \left(d + e x\right)\right)^{\frac{5}{2}}}{x^{5} \left(d + e x\right)^{4}}\, dx"," ",0,"Integral((-(-d + e*x)*(d + e*x))**(5/2)/(x**5*(d + e*x)**4), x)","F",0
209,0,0,0,0.000000," ","integrate((-e**2*x**2+d**2)**(5/2)/x**6/(e*x+d)**4,x)","\int \frac{\left(- \left(- d + e x\right) \left(d + e x\right)\right)^{\frac{5}{2}}}{x^{6} \left(d + e x\right)^{4}}\, dx"," ",0,"Integral((-(-d + e*x)*(d + e*x))**(5/2)/(x**6*(d + e*x)**4), x)","F",0
210,0,0,0,0.000000," ","integrate(x**2*(-a**2*x**2+1)**(1/2)/(-a*x+1)**4,x)","\int \frac{x^{2} \sqrt{- \left(a x - 1\right) \left(a x + 1\right)}}{\left(a x - 1\right)^{4}}\, dx"," ",0,"Integral(x**2*sqrt(-(a*x - 1)*(a*x + 1))/(a*x - 1)**4, x)","F",0
211,0,0,0,0.000000," ","integrate(x**2*(-a**2*x**2+1)**(1/2)/(-a*x+1)**5,x)","- \int \frac{x^{2} \sqrt{- a^{2} x^{2} + 1}}{a^{5} x^{5} - 5 a^{4} x^{4} + 10 a^{3} x^{3} - 10 a^{2} x^{2} + 5 a x - 1}\, dx"," ",0,"-Integral(x**2*sqrt(-a**2*x**2 + 1)/(a**5*x**5 - 5*a**4*x**4 + 10*a**3*x**3 - 10*a**2*x**2 + 5*a*x - 1), x)","F",0
212,0,0,0,0.000000," ","integrate(x**3/(e*x+d)**4/(-e**2*x**2+d**2)**(7/2),x)","\int \frac{x^{3}}{\left(- \left(- d + e x\right) \left(d + e x\right)\right)^{\frac{7}{2}} \left(d + e x\right)^{4}}\, dx"," ",0,"Integral(x**3/((-(-d + e*x)*(d + e*x))**(7/2)*(d + e*x)**4), x)","F",0
213,0,0,0,0.000000," ","integrate(x**2/(e*x+d)**4/(-e**2*x**2+d**2)**(7/2),x)","\int \frac{x^{2}}{\left(- \left(- d + e x\right) \left(d + e x\right)\right)^{\frac{7}{2}} \left(d + e x\right)^{4}}\, dx"," ",0,"Integral(x**2/((-(-d + e*x)*(d + e*x))**(7/2)*(d + e*x)**4), x)","F",0
214,0,0,0,0.000000," ","integrate(x/(e*x+d)**4/(-e**2*x**2+d**2)**(7/2),x)","\int \frac{x}{\left(- \left(- d + e x\right) \left(d + e x\right)\right)^{\frac{7}{2}} \left(d + e x\right)^{4}}\, dx"," ",0,"Integral(x/((-(-d + e*x)*(d + e*x))**(7/2)*(d + e*x)**4), x)","F",0
215,0,0,0,0.000000," ","integrate(1/(e*x+d)**4/(-e**2*x**2+d**2)**(7/2),x)","\int \frac{1}{\left(- \left(- d + e x\right) \left(d + e x\right)\right)^{\frac{7}{2}} \left(d + e x\right)^{4}}\, dx"," ",0,"Integral(1/((-(-d + e*x)*(d + e*x))**(7/2)*(d + e*x)**4), x)","F",0
216,0,0,0,0.000000," ","integrate(1/x/(e*x+d)**4/(-e**2*x**2+d**2)**(7/2),x)","\int \frac{1}{x \left(- \left(- d + e x\right) \left(d + e x\right)\right)^{\frac{7}{2}} \left(d + e x\right)^{4}}\, dx"," ",0,"Integral(1/(x*(-(-d + e*x)*(d + e*x))**(7/2)*(d + e*x)**4), x)","F",0
217,0,0,0,0.000000," ","integrate(1/x**2/(e*x+d)**4/(-e**2*x**2+d**2)**(7/2),x)","\int \frac{1}{x^{2} \left(- \left(- d + e x\right) \left(d + e x\right)\right)^{\frac{7}{2}} \left(d + e x\right)^{4}}\, dx"," ",0,"Integral(1/(x**2*(-(-d + e*x)*(d + e*x))**(7/2)*(d + e*x)**4), x)","F",0
218,0,0,0,0.000000," ","integrate((-a*c*x+c)**(1/2)*(-a**2*x**2+1)**(1/2)/x**2,x)","\int \frac{\sqrt{- c \left(a x - 1\right)} \sqrt{- \left(a x - 1\right) \left(a x + 1\right)}}{x^{2}}\, dx"," ",0,"Integral(sqrt(-c*(a*x - 1))*sqrt(-(a*x - 1)*(a*x + 1))/x**2, x)","F",0
219,0,0,0,0.000000," ","integrate((-a*c*x+c)**(1/2)/x/(-a**2*x**2+1)**(1/2),x)","\int \frac{\sqrt{- c \left(a x - 1\right)}}{x \sqrt{- \left(a x - 1\right) \left(a x + 1\right)}}\, dx"," ",0,"Integral(sqrt(-c*(a*x - 1))/(x*sqrt(-(a*x - 1)*(a*x + 1))), x)","F",0
220,1,83,0,1.904180," ","integrate((-a*x+1)**(1/2)/x**(1/2),x)","\begin{cases} \frac{i a x^{\frac{3}{2}}}{\sqrt{a x - 1}} - \frac{i \sqrt{x}}{\sqrt{a x - 1}} - \frac{i \operatorname{acosh}{\left(\sqrt{a} \sqrt{x} \right)}}{\sqrt{a}} & \text{for}\: \left|{a x}\right| > 1 \\\sqrt{x} \sqrt{- a x + 1} + \frac{\operatorname{asin}{\left(\sqrt{a} \sqrt{x} \right)}}{\sqrt{a}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((I*a*x**(3/2)/sqrt(a*x - 1) - I*sqrt(x)/sqrt(a*x - 1) - I*acosh(sqrt(a)*sqrt(x))/sqrt(a), Abs(a*x) > 1), (sqrt(x)*sqrt(-a*x + 1) + asin(sqrt(a)*sqrt(x))/sqrt(a), True))","A",0
221,0,0,0,0.000000," ","integrate((-a**2*x**2+1)**(1/2)/x**(1/2)/(a*x+1)**(1/2),x)","\int \frac{\sqrt{- \left(a x - 1\right) \left(a x + 1\right)}}{\sqrt{x} \sqrt{a x + 1}}\, dx"," ",0,"Integral(sqrt(-(a*x - 1)*(a*x + 1))/(sqrt(x)*sqrt(a*x + 1)), x)","F",0
222,1,29,0,1.966493," ","integrate((a*x+1)**(1/2)/x**(1/2),x)","\sqrt{x} \sqrt{a x + 1} + \frac{\operatorname{asinh}{\left(\sqrt{a} \sqrt{x} \right)}}{\sqrt{a}}"," ",0,"sqrt(x)*sqrt(a*x + 1) + asinh(sqrt(a)*sqrt(x))/sqrt(a)","A",0
223,0,0,0,0.000000," ","integrate((-a**2*x**2+1)**(1/2)/x**(1/2)/(-a*x+1)**(1/2),x)","\int \frac{\sqrt{- \left(a x - 1\right) \left(a x + 1\right)}}{\sqrt{x} \sqrt{- a x + 1}}\, dx"," ",0,"Integral(sqrt(-(a*x - 1)*(a*x + 1))/(sqrt(x)*sqrt(-a*x + 1)), x)","F",0
224,1,148,0,3.391433," ","integrate(x**(1/2)*(-a*x+1)**(1/2),x)","\begin{cases} \frac{i a x^{\frac{5}{2}}}{2 \sqrt{a x - 1}} - \frac{3 i x^{\frac{3}{2}}}{4 \sqrt{a x - 1}} + \frac{i \sqrt{x}}{4 a \sqrt{a x - 1}} - \frac{i \operatorname{acosh}{\left(\sqrt{a} \sqrt{x} \right)}}{4 a^{\frac{3}{2}}} & \text{for}\: \left|{a x}\right| > 1 \\- \frac{a x^{\frac{5}{2}}}{2 \sqrt{- a x + 1}} + \frac{3 x^{\frac{3}{2}}}{4 \sqrt{- a x + 1}} - \frac{\sqrt{x}}{4 a \sqrt{- a x + 1}} + \frac{\operatorname{asin}{\left(\sqrt{a} \sqrt{x} \right)}}{4 a^{\frac{3}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((I*a*x**(5/2)/(2*sqrt(a*x - 1)) - 3*I*x**(3/2)/(4*sqrt(a*x - 1)) + I*sqrt(x)/(4*a*sqrt(a*x - 1)) - I*acosh(sqrt(a)*sqrt(x))/(4*a**(3/2)), Abs(a*x) > 1), (-a*x**(5/2)/(2*sqrt(-a*x + 1)) + 3*x**(3/2)/(4*sqrt(-a*x + 1)) - sqrt(x)/(4*a*sqrt(-a*x + 1)) + asin(sqrt(a)*sqrt(x))/(4*a**(3/2)), True))","A",0
225,0,0,0,0.000000," ","integrate(x**(1/2)*(-a**2*x**2+1)**(1/2)/(a*x+1)**(1/2),x)","\int \frac{\sqrt{x} \sqrt{- \left(a x - 1\right) \left(a x + 1\right)}}{\sqrt{a x + 1}}\, dx"," ",0,"Integral(sqrt(x)*sqrt(-(a*x - 1)*(a*x + 1))/sqrt(a*x + 1), x)","F",0
226,1,513,0,45.913677," ","integrate((g*x)**m*(e*x+d)**3*(-e**2*x**2+d**2)**(5/2),x)","\frac{d^{8} g^{m} x x^{m} \Gamma\left(\frac{m}{2} + \frac{1}{2}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{m}{2} + \frac{1}{2} \\ \frac{m}{2} + \frac{3}{2} \end{matrix}\middle| {\frac{e^{2} x^{2} e^{2 i \pi}}{d^{2}}} \right)}}{2 \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)} + \frac{3 d^{7} e g^{m} x^{2} x^{m} \Gamma\left(\frac{m}{2} + 1\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{m}{2} + 1 \\ \frac{m}{2} + 2 \end{matrix}\middle| {\frac{e^{2} x^{2} e^{2 i \pi}}{d^{2}}} \right)}}{2 \Gamma\left(\frac{m}{2} + 2\right)} + \frac{d^{6} e^{2} g^{m} x^{3} x^{m} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{m}{2} + \frac{3}{2} \\ \frac{m}{2} + \frac{5}{2} \end{matrix}\middle| {\frac{e^{2} x^{2} e^{2 i \pi}}{d^{2}}} \right)}}{2 \Gamma\left(\frac{m}{2} + \frac{5}{2}\right)} - \frac{5 d^{5} e^{3} g^{m} x^{4} x^{m} \Gamma\left(\frac{m}{2} + 2\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{m}{2} + 2 \\ \frac{m}{2} + 3 \end{matrix}\middle| {\frac{e^{2} x^{2} e^{2 i \pi}}{d^{2}}} \right)}}{2 \Gamma\left(\frac{m}{2} + 3\right)} - \frac{5 d^{4} e^{4} g^{m} x^{5} x^{m} \Gamma\left(\frac{m}{2} + \frac{5}{2}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{m}{2} + \frac{5}{2} \\ \frac{m}{2} + \frac{7}{2} \end{matrix}\middle| {\frac{e^{2} x^{2} e^{2 i \pi}}{d^{2}}} \right)}}{2 \Gamma\left(\frac{m}{2} + \frac{7}{2}\right)} + \frac{d^{3} e^{5} g^{m} x^{6} x^{m} \Gamma\left(\frac{m}{2} + 3\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{m}{2} + 3 \\ \frac{m}{2} + 4 \end{matrix}\middle| {\frac{e^{2} x^{2} e^{2 i \pi}}{d^{2}}} \right)}}{2 \Gamma\left(\frac{m}{2} + 4\right)} + \frac{3 d^{2} e^{6} g^{m} x^{7} x^{m} \Gamma\left(\frac{m}{2} + \frac{7}{2}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{m}{2} + \frac{7}{2} \\ \frac{m}{2} + \frac{9}{2} \end{matrix}\middle| {\frac{e^{2} x^{2} e^{2 i \pi}}{d^{2}}} \right)}}{2 \Gamma\left(\frac{m}{2} + \frac{9}{2}\right)} + \frac{d e^{7} g^{m} x^{8} x^{m} \Gamma\left(\frac{m}{2} + 4\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{m}{2} + 4 \\ \frac{m}{2} + 5 \end{matrix}\middle| {\frac{e^{2} x^{2} e^{2 i \pi}}{d^{2}}} \right)}}{2 \Gamma\left(\frac{m}{2} + 5\right)}"," ",0,"d**8*g**m*x*x**m*gamma(m/2 + 1/2)*hyper((-1/2, m/2 + 1/2), (m/2 + 3/2,), e**2*x**2*exp_polar(2*I*pi)/d**2)/(2*gamma(m/2 + 3/2)) + 3*d**7*e*g**m*x**2*x**m*gamma(m/2 + 1)*hyper((-1/2, m/2 + 1), (m/2 + 2,), e**2*x**2*exp_polar(2*I*pi)/d**2)/(2*gamma(m/2 + 2)) + d**6*e**2*g**m*x**3*x**m*gamma(m/2 + 3/2)*hyper((-1/2, m/2 + 3/2), (m/2 + 5/2,), e**2*x**2*exp_polar(2*I*pi)/d**2)/(2*gamma(m/2 + 5/2)) - 5*d**5*e**3*g**m*x**4*x**m*gamma(m/2 + 2)*hyper((-1/2, m/2 + 2), (m/2 + 3,), e**2*x**2*exp_polar(2*I*pi)/d**2)/(2*gamma(m/2 + 3)) - 5*d**4*e**4*g**m*x**5*x**m*gamma(m/2 + 5/2)*hyper((-1/2, m/2 + 5/2), (m/2 + 7/2,), e**2*x**2*exp_polar(2*I*pi)/d**2)/(2*gamma(m/2 + 7/2)) + d**3*e**5*g**m*x**6*x**m*gamma(m/2 + 3)*hyper((-1/2, m/2 + 3), (m/2 + 4,), e**2*x**2*exp_polar(2*I*pi)/d**2)/(2*gamma(m/2 + 4)) + 3*d**2*e**6*g**m*x**7*x**m*gamma(m/2 + 7/2)*hyper((-1/2, m/2 + 7/2), (m/2 + 9/2,), e**2*x**2*exp_polar(2*I*pi)/d**2)/(2*gamma(m/2 + 9/2)) + d*e**7*g**m*x**8*x**m*gamma(m/2 + 4)*hyper((-1/2, m/2 + 4), (m/2 + 5,), e**2*x**2*exp_polar(2*I*pi)/d**2)/(2*gamma(m/2 + 5))","C",0
227,1,442,0,33.194143," ","integrate((g*x)**m*(e*x+d)**2*(-e**2*x**2+d**2)**(5/2),x)","\frac{d^{7} g^{m} x x^{m} \Gamma\left(\frac{m}{2} + \frac{1}{2}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{m}{2} + \frac{1}{2} \\ \frac{m}{2} + \frac{3}{2} \end{matrix}\middle| {\frac{e^{2} x^{2} e^{2 i \pi}}{d^{2}}} \right)}}{2 \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)} + \frac{d^{6} e g^{m} x^{2} x^{m} \Gamma\left(\frac{m}{2} + 1\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{m}{2} + 1 \\ \frac{m}{2} + 2 \end{matrix}\middle| {\frac{e^{2} x^{2} e^{2 i \pi}}{d^{2}}} \right)}}{\Gamma\left(\frac{m}{2} + 2\right)} - \frac{d^{5} e^{2} g^{m} x^{3} x^{m} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{m}{2} + \frac{3}{2} \\ \frac{m}{2} + \frac{5}{2} \end{matrix}\middle| {\frac{e^{2} x^{2} e^{2 i \pi}}{d^{2}}} \right)}}{2 \Gamma\left(\frac{m}{2} + \frac{5}{2}\right)} - \frac{2 d^{4} e^{3} g^{m} x^{4} x^{m} \Gamma\left(\frac{m}{2} + 2\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{m}{2} + 2 \\ \frac{m}{2} + 3 \end{matrix}\middle| {\frac{e^{2} x^{2} e^{2 i \pi}}{d^{2}}} \right)}}{\Gamma\left(\frac{m}{2} + 3\right)} - \frac{d^{3} e^{4} g^{m} x^{5} x^{m} \Gamma\left(\frac{m}{2} + \frac{5}{2}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{m}{2} + \frac{5}{2} \\ \frac{m}{2} + \frac{7}{2} \end{matrix}\middle| {\frac{e^{2} x^{2} e^{2 i \pi}}{d^{2}}} \right)}}{2 \Gamma\left(\frac{m}{2} + \frac{7}{2}\right)} + \frac{d^{2} e^{5} g^{m} x^{6} x^{m} \Gamma\left(\frac{m}{2} + 3\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{m}{2} + 3 \\ \frac{m}{2} + 4 \end{matrix}\middle| {\frac{e^{2} x^{2} e^{2 i \pi}}{d^{2}}} \right)}}{\Gamma\left(\frac{m}{2} + 4\right)} + \frac{d e^{6} g^{m} x^{7} x^{m} \Gamma\left(\frac{m}{2} + \frac{7}{2}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{m}{2} + \frac{7}{2} \\ \frac{m}{2} + \frac{9}{2} \end{matrix}\middle| {\frac{e^{2} x^{2} e^{2 i \pi}}{d^{2}}} \right)}}{2 \Gamma\left(\frac{m}{2} + \frac{9}{2}\right)}"," ",0,"d**7*g**m*x*x**m*gamma(m/2 + 1/2)*hyper((-1/2, m/2 + 1/2), (m/2 + 3/2,), e**2*x**2*exp_polar(2*I*pi)/d**2)/(2*gamma(m/2 + 3/2)) + d**6*e*g**m*x**2*x**m*gamma(m/2 + 1)*hyper((-1/2, m/2 + 1), (m/2 + 2,), e**2*x**2*exp_polar(2*I*pi)/d**2)/gamma(m/2 + 2) - d**5*e**2*g**m*x**3*x**m*gamma(m/2 + 3/2)*hyper((-1/2, m/2 + 3/2), (m/2 + 5/2,), e**2*x**2*exp_polar(2*I*pi)/d**2)/(2*gamma(m/2 + 5/2)) - 2*d**4*e**3*g**m*x**4*x**m*gamma(m/2 + 2)*hyper((-1/2, m/2 + 2), (m/2 + 3,), e**2*x**2*exp_polar(2*I*pi)/d**2)/gamma(m/2 + 3) - d**3*e**4*g**m*x**5*x**m*gamma(m/2 + 5/2)*hyper((-1/2, m/2 + 5/2), (m/2 + 7/2,), e**2*x**2*exp_polar(2*I*pi)/d**2)/(2*gamma(m/2 + 7/2)) + d**2*e**5*g**m*x**6*x**m*gamma(m/2 + 3)*hyper((-1/2, m/2 + 3), (m/2 + 4,), e**2*x**2*exp_polar(2*I*pi)/d**2)/gamma(m/2 + 4) + d*e**6*g**m*x**7*x**m*gamma(m/2 + 7/2)*hyper((-1/2, m/2 + 7/2), (m/2 + 9/2,), e**2*x**2*exp_polar(2*I*pi)/d**2)/(2*gamma(m/2 + 9/2))","C",0
228,1,374,0,24.576956," ","integrate((g*x)**m*(e*x+d)*(-e**2*x**2+d**2)**(5/2),x)","\frac{d^{6} g^{m} x x^{m} \Gamma\left(\frac{m}{2} + \frac{1}{2}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{m}{2} + \frac{1}{2} \\ \frac{m}{2} + \frac{3}{2} \end{matrix}\middle| {\frac{e^{2} x^{2} e^{2 i \pi}}{d^{2}}} \right)}}{2 \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)} + \frac{d^{5} e g^{m} x^{2} x^{m} \Gamma\left(\frac{m}{2} + 1\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{m}{2} + 1 \\ \frac{m}{2} + 2 \end{matrix}\middle| {\frac{e^{2} x^{2} e^{2 i \pi}}{d^{2}}} \right)}}{2 \Gamma\left(\frac{m}{2} + 2\right)} - \frac{d^{4} e^{2} g^{m} x^{3} x^{m} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{m}{2} + \frac{3}{2} \\ \frac{m}{2} + \frac{5}{2} \end{matrix}\middle| {\frac{e^{2} x^{2} e^{2 i \pi}}{d^{2}}} \right)}}{\Gamma\left(\frac{m}{2} + \frac{5}{2}\right)} - \frac{d^{3} e^{3} g^{m} x^{4} x^{m} \Gamma\left(\frac{m}{2} + 2\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{m}{2} + 2 \\ \frac{m}{2} + 3 \end{matrix}\middle| {\frac{e^{2} x^{2} e^{2 i \pi}}{d^{2}}} \right)}}{\Gamma\left(\frac{m}{2} + 3\right)} + \frac{d^{2} e^{4} g^{m} x^{5} x^{m} \Gamma\left(\frac{m}{2} + \frac{5}{2}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{m}{2} + \frac{5}{2} \\ \frac{m}{2} + \frac{7}{2} \end{matrix}\middle| {\frac{e^{2} x^{2} e^{2 i \pi}}{d^{2}}} \right)}}{2 \Gamma\left(\frac{m}{2} + \frac{7}{2}\right)} + \frac{d e^{5} g^{m} x^{6} x^{m} \Gamma\left(\frac{m}{2} + 3\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{m}{2} + 3 \\ \frac{m}{2} + 4 \end{matrix}\middle| {\frac{e^{2} x^{2} e^{2 i \pi}}{d^{2}}} \right)}}{2 \Gamma\left(\frac{m}{2} + 4\right)}"," ",0,"d**6*g**m*x*x**m*gamma(m/2 + 1/2)*hyper((-1/2, m/2 + 1/2), (m/2 + 3/2,), e**2*x**2*exp_polar(2*I*pi)/d**2)/(2*gamma(m/2 + 3/2)) + d**5*e*g**m*x**2*x**m*gamma(m/2 + 1)*hyper((-1/2, m/2 + 1), (m/2 + 2,), e**2*x**2*exp_polar(2*I*pi)/d**2)/(2*gamma(m/2 + 2)) - d**4*e**2*g**m*x**3*x**m*gamma(m/2 + 3/2)*hyper((-1/2, m/2 + 3/2), (m/2 + 5/2,), e**2*x**2*exp_polar(2*I*pi)/d**2)/gamma(m/2 + 5/2) - d**3*e**3*g**m*x**4*x**m*gamma(m/2 + 2)*hyper((-1/2, m/2 + 2), (m/2 + 3,), e**2*x**2*exp_polar(2*I*pi)/d**2)/gamma(m/2 + 3) + d**2*e**4*g**m*x**5*x**m*gamma(m/2 + 5/2)*hyper((-1/2, m/2 + 5/2), (m/2 + 7/2,), e**2*x**2*exp_polar(2*I*pi)/d**2)/(2*gamma(m/2 + 7/2)) + d*e**5*g**m*x**6*x**m*gamma(m/2 + 3)*hyper((-1/2, m/2 + 3), (m/2 + 4,), e**2*x**2*exp_polar(2*I*pi)/d**2)/(2*gamma(m/2 + 4))","C",0
229,1,61,0,10.073767," ","integrate((g*x)**m*(-e**2*x**2+d**2)**(5/2),x)","\frac{d^{5} g^{m} x x^{m} \Gamma\left(\frac{m}{2} + \frac{1}{2}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{2}, \frac{m}{2} + \frac{1}{2} \\ \frac{m}{2} + \frac{3}{2} \end{matrix}\middle| {\frac{e^{2} x^{2} e^{2 i \pi}}{d^{2}}} \right)}}{2 \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)}"," ",0,"d**5*g**m*x*x**m*gamma(m/2 + 1/2)*hyper((-5/2, m/2 + 1/2), (m/2 + 3/2,), e**2*x**2*exp_polar(2*I*pi)/d**2)/(2*gamma(m/2 + 3/2))","C",0
230,1,248,0,25.455405," ","integrate((g*x)**m*(-e**2*x**2+d**2)**(5/2)/(e*x+d),x)","\frac{d^{4} g^{m} x x^{m} \Gamma\left(\frac{m}{2} + \frac{1}{2}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{m}{2} + \frac{1}{2} \\ \frac{m}{2} + \frac{3}{2} \end{matrix}\middle| {\frac{e^{2} x^{2} e^{2 i \pi}}{d^{2}}} \right)}}{2 \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)} - \frac{d^{3} e g^{m} x^{2} x^{m} \Gamma\left(\frac{m}{2} + 1\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{m}{2} + 1 \\ \frac{m}{2} + 2 \end{matrix}\middle| {\frac{e^{2} x^{2} e^{2 i \pi}}{d^{2}}} \right)}}{2 \Gamma\left(\frac{m}{2} + 2\right)} - \frac{d^{2} e^{2} g^{m} x^{3} x^{m} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{m}{2} + \frac{3}{2} \\ \frac{m}{2} + \frac{5}{2} \end{matrix}\middle| {\frac{e^{2} x^{2} e^{2 i \pi}}{d^{2}}} \right)}}{2 \Gamma\left(\frac{m}{2} + \frac{5}{2}\right)} + \frac{d e^{3} g^{m} x^{4} x^{m} \Gamma\left(\frac{m}{2} + 2\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{m}{2} + 2 \\ \frac{m}{2} + 3 \end{matrix}\middle| {\frac{e^{2} x^{2} e^{2 i \pi}}{d^{2}}} \right)}}{2 \Gamma\left(\frac{m}{2} + 3\right)}"," ",0,"d**4*g**m*x*x**m*gamma(m/2 + 1/2)*hyper((-1/2, m/2 + 1/2), (m/2 + 3/2,), e**2*x**2*exp_polar(2*I*pi)/d**2)/(2*gamma(m/2 + 3/2)) - d**3*e*g**m*x**2*x**m*gamma(m/2 + 1)*hyper((-1/2, m/2 + 1), (m/2 + 2,), e**2*x**2*exp_polar(2*I*pi)/d**2)/(2*gamma(m/2 + 2)) - d**2*e**2*g**m*x**3*x**m*gamma(m/2 + 3/2)*hyper((-1/2, m/2 + 3/2), (m/2 + 5/2,), e**2*x**2*exp_polar(2*I*pi)/d**2)/(2*gamma(m/2 + 5/2)) + d*e**3*g**m*x**4*x**m*gamma(m/2 + 2)*hyper((-1/2, m/2 + 2), (m/2 + 3,), e**2*x**2*exp_polar(2*I*pi)/d**2)/(2*gamma(m/2 + 3))","C",0
231,1,185,0,91.468723," ","integrate((g*x)**m*(-e**2*x**2+d**2)**(5/2)/(e*x+d)**2,x)","\frac{d^{3} g^{m} x x^{m} \Gamma\left(\frac{m}{2} + \frac{1}{2}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{m}{2} + \frac{1}{2} \\ \frac{m}{2} + \frac{3}{2} \end{matrix}\middle| {\frac{e^{2} x^{2} e^{2 i \pi}}{d^{2}}} \right)}}{2 \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)} - \frac{d^{2} e g^{m} x^{2} x^{m} \Gamma\left(\frac{m}{2} + 1\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{m}{2} + 1 \\ \frac{m}{2} + 2 \end{matrix}\middle| {\frac{e^{2} x^{2} e^{2 i \pi}}{d^{2}}} \right)}}{\Gamma\left(\frac{m}{2} + 2\right)} + \frac{d e^{2} g^{m} x^{3} x^{m} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{m}{2} + \frac{3}{2} \\ \frac{m}{2} + \frac{5}{2} \end{matrix}\middle| {\frac{e^{2} x^{2} e^{2 i \pi}}{d^{2}}} \right)}}{2 \Gamma\left(\frac{m}{2} + \frac{5}{2}\right)}"," ",0,"d**3*g**m*x*x**m*gamma(m/2 + 1/2)*hyper((-1/2, m/2 + 1/2), (m/2 + 3/2,), e**2*x**2*exp_polar(2*I*pi)/d**2)/(2*gamma(m/2 + 3/2)) - d**2*e*g**m*x**2*x**m*gamma(m/2 + 1)*hyper((-1/2, m/2 + 1), (m/2 + 2,), e**2*x**2*exp_polar(2*I*pi)/d**2)/gamma(m/2 + 2) + d*e**2*g**m*x**3*x**m*gamma(m/2 + 3/2)*hyper((-1/2, m/2 + 3/2), (m/2 + 5/2,), e**2*x**2*exp_polar(2*I*pi)/d**2)/(2*gamma(m/2 + 5/2))","C",0
232,-2,0,0,0.000000," ","integrate((g*x)**m*(-e**2*x**2+d**2)**(5/2)/(e*x+d)**3,x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
233,0,0,0,0.000000," ","integrate((g*x)**m*(e*x+d)**3/(-e**2*x**2+d**2)**(7/2),x)","\int \frac{\left(g x\right)^{m} \left(d + e x\right)^{3}}{\left(- \left(- d + e x\right) \left(d + e x\right)\right)^{\frac{7}{2}}}\, dx"," ",0,"Integral((g*x)**m*(d + e*x)**3/(-(-d + e*x)*(d + e*x))**(7/2), x)","F",0
234,0,0,0,0.000000," ","integrate((g*x)**m*(e*x+d)**2/(-e**2*x**2+d**2)**(7/2),x)","\int \frac{\left(g x\right)^{m} \left(d + e x\right)^{2}}{\left(- \left(- d + e x\right) \left(d + e x\right)\right)^{\frac{7}{2}}}\, dx"," ",0,"Integral((g*x)**m*(d + e*x)**2/(-(-d + e*x)*(d + e*x))**(7/2), x)","F",0
235,1,117,0,63.251011," ","integrate((g*x)**m*(e*x+d)/(-e**2*x**2+d**2)**(7/2),x)","\frac{g^{m} x x^{m} \Gamma\left(\frac{m}{2} + \frac{1}{2}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{7}{2}, \frac{m}{2} + \frac{1}{2} \\ \frac{m}{2} + \frac{3}{2} \end{matrix}\middle| {\frac{e^{2} x^{2} e^{2 i \pi}}{d^{2}}} \right)}}{2 d^{6} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)} + \frac{e g^{m} x^{2} x^{m} \Gamma\left(\frac{m}{2} + 1\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{7}{2}, \frac{m}{2} + 1 \\ \frac{m}{2} + 2 \end{matrix}\middle| {\frac{e^{2} x^{2} e^{2 i \pi}}{d^{2}}} \right)}}{2 d^{7} \Gamma\left(\frac{m}{2} + 2\right)}"," ",0,"g**m*x*x**m*gamma(m/2 + 1/2)*hyper((7/2, m/2 + 1/2), (m/2 + 3/2,), e**2*x**2*exp_polar(2*I*pi)/d**2)/(2*d**6*gamma(m/2 + 3/2)) + e*g**m*x**2*x**m*gamma(m/2 + 1)*hyper((7/2, m/2 + 1), (m/2 + 2,), e**2*x**2*exp_polar(2*I*pi)/d**2)/(2*d**7*gamma(m/2 + 2))","C",0
236,1,60,0,11.402138," ","integrate((g*x)**m/(-e**2*x**2+d**2)**(7/2),x)","\frac{g^{m} x x^{m} \Gamma\left(\frac{m}{2} + \frac{1}{2}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{7}{2}, \frac{m}{2} + \frac{1}{2} \\ \frac{m}{2} + \frac{3}{2} \end{matrix}\middle| {\frac{e^{2} x^{2} e^{2 i \pi}}{d^{2}}} \right)}}{2 d^{7} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)}"," ",0,"g**m*x*x**m*gamma(m/2 + 1/2)*hyper((7/2, m/2 + 1/2), (m/2 + 3/2,), e**2*x**2*exp_polar(2*I*pi)/d**2)/(2*d**7*gamma(m/2 + 3/2))","C",0
237,0,0,0,0.000000," ","integrate((g*x)**m/(e*x+d)/(-e**2*x**2+d**2)**(7/2),x)","\int \frac{\left(g x\right)^{m}}{\left(- \left(- d + e x\right) \left(d + e x\right)\right)^{\frac{7}{2}} \left(d + e x\right)}\, dx"," ",0,"Integral((g*x)**m/((-(-d + e*x)*(d + e*x))**(7/2)*(d + e*x)), x)","F",0
238,-2,0,0,0.000000," ","integrate((g*x)**m/(e*x+d)**2/(-e**2*x**2+d**2)**(7/2),x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
239,-2,0,0,0.000000," ","integrate((g*x)**m/(e*x+d)**3/(-e**2*x**2+d**2)**(7/2),x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
240,1,972,0,7.456496," ","integrate(x**5*(e*x+d)*(-e**2*x**2+d**2)**p,x)","d \left(\begin{cases} \frac{x^{6} \left(d^{2}\right)^{p}}{6} & \text{for}\: e = 0 \\- \frac{2 d^{4} \log{\left(- \frac{d}{e} + x \right)}}{4 d^{4} e^{6} - 8 d^{2} e^{8} x^{2} + 4 e^{10} x^{4}} - \frac{2 d^{4} \log{\left(\frac{d}{e} + x \right)}}{4 d^{4} e^{6} - 8 d^{2} e^{8} x^{2} + 4 e^{10} x^{4}} - \frac{3 d^{4}}{4 d^{4} e^{6} - 8 d^{2} e^{8} x^{2} + 4 e^{10} x^{4}} + \frac{4 d^{2} e^{2} x^{2} \log{\left(- \frac{d}{e} + x \right)}}{4 d^{4} e^{6} - 8 d^{2} e^{8} x^{2} + 4 e^{10} x^{4}} + \frac{4 d^{2} e^{2} x^{2} \log{\left(\frac{d}{e} + x \right)}}{4 d^{4} e^{6} - 8 d^{2} e^{8} x^{2} + 4 e^{10} x^{4}} + \frac{4 d^{2} e^{2} x^{2}}{4 d^{4} e^{6} - 8 d^{2} e^{8} x^{2} + 4 e^{10} x^{4}} - \frac{2 e^{4} x^{4} \log{\left(- \frac{d}{e} + x \right)}}{4 d^{4} e^{6} - 8 d^{2} e^{8} x^{2} + 4 e^{10} x^{4}} - \frac{2 e^{4} x^{4} \log{\left(\frac{d}{e} + x \right)}}{4 d^{4} e^{6} - 8 d^{2} e^{8} x^{2} + 4 e^{10} x^{4}} & \text{for}\: p = -3 \\- \frac{2 d^{4} \log{\left(- \frac{d}{e} + x \right)}}{- 2 d^{2} e^{6} + 2 e^{8} x^{2}} - \frac{2 d^{4} \log{\left(\frac{d}{e} + x \right)}}{- 2 d^{2} e^{6} + 2 e^{8} x^{2}} - \frac{2 d^{4}}{- 2 d^{2} e^{6} + 2 e^{8} x^{2}} + \frac{2 d^{2} e^{2} x^{2} \log{\left(- \frac{d}{e} + x \right)}}{- 2 d^{2} e^{6} + 2 e^{8} x^{2}} + \frac{2 d^{2} e^{2} x^{2} \log{\left(\frac{d}{e} + x \right)}}{- 2 d^{2} e^{6} + 2 e^{8} x^{2}} + \frac{e^{4} x^{4}}{- 2 d^{2} e^{6} + 2 e^{8} x^{2}} & \text{for}\: p = -2 \\- \frac{d^{4} \log{\left(- \frac{d}{e} + x \right)}}{2 e^{6}} - \frac{d^{4} \log{\left(\frac{d}{e} + x \right)}}{2 e^{6}} - \frac{d^{2} x^{2}}{2 e^{4}} - \frac{x^{4}}{4 e^{2}} & \text{for}\: p = -1 \\- \frac{2 d^{6} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{6} p^{3} + 12 e^{6} p^{2} + 22 e^{6} p + 12 e^{6}} - \frac{2 d^{4} e^{2} p x^{2} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{6} p^{3} + 12 e^{6} p^{2} + 22 e^{6} p + 12 e^{6}} - \frac{d^{2} e^{4} p^{2} x^{4} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{6} p^{3} + 12 e^{6} p^{2} + 22 e^{6} p + 12 e^{6}} - \frac{d^{2} e^{4} p x^{4} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{6} p^{3} + 12 e^{6} p^{2} + 22 e^{6} p + 12 e^{6}} + \frac{e^{6} p^{2} x^{6} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{6} p^{3} + 12 e^{6} p^{2} + 22 e^{6} p + 12 e^{6}} + \frac{3 e^{6} p x^{6} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{6} p^{3} + 12 e^{6} p^{2} + 22 e^{6} p + 12 e^{6}} + \frac{2 e^{6} x^{6} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{6} p^{3} + 12 e^{6} p^{2} + 22 e^{6} p + 12 e^{6}} & \text{otherwise} \end{cases}\right) + \frac{d^{2 p} e x^{7} {{}_{2}F_{1}\left(\begin{matrix} \frac{7}{2}, - p \\ \frac{9}{2} \end{matrix}\middle| {\frac{e^{2} x^{2} e^{2 i \pi}}{d^{2}}} \right)}}{7}"," ",0,"d*Piecewise((x**6*(d**2)**p/6, Eq(e, 0)), (-2*d**4*log(-d/e + x)/(4*d**4*e**6 - 8*d**2*e**8*x**2 + 4*e**10*x**4) - 2*d**4*log(d/e + x)/(4*d**4*e**6 - 8*d**2*e**8*x**2 + 4*e**10*x**4) - 3*d**4/(4*d**4*e**6 - 8*d**2*e**8*x**2 + 4*e**10*x**4) + 4*d**2*e**2*x**2*log(-d/e + x)/(4*d**4*e**6 - 8*d**2*e**8*x**2 + 4*e**10*x**4) + 4*d**2*e**2*x**2*log(d/e + x)/(4*d**4*e**6 - 8*d**2*e**8*x**2 + 4*e**10*x**4) + 4*d**2*e**2*x**2/(4*d**4*e**6 - 8*d**2*e**8*x**2 + 4*e**10*x**4) - 2*e**4*x**4*log(-d/e + x)/(4*d**4*e**6 - 8*d**2*e**8*x**2 + 4*e**10*x**4) - 2*e**4*x**4*log(d/e + x)/(4*d**4*e**6 - 8*d**2*e**8*x**2 + 4*e**10*x**4), Eq(p, -3)), (-2*d**4*log(-d/e + x)/(-2*d**2*e**6 + 2*e**8*x**2) - 2*d**4*log(d/e + x)/(-2*d**2*e**6 + 2*e**8*x**2) - 2*d**4/(-2*d**2*e**6 + 2*e**8*x**2) + 2*d**2*e**2*x**2*log(-d/e + x)/(-2*d**2*e**6 + 2*e**8*x**2) + 2*d**2*e**2*x**2*log(d/e + x)/(-2*d**2*e**6 + 2*e**8*x**2) + e**4*x**4/(-2*d**2*e**6 + 2*e**8*x**2), Eq(p, -2)), (-d**4*log(-d/e + x)/(2*e**6) - d**4*log(d/e + x)/(2*e**6) - d**2*x**2/(2*e**4) - x**4/(4*e**2), Eq(p, -1)), (-2*d**6*(d**2 - e**2*x**2)**p/(2*e**6*p**3 + 12*e**6*p**2 + 22*e**6*p + 12*e**6) - 2*d**4*e**2*p*x**2*(d**2 - e**2*x**2)**p/(2*e**6*p**3 + 12*e**6*p**2 + 22*e**6*p + 12*e**6) - d**2*e**4*p**2*x**4*(d**2 - e**2*x**2)**p/(2*e**6*p**3 + 12*e**6*p**2 + 22*e**6*p + 12*e**6) - d**2*e**4*p*x**4*(d**2 - e**2*x**2)**p/(2*e**6*p**3 + 12*e**6*p**2 + 22*e**6*p + 12*e**6) + e**6*p**2*x**6*(d**2 - e**2*x**2)**p/(2*e**6*p**3 + 12*e**6*p**2 + 22*e**6*p + 12*e**6) + 3*e**6*p*x**6*(d**2 - e**2*x**2)**p/(2*e**6*p**3 + 12*e**6*p**2 + 22*e**6*p + 12*e**6) + 2*e**6*x**6*(d**2 - e**2*x**2)**p/(2*e**6*p**3 + 12*e**6*p**2 + 22*e**6*p + 12*e**6), True)) + d**(2*p)*e*x**7*hyper((7/2, -p), (9/2,), e**2*x**2*exp_polar(2*I*pi)/d**2)/7","B",0
241,1,972,0,7.100584," ","integrate(x**4*(e*x+d)*(-e**2*x**2+d**2)**p,x)","\frac{d d^{2 p} x^{5} {{}_{2}F_{1}\left(\begin{matrix} \frac{5}{2}, - p \\ \frac{7}{2} \end{matrix}\middle| {\frac{e^{2} x^{2} e^{2 i \pi}}{d^{2}}} \right)}}{5} + e \left(\begin{cases} \frac{x^{6} \left(d^{2}\right)^{p}}{6} & \text{for}\: e = 0 \\- \frac{2 d^{4} \log{\left(- \frac{d}{e} + x \right)}}{4 d^{4} e^{6} - 8 d^{2} e^{8} x^{2} + 4 e^{10} x^{4}} - \frac{2 d^{4} \log{\left(\frac{d}{e} + x \right)}}{4 d^{4} e^{6} - 8 d^{2} e^{8} x^{2} + 4 e^{10} x^{4}} - \frac{3 d^{4}}{4 d^{4} e^{6} - 8 d^{2} e^{8} x^{2} + 4 e^{10} x^{4}} + \frac{4 d^{2} e^{2} x^{2} \log{\left(- \frac{d}{e} + x \right)}}{4 d^{4} e^{6} - 8 d^{2} e^{8} x^{2} + 4 e^{10} x^{4}} + \frac{4 d^{2} e^{2} x^{2} \log{\left(\frac{d}{e} + x \right)}}{4 d^{4} e^{6} - 8 d^{2} e^{8} x^{2} + 4 e^{10} x^{4}} + \frac{4 d^{2} e^{2} x^{2}}{4 d^{4} e^{6} - 8 d^{2} e^{8} x^{2} + 4 e^{10} x^{4}} - \frac{2 e^{4} x^{4} \log{\left(- \frac{d}{e} + x \right)}}{4 d^{4} e^{6} - 8 d^{2} e^{8} x^{2} + 4 e^{10} x^{4}} - \frac{2 e^{4} x^{4} \log{\left(\frac{d}{e} + x \right)}}{4 d^{4} e^{6} - 8 d^{2} e^{8} x^{2} + 4 e^{10} x^{4}} & \text{for}\: p = -3 \\- \frac{2 d^{4} \log{\left(- \frac{d}{e} + x \right)}}{- 2 d^{2} e^{6} + 2 e^{8} x^{2}} - \frac{2 d^{4} \log{\left(\frac{d}{e} + x \right)}}{- 2 d^{2} e^{6} + 2 e^{8} x^{2}} - \frac{2 d^{4}}{- 2 d^{2} e^{6} + 2 e^{8} x^{2}} + \frac{2 d^{2} e^{2} x^{2} \log{\left(- \frac{d}{e} + x \right)}}{- 2 d^{2} e^{6} + 2 e^{8} x^{2}} + \frac{2 d^{2} e^{2} x^{2} \log{\left(\frac{d}{e} + x \right)}}{- 2 d^{2} e^{6} + 2 e^{8} x^{2}} + \frac{e^{4} x^{4}}{- 2 d^{2} e^{6} + 2 e^{8} x^{2}} & \text{for}\: p = -2 \\- \frac{d^{4} \log{\left(- \frac{d}{e} + x \right)}}{2 e^{6}} - \frac{d^{4} \log{\left(\frac{d}{e} + x \right)}}{2 e^{6}} - \frac{d^{2} x^{2}}{2 e^{4}} - \frac{x^{4}}{4 e^{2}} & \text{for}\: p = -1 \\- \frac{2 d^{6} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{6} p^{3} + 12 e^{6} p^{2} + 22 e^{6} p + 12 e^{6}} - \frac{2 d^{4} e^{2} p x^{2} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{6} p^{3} + 12 e^{6} p^{2} + 22 e^{6} p + 12 e^{6}} - \frac{d^{2} e^{4} p^{2} x^{4} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{6} p^{3} + 12 e^{6} p^{2} + 22 e^{6} p + 12 e^{6}} - \frac{d^{2} e^{4} p x^{4} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{6} p^{3} + 12 e^{6} p^{2} + 22 e^{6} p + 12 e^{6}} + \frac{e^{6} p^{2} x^{6} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{6} p^{3} + 12 e^{6} p^{2} + 22 e^{6} p + 12 e^{6}} + \frac{3 e^{6} p x^{6} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{6} p^{3} + 12 e^{6} p^{2} + 22 e^{6} p + 12 e^{6}} + \frac{2 e^{6} x^{6} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{6} p^{3} + 12 e^{6} p^{2} + 22 e^{6} p + 12 e^{6}} & \text{otherwise} \end{cases}\right)"," ",0,"d*d**(2*p)*x**5*hyper((5/2, -p), (7/2,), e**2*x**2*exp_polar(2*I*pi)/d**2)/5 + e*Piecewise((x**6*(d**2)**p/6, Eq(e, 0)), (-2*d**4*log(-d/e + x)/(4*d**4*e**6 - 8*d**2*e**8*x**2 + 4*e**10*x**4) - 2*d**4*log(d/e + x)/(4*d**4*e**6 - 8*d**2*e**8*x**2 + 4*e**10*x**4) - 3*d**4/(4*d**4*e**6 - 8*d**2*e**8*x**2 + 4*e**10*x**4) + 4*d**2*e**2*x**2*log(-d/e + x)/(4*d**4*e**6 - 8*d**2*e**8*x**2 + 4*e**10*x**4) + 4*d**2*e**2*x**2*log(d/e + x)/(4*d**4*e**6 - 8*d**2*e**8*x**2 + 4*e**10*x**4) + 4*d**2*e**2*x**2/(4*d**4*e**6 - 8*d**2*e**8*x**2 + 4*e**10*x**4) - 2*e**4*x**4*log(-d/e + x)/(4*d**4*e**6 - 8*d**2*e**8*x**2 + 4*e**10*x**4) - 2*e**4*x**4*log(d/e + x)/(4*d**4*e**6 - 8*d**2*e**8*x**2 + 4*e**10*x**4), Eq(p, -3)), (-2*d**4*log(-d/e + x)/(-2*d**2*e**6 + 2*e**8*x**2) - 2*d**4*log(d/e + x)/(-2*d**2*e**6 + 2*e**8*x**2) - 2*d**4/(-2*d**2*e**6 + 2*e**8*x**2) + 2*d**2*e**2*x**2*log(-d/e + x)/(-2*d**2*e**6 + 2*e**8*x**2) + 2*d**2*e**2*x**2*log(d/e + x)/(-2*d**2*e**6 + 2*e**8*x**2) + e**4*x**4/(-2*d**2*e**6 + 2*e**8*x**2), Eq(p, -2)), (-d**4*log(-d/e + x)/(2*e**6) - d**4*log(d/e + x)/(2*e**6) - d**2*x**2/(2*e**4) - x**4/(4*e**2), Eq(p, -1)), (-2*d**6*(d**2 - e**2*x**2)**p/(2*e**6*p**3 + 12*e**6*p**2 + 22*e**6*p + 12*e**6) - 2*d**4*e**2*p*x**2*(d**2 - e**2*x**2)**p/(2*e**6*p**3 + 12*e**6*p**2 + 22*e**6*p + 12*e**6) - d**2*e**4*p**2*x**4*(d**2 - e**2*x**2)**p/(2*e**6*p**3 + 12*e**6*p**2 + 22*e**6*p + 12*e**6) - d**2*e**4*p*x**4*(d**2 - e**2*x**2)**p/(2*e**6*p**3 + 12*e**6*p**2 + 22*e**6*p + 12*e**6) + e**6*p**2*x**6*(d**2 - e**2*x**2)**p/(2*e**6*p**3 + 12*e**6*p**2 + 22*e**6*p + 12*e**6) + 3*e**6*p*x**6*(d**2 - e**2*x**2)**p/(2*e**6*p**3 + 12*e**6*p**2 + 22*e**6*p + 12*e**6) + 2*e**6*x**6*(d**2 - e**2*x**2)**p/(2*e**6*p**3 + 12*e**6*p**2 + 22*e**6*p + 12*e**6), True))","B",0
242,1,382,0,5.456663," ","integrate(x**3*(e*x+d)*(-e**2*x**2+d**2)**p,x)","d \left(\begin{cases} \frac{x^{4} \left(d^{2}\right)^{p}}{4} & \text{for}\: e = 0 \\- \frac{d^{2} \log{\left(- \frac{d}{e} + x \right)}}{- 2 d^{2} e^{4} + 2 e^{6} x^{2}} - \frac{d^{2} \log{\left(\frac{d}{e} + x \right)}}{- 2 d^{2} e^{4} + 2 e^{6} x^{2}} - \frac{d^{2}}{- 2 d^{2} e^{4} + 2 e^{6} x^{2}} + \frac{e^{2} x^{2} \log{\left(- \frac{d}{e} + x \right)}}{- 2 d^{2} e^{4} + 2 e^{6} x^{2}} + \frac{e^{2} x^{2} \log{\left(\frac{d}{e} + x \right)}}{- 2 d^{2} e^{4} + 2 e^{6} x^{2}} & \text{for}\: p = -2 \\- \frac{d^{2} \log{\left(- \frac{d}{e} + x \right)}}{2 e^{4}} - \frac{d^{2} \log{\left(\frac{d}{e} + x \right)}}{2 e^{4}} - \frac{x^{2}}{2 e^{2}} & \text{for}\: p = -1 \\- \frac{d^{4} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{4} p^{2} + 6 e^{4} p + 4 e^{4}} - \frac{d^{2} e^{2} p x^{2} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{4} p^{2} + 6 e^{4} p + 4 e^{4}} + \frac{e^{4} p x^{4} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{4} p^{2} + 6 e^{4} p + 4 e^{4}} + \frac{e^{4} x^{4} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{4} p^{2} + 6 e^{4} p + 4 e^{4}} & \text{otherwise} \end{cases}\right) + \frac{d^{2 p} e x^{5} {{}_{2}F_{1}\left(\begin{matrix} \frac{5}{2}, - p \\ \frac{7}{2} \end{matrix}\middle| {\frac{e^{2} x^{2} e^{2 i \pi}}{d^{2}}} \right)}}{5}"," ",0,"d*Piecewise((x**4*(d**2)**p/4, Eq(e, 0)), (-d**2*log(-d/e + x)/(-2*d**2*e**4 + 2*e**6*x**2) - d**2*log(d/e + x)/(-2*d**2*e**4 + 2*e**6*x**2) - d**2/(-2*d**2*e**4 + 2*e**6*x**2) + e**2*x**2*log(-d/e + x)/(-2*d**2*e**4 + 2*e**6*x**2) + e**2*x**2*log(d/e + x)/(-2*d**2*e**4 + 2*e**6*x**2), Eq(p, -2)), (-d**2*log(-d/e + x)/(2*e**4) - d**2*log(d/e + x)/(2*e**4) - x**2/(2*e**2), Eq(p, -1)), (-d**4*(d**2 - e**2*x**2)**p/(2*e**4*p**2 + 6*e**4*p + 4*e**4) - d**2*e**2*p*x**2*(d**2 - e**2*x**2)**p/(2*e**4*p**2 + 6*e**4*p + 4*e**4) + e**4*p*x**4*(d**2 - e**2*x**2)**p/(2*e**4*p**2 + 6*e**4*p + 4*e**4) + e**4*x**4*(d**2 - e**2*x**2)**p/(2*e**4*p**2 + 6*e**4*p + 4*e**4), True)) + d**(2*p)*e*x**5*hyper((5/2, -p), (7/2,), e**2*x**2*exp_polar(2*I*pi)/d**2)/5","B",0
243,1,382,0,5.073282," ","integrate(x**2*(e*x+d)*(-e**2*x**2+d**2)**p,x)","\frac{d d^{2 p} x^{3} {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{2}, - p \\ \frac{5}{2} \end{matrix}\middle| {\frac{e^{2} x^{2} e^{2 i \pi}}{d^{2}}} \right)}}{3} + e \left(\begin{cases} \frac{x^{4} \left(d^{2}\right)^{p}}{4} & \text{for}\: e = 0 \\- \frac{d^{2} \log{\left(- \frac{d}{e} + x \right)}}{- 2 d^{2} e^{4} + 2 e^{6} x^{2}} - \frac{d^{2} \log{\left(\frac{d}{e} + x \right)}}{- 2 d^{2} e^{4} + 2 e^{6} x^{2}} - \frac{d^{2}}{- 2 d^{2} e^{4} + 2 e^{6} x^{2}} + \frac{e^{2} x^{2} \log{\left(- \frac{d}{e} + x \right)}}{- 2 d^{2} e^{4} + 2 e^{6} x^{2}} + \frac{e^{2} x^{2} \log{\left(\frac{d}{e} + x \right)}}{- 2 d^{2} e^{4} + 2 e^{6} x^{2}} & \text{for}\: p = -2 \\- \frac{d^{2} \log{\left(- \frac{d}{e} + x \right)}}{2 e^{4}} - \frac{d^{2} \log{\left(\frac{d}{e} + x \right)}}{2 e^{4}} - \frac{x^{2}}{2 e^{2}} & \text{for}\: p = -1 \\- \frac{d^{4} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{4} p^{2} + 6 e^{4} p + 4 e^{4}} - \frac{d^{2} e^{2} p x^{2} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{4} p^{2} + 6 e^{4} p + 4 e^{4}} + \frac{e^{4} p x^{4} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{4} p^{2} + 6 e^{4} p + 4 e^{4}} + \frac{e^{4} x^{4} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{4} p^{2} + 6 e^{4} p + 4 e^{4}} & \text{otherwise} \end{cases}\right)"," ",0,"d*d**(2*p)*x**3*hyper((3/2, -p), (5/2,), e**2*x**2*exp_polar(2*I*pi)/d**2)/3 + e*Piecewise((x**4*(d**2)**p/4, Eq(e, 0)), (-d**2*log(-d/e + x)/(-2*d**2*e**4 + 2*e**6*x**2) - d**2*log(d/e + x)/(-2*d**2*e**4 + 2*e**6*x**2) - d**2/(-2*d**2*e**4 + 2*e**6*x**2) + e**2*x**2*log(-d/e + x)/(-2*d**2*e**4 + 2*e**6*x**2) + e**2*x**2*log(d/e + x)/(-2*d**2*e**4 + 2*e**6*x**2), Eq(p, -2)), (-d**2*log(-d/e + x)/(2*e**4) - d**2*log(d/e + x)/(2*e**4) - x**2/(2*e**2), Eq(p, -1)), (-d**4*(d**2 - e**2*x**2)**p/(2*e**4*p**2 + 6*e**4*p + 4*e**4) - d**2*e**2*p*x**2*(d**2 - e**2*x**2)**p/(2*e**4*p**2 + 6*e**4*p + 4*e**4) + e**4*p*x**4*(d**2 - e**2*x**2)**p/(2*e**4*p**2 + 6*e**4*p + 4*e**4) + e**4*x**4*(d**2 - e**2*x**2)**p/(2*e**4*p**2 + 6*e**4*p + 4*e**4), True))","B",0
244,1,85,0,3.523836," ","integrate(x*(e*x+d)*(-e**2*x**2+d**2)**p,x)","d \left(\begin{cases} \frac{x^{2} \left(d^{2}\right)^{p}}{2} & \text{for}\: e^{2} = 0 \\- \frac{\begin{cases} \frac{\left(d^{2} - e^{2} x^{2}\right)^{p + 1}}{p + 1} & \text{for}\: p \neq -1 \\\log{\left(d^{2} - e^{2} x^{2} \right)} & \text{otherwise} \end{cases}}{2 e^{2}} & \text{otherwise} \end{cases}\right) + \frac{d^{2 p} e x^{3} {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{2}, - p \\ \frac{5}{2} \end{matrix}\middle| {\frac{e^{2} x^{2} e^{2 i \pi}}{d^{2}}} \right)}}{3}"," ",0,"d*Piecewise((x**2*(d**2)**p/2, Eq(e**2, 0)), (-Piecewise(((d**2 - e**2*x**2)**(p + 1)/(p + 1), Ne(p, -1)), (log(d**2 - e**2*x**2), True))/(2*e**2), True)) + d**(2*p)*e*x**3*hyper((3/2, -p), (5/2,), e**2*x**2*exp_polar(2*I*pi)/d**2)/3","A",0
245,1,82,0,4.176990," ","integrate((e*x+d)*(-e**2*x**2+d**2)**p,x)","d d^{2 p} x {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, - p \\ \frac{3}{2} \end{matrix}\middle| {\frac{e^{2} x^{2} e^{2 i \pi}}{d^{2}}} \right)} + e \left(\begin{cases} \frac{x^{2} \left(d^{2}\right)^{p}}{2} & \text{for}\: e^{2} = 0 \\- \frac{\begin{cases} \frac{\left(d^{2} - e^{2} x^{2}\right)^{p + 1}}{p + 1} & \text{for}\: p \neq -1 \\\log{\left(d^{2} - e^{2} x^{2} \right)} & \text{otherwise} \end{cases}}{2 e^{2}} & \text{otherwise} \end{cases}\right)"," ",0,"d*d**(2*p)*x*hyper((1/2, -p), (3/2,), e**2*x**2*exp_polar(2*I*pi)/d**2) + e*Piecewise((x**2*(d**2)**p/2, Eq(e**2, 0)), (-Piecewise(((d**2 - e**2*x**2)**(p + 1)/(p + 1), Ne(p, -1)), (log(d**2 - e**2*x**2), True))/(2*e**2), True))","A",0
246,1,78,0,9.367409," ","integrate((e*x+d)*(-e**2*x**2+d**2)**p/x,x)","- \frac{d e^{2 p} x^{2 p} e^{i \pi p} \Gamma\left(- p\right) {{}_{2}F_{1}\left(\begin{matrix} - p, - p \\ 1 - p \end{matrix}\middle| {\frac{d^{2}}{e^{2} x^{2}}} \right)}}{2 \Gamma\left(1 - p\right)} + d^{2 p} e x {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, - p \\ \frac{3}{2} \end{matrix}\middle| {\frac{e^{2} x^{2} e^{2 i \pi}}{d^{2}}} \right)}"," ",0,"-d*e**(2*p)*x**(2*p)*exp(I*pi*p)*gamma(-p)*hyper((-p, -p), (1 - p,), d**2/(e**2*x**2))/(2*gamma(1 - p)) + d**(2*p)*e*x*hyper((1/2, -p), (3/2,), e**2*x**2*exp_polar(2*I*pi)/d**2)","C",0
247,1,82,0,5.526821," ","integrate((e*x+d)*(-e**2*x**2+d**2)**p/x**2,x)","- \frac{d d^{2 p} {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, - p \\ \frac{1}{2} \end{matrix}\middle| {\frac{e^{2} x^{2} e^{2 i \pi}}{d^{2}}} \right)}}{x} - \frac{e e^{2 p} x^{2 p} e^{i \pi p} \Gamma\left(- p\right) {{}_{2}F_{1}\left(\begin{matrix} - p, - p \\ 1 - p \end{matrix}\middle| {\frac{d^{2}}{e^{2} x^{2}}} \right)}}{2 \Gamma\left(1 - p\right)}"," ",0,"-d*d**(2*p)*hyper((-1/2, -p), (1/2,), e**2*x**2*exp_polar(2*I*pi)/d**2)/x - e*e**(2*p)*x**(2*p)*exp(I*pi*p)*gamma(-p)*hyper((-p, -p), (1 - p,), d**2/(e**2*x**2))/(2*gamma(1 - p))","C",0
248,1,85,0,5.072889," ","integrate((e*x+d)*(-e**2*x**2+d**2)**p/x**3,x)","- \frac{d e^{2 p} x^{2 p} e^{i \pi p} \Gamma\left(1 - p\right) {{}_{2}F_{1}\left(\begin{matrix} - p, 1 - p \\ 2 - p \end{matrix}\middle| {\frac{d^{2}}{e^{2} x^{2}}} \right)}}{2 x^{2} \Gamma\left(2 - p\right)} - \frac{d^{2 p} e {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, - p \\ \frac{1}{2} \end{matrix}\middle| {\frac{e^{2} x^{2} e^{2 i \pi}}{d^{2}}} \right)}}{x}"," ",0,"-d*e**(2*p)*x**(2*p)*exp(I*pi*p)*gamma(1 - p)*hyper((-p, 1 - p), (2 - p,), d**2/(e**2*x**2))/(2*x**2*gamma(2 - p)) - d**(2*p)*e*hyper((-1/2, -p), (1/2,), e**2*x**2*exp_polar(2*I*pi)/d**2)/x","C",0
249,1,2924,0,14.933202," ","integrate(x**5*(e*x+d)**2*(-e**2*x**2+d**2)**p,x)","d^{2} \left(\begin{cases} \frac{x^{6} \left(d^{2}\right)^{p}}{6} & \text{for}\: e = 0 \\- \frac{2 d^{4} \log{\left(- \frac{d}{e} + x \right)}}{4 d^{4} e^{6} - 8 d^{2} e^{8} x^{2} + 4 e^{10} x^{4}} - \frac{2 d^{4} \log{\left(\frac{d}{e} + x \right)}}{4 d^{4} e^{6} - 8 d^{2} e^{8} x^{2} + 4 e^{10} x^{4}} - \frac{3 d^{4}}{4 d^{4} e^{6} - 8 d^{2} e^{8} x^{2} + 4 e^{10} x^{4}} + \frac{4 d^{2} e^{2} x^{2} \log{\left(- \frac{d}{e} + x \right)}}{4 d^{4} e^{6} - 8 d^{2} e^{8} x^{2} + 4 e^{10} x^{4}} + \frac{4 d^{2} e^{2} x^{2} \log{\left(\frac{d}{e} + x \right)}}{4 d^{4} e^{6} - 8 d^{2} e^{8} x^{2} + 4 e^{10} x^{4}} + \frac{4 d^{2} e^{2} x^{2}}{4 d^{4} e^{6} - 8 d^{2} e^{8} x^{2} + 4 e^{10} x^{4}} - \frac{2 e^{4} x^{4} \log{\left(- \frac{d}{e} + x \right)}}{4 d^{4} e^{6} - 8 d^{2} e^{8} x^{2} + 4 e^{10} x^{4}} - \frac{2 e^{4} x^{4} \log{\left(\frac{d}{e} + x \right)}}{4 d^{4} e^{6} - 8 d^{2} e^{8} x^{2} + 4 e^{10} x^{4}} & \text{for}\: p = -3 \\- \frac{2 d^{4} \log{\left(- \frac{d}{e} + x \right)}}{- 2 d^{2} e^{6} + 2 e^{8} x^{2}} - \frac{2 d^{4} \log{\left(\frac{d}{e} + x \right)}}{- 2 d^{2} e^{6} + 2 e^{8} x^{2}} - \frac{2 d^{4}}{- 2 d^{2} e^{6} + 2 e^{8} x^{2}} + \frac{2 d^{2} e^{2} x^{2} \log{\left(- \frac{d}{e} + x \right)}}{- 2 d^{2} e^{6} + 2 e^{8} x^{2}} + \frac{2 d^{2} e^{2} x^{2} \log{\left(\frac{d}{e} + x \right)}}{- 2 d^{2} e^{6} + 2 e^{8} x^{2}} + \frac{e^{4} x^{4}}{- 2 d^{2} e^{6} + 2 e^{8} x^{2}} & \text{for}\: p = -2 \\- \frac{d^{4} \log{\left(- \frac{d}{e} + x \right)}}{2 e^{6}} - \frac{d^{4} \log{\left(\frac{d}{e} + x \right)}}{2 e^{6}} - \frac{d^{2} x^{2}}{2 e^{4}} - \frac{x^{4}}{4 e^{2}} & \text{for}\: p = -1 \\- \frac{2 d^{6} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{6} p^{3} + 12 e^{6} p^{2} + 22 e^{6} p + 12 e^{6}} - \frac{2 d^{4} e^{2} p x^{2} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{6} p^{3} + 12 e^{6} p^{2} + 22 e^{6} p + 12 e^{6}} - \frac{d^{2} e^{4} p^{2} x^{4} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{6} p^{3} + 12 e^{6} p^{2} + 22 e^{6} p + 12 e^{6}} - \frac{d^{2} e^{4} p x^{4} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{6} p^{3} + 12 e^{6} p^{2} + 22 e^{6} p + 12 e^{6}} + \frac{e^{6} p^{2} x^{6} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{6} p^{3} + 12 e^{6} p^{2} + 22 e^{6} p + 12 e^{6}} + \frac{3 e^{6} p x^{6} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{6} p^{3} + 12 e^{6} p^{2} + 22 e^{6} p + 12 e^{6}} + \frac{2 e^{6} x^{6} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{6} p^{3} + 12 e^{6} p^{2} + 22 e^{6} p + 12 e^{6}} & \text{otherwise} \end{cases}\right) + \frac{2 d d^{2 p} e x^{7} {{}_{2}F_{1}\left(\begin{matrix} \frac{7}{2}, - p \\ \frac{9}{2} \end{matrix}\middle| {\frac{e^{2} x^{2} e^{2 i \pi}}{d^{2}}} \right)}}{7} + e^{2} \left(\begin{cases} \frac{x^{8} \left(d^{2}\right)^{p}}{8} & \text{for}\: e = 0 \\- \frac{6 d^{6} \log{\left(- \frac{d}{e} + x \right)}}{- 12 d^{6} e^{8} + 36 d^{4} e^{10} x^{2} - 36 d^{2} e^{12} x^{4} + 12 e^{14} x^{6}} - \frac{6 d^{6} \log{\left(\frac{d}{e} + x \right)}}{- 12 d^{6} e^{8} + 36 d^{4} e^{10} x^{2} - 36 d^{2} e^{12} x^{4} + 12 e^{14} x^{6}} - \frac{11 d^{6}}{- 12 d^{6} e^{8} + 36 d^{4} e^{10} x^{2} - 36 d^{2} e^{12} x^{4} + 12 e^{14} x^{6}} + \frac{18 d^{4} e^{2} x^{2} \log{\left(- \frac{d}{e} + x \right)}}{- 12 d^{6} e^{8} + 36 d^{4} e^{10} x^{2} - 36 d^{2} e^{12} x^{4} + 12 e^{14} x^{6}} + \frac{18 d^{4} e^{2} x^{2} \log{\left(\frac{d}{e} + x \right)}}{- 12 d^{6} e^{8} + 36 d^{4} e^{10} x^{2} - 36 d^{2} e^{12} x^{4} + 12 e^{14} x^{6}} + \frac{27 d^{4} e^{2} x^{2}}{- 12 d^{6} e^{8} + 36 d^{4} e^{10} x^{2} - 36 d^{2} e^{12} x^{4} + 12 e^{14} x^{6}} - \frac{18 d^{2} e^{4} x^{4} \log{\left(- \frac{d}{e} + x \right)}}{- 12 d^{6} e^{8} + 36 d^{4} e^{10} x^{2} - 36 d^{2} e^{12} x^{4} + 12 e^{14} x^{6}} - \frac{18 d^{2} e^{4} x^{4} \log{\left(\frac{d}{e} + x \right)}}{- 12 d^{6} e^{8} + 36 d^{4} e^{10} x^{2} - 36 d^{2} e^{12} x^{4} + 12 e^{14} x^{6}} - \frac{18 d^{2} e^{4} x^{4}}{- 12 d^{6} e^{8} + 36 d^{4} e^{10} x^{2} - 36 d^{2} e^{12} x^{4} + 12 e^{14} x^{6}} + \frac{6 e^{6} x^{6} \log{\left(- \frac{d}{e} + x \right)}}{- 12 d^{6} e^{8} + 36 d^{4} e^{10} x^{2} - 36 d^{2} e^{12} x^{4} + 12 e^{14} x^{6}} + \frac{6 e^{6} x^{6} \log{\left(\frac{d}{e} + x \right)}}{- 12 d^{6} e^{8} + 36 d^{4} e^{10} x^{2} - 36 d^{2} e^{12} x^{4} + 12 e^{14} x^{6}} & \text{for}\: p = -4 \\- \frac{6 d^{6} \log{\left(- \frac{d}{e} + x \right)}}{4 d^{4} e^{8} - 8 d^{2} e^{10} x^{2} + 4 e^{12} x^{4}} - \frac{6 d^{6} \log{\left(\frac{d}{e} + x \right)}}{4 d^{4} e^{8} - 8 d^{2} e^{10} x^{2} + 4 e^{12} x^{4}} - \frac{9 d^{6}}{4 d^{4} e^{8} - 8 d^{2} e^{10} x^{2} + 4 e^{12} x^{4}} + \frac{12 d^{4} e^{2} x^{2} \log{\left(- \frac{d}{e} + x \right)}}{4 d^{4} e^{8} - 8 d^{2} e^{10} x^{2} + 4 e^{12} x^{4}} + \frac{12 d^{4} e^{2} x^{2} \log{\left(\frac{d}{e} + x \right)}}{4 d^{4} e^{8} - 8 d^{2} e^{10} x^{2} + 4 e^{12} x^{4}} + \frac{12 d^{4} e^{2} x^{2}}{4 d^{4} e^{8} - 8 d^{2} e^{10} x^{2} + 4 e^{12} x^{4}} - \frac{6 d^{2} e^{4} x^{4} \log{\left(- \frac{d}{e} + x \right)}}{4 d^{4} e^{8} - 8 d^{2} e^{10} x^{2} + 4 e^{12} x^{4}} - \frac{6 d^{2} e^{4} x^{4} \log{\left(\frac{d}{e} + x \right)}}{4 d^{4} e^{8} - 8 d^{2} e^{10} x^{2} + 4 e^{12} x^{4}} - \frac{2 e^{6} x^{6}}{4 d^{4} e^{8} - 8 d^{2} e^{10} x^{2} + 4 e^{12} x^{4}} & \text{for}\: p = -3 \\- \frac{6 d^{6} \log{\left(- \frac{d}{e} + x \right)}}{- 4 d^{2} e^{8} + 4 e^{10} x^{2}} - \frac{6 d^{6} \log{\left(\frac{d}{e} + x \right)}}{- 4 d^{2} e^{8} + 4 e^{10} x^{2}} - \frac{6 d^{6}}{- 4 d^{2} e^{8} + 4 e^{10} x^{2}} + \frac{6 d^{4} e^{2} x^{2} \log{\left(- \frac{d}{e} + x \right)}}{- 4 d^{2} e^{8} + 4 e^{10} x^{2}} + \frac{6 d^{4} e^{2} x^{2} \log{\left(\frac{d}{e} + x \right)}}{- 4 d^{2} e^{8} + 4 e^{10} x^{2}} + \frac{3 d^{2} e^{4} x^{4}}{- 4 d^{2} e^{8} + 4 e^{10} x^{2}} + \frac{e^{6} x^{6}}{- 4 d^{2} e^{8} + 4 e^{10} x^{2}} & \text{for}\: p = -2 \\- \frac{d^{6} \log{\left(- \frac{d}{e} + x \right)}}{2 e^{8}} - \frac{d^{6} \log{\left(\frac{d}{e} + x \right)}}{2 e^{8}} - \frac{d^{4} x^{2}}{2 e^{6}} - \frac{d^{2} x^{4}}{4 e^{4}} - \frac{x^{6}}{6 e^{2}} & \text{for}\: p = -1 \\- \frac{6 d^{8} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{8} p^{4} + 20 e^{8} p^{3} + 70 e^{8} p^{2} + 100 e^{8} p + 48 e^{8}} - \frac{6 d^{6} e^{2} p x^{2} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{8} p^{4} + 20 e^{8} p^{3} + 70 e^{8} p^{2} + 100 e^{8} p + 48 e^{8}} - \frac{3 d^{4} e^{4} p^{2} x^{4} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{8} p^{4} + 20 e^{8} p^{3} + 70 e^{8} p^{2} + 100 e^{8} p + 48 e^{8}} - \frac{3 d^{4} e^{4} p x^{4} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{8} p^{4} + 20 e^{8} p^{3} + 70 e^{8} p^{2} + 100 e^{8} p + 48 e^{8}} - \frac{d^{2} e^{6} p^{3} x^{6} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{8} p^{4} + 20 e^{8} p^{3} + 70 e^{8} p^{2} + 100 e^{8} p + 48 e^{8}} - \frac{3 d^{2} e^{6} p^{2} x^{6} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{8} p^{4} + 20 e^{8} p^{3} + 70 e^{8} p^{2} + 100 e^{8} p + 48 e^{8}} - \frac{2 d^{2} e^{6} p x^{6} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{8} p^{4} + 20 e^{8} p^{3} + 70 e^{8} p^{2} + 100 e^{8} p + 48 e^{8}} + \frac{e^{8} p^{3} x^{8} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{8} p^{4} + 20 e^{8} p^{3} + 70 e^{8} p^{2} + 100 e^{8} p + 48 e^{8}} + \frac{6 e^{8} p^{2} x^{8} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{8} p^{4} + 20 e^{8} p^{3} + 70 e^{8} p^{2} + 100 e^{8} p + 48 e^{8}} + \frac{11 e^{8} p x^{8} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{8} p^{4} + 20 e^{8} p^{3} + 70 e^{8} p^{2} + 100 e^{8} p + 48 e^{8}} + \frac{6 e^{8} x^{8} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{8} p^{4} + 20 e^{8} p^{3} + 70 e^{8} p^{2} + 100 e^{8} p + 48 e^{8}} & \text{otherwise} \end{cases}\right)"," ",0,"d**2*Piecewise((x**6*(d**2)**p/6, Eq(e, 0)), (-2*d**4*log(-d/e + x)/(4*d**4*e**6 - 8*d**2*e**8*x**2 + 4*e**10*x**4) - 2*d**4*log(d/e + x)/(4*d**4*e**6 - 8*d**2*e**8*x**2 + 4*e**10*x**4) - 3*d**4/(4*d**4*e**6 - 8*d**2*e**8*x**2 + 4*e**10*x**4) + 4*d**2*e**2*x**2*log(-d/e + x)/(4*d**4*e**6 - 8*d**2*e**8*x**2 + 4*e**10*x**4) + 4*d**2*e**2*x**2*log(d/e + x)/(4*d**4*e**6 - 8*d**2*e**8*x**2 + 4*e**10*x**4) + 4*d**2*e**2*x**2/(4*d**4*e**6 - 8*d**2*e**8*x**2 + 4*e**10*x**4) - 2*e**4*x**4*log(-d/e + x)/(4*d**4*e**6 - 8*d**2*e**8*x**2 + 4*e**10*x**4) - 2*e**4*x**4*log(d/e + x)/(4*d**4*e**6 - 8*d**2*e**8*x**2 + 4*e**10*x**4), Eq(p, -3)), (-2*d**4*log(-d/e + x)/(-2*d**2*e**6 + 2*e**8*x**2) - 2*d**4*log(d/e + x)/(-2*d**2*e**6 + 2*e**8*x**2) - 2*d**4/(-2*d**2*e**6 + 2*e**8*x**2) + 2*d**2*e**2*x**2*log(-d/e + x)/(-2*d**2*e**6 + 2*e**8*x**2) + 2*d**2*e**2*x**2*log(d/e + x)/(-2*d**2*e**6 + 2*e**8*x**2) + e**4*x**4/(-2*d**2*e**6 + 2*e**8*x**2), Eq(p, -2)), (-d**4*log(-d/e + x)/(2*e**6) - d**4*log(d/e + x)/(2*e**6) - d**2*x**2/(2*e**4) - x**4/(4*e**2), Eq(p, -1)), (-2*d**6*(d**2 - e**2*x**2)**p/(2*e**6*p**3 + 12*e**6*p**2 + 22*e**6*p + 12*e**6) - 2*d**4*e**2*p*x**2*(d**2 - e**2*x**2)**p/(2*e**6*p**3 + 12*e**6*p**2 + 22*e**6*p + 12*e**6) - d**2*e**4*p**2*x**4*(d**2 - e**2*x**2)**p/(2*e**6*p**3 + 12*e**6*p**2 + 22*e**6*p + 12*e**6) - d**2*e**4*p*x**4*(d**2 - e**2*x**2)**p/(2*e**6*p**3 + 12*e**6*p**2 + 22*e**6*p + 12*e**6) + e**6*p**2*x**6*(d**2 - e**2*x**2)**p/(2*e**6*p**3 + 12*e**6*p**2 + 22*e**6*p + 12*e**6) + 3*e**6*p*x**6*(d**2 - e**2*x**2)**p/(2*e**6*p**3 + 12*e**6*p**2 + 22*e**6*p + 12*e**6) + 2*e**6*x**6*(d**2 - e**2*x**2)**p/(2*e**6*p**3 + 12*e**6*p**2 + 22*e**6*p + 12*e**6), True)) + 2*d*d**(2*p)*e*x**7*hyper((7/2, -p), (9/2,), e**2*x**2*exp_polar(2*I*pi)/d**2)/7 + e**2*Piecewise((x**8*(d**2)**p/8, Eq(e, 0)), (-6*d**6*log(-d/e + x)/(-12*d**6*e**8 + 36*d**4*e**10*x**2 - 36*d**2*e**12*x**4 + 12*e**14*x**6) - 6*d**6*log(d/e + x)/(-12*d**6*e**8 + 36*d**4*e**10*x**2 - 36*d**2*e**12*x**4 + 12*e**14*x**6) - 11*d**6/(-12*d**6*e**8 + 36*d**4*e**10*x**2 - 36*d**2*e**12*x**4 + 12*e**14*x**6) + 18*d**4*e**2*x**2*log(-d/e + x)/(-12*d**6*e**8 + 36*d**4*e**10*x**2 - 36*d**2*e**12*x**4 + 12*e**14*x**6) + 18*d**4*e**2*x**2*log(d/e + x)/(-12*d**6*e**8 + 36*d**4*e**10*x**2 - 36*d**2*e**12*x**4 + 12*e**14*x**6) + 27*d**4*e**2*x**2/(-12*d**6*e**8 + 36*d**4*e**10*x**2 - 36*d**2*e**12*x**4 + 12*e**14*x**6) - 18*d**2*e**4*x**4*log(-d/e + x)/(-12*d**6*e**8 + 36*d**4*e**10*x**2 - 36*d**2*e**12*x**4 + 12*e**14*x**6) - 18*d**2*e**4*x**4*log(d/e + x)/(-12*d**6*e**8 + 36*d**4*e**10*x**2 - 36*d**2*e**12*x**4 + 12*e**14*x**6) - 18*d**2*e**4*x**4/(-12*d**6*e**8 + 36*d**4*e**10*x**2 - 36*d**2*e**12*x**4 + 12*e**14*x**6) + 6*e**6*x**6*log(-d/e + x)/(-12*d**6*e**8 + 36*d**4*e**10*x**2 - 36*d**2*e**12*x**4 + 12*e**14*x**6) + 6*e**6*x**6*log(d/e + x)/(-12*d**6*e**8 + 36*d**4*e**10*x**2 - 36*d**2*e**12*x**4 + 12*e**14*x**6), Eq(p, -4)), (-6*d**6*log(-d/e + x)/(4*d**4*e**8 - 8*d**2*e**10*x**2 + 4*e**12*x**4) - 6*d**6*log(d/e + x)/(4*d**4*e**8 - 8*d**2*e**10*x**2 + 4*e**12*x**4) - 9*d**6/(4*d**4*e**8 - 8*d**2*e**10*x**2 + 4*e**12*x**4) + 12*d**4*e**2*x**2*log(-d/e + x)/(4*d**4*e**8 - 8*d**2*e**10*x**2 + 4*e**12*x**4) + 12*d**4*e**2*x**2*log(d/e + x)/(4*d**4*e**8 - 8*d**2*e**10*x**2 + 4*e**12*x**4) + 12*d**4*e**2*x**2/(4*d**4*e**8 - 8*d**2*e**10*x**2 + 4*e**12*x**4) - 6*d**2*e**4*x**4*log(-d/e + x)/(4*d**4*e**8 - 8*d**2*e**10*x**2 + 4*e**12*x**4) - 6*d**2*e**4*x**4*log(d/e + x)/(4*d**4*e**8 - 8*d**2*e**10*x**2 + 4*e**12*x**4) - 2*e**6*x**6/(4*d**4*e**8 - 8*d**2*e**10*x**2 + 4*e**12*x**4), Eq(p, -3)), (-6*d**6*log(-d/e + x)/(-4*d**2*e**8 + 4*e**10*x**2) - 6*d**6*log(d/e + x)/(-4*d**2*e**8 + 4*e**10*x**2) - 6*d**6/(-4*d**2*e**8 + 4*e**10*x**2) + 6*d**4*e**2*x**2*log(-d/e + x)/(-4*d**2*e**8 + 4*e**10*x**2) + 6*d**4*e**2*x**2*log(d/e + x)/(-4*d**2*e**8 + 4*e**10*x**2) + 3*d**2*e**4*x**4/(-4*d**2*e**8 + 4*e**10*x**2) + e**6*x**6/(-4*d**2*e**8 + 4*e**10*x**2), Eq(p, -2)), (-d**6*log(-d/e + x)/(2*e**8) - d**6*log(d/e + x)/(2*e**8) - d**4*x**2/(2*e**6) - d**2*x**4/(4*e**4) - x**6/(6*e**2), Eq(p, -1)), (-6*d**8*(d**2 - e**2*x**2)**p/(2*e**8*p**4 + 20*e**8*p**3 + 70*e**8*p**2 + 100*e**8*p + 48*e**8) - 6*d**6*e**2*p*x**2*(d**2 - e**2*x**2)**p/(2*e**8*p**4 + 20*e**8*p**3 + 70*e**8*p**2 + 100*e**8*p + 48*e**8) - 3*d**4*e**4*p**2*x**4*(d**2 - e**2*x**2)**p/(2*e**8*p**4 + 20*e**8*p**3 + 70*e**8*p**2 + 100*e**8*p + 48*e**8) - 3*d**4*e**4*p*x**4*(d**2 - e**2*x**2)**p/(2*e**8*p**4 + 20*e**8*p**3 + 70*e**8*p**2 + 100*e**8*p + 48*e**8) - d**2*e**6*p**3*x**6*(d**2 - e**2*x**2)**p/(2*e**8*p**4 + 20*e**8*p**3 + 70*e**8*p**2 + 100*e**8*p + 48*e**8) - 3*d**2*e**6*p**2*x**6*(d**2 - e**2*x**2)**p/(2*e**8*p**4 + 20*e**8*p**3 + 70*e**8*p**2 + 100*e**8*p + 48*e**8) - 2*d**2*e**6*p*x**6*(d**2 - e**2*x**2)**p/(2*e**8*p**4 + 20*e**8*p**3 + 70*e**8*p**2 + 100*e**8*p + 48*e**8) + e**8*p**3*x**8*(d**2 - e**2*x**2)**p/(2*e**8*p**4 + 20*e**8*p**3 + 70*e**8*p**2 + 100*e**8*p + 48*e**8) + 6*e**8*p**2*x**8*(d**2 - e**2*x**2)**p/(2*e**8*p**4 + 20*e**8*p**3 + 70*e**8*p**2 + 100*e**8*p + 48*e**8) + 11*e**8*p*x**8*(d**2 - e**2*x**2)**p/(2*e**8*p**4 + 20*e**8*p**3 + 70*e**8*p**2 + 100*e**8*p + 48*e**8) + 6*e**8*x**8*(d**2 - e**2*x**2)**p/(2*e**8*p**4 + 20*e**8*p**3 + 70*e**8*p**2 + 100*e**8*p + 48*e**8), True))","B",0
250,1,1015,0,8.903341," ","integrate(x**4*(e*x+d)**2*(-e**2*x**2+d**2)**p,x)","\frac{d^{2} d^{2 p} x^{5} {{}_{2}F_{1}\left(\begin{matrix} \frac{5}{2}, - p \\ \frac{7}{2} \end{matrix}\middle| {\frac{e^{2} x^{2} e^{2 i \pi}}{d^{2}}} \right)}}{5} + 2 d e \left(\begin{cases} \frac{x^{6} \left(d^{2}\right)^{p}}{6} & \text{for}\: e = 0 \\- \frac{2 d^{4} \log{\left(- \frac{d}{e} + x \right)}}{4 d^{4} e^{6} - 8 d^{2} e^{8} x^{2} + 4 e^{10} x^{4}} - \frac{2 d^{4} \log{\left(\frac{d}{e} + x \right)}}{4 d^{4} e^{6} - 8 d^{2} e^{8} x^{2} + 4 e^{10} x^{4}} - \frac{3 d^{4}}{4 d^{4} e^{6} - 8 d^{2} e^{8} x^{2} + 4 e^{10} x^{4}} + \frac{4 d^{2} e^{2} x^{2} \log{\left(- \frac{d}{e} + x \right)}}{4 d^{4} e^{6} - 8 d^{2} e^{8} x^{2} + 4 e^{10} x^{4}} + \frac{4 d^{2} e^{2} x^{2} \log{\left(\frac{d}{e} + x \right)}}{4 d^{4} e^{6} - 8 d^{2} e^{8} x^{2} + 4 e^{10} x^{4}} + \frac{4 d^{2} e^{2} x^{2}}{4 d^{4} e^{6} - 8 d^{2} e^{8} x^{2} + 4 e^{10} x^{4}} - \frac{2 e^{4} x^{4} \log{\left(- \frac{d}{e} + x \right)}}{4 d^{4} e^{6} - 8 d^{2} e^{8} x^{2} + 4 e^{10} x^{4}} - \frac{2 e^{4} x^{4} \log{\left(\frac{d}{e} + x \right)}}{4 d^{4} e^{6} - 8 d^{2} e^{8} x^{2} + 4 e^{10} x^{4}} & \text{for}\: p = -3 \\- \frac{2 d^{4} \log{\left(- \frac{d}{e} + x \right)}}{- 2 d^{2} e^{6} + 2 e^{8} x^{2}} - \frac{2 d^{4} \log{\left(\frac{d}{e} + x \right)}}{- 2 d^{2} e^{6} + 2 e^{8} x^{2}} - \frac{2 d^{4}}{- 2 d^{2} e^{6} + 2 e^{8} x^{2}} + \frac{2 d^{2} e^{2} x^{2} \log{\left(- \frac{d}{e} + x \right)}}{- 2 d^{2} e^{6} + 2 e^{8} x^{2}} + \frac{2 d^{2} e^{2} x^{2} \log{\left(\frac{d}{e} + x \right)}}{- 2 d^{2} e^{6} + 2 e^{8} x^{2}} + \frac{e^{4} x^{4}}{- 2 d^{2} e^{6} + 2 e^{8} x^{2}} & \text{for}\: p = -2 \\- \frac{d^{4} \log{\left(- \frac{d}{e} + x \right)}}{2 e^{6}} - \frac{d^{4} \log{\left(\frac{d}{e} + x \right)}}{2 e^{6}} - \frac{d^{2} x^{2}}{2 e^{4}} - \frac{x^{4}}{4 e^{2}} & \text{for}\: p = -1 \\- \frac{2 d^{6} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{6} p^{3} + 12 e^{6} p^{2} + 22 e^{6} p + 12 e^{6}} - \frac{2 d^{4} e^{2} p x^{2} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{6} p^{3} + 12 e^{6} p^{2} + 22 e^{6} p + 12 e^{6}} - \frac{d^{2} e^{4} p^{2} x^{4} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{6} p^{3} + 12 e^{6} p^{2} + 22 e^{6} p + 12 e^{6}} - \frac{d^{2} e^{4} p x^{4} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{6} p^{3} + 12 e^{6} p^{2} + 22 e^{6} p + 12 e^{6}} + \frac{e^{6} p^{2} x^{6} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{6} p^{3} + 12 e^{6} p^{2} + 22 e^{6} p + 12 e^{6}} + \frac{3 e^{6} p x^{6} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{6} p^{3} + 12 e^{6} p^{2} + 22 e^{6} p + 12 e^{6}} + \frac{2 e^{6} x^{6} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{6} p^{3} + 12 e^{6} p^{2} + 22 e^{6} p + 12 e^{6}} & \text{otherwise} \end{cases}\right) + \frac{d^{2 p} e^{2} x^{7} {{}_{2}F_{1}\left(\begin{matrix} \frac{7}{2}, - p \\ \frac{9}{2} \end{matrix}\middle| {\frac{e^{2} x^{2} e^{2 i \pi}}{d^{2}}} \right)}}{7}"," ",0,"d**2*d**(2*p)*x**5*hyper((5/2, -p), (7/2,), e**2*x**2*exp_polar(2*I*pi)/d**2)/5 + 2*d*e*Piecewise((x**6*(d**2)**p/6, Eq(e, 0)), (-2*d**4*log(-d/e + x)/(4*d**4*e**6 - 8*d**2*e**8*x**2 + 4*e**10*x**4) - 2*d**4*log(d/e + x)/(4*d**4*e**6 - 8*d**2*e**8*x**2 + 4*e**10*x**4) - 3*d**4/(4*d**4*e**6 - 8*d**2*e**8*x**2 + 4*e**10*x**4) + 4*d**2*e**2*x**2*log(-d/e + x)/(4*d**4*e**6 - 8*d**2*e**8*x**2 + 4*e**10*x**4) + 4*d**2*e**2*x**2*log(d/e + x)/(4*d**4*e**6 - 8*d**2*e**8*x**2 + 4*e**10*x**4) + 4*d**2*e**2*x**2/(4*d**4*e**6 - 8*d**2*e**8*x**2 + 4*e**10*x**4) - 2*e**4*x**4*log(-d/e + x)/(4*d**4*e**6 - 8*d**2*e**8*x**2 + 4*e**10*x**4) - 2*e**4*x**4*log(d/e + x)/(4*d**4*e**6 - 8*d**2*e**8*x**2 + 4*e**10*x**4), Eq(p, -3)), (-2*d**4*log(-d/e + x)/(-2*d**2*e**6 + 2*e**8*x**2) - 2*d**4*log(d/e + x)/(-2*d**2*e**6 + 2*e**8*x**2) - 2*d**4/(-2*d**2*e**6 + 2*e**8*x**2) + 2*d**2*e**2*x**2*log(-d/e + x)/(-2*d**2*e**6 + 2*e**8*x**2) + 2*d**2*e**2*x**2*log(d/e + x)/(-2*d**2*e**6 + 2*e**8*x**2) + e**4*x**4/(-2*d**2*e**6 + 2*e**8*x**2), Eq(p, -2)), (-d**4*log(-d/e + x)/(2*e**6) - d**4*log(d/e + x)/(2*e**6) - d**2*x**2/(2*e**4) - x**4/(4*e**2), Eq(p, -1)), (-2*d**6*(d**2 - e**2*x**2)**p/(2*e**6*p**3 + 12*e**6*p**2 + 22*e**6*p + 12*e**6) - 2*d**4*e**2*p*x**2*(d**2 - e**2*x**2)**p/(2*e**6*p**3 + 12*e**6*p**2 + 22*e**6*p + 12*e**6) - d**2*e**4*p**2*x**4*(d**2 - e**2*x**2)**p/(2*e**6*p**3 + 12*e**6*p**2 + 22*e**6*p + 12*e**6) - d**2*e**4*p*x**4*(d**2 - e**2*x**2)**p/(2*e**6*p**3 + 12*e**6*p**2 + 22*e**6*p + 12*e**6) + e**6*p**2*x**6*(d**2 - e**2*x**2)**p/(2*e**6*p**3 + 12*e**6*p**2 + 22*e**6*p + 12*e**6) + 3*e**6*p*x**6*(d**2 - e**2*x**2)**p/(2*e**6*p**3 + 12*e**6*p**2 + 22*e**6*p + 12*e**6) + 2*e**6*x**6*(d**2 - e**2*x**2)**p/(2*e**6*p**3 + 12*e**6*p**2 + 22*e**6*p + 12*e**6), True)) + d**(2*p)*e**2*x**7*hyper((7/2, -p), (9/2,), e**2*x**2*exp_polar(2*I*pi)/d**2)/7","B",0
251,1,1328,0,9.141547," ","integrate(x**3*(e*x+d)**2*(-e**2*x**2+d**2)**p,x)","d^{2} \left(\begin{cases} \frac{x^{4} \left(d^{2}\right)^{p}}{4} & \text{for}\: e = 0 \\- \frac{d^{2} \log{\left(- \frac{d}{e} + x \right)}}{- 2 d^{2} e^{4} + 2 e^{6} x^{2}} - \frac{d^{2} \log{\left(\frac{d}{e} + x \right)}}{- 2 d^{2} e^{4} + 2 e^{6} x^{2}} - \frac{d^{2}}{- 2 d^{2} e^{4} + 2 e^{6} x^{2}} + \frac{e^{2} x^{2} \log{\left(- \frac{d}{e} + x \right)}}{- 2 d^{2} e^{4} + 2 e^{6} x^{2}} + \frac{e^{2} x^{2} \log{\left(\frac{d}{e} + x \right)}}{- 2 d^{2} e^{4} + 2 e^{6} x^{2}} & \text{for}\: p = -2 \\- \frac{d^{2} \log{\left(- \frac{d}{e} + x \right)}}{2 e^{4}} - \frac{d^{2} \log{\left(\frac{d}{e} + x \right)}}{2 e^{4}} - \frac{x^{2}}{2 e^{2}} & \text{for}\: p = -1 \\- \frac{d^{4} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{4} p^{2} + 6 e^{4} p + 4 e^{4}} - \frac{d^{2} e^{2} p x^{2} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{4} p^{2} + 6 e^{4} p + 4 e^{4}} + \frac{e^{4} p x^{4} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{4} p^{2} + 6 e^{4} p + 4 e^{4}} + \frac{e^{4} x^{4} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{4} p^{2} + 6 e^{4} p + 4 e^{4}} & \text{otherwise} \end{cases}\right) + \frac{2 d d^{2 p} e x^{5} {{}_{2}F_{1}\left(\begin{matrix} \frac{5}{2}, - p \\ \frac{7}{2} \end{matrix}\middle| {\frac{e^{2} x^{2} e^{2 i \pi}}{d^{2}}} \right)}}{5} + e^{2} \left(\begin{cases} \frac{x^{6} \left(d^{2}\right)^{p}}{6} & \text{for}\: e = 0 \\- \frac{2 d^{4} \log{\left(- \frac{d}{e} + x \right)}}{4 d^{4} e^{6} - 8 d^{2} e^{8} x^{2} + 4 e^{10} x^{4}} - \frac{2 d^{4} \log{\left(\frac{d}{e} + x \right)}}{4 d^{4} e^{6} - 8 d^{2} e^{8} x^{2} + 4 e^{10} x^{4}} - \frac{3 d^{4}}{4 d^{4} e^{6} - 8 d^{2} e^{8} x^{2} + 4 e^{10} x^{4}} + \frac{4 d^{2} e^{2} x^{2} \log{\left(- \frac{d}{e} + x \right)}}{4 d^{4} e^{6} - 8 d^{2} e^{8} x^{2} + 4 e^{10} x^{4}} + \frac{4 d^{2} e^{2} x^{2} \log{\left(\frac{d}{e} + x \right)}}{4 d^{4} e^{6} - 8 d^{2} e^{8} x^{2} + 4 e^{10} x^{4}} + \frac{4 d^{2} e^{2} x^{2}}{4 d^{4} e^{6} - 8 d^{2} e^{8} x^{2} + 4 e^{10} x^{4}} - \frac{2 e^{4} x^{4} \log{\left(- \frac{d}{e} + x \right)}}{4 d^{4} e^{6} - 8 d^{2} e^{8} x^{2} + 4 e^{10} x^{4}} - \frac{2 e^{4} x^{4} \log{\left(\frac{d}{e} + x \right)}}{4 d^{4} e^{6} - 8 d^{2} e^{8} x^{2} + 4 e^{10} x^{4}} & \text{for}\: p = -3 \\- \frac{2 d^{4} \log{\left(- \frac{d}{e} + x \right)}}{- 2 d^{2} e^{6} + 2 e^{8} x^{2}} - \frac{2 d^{4} \log{\left(\frac{d}{e} + x \right)}}{- 2 d^{2} e^{6} + 2 e^{8} x^{2}} - \frac{2 d^{4}}{- 2 d^{2} e^{6} + 2 e^{8} x^{2}} + \frac{2 d^{2} e^{2} x^{2} \log{\left(- \frac{d}{e} + x \right)}}{- 2 d^{2} e^{6} + 2 e^{8} x^{2}} + \frac{2 d^{2} e^{2} x^{2} \log{\left(\frac{d}{e} + x \right)}}{- 2 d^{2} e^{6} + 2 e^{8} x^{2}} + \frac{e^{4} x^{4}}{- 2 d^{2} e^{6} + 2 e^{8} x^{2}} & \text{for}\: p = -2 \\- \frac{d^{4} \log{\left(- \frac{d}{e} + x \right)}}{2 e^{6}} - \frac{d^{4} \log{\left(\frac{d}{e} + x \right)}}{2 e^{6}} - \frac{d^{2} x^{2}}{2 e^{4}} - \frac{x^{4}}{4 e^{2}} & \text{for}\: p = -1 \\- \frac{2 d^{6} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{6} p^{3} + 12 e^{6} p^{2} + 22 e^{6} p + 12 e^{6}} - \frac{2 d^{4} e^{2} p x^{2} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{6} p^{3} + 12 e^{6} p^{2} + 22 e^{6} p + 12 e^{6}} - \frac{d^{2} e^{4} p^{2} x^{4} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{6} p^{3} + 12 e^{6} p^{2} + 22 e^{6} p + 12 e^{6}} - \frac{d^{2} e^{4} p x^{4} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{6} p^{3} + 12 e^{6} p^{2} + 22 e^{6} p + 12 e^{6}} + \frac{e^{6} p^{2} x^{6} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{6} p^{3} + 12 e^{6} p^{2} + 22 e^{6} p + 12 e^{6}} + \frac{3 e^{6} p x^{6} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{6} p^{3} + 12 e^{6} p^{2} + 22 e^{6} p + 12 e^{6}} + \frac{2 e^{6} x^{6} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{6} p^{3} + 12 e^{6} p^{2} + 22 e^{6} p + 12 e^{6}} & \text{otherwise} \end{cases}\right)"," ",0,"d**2*Piecewise((x**4*(d**2)**p/4, Eq(e, 0)), (-d**2*log(-d/e + x)/(-2*d**2*e**4 + 2*e**6*x**2) - d**2*log(d/e + x)/(-2*d**2*e**4 + 2*e**6*x**2) - d**2/(-2*d**2*e**4 + 2*e**6*x**2) + e**2*x**2*log(-d/e + x)/(-2*d**2*e**4 + 2*e**6*x**2) + e**2*x**2*log(d/e + x)/(-2*d**2*e**4 + 2*e**6*x**2), Eq(p, -2)), (-d**2*log(-d/e + x)/(2*e**4) - d**2*log(d/e + x)/(2*e**4) - x**2/(2*e**2), Eq(p, -1)), (-d**4*(d**2 - e**2*x**2)**p/(2*e**4*p**2 + 6*e**4*p + 4*e**4) - d**2*e**2*p*x**2*(d**2 - e**2*x**2)**p/(2*e**4*p**2 + 6*e**4*p + 4*e**4) + e**4*p*x**4*(d**2 - e**2*x**2)**p/(2*e**4*p**2 + 6*e**4*p + 4*e**4) + e**4*x**4*(d**2 - e**2*x**2)**p/(2*e**4*p**2 + 6*e**4*p + 4*e**4), True)) + 2*d*d**(2*p)*e*x**5*hyper((5/2, -p), (7/2,), e**2*x**2*exp_polar(2*I*pi)/d**2)/5 + e**2*Piecewise((x**6*(d**2)**p/6, Eq(e, 0)), (-2*d**4*log(-d/e + x)/(4*d**4*e**6 - 8*d**2*e**8*x**2 + 4*e**10*x**4) - 2*d**4*log(d/e + x)/(4*d**4*e**6 - 8*d**2*e**8*x**2 + 4*e**10*x**4) - 3*d**4/(4*d**4*e**6 - 8*d**2*e**8*x**2 + 4*e**10*x**4) + 4*d**2*e**2*x**2*log(-d/e + x)/(4*d**4*e**6 - 8*d**2*e**8*x**2 + 4*e**10*x**4) + 4*d**2*e**2*x**2*log(d/e + x)/(4*d**4*e**6 - 8*d**2*e**8*x**2 + 4*e**10*x**4) + 4*d**2*e**2*x**2/(4*d**4*e**6 - 8*d**2*e**8*x**2 + 4*e**10*x**4) - 2*e**4*x**4*log(-d/e + x)/(4*d**4*e**6 - 8*d**2*e**8*x**2 + 4*e**10*x**4) - 2*e**4*x**4*log(d/e + x)/(4*d**4*e**6 - 8*d**2*e**8*x**2 + 4*e**10*x**4), Eq(p, -3)), (-2*d**4*log(-d/e + x)/(-2*d**2*e**6 + 2*e**8*x**2) - 2*d**4*log(d/e + x)/(-2*d**2*e**6 + 2*e**8*x**2) - 2*d**4/(-2*d**2*e**6 + 2*e**8*x**2) + 2*d**2*e**2*x**2*log(-d/e + x)/(-2*d**2*e**6 + 2*e**8*x**2) + 2*d**2*e**2*x**2*log(d/e + x)/(-2*d**2*e**6 + 2*e**8*x**2) + e**4*x**4/(-2*d**2*e**6 + 2*e**8*x**2), Eq(p, -2)), (-d**4*log(-d/e + x)/(2*e**6) - d**4*log(d/e + x)/(2*e**6) - d**2*x**2/(2*e**4) - x**4/(4*e**2), Eq(p, -1)), (-2*d**6*(d**2 - e**2*x**2)**p/(2*e**6*p**3 + 12*e**6*p**2 + 22*e**6*p + 12*e**6) - 2*d**4*e**2*p*x**2*(d**2 - e**2*x**2)**p/(2*e**6*p**3 + 12*e**6*p**2 + 22*e**6*p + 12*e**6) - d**2*e**4*p**2*x**4*(d**2 - e**2*x**2)**p/(2*e**6*p**3 + 12*e**6*p**2 + 22*e**6*p + 12*e**6) - d**2*e**4*p*x**4*(d**2 - e**2*x**2)**p/(2*e**6*p**3 + 12*e**6*p**2 + 22*e**6*p + 12*e**6) + e**6*p**2*x**6*(d**2 - e**2*x**2)**p/(2*e**6*p**3 + 12*e**6*p**2 + 22*e**6*p + 12*e**6) + 3*e**6*p*x**6*(d**2 - e**2*x**2)**p/(2*e**6*p**3 + 12*e**6*p**2 + 22*e**6*p + 12*e**6) + 2*e**6*x**6*(d**2 - e**2*x**2)**p/(2*e**6*p**3 + 12*e**6*p**2 + 22*e**6*p + 12*e**6), True))","B",0
252,1,425,0,6.427926," ","integrate(x**2*(e*x+d)**2*(-e**2*x**2+d**2)**p,x)","\frac{d^{2} d^{2 p} x^{3} {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{2}, - p \\ \frac{5}{2} \end{matrix}\middle| {\frac{e^{2} x^{2} e^{2 i \pi}}{d^{2}}} \right)}}{3} + 2 d e \left(\begin{cases} \frac{x^{4} \left(d^{2}\right)^{p}}{4} & \text{for}\: e = 0 \\- \frac{d^{2} \log{\left(- \frac{d}{e} + x \right)}}{- 2 d^{2} e^{4} + 2 e^{6} x^{2}} - \frac{d^{2} \log{\left(\frac{d}{e} + x \right)}}{- 2 d^{2} e^{4} + 2 e^{6} x^{2}} - \frac{d^{2}}{- 2 d^{2} e^{4} + 2 e^{6} x^{2}} + \frac{e^{2} x^{2} \log{\left(- \frac{d}{e} + x \right)}}{- 2 d^{2} e^{4} + 2 e^{6} x^{2}} + \frac{e^{2} x^{2} \log{\left(\frac{d}{e} + x \right)}}{- 2 d^{2} e^{4} + 2 e^{6} x^{2}} & \text{for}\: p = -2 \\- \frac{d^{2} \log{\left(- \frac{d}{e} + x \right)}}{2 e^{4}} - \frac{d^{2} \log{\left(\frac{d}{e} + x \right)}}{2 e^{4}} - \frac{x^{2}}{2 e^{2}} & \text{for}\: p = -1 \\- \frac{d^{4} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{4} p^{2} + 6 e^{4} p + 4 e^{4}} - \frac{d^{2} e^{2} p x^{2} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{4} p^{2} + 6 e^{4} p + 4 e^{4}} + \frac{e^{4} p x^{4} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{4} p^{2} + 6 e^{4} p + 4 e^{4}} + \frac{e^{4} x^{4} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{4} p^{2} + 6 e^{4} p + 4 e^{4}} & \text{otherwise} \end{cases}\right) + \frac{d^{2 p} e^{2} x^{5} {{}_{2}F_{1}\left(\begin{matrix} \frac{5}{2}, - p \\ \frac{7}{2} \end{matrix}\middle| {\frac{e^{2} x^{2} e^{2 i \pi}}{d^{2}}} \right)}}{5}"," ",0,"d**2*d**(2*p)*x**3*hyper((3/2, -p), (5/2,), e**2*x**2*exp_polar(2*I*pi)/d**2)/3 + 2*d*e*Piecewise((x**4*(d**2)**p/4, Eq(e, 0)), (-d**2*log(-d/e + x)/(-2*d**2*e**4 + 2*e**6*x**2) - d**2*log(d/e + x)/(-2*d**2*e**4 + 2*e**6*x**2) - d**2/(-2*d**2*e**4 + 2*e**6*x**2) + e**2*x**2*log(-d/e + x)/(-2*d**2*e**4 + 2*e**6*x**2) + e**2*x**2*log(d/e + x)/(-2*d**2*e**4 + 2*e**6*x**2), Eq(p, -2)), (-d**2*log(-d/e + x)/(2*e**4) - d**2*log(d/e + x)/(2*e**4) - x**2/(2*e**2), Eq(p, -1)), (-d**4*(d**2 - e**2*x**2)**p/(2*e**4*p**2 + 6*e**4*p + 4*e**4) - d**2*e**2*p*x**2*(d**2 - e**2*x**2)**p/(2*e**4*p**2 + 6*e**4*p + 4*e**4) + e**4*p*x**4*(d**2 - e**2*x**2)**p/(2*e**4*p**2 + 6*e**4*p + 4*e**4) + e**4*x**4*(d**2 - e**2*x**2)**p/(2*e**4*p**2 + 6*e**4*p + 4*e**4), True)) + d**(2*p)*e**2*x**5*hyper((5/2, -p), (7/2,), e**2*x**2*exp_polar(2*I*pi)/d**2)/5","B",0
253,1,440,0,5.924443," ","integrate(x*(e*x+d)**2*(-e**2*x**2+d**2)**p,x)","d^{2} \left(\begin{cases} \frac{x^{2} \left(d^{2}\right)^{p}}{2} & \text{for}\: e^{2} = 0 \\- \frac{\begin{cases} \frac{\left(d^{2} - e^{2} x^{2}\right)^{p + 1}}{p + 1} & \text{for}\: p \neq -1 \\\log{\left(d^{2} - e^{2} x^{2} \right)} & \text{otherwise} \end{cases}}{2 e^{2}} & \text{otherwise} \end{cases}\right) + \frac{2 d d^{2 p} e x^{3} {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{2}, - p \\ \frac{5}{2} \end{matrix}\middle| {\frac{e^{2} x^{2} e^{2 i \pi}}{d^{2}}} \right)}}{3} + e^{2} \left(\begin{cases} \frac{x^{4} \left(d^{2}\right)^{p}}{4} & \text{for}\: e = 0 \\- \frac{d^{2} \log{\left(- \frac{d}{e} + x \right)}}{- 2 d^{2} e^{4} + 2 e^{6} x^{2}} - \frac{d^{2} \log{\left(\frac{d}{e} + x \right)}}{- 2 d^{2} e^{4} + 2 e^{6} x^{2}} - \frac{d^{2}}{- 2 d^{2} e^{4} + 2 e^{6} x^{2}} + \frac{e^{2} x^{2} \log{\left(- \frac{d}{e} + x \right)}}{- 2 d^{2} e^{4} + 2 e^{6} x^{2}} + \frac{e^{2} x^{2} \log{\left(\frac{d}{e} + x \right)}}{- 2 d^{2} e^{4} + 2 e^{6} x^{2}} & \text{for}\: p = -2 \\- \frac{d^{2} \log{\left(- \frac{d}{e} + x \right)}}{2 e^{4}} - \frac{d^{2} \log{\left(\frac{d}{e} + x \right)}}{2 e^{4}} - \frac{x^{2}}{2 e^{2}} & \text{for}\: p = -1 \\- \frac{d^{4} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{4} p^{2} + 6 e^{4} p + 4 e^{4}} - \frac{d^{2} e^{2} p x^{2} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{4} p^{2} + 6 e^{4} p + 4 e^{4}} + \frac{e^{4} p x^{4} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{4} p^{2} + 6 e^{4} p + 4 e^{4}} + \frac{e^{4} x^{4} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{4} p^{2} + 6 e^{4} p + 4 e^{4}} & \text{otherwise} \end{cases}\right)"," ",0,"d**2*Piecewise((x**2*(d**2)**p/2, Eq(e**2, 0)), (-Piecewise(((d**2 - e**2*x**2)**(p + 1)/(p + 1), Ne(p, -1)), (log(d**2 - e**2*x**2), True))/(2*e**2), True)) + 2*d*d**(2*p)*e*x**3*hyper((3/2, -p), (5/2,), e**2*x**2*exp_polar(2*I*pi)/d**2)/3 + e**2*Piecewise((x**4*(d**2)**p/4, Eq(e, 0)), (-d**2*log(-d/e + x)/(-2*d**2*e**4 + 2*e**6*x**2) - d**2*log(d/e + x)/(-2*d**2*e**4 + 2*e**6*x**2) - d**2/(-2*d**2*e**4 + 2*e**6*x**2) + e**2*x**2*log(-d/e + x)/(-2*d**2*e**4 + 2*e**6*x**2) + e**2*x**2*log(d/e + x)/(-2*d**2*e**4 + 2*e**6*x**2), Eq(p, -2)), (-d**2*log(-d/e + x)/(2*e**4) - d**2*log(d/e + x)/(2*e**4) - x**2/(2*e**2), Eq(p, -1)), (-d**4*(d**2 - e**2*x**2)**p/(2*e**4*p**2 + 6*e**4*p + 4*e**4) - d**2*e**2*p*x**2*(d**2 - e**2*x**2)**p/(2*e**4*p**2 + 6*e**4*p + 4*e**4) + e**4*p*x**4*(d**2 - e**2*x**2)**p/(2*e**4*p**2 + 6*e**4*p + 4*e**4) + e**4*x**4*(d**2 - e**2*x**2)**p/(2*e**4*p**2 + 6*e**4*p + 4*e**4), True))","A",0
254,1,124,0,4.949948," ","integrate((e*x+d)**2*(-e**2*x**2+d**2)**p,x)","d^{2} d^{2 p} x {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, - p \\ \frac{3}{2} \end{matrix}\middle| {\frac{e^{2} x^{2} e^{2 i \pi}}{d^{2}}} \right)} + 2 d e \left(\begin{cases} \frac{x^{2} \left(d^{2}\right)^{p}}{2} & \text{for}\: e^{2} = 0 \\- \frac{\begin{cases} \frac{\left(d^{2} - e^{2} x^{2}\right)^{p + 1}}{p + 1} & \text{for}\: p \neq -1 \\\log{\left(d^{2} - e^{2} x^{2} \right)} & \text{otherwise} \end{cases}}{2 e^{2}} & \text{otherwise} \end{cases}\right) + \frac{d^{2 p} e^{2} x^{3} {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{2}, - p \\ \frac{5}{2} \end{matrix}\middle| {\frac{e^{2} x^{2} e^{2 i \pi}}{d^{2}}} \right)}}{3}"," ",0,"d**2*d**(2*p)*x*hyper((1/2, -p), (3/2,), e**2*x**2*exp_polar(2*I*pi)/d**2) + 2*d*e*Piecewise((x**2*(d**2)**p/2, Eq(e**2, 0)), (-Piecewise(((d**2 - e**2*x**2)**(p + 1)/(p + 1), Ne(p, -1)), (log(d**2 - e**2*x**2), True))/(2*e**2), True)) + d**(2*p)*e**2*x**3*hyper((3/2, -p), (5/2,), e**2*x**2*exp_polar(2*I*pi)/d**2)/3","A",0
255,1,136,0,9.045894," ","integrate((e*x+d)**2*(-e**2*x**2+d**2)**p/x,x)","- \frac{d^{2} e^{2 p} x^{2 p} e^{i \pi p} \Gamma\left(- p\right) {{}_{2}F_{1}\left(\begin{matrix} - p, - p \\ 1 - p \end{matrix}\middle| {\frac{d^{2}}{e^{2} x^{2}}} \right)}}{2 \Gamma\left(1 - p\right)} + 2 d d^{2 p} e x {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, - p \\ \frac{3}{2} \end{matrix}\middle| {\frac{e^{2} x^{2} e^{2 i \pi}}{d^{2}}} \right)} + e^{2} \left(\begin{cases} \frac{x^{2} \left(d^{2}\right)^{p}}{2} & \text{for}\: e^{2} = 0 \\- \frac{\begin{cases} \frac{\left(d^{2} - e^{2} x^{2}\right)^{p + 1}}{p + 1} & \text{for}\: p \neq -1 \\\log{\left(d^{2} - e^{2} x^{2} \right)} & \text{otherwise} \end{cases}}{2 e^{2}} & \text{otherwise} \end{cases}\right)"," ",0,"-d**2*e**(2*p)*x**(2*p)*exp(I*pi*p)*gamma(-p)*hyper((-p, -p), (1 - p,), d**2/(e**2*x**2))/(2*gamma(1 - p)) + 2*d*d**(2*p)*e*x*hyper((1/2, -p), (3/2,), e**2*x**2*exp_polar(2*I*pi)/d**2) + e**2*Piecewise((x**2*(d**2)**p/2, Eq(e**2, 0)), (-Piecewise(((d**2 - e**2*x**2)**(p + 1)/(p + 1), Ne(p, -1)), (log(d**2 - e**2*x**2), True))/(2*e**2), True))","A",0
256,1,116,0,6.894738," ","integrate((e*x+d)**2*(-e**2*x**2+d**2)**p/x**2,x)","- \frac{d^{2} d^{2 p} {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, - p \\ \frac{1}{2} \end{matrix}\middle| {\frac{e^{2} x^{2} e^{2 i \pi}}{d^{2}}} \right)}}{x} - \frac{d e e^{2 p} x^{2 p} e^{i \pi p} \Gamma\left(- p\right) {{}_{2}F_{1}\left(\begin{matrix} - p, - p \\ 1 - p \end{matrix}\middle| {\frac{d^{2}}{e^{2} x^{2}}} \right)}}{\Gamma\left(1 - p\right)} + d^{2 p} e^{2} x {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, - p \\ \frac{3}{2} \end{matrix}\middle| {\frac{e^{2} x^{2} e^{2 i \pi}}{d^{2}}} \right)}"," ",0,"-d**2*d**(2*p)*hyper((-1/2, -p), (1/2,), e**2*x**2*exp_polar(2*I*pi)/d**2)/x - d*e*e**(2*p)*x**(2*p)*exp(I*pi*p)*gamma(-p)*hyper((-p, -p), (1 - p,), d**2/(e**2*x**2))/gamma(1 - p) + d**(2*p)*e**2*x*hyper((1/2, -p), (3/2,), e**2*x**2*exp_polar(2*I*pi)/d**2)","C",0
257,1,139,0,6.917206," ","integrate((e*x+d)**2*(-e**2*x**2+d**2)**p/x**3,x)","- \frac{d^{2} e^{2 p} x^{2 p} e^{i \pi p} \Gamma\left(1 - p\right) {{}_{2}F_{1}\left(\begin{matrix} - p, 1 - p \\ 2 - p \end{matrix}\middle| {\frac{d^{2}}{e^{2} x^{2}}} \right)}}{2 x^{2} \Gamma\left(2 - p\right)} - \frac{2 d d^{2 p} e {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, - p \\ \frac{1}{2} \end{matrix}\middle| {\frac{e^{2} x^{2} e^{2 i \pi}}{d^{2}}} \right)}}{x} - \frac{e^{2} e^{2 p} x^{2 p} e^{i \pi p} \Gamma\left(- p\right) {{}_{2}F_{1}\left(\begin{matrix} - p, - p \\ 1 - p \end{matrix}\middle| {\frac{d^{2}}{e^{2} x^{2}}} \right)}}{2 \Gamma\left(1 - p\right)}"," ",0,"-d**2*e**(2*p)*x**(2*p)*exp(I*pi*p)*gamma(1 - p)*hyper((-p, 1 - p), (2 - p,), d**2/(e**2*x**2))/(2*x**2*gamma(2 - p)) - 2*d*d**(2*p)*e*hyper((-1/2, -p), (1/2,), e**2*x**2*exp_polar(2*I*pi)/d**2)/x - e**2*e**(2*p)*x**(2*p)*exp(I*pi*p)*gamma(-p)*hyper((-p, -p), (1 - p,), d**2/(e**2*x**2))/(2*gamma(1 - p))","C",0
258,1,2966,0,16.245814," ","integrate(x**5*(e*x+d)**3*(-e**2*x**2+d**2)**p,x)","d^{3} \left(\begin{cases} \frac{x^{6} \left(d^{2}\right)^{p}}{6} & \text{for}\: e = 0 \\- \frac{2 d^{4} \log{\left(- \frac{d}{e} + x \right)}}{4 d^{4} e^{6} - 8 d^{2} e^{8} x^{2} + 4 e^{10} x^{4}} - \frac{2 d^{4} \log{\left(\frac{d}{e} + x \right)}}{4 d^{4} e^{6} - 8 d^{2} e^{8} x^{2} + 4 e^{10} x^{4}} - \frac{3 d^{4}}{4 d^{4} e^{6} - 8 d^{2} e^{8} x^{2} + 4 e^{10} x^{4}} + \frac{4 d^{2} e^{2} x^{2} \log{\left(- \frac{d}{e} + x \right)}}{4 d^{4} e^{6} - 8 d^{2} e^{8} x^{2} + 4 e^{10} x^{4}} + \frac{4 d^{2} e^{2} x^{2} \log{\left(\frac{d}{e} + x \right)}}{4 d^{4} e^{6} - 8 d^{2} e^{8} x^{2} + 4 e^{10} x^{4}} + \frac{4 d^{2} e^{2} x^{2}}{4 d^{4} e^{6} - 8 d^{2} e^{8} x^{2} + 4 e^{10} x^{4}} - \frac{2 e^{4} x^{4} \log{\left(- \frac{d}{e} + x \right)}}{4 d^{4} e^{6} - 8 d^{2} e^{8} x^{2} + 4 e^{10} x^{4}} - \frac{2 e^{4} x^{4} \log{\left(\frac{d}{e} + x \right)}}{4 d^{4} e^{6} - 8 d^{2} e^{8} x^{2} + 4 e^{10} x^{4}} & \text{for}\: p = -3 \\- \frac{2 d^{4} \log{\left(- \frac{d}{e} + x \right)}}{- 2 d^{2} e^{6} + 2 e^{8} x^{2}} - \frac{2 d^{4} \log{\left(\frac{d}{e} + x \right)}}{- 2 d^{2} e^{6} + 2 e^{8} x^{2}} - \frac{2 d^{4}}{- 2 d^{2} e^{6} + 2 e^{8} x^{2}} + \frac{2 d^{2} e^{2} x^{2} \log{\left(- \frac{d}{e} + x \right)}}{- 2 d^{2} e^{6} + 2 e^{8} x^{2}} + \frac{2 d^{2} e^{2} x^{2} \log{\left(\frac{d}{e} + x \right)}}{- 2 d^{2} e^{6} + 2 e^{8} x^{2}} + \frac{e^{4} x^{4}}{- 2 d^{2} e^{6} + 2 e^{8} x^{2}} & \text{for}\: p = -2 \\- \frac{d^{4} \log{\left(- \frac{d}{e} + x \right)}}{2 e^{6}} - \frac{d^{4} \log{\left(\frac{d}{e} + x \right)}}{2 e^{6}} - \frac{d^{2} x^{2}}{2 e^{4}} - \frac{x^{4}}{4 e^{2}} & \text{for}\: p = -1 \\- \frac{2 d^{6} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{6} p^{3} + 12 e^{6} p^{2} + 22 e^{6} p + 12 e^{6}} - \frac{2 d^{4} e^{2} p x^{2} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{6} p^{3} + 12 e^{6} p^{2} + 22 e^{6} p + 12 e^{6}} - \frac{d^{2} e^{4} p^{2} x^{4} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{6} p^{3} + 12 e^{6} p^{2} + 22 e^{6} p + 12 e^{6}} - \frac{d^{2} e^{4} p x^{4} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{6} p^{3} + 12 e^{6} p^{2} + 22 e^{6} p + 12 e^{6}} + \frac{e^{6} p^{2} x^{6} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{6} p^{3} + 12 e^{6} p^{2} + 22 e^{6} p + 12 e^{6}} + \frac{3 e^{6} p x^{6} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{6} p^{3} + 12 e^{6} p^{2} + 22 e^{6} p + 12 e^{6}} + \frac{2 e^{6} x^{6} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{6} p^{3} + 12 e^{6} p^{2} + 22 e^{6} p + 12 e^{6}} & \text{otherwise} \end{cases}\right) + \frac{3 d^{2} d^{2 p} e x^{7} {{}_{2}F_{1}\left(\begin{matrix} \frac{7}{2}, - p \\ \frac{9}{2} \end{matrix}\middle| {\frac{e^{2} x^{2} e^{2 i \pi}}{d^{2}}} \right)}}{7} + 3 d e^{2} \left(\begin{cases} \frac{x^{8} \left(d^{2}\right)^{p}}{8} & \text{for}\: e = 0 \\- \frac{6 d^{6} \log{\left(- \frac{d}{e} + x \right)}}{- 12 d^{6} e^{8} + 36 d^{4} e^{10} x^{2} - 36 d^{2} e^{12} x^{4} + 12 e^{14} x^{6}} - \frac{6 d^{6} \log{\left(\frac{d}{e} + x \right)}}{- 12 d^{6} e^{8} + 36 d^{4} e^{10} x^{2} - 36 d^{2} e^{12} x^{4} + 12 e^{14} x^{6}} - \frac{11 d^{6}}{- 12 d^{6} e^{8} + 36 d^{4} e^{10} x^{2} - 36 d^{2} e^{12} x^{4} + 12 e^{14} x^{6}} + \frac{18 d^{4} e^{2} x^{2} \log{\left(- \frac{d}{e} + x \right)}}{- 12 d^{6} e^{8} + 36 d^{4} e^{10} x^{2} - 36 d^{2} e^{12} x^{4} + 12 e^{14} x^{6}} + \frac{18 d^{4} e^{2} x^{2} \log{\left(\frac{d}{e} + x \right)}}{- 12 d^{6} e^{8} + 36 d^{4} e^{10} x^{2} - 36 d^{2} e^{12} x^{4} + 12 e^{14} x^{6}} + \frac{27 d^{4} e^{2} x^{2}}{- 12 d^{6} e^{8} + 36 d^{4} e^{10} x^{2} - 36 d^{2} e^{12} x^{4} + 12 e^{14} x^{6}} - \frac{18 d^{2} e^{4} x^{4} \log{\left(- \frac{d}{e} + x \right)}}{- 12 d^{6} e^{8} + 36 d^{4} e^{10} x^{2} - 36 d^{2} e^{12} x^{4} + 12 e^{14} x^{6}} - \frac{18 d^{2} e^{4} x^{4} \log{\left(\frac{d}{e} + x \right)}}{- 12 d^{6} e^{8} + 36 d^{4} e^{10} x^{2} - 36 d^{2} e^{12} x^{4} + 12 e^{14} x^{6}} - \frac{18 d^{2} e^{4} x^{4}}{- 12 d^{6} e^{8} + 36 d^{4} e^{10} x^{2} - 36 d^{2} e^{12} x^{4} + 12 e^{14} x^{6}} + \frac{6 e^{6} x^{6} \log{\left(- \frac{d}{e} + x \right)}}{- 12 d^{6} e^{8} + 36 d^{4} e^{10} x^{2} - 36 d^{2} e^{12} x^{4} + 12 e^{14} x^{6}} + \frac{6 e^{6} x^{6} \log{\left(\frac{d}{e} + x \right)}}{- 12 d^{6} e^{8} + 36 d^{4} e^{10} x^{2} - 36 d^{2} e^{12} x^{4} + 12 e^{14} x^{6}} & \text{for}\: p = -4 \\- \frac{6 d^{6} \log{\left(- \frac{d}{e} + x \right)}}{4 d^{4} e^{8} - 8 d^{2} e^{10} x^{2} + 4 e^{12} x^{4}} - \frac{6 d^{6} \log{\left(\frac{d}{e} + x \right)}}{4 d^{4} e^{8} - 8 d^{2} e^{10} x^{2} + 4 e^{12} x^{4}} - \frac{9 d^{6}}{4 d^{4} e^{8} - 8 d^{2} e^{10} x^{2} + 4 e^{12} x^{4}} + \frac{12 d^{4} e^{2} x^{2} \log{\left(- \frac{d}{e} + x \right)}}{4 d^{4} e^{8} - 8 d^{2} e^{10} x^{2} + 4 e^{12} x^{4}} + \frac{12 d^{4} e^{2} x^{2} \log{\left(\frac{d}{e} + x \right)}}{4 d^{4} e^{8} - 8 d^{2} e^{10} x^{2} + 4 e^{12} x^{4}} + \frac{12 d^{4} e^{2} x^{2}}{4 d^{4} e^{8} - 8 d^{2} e^{10} x^{2} + 4 e^{12} x^{4}} - \frac{6 d^{2} e^{4} x^{4} \log{\left(- \frac{d}{e} + x \right)}}{4 d^{4} e^{8} - 8 d^{2} e^{10} x^{2} + 4 e^{12} x^{4}} - \frac{6 d^{2} e^{4} x^{4} \log{\left(\frac{d}{e} + x \right)}}{4 d^{4} e^{8} - 8 d^{2} e^{10} x^{2} + 4 e^{12} x^{4}} - \frac{2 e^{6} x^{6}}{4 d^{4} e^{8} - 8 d^{2} e^{10} x^{2} + 4 e^{12} x^{4}} & \text{for}\: p = -3 \\- \frac{6 d^{6} \log{\left(- \frac{d}{e} + x \right)}}{- 4 d^{2} e^{8} + 4 e^{10} x^{2}} - \frac{6 d^{6} \log{\left(\frac{d}{e} + x \right)}}{- 4 d^{2} e^{8} + 4 e^{10} x^{2}} - \frac{6 d^{6}}{- 4 d^{2} e^{8} + 4 e^{10} x^{2}} + \frac{6 d^{4} e^{2} x^{2} \log{\left(- \frac{d}{e} + x \right)}}{- 4 d^{2} e^{8} + 4 e^{10} x^{2}} + \frac{6 d^{4} e^{2} x^{2} \log{\left(\frac{d}{e} + x \right)}}{- 4 d^{2} e^{8} + 4 e^{10} x^{2}} + \frac{3 d^{2} e^{4} x^{4}}{- 4 d^{2} e^{8} + 4 e^{10} x^{2}} + \frac{e^{6} x^{6}}{- 4 d^{2} e^{8} + 4 e^{10} x^{2}} & \text{for}\: p = -2 \\- \frac{d^{6} \log{\left(- \frac{d}{e} + x \right)}}{2 e^{8}} - \frac{d^{6} \log{\left(\frac{d}{e} + x \right)}}{2 e^{8}} - \frac{d^{4} x^{2}}{2 e^{6}} - \frac{d^{2} x^{4}}{4 e^{4}} - \frac{x^{6}}{6 e^{2}} & \text{for}\: p = -1 \\- \frac{6 d^{8} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{8} p^{4} + 20 e^{8} p^{3} + 70 e^{8} p^{2} + 100 e^{8} p + 48 e^{8}} - \frac{6 d^{6} e^{2} p x^{2} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{8} p^{4} + 20 e^{8} p^{3} + 70 e^{8} p^{2} + 100 e^{8} p + 48 e^{8}} - \frac{3 d^{4} e^{4} p^{2} x^{4} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{8} p^{4} + 20 e^{8} p^{3} + 70 e^{8} p^{2} + 100 e^{8} p + 48 e^{8}} - \frac{3 d^{4} e^{4} p x^{4} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{8} p^{4} + 20 e^{8} p^{3} + 70 e^{8} p^{2} + 100 e^{8} p + 48 e^{8}} - \frac{d^{2} e^{6} p^{3} x^{6} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{8} p^{4} + 20 e^{8} p^{3} + 70 e^{8} p^{2} + 100 e^{8} p + 48 e^{8}} - \frac{3 d^{2} e^{6} p^{2} x^{6} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{8} p^{4} + 20 e^{8} p^{3} + 70 e^{8} p^{2} + 100 e^{8} p + 48 e^{8}} - \frac{2 d^{2} e^{6} p x^{6} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{8} p^{4} + 20 e^{8} p^{3} + 70 e^{8} p^{2} + 100 e^{8} p + 48 e^{8}} + \frac{e^{8} p^{3} x^{8} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{8} p^{4} + 20 e^{8} p^{3} + 70 e^{8} p^{2} + 100 e^{8} p + 48 e^{8}} + \frac{6 e^{8} p^{2} x^{8} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{8} p^{4} + 20 e^{8} p^{3} + 70 e^{8} p^{2} + 100 e^{8} p + 48 e^{8}} + \frac{11 e^{8} p x^{8} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{8} p^{4} + 20 e^{8} p^{3} + 70 e^{8} p^{2} + 100 e^{8} p + 48 e^{8}} + \frac{6 e^{8} x^{8} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{8} p^{4} + 20 e^{8} p^{3} + 70 e^{8} p^{2} + 100 e^{8} p + 48 e^{8}} & \text{otherwise} \end{cases}\right) + \frac{d^{2 p} e^{3} x^{9} {{}_{2}F_{1}\left(\begin{matrix} \frac{9}{2}, - p \\ \frac{11}{2} \end{matrix}\middle| {\frac{e^{2} x^{2} e^{2 i \pi}}{d^{2}}} \right)}}{9}"," ",0,"d**3*Piecewise((x**6*(d**2)**p/6, Eq(e, 0)), (-2*d**4*log(-d/e + x)/(4*d**4*e**6 - 8*d**2*e**8*x**2 + 4*e**10*x**4) - 2*d**4*log(d/e + x)/(4*d**4*e**6 - 8*d**2*e**8*x**2 + 4*e**10*x**4) - 3*d**4/(4*d**4*e**6 - 8*d**2*e**8*x**2 + 4*e**10*x**4) + 4*d**2*e**2*x**2*log(-d/e + x)/(4*d**4*e**6 - 8*d**2*e**8*x**2 + 4*e**10*x**4) + 4*d**2*e**2*x**2*log(d/e + x)/(4*d**4*e**6 - 8*d**2*e**8*x**2 + 4*e**10*x**4) + 4*d**2*e**2*x**2/(4*d**4*e**6 - 8*d**2*e**8*x**2 + 4*e**10*x**4) - 2*e**4*x**4*log(-d/e + x)/(4*d**4*e**6 - 8*d**2*e**8*x**2 + 4*e**10*x**4) - 2*e**4*x**4*log(d/e + x)/(4*d**4*e**6 - 8*d**2*e**8*x**2 + 4*e**10*x**4), Eq(p, -3)), (-2*d**4*log(-d/e + x)/(-2*d**2*e**6 + 2*e**8*x**2) - 2*d**4*log(d/e + x)/(-2*d**2*e**6 + 2*e**8*x**2) - 2*d**4/(-2*d**2*e**6 + 2*e**8*x**2) + 2*d**2*e**2*x**2*log(-d/e + x)/(-2*d**2*e**6 + 2*e**8*x**2) + 2*d**2*e**2*x**2*log(d/e + x)/(-2*d**2*e**6 + 2*e**8*x**2) + e**4*x**4/(-2*d**2*e**6 + 2*e**8*x**2), Eq(p, -2)), (-d**4*log(-d/e + x)/(2*e**6) - d**4*log(d/e + x)/(2*e**6) - d**2*x**2/(2*e**4) - x**4/(4*e**2), Eq(p, -1)), (-2*d**6*(d**2 - e**2*x**2)**p/(2*e**6*p**3 + 12*e**6*p**2 + 22*e**6*p + 12*e**6) - 2*d**4*e**2*p*x**2*(d**2 - e**2*x**2)**p/(2*e**6*p**3 + 12*e**6*p**2 + 22*e**6*p + 12*e**6) - d**2*e**4*p**2*x**4*(d**2 - e**2*x**2)**p/(2*e**6*p**3 + 12*e**6*p**2 + 22*e**6*p + 12*e**6) - d**2*e**4*p*x**4*(d**2 - e**2*x**2)**p/(2*e**6*p**3 + 12*e**6*p**2 + 22*e**6*p + 12*e**6) + e**6*p**2*x**6*(d**2 - e**2*x**2)**p/(2*e**6*p**3 + 12*e**6*p**2 + 22*e**6*p + 12*e**6) + 3*e**6*p*x**6*(d**2 - e**2*x**2)**p/(2*e**6*p**3 + 12*e**6*p**2 + 22*e**6*p + 12*e**6) + 2*e**6*x**6*(d**2 - e**2*x**2)**p/(2*e**6*p**3 + 12*e**6*p**2 + 22*e**6*p + 12*e**6), True)) + 3*d**2*d**(2*p)*e*x**7*hyper((7/2, -p), (9/2,), e**2*x**2*exp_polar(2*I*pi)/d**2)/7 + 3*d*e**2*Piecewise((x**8*(d**2)**p/8, Eq(e, 0)), (-6*d**6*log(-d/e + x)/(-12*d**6*e**8 + 36*d**4*e**10*x**2 - 36*d**2*e**12*x**4 + 12*e**14*x**6) - 6*d**6*log(d/e + x)/(-12*d**6*e**8 + 36*d**4*e**10*x**2 - 36*d**2*e**12*x**4 + 12*e**14*x**6) - 11*d**6/(-12*d**6*e**8 + 36*d**4*e**10*x**2 - 36*d**2*e**12*x**4 + 12*e**14*x**6) + 18*d**4*e**2*x**2*log(-d/e + x)/(-12*d**6*e**8 + 36*d**4*e**10*x**2 - 36*d**2*e**12*x**4 + 12*e**14*x**6) + 18*d**4*e**2*x**2*log(d/e + x)/(-12*d**6*e**8 + 36*d**4*e**10*x**2 - 36*d**2*e**12*x**4 + 12*e**14*x**6) + 27*d**4*e**2*x**2/(-12*d**6*e**8 + 36*d**4*e**10*x**2 - 36*d**2*e**12*x**4 + 12*e**14*x**6) - 18*d**2*e**4*x**4*log(-d/e + x)/(-12*d**6*e**8 + 36*d**4*e**10*x**2 - 36*d**2*e**12*x**4 + 12*e**14*x**6) - 18*d**2*e**4*x**4*log(d/e + x)/(-12*d**6*e**8 + 36*d**4*e**10*x**2 - 36*d**2*e**12*x**4 + 12*e**14*x**6) - 18*d**2*e**4*x**4/(-12*d**6*e**8 + 36*d**4*e**10*x**2 - 36*d**2*e**12*x**4 + 12*e**14*x**6) + 6*e**6*x**6*log(-d/e + x)/(-12*d**6*e**8 + 36*d**4*e**10*x**2 - 36*d**2*e**12*x**4 + 12*e**14*x**6) + 6*e**6*x**6*log(d/e + x)/(-12*d**6*e**8 + 36*d**4*e**10*x**2 - 36*d**2*e**12*x**4 + 12*e**14*x**6), Eq(p, -4)), (-6*d**6*log(-d/e + x)/(4*d**4*e**8 - 8*d**2*e**10*x**2 + 4*e**12*x**4) - 6*d**6*log(d/e + x)/(4*d**4*e**8 - 8*d**2*e**10*x**2 + 4*e**12*x**4) - 9*d**6/(4*d**4*e**8 - 8*d**2*e**10*x**2 + 4*e**12*x**4) + 12*d**4*e**2*x**2*log(-d/e + x)/(4*d**4*e**8 - 8*d**2*e**10*x**2 + 4*e**12*x**4) + 12*d**4*e**2*x**2*log(d/e + x)/(4*d**4*e**8 - 8*d**2*e**10*x**2 + 4*e**12*x**4) + 12*d**4*e**2*x**2/(4*d**4*e**8 - 8*d**2*e**10*x**2 + 4*e**12*x**4) - 6*d**2*e**4*x**4*log(-d/e + x)/(4*d**4*e**8 - 8*d**2*e**10*x**2 + 4*e**12*x**4) - 6*d**2*e**4*x**4*log(d/e + x)/(4*d**4*e**8 - 8*d**2*e**10*x**2 + 4*e**12*x**4) - 2*e**6*x**6/(4*d**4*e**8 - 8*d**2*e**10*x**2 + 4*e**12*x**4), Eq(p, -3)), (-6*d**6*log(-d/e + x)/(-4*d**2*e**8 + 4*e**10*x**2) - 6*d**6*log(d/e + x)/(-4*d**2*e**8 + 4*e**10*x**2) - 6*d**6/(-4*d**2*e**8 + 4*e**10*x**2) + 6*d**4*e**2*x**2*log(-d/e + x)/(-4*d**2*e**8 + 4*e**10*x**2) + 6*d**4*e**2*x**2*log(d/e + x)/(-4*d**2*e**8 + 4*e**10*x**2) + 3*d**2*e**4*x**4/(-4*d**2*e**8 + 4*e**10*x**2) + e**6*x**6/(-4*d**2*e**8 + 4*e**10*x**2), Eq(p, -2)), (-d**6*log(-d/e + x)/(2*e**8) - d**6*log(d/e + x)/(2*e**8) - d**4*x**2/(2*e**6) - d**2*x**4/(4*e**4) - x**6/(6*e**2), Eq(p, -1)), (-6*d**8*(d**2 - e**2*x**2)**p/(2*e**8*p**4 + 20*e**8*p**3 + 70*e**8*p**2 + 100*e**8*p + 48*e**8) - 6*d**6*e**2*p*x**2*(d**2 - e**2*x**2)**p/(2*e**8*p**4 + 20*e**8*p**3 + 70*e**8*p**2 + 100*e**8*p + 48*e**8) - 3*d**4*e**4*p**2*x**4*(d**2 - e**2*x**2)**p/(2*e**8*p**4 + 20*e**8*p**3 + 70*e**8*p**2 + 100*e**8*p + 48*e**8) - 3*d**4*e**4*p*x**4*(d**2 - e**2*x**2)**p/(2*e**8*p**4 + 20*e**8*p**3 + 70*e**8*p**2 + 100*e**8*p + 48*e**8) - d**2*e**6*p**3*x**6*(d**2 - e**2*x**2)**p/(2*e**8*p**4 + 20*e**8*p**3 + 70*e**8*p**2 + 100*e**8*p + 48*e**8) - 3*d**2*e**6*p**2*x**6*(d**2 - e**2*x**2)**p/(2*e**8*p**4 + 20*e**8*p**3 + 70*e**8*p**2 + 100*e**8*p + 48*e**8) - 2*d**2*e**6*p*x**6*(d**2 - e**2*x**2)**p/(2*e**8*p**4 + 20*e**8*p**3 + 70*e**8*p**2 + 100*e**8*p + 48*e**8) + e**8*p**3*x**8*(d**2 - e**2*x**2)**p/(2*e**8*p**4 + 20*e**8*p**3 + 70*e**8*p**2 + 100*e**8*p + 48*e**8) + 6*e**8*p**2*x**8*(d**2 - e**2*x**2)**p/(2*e**8*p**4 + 20*e**8*p**3 + 70*e**8*p**2 + 100*e**8*p + 48*e**8) + 11*e**8*p*x**8*(d**2 - e**2*x**2)**p/(2*e**8*p**4 + 20*e**8*p**3 + 70*e**8*p**2 + 100*e**8*p + 48*e**8) + 6*e**8*x**8*(d**2 - e**2*x**2)**p/(2*e**8*p**4 + 20*e**8*p**3 + 70*e**8*p**2 + 100*e**8*p + 48*e**8), True)) + d**(2*p)*e**3*x**9*hyper((9/2, -p), (11/2,), e**2*x**2*exp_polar(2*I*pi)/d**2)/9","B",0
259,1,2966,0,16.045946," ","integrate(x**4*(e*x+d)**3*(-e**2*x**2+d**2)**p,x)","\frac{d^{3} d^{2 p} x^{5} {{}_{2}F_{1}\left(\begin{matrix} \frac{5}{2}, - p \\ \frac{7}{2} \end{matrix}\middle| {\frac{e^{2} x^{2} e^{2 i \pi}}{d^{2}}} \right)}}{5} + 3 d^{2} e \left(\begin{cases} \frac{x^{6} \left(d^{2}\right)^{p}}{6} & \text{for}\: e = 0 \\- \frac{2 d^{4} \log{\left(- \frac{d}{e} + x \right)}}{4 d^{4} e^{6} - 8 d^{2} e^{8} x^{2} + 4 e^{10} x^{4}} - \frac{2 d^{4} \log{\left(\frac{d}{e} + x \right)}}{4 d^{4} e^{6} - 8 d^{2} e^{8} x^{2} + 4 e^{10} x^{4}} - \frac{3 d^{4}}{4 d^{4} e^{6} - 8 d^{2} e^{8} x^{2} + 4 e^{10} x^{4}} + \frac{4 d^{2} e^{2} x^{2} \log{\left(- \frac{d}{e} + x \right)}}{4 d^{4} e^{6} - 8 d^{2} e^{8} x^{2} + 4 e^{10} x^{4}} + \frac{4 d^{2} e^{2} x^{2} \log{\left(\frac{d}{e} + x \right)}}{4 d^{4} e^{6} - 8 d^{2} e^{8} x^{2} + 4 e^{10} x^{4}} + \frac{4 d^{2} e^{2} x^{2}}{4 d^{4} e^{6} - 8 d^{2} e^{8} x^{2} + 4 e^{10} x^{4}} - \frac{2 e^{4} x^{4} \log{\left(- \frac{d}{e} + x \right)}}{4 d^{4} e^{6} - 8 d^{2} e^{8} x^{2} + 4 e^{10} x^{4}} - \frac{2 e^{4} x^{4} \log{\left(\frac{d}{e} + x \right)}}{4 d^{4} e^{6} - 8 d^{2} e^{8} x^{2} + 4 e^{10} x^{4}} & \text{for}\: p = -3 \\- \frac{2 d^{4} \log{\left(- \frac{d}{e} + x \right)}}{- 2 d^{2} e^{6} + 2 e^{8} x^{2}} - \frac{2 d^{4} \log{\left(\frac{d}{e} + x \right)}}{- 2 d^{2} e^{6} + 2 e^{8} x^{2}} - \frac{2 d^{4}}{- 2 d^{2} e^{6} + 2 e^{8} x^{2}} + \frac{2 d^{2} e^{2} x^{2} \log{\left(- \frac{d}{e} + x \right)}}{- 2 d^{2} e^{6} + 2 e^{8} x^{2}} + \frac{2 d^{2} e^{2} x^{2} \log{\left(\frac{d}{e} + x \right)}}{- 2 d^{2} e^{6} + 2 e^{8} x^{2}} + \frac{e^{4} x^{4}}{- 2 d^{2} e^{6} + 2 e^{8} x^{2}} & \text{for}\: p = -2 \\- \frac{d^{4} \log{\left(- \frac{d}{e} + x \right)}}{2 e^{6}} - \frac{d^{4} \log{\left(\frac{d}{e} + x \right)}}{2 e^{6}} - \frac{d^{2} x^{2}}{2 e^{4}} - \frac{x^{4}}{4 e^{2}} & \text{for}\: p = -1 \\- \frac{2 d^{6} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{6} p^{3} + 12 e^{6} p^{2} + 22 e^{6} p + 12 e^{6}} - \frac{2 d^{4} e^{2} p x^{2} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{6} p^{3} + 12 e^{6} p^{2} + 22 e^{6} p + 12 e^{6}} - \frac{d^{2} e^{4} p^{2} x^{4} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{6} p^{3} + 12 e^{6} p^{2} + 22 e^{6} p + 12 e^{6}} - \frac{d^{2} e^{4} p x^{4} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{6} p^{3} + 12 e^{6} p^{2} + 22 e^{6} p + 12 e^{6}} + \frac{e^{6} p^{2} x^{6} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{6} p^{3} + 12 e^{6} p^{2} + 22 e^{6} p + 12 e^{6}} + \frac{3 e^{6} p x^{6} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{6} p^{3} + 12 e^{6} p^{2} + 22 e^{6} p + 12 e^{6}} + \frac{2 e^{6} x^{6} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{6} p^{3} + 12 e^{6} p^{2} + 22 e^{6} p + 12 e^{6}} & \text{otherwise} \end{cases}\right) + \frac{3 d d^{2 p} e^{2} x^{7} {{}_{2}F_{1}\left(\begin{matrix} \frac{7}{2}, - p \\ \frac{9}{2} \end{matrix}\middle| {\frac{e^{2} x^{2} e^{2 i \pi}}{d^{2}}} \right)}}{7} + e^{3} \left(\begin{cases} \frac{x^{8} \left(d^{2}\right)^{p}}{8} & \text{for}\: e = 0 \\- \frac{6 d^{6} \log{\left(- \frac{d}{e} + x \right)}}{- 12 d^{6} e^{8} + 36 d^{4} e^{10} x^{2} - 36 d^{2} e^{12} x^{4} + 12 e^{14} x^{6}} - \frac{6 d^{6} \log{\left(\frac{d}{e} + x \right)}}{- 12 d^{6} e^{8} + 36 d^{4} e^{10} x^{2} - 36 d^{2} e^{12} x^{4} + 12 e^{14} x^{6}} - \frac{11 d^{6}}{- 12 d^{6} e^{8} + 36 d^{4} e^{10} x^{2} - 36 d^{2} e^{12} x^{4} + 12 e^{14} x^{6}} + \frac{18 d^{4} e^{2} x^{2} \log{\left(- \frac{d}{e} + x \right)}}{- 12 d^{6} e^{8} + 36 d^{4} e^{10} x^{2} - 36 d^{2} e^{12} x^{4} + 12 e^{14} x^{6}} + \frac{18 d^{4} e^{2} x^{2} \log{\left(\frac{d}{e} + x \right)}}{- 12 d^{6} e^{8} + 36 d^{4} e^{10} x^{2} - 36 d^{2} e^{12} x^{4} + 12 e^{14} x^{6}} + \frac{27 d^{4} e^{2} x^{2}}{- 12 d^{6} e^{8} + 36 d^{4} e^{10} x^{2} - 36 d^{2} e^{12} x^{4} + 12 e^{14} x^{6}} - \frac{18 d^{2} e^{4} x^{4} \log{\left(- \frac{d}{e} + x \right)}}{- 12 d^{6} e^{8} + 36 d^{4} e^{10} x^{2} - 36 d^{2} e^{12} x^{4} + 12 e^{14} x^{6}} - \frac{18 d^{2} e^{4} x^{4} \log{\left(\frac{d}{e} + x \right)}}{- 12 d^{6} e^{8} + 36 d^{4} e^{10} x^{2} - 36 d^{2} e^{12} x^{4} + 12 e^{14} x^{6}} - \frac{18 d^{2} e^{4} x^{4}}{- 12 d^{6} e^{8} + 36 d^{4} e^{10} x^{2} - 36 d^{2} e^{12} x^{4} + 12 e^{14} x^{6}} + \frac{6 e^{6} x^{6} \log{\left(- \frac{d}{e} + x \right)}}{- 12 d^{6} e^{8} + 36 d^{4} e^{10} x^{2} - 36 d^{2} e^{12} x^{4} + 12 e^{14} x^{6}} + \frac{6 e^{6} x^{6} \log{\left(\frac{d}{e} + x \right)}}{- 12 d^{6} e^{8} + 36 d^{4} e^{10} x^{2} - 36 d^{2} e^{12} x^{4} + 12 e^{14} x^{6}} & \text{for}\: p = -4 \\- \frac{6 d^{6} \log{\left(- \frac{d}{e} + x \right)}}{4 d^{4} e^{8} - 8 d^{2} e^{10} x^{2} + 4 e^{12} x^{4}} - \frac{6 d^{6} \log{\left(\frac{d}{e} + x \right)}}{4 d^{4} e^{8} - 8 d^{2} e^{10} x^{2} + 4 e^{12} x^{4}} - \frac{9 d^{6}}{4 d^{4} e^{8} - 8 d^{2} e^{10} x^{2} + 4 e^{12} x^{4}} + \frac{12 d^{4} e^{2} x^{2} \log{\left(- \frac{d}{e} + x \right)}}{4 d^{4} e^{8} - 8 d^{2} e^{10} x^{2} + 4 e^{12} x^{4}} + \frac{12 d^{4} e^{2} x^{2} \log{\left(\frac{d}{e} + x \right)}}{4 d^{4} e^{8} - 8 d^{2} e^{10} x^{2} + 4 e^{12} x^{4}} + \frac{12 d^{4} e^{2} x^{2}}{4 d^{4} e^{8} - 8 d^{2} e^{10} x^{2} + 4 e^{12} x^{4}} - \frac{6 d^{2} e^{4} x^{4} \log{\left(- \frac{d}{e} + x \right)}}{4 d^{4} e^{8} - 8 d^{2} e^{10} x^{2} + 4 e^{12} x^{4}} - \frac{6 d^{2} e^{4} x^{4} \log{\left(\frac{d}{e} + x \right)}}{4 d^{4} e^{8} - 8 d^{2} e^{10} x^{2} + 4 e^{12} x^{4}} - \frac{2 e^{6} x^{6}}{4 d^{4} e^{8} - 8 d^{2} e^{10} x^{2} + 4 e^{12} x^{4}} & \text{for}\: p = -3 \\- \frac{6 d^{6} \log{\left(- \frac{d}{e} + x \right)}}{- 4 d^{2} e^{8} + 4 e^{10} x^{2}} - \frac{6 d^{6} \log{\left(\frac{d}{e} + x \right)}}{- 4 d^{2} e^{8} + 4 e^{10} x^{2}} - \frac{6 d^{6}}{- 4 d^{2} e^{8} + 4 e^{10} x^{2}} + \frac{6 d^{4} e^{2} x^{2} \log{\left(- \frac{d}{e} + x \right)}}{- 4 d^{2} e^{8} + 4 e^{10} x^{2}} + \frac{6 d^{4} e^{2} x^{2} \log{\left(\frac{d}{e} + x \right)}}{- 4 d^{2} e^{8} + 4 e^{10} x^{2}} + \frac{3 d^{2} e^{4} x^{4}}{- 4 d^{2} e^{8} + 4 e^{10} x^{2}} + \frac{e^{6} x^{6}}{- 4 d^{2} e^{8} + 4 e^{10} x^{2}} & \text{for}\: p = -2 \\- \frac{d^{6} \log{\left(- \frac{d}{e} + x \right)}}{2 e^{8}} - \frac{d^{6} \log{\left(\frac{d}{e} + x \right)}}{2 e^{8}} - \frac{d^{4} x^{2}}{2 e^{6}} - \frac{d^{2} x^{4}}{4 e^{4}} - \frac{x^{6}}{6 e^{2}} & \text{for}\: p = -1 \\- \frac{6 d^{8} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{8} p^{4} + 20 e^{8} p^{3} + 70 e^{8} p^{2} + 100 e^{8} p + 48 e^{8}} - \frac{6 d^{6} e^{2} p x^{2} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{8} p^{4} + 20 e^{8} p^{3} + 70 e^{8} p^{2} + 100 e^{8} p + 48 e^{8}} - \frac{3 d^{4} e^{4} p^{2} x^{4} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{8} p^{4} + 20 e^{8} p^{3} + 70 e^{8} p^{2} + 100 e^{8} p + 48 e^{8}} - \frac{3 d^{4} e^{4} p x^{4} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{8} p^{4} + 20 e^{8} p^{3} + 70 e^{8} p^{2} + 100 e^{8} p + 48 e^{8}} - \frac{d^{2} e^{6} p^{3} x^{6} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{8} p^{4} + 20 e^{8} p^{3} + 70 e^{8} p^{2} + 100 e^{8} p + 48 e^{8}} - \frac{3 d^{2} e^{6} p^{2} x^{6} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{8} p^{4} + 20 e^{8} p^{3} + 70 e^{8} p^{2} + 100 e^{8} p + 48 e^{8}} - \frac{2 d^{2} e^{6} p x^{6} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{8} p^{4} + 20 e^{8} p^{3} + 70 e^{8} p^{2} + 100 e^{8} p + 48 e^{8}} + \frac{e^{8} p^{3} x^{8} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{8} p^{4} + 20 e^{8} p^{3} + 70 e^{8} p^{2} + 100 e^{8} p + 48 e^{8}} + \frac{6 e^{8} p^{2} x^{8} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{8} p^{4} + 20 e^{8} p^{3} + 70 e^{8} p^{2} + 100 e^{8} p + 48 e^{8}} + \frac{11 e^{8} p x^{8} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{8} p^{4} + 20 e^{8} p^{3} + 70 e^{8} p^{2} + 100 e^{8} p + 48 e^{8}} + \frac{6 e^{8} x^{8} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{8} p^{4} + 20 e^{8} p^{3} + 70 e^{8} p^{2} + 100 e^{8} p + 48 e^{8}} & \text{otherwise} \end{cases}\right)"," ",0,"d**3*d**(2*p)*x**5*hyper((5/2, -p), (7/2,), e**2*x**2*exp_polar(2*I*pi)/d**2)/5 + 3*d**2*e*Piecewise((x**6*(d**2)**p/6, Eq(e, 0)), (-2*d**4*log(-d/e + x)/(4*d**4*e**6 - 8*d**2*e**8*x**2 + 4*e**10*x**4) - 2*d**4*log(d/e + x)/(4*d**4*e**6 - 8*d**2*e**8*x**2 + 4*e**10*x**4) - 3*d**4/(4*d**4*e**6 - 8*d**2*e**8*x**2 + 4*e**10*x**4) + 4*d**2*e**2*x**2*log(-d/e + x)/(4*d**4*e**6 - 8*d**2*e**8*x**2 + 4*e**10*x**4) + 4*d**2*e**2*x**2*log(d/e + x)/(4*d**4*e**6 - 8*d**2*e**8*x**2 + 4*e**10*x**4) + 4*d**2*e**2*x**2/(4*d**4*e**6 - 8*d**2*e**8*x**2 + 4*e**10*x**4) - 2*e**4*x**4*log(-d/e + x)/(4*d**4*e**6 - 8*d**2*e**8*x**2 + 4*e**10*x**4) - 2*e**4*x**4*log(d/e + x)/(4*d**4*e**6 - 8*d**2*e**8*x**2 + 4*e**10*x**4), Eq(p, -3)), (-2*d**4*log(-d/e + x)/(-2*d**2*e**6 + 2*e**8*x**2) - 2*d**4*log(d/e + x)/(-2*d**2*e**6 + 2*e**8*x**2) - 2*d**4/(-2*d**2*e**6 + 2*e**8*x**2) + 2*d**2*e**2*x**2*log(-d/e + x)/(-2*d**2*e**6 + 2*e**8*x**2) + 2*d**2*e**2*x**2*log(d/e + x)/(-2*d**2*e**6 + 2*e**8*x**2) + e**4*x**4/(-2*d**2*e**6 + 2*e**8*x**2), Eq(p, -2)), (-d**4*log(-d/e + x)/(2*e**6) - d**4*log(d/e + x)/(2*e**6) - d**2*x**2/(2*e**4) - x**4/(4*e**2), Eq(p, -1)), (-2*d**6*(d**2 - e**2*x**2)**p/(2*e**6*p**3 + 12*e**6*p**2 + 22*e**6*p + 12*e**6) - 2*d**4*e**2*p*x**2*(d**2 - e**2*x**2)**p/(2*e**6*p**3 + 12*e**6*p**2 + 22*e**6*p + 12*e**6) - d**2*e**4*p**2*x**4*(d**2 - e**2*x**2)**p/(2*e**6*p**3 + 12*e**6*p**2 + 22*e**6*p + 12*e**6) - d**2*e**4*p*x**4*(d**2 - e**2*x**2)**p/(2*e**6*p**3 + 12*e**6*p**2 + 22*e**6*p + 12*e**6) + e**6*p**2*x**6*(d**2 - e**2*x**2)**p/(2*e**6*p**3 + 12*e**6*p**2 + 22*e**6*p + 12*e**6) + 3*e**6*p*x**6*(d**2 - e**2*x**2)**p/(2*e**6*p**3 + 12*e**6*p**2 + 22*e**6*p + 12*e**6) + 2*e**6*x**6*(d**2 - e**2*x**2)**p/(2*e**6*p**3 + 12*e**6*p**2 + 22*e**6*p + 12*e**6), True)) + 3*d*d**(2*p)*e**2*x**7*hyper((7/2, -p), (9/2,), e**2*x**2*exp_polar(2*I*pi)/d**2)/7 + e**3*Piecewise((x**8*(d**2)**p/8, Eq(e, 0)), (-6*d**6*log(-d/e + x)/(-12*d**6*e**8 + 36*d**4*e**10*x**2 - 36*d**2*e**12*x**4 + 12*e**14*x**6) - 6*d**6*log(d/e + x)/(-12*d**6*e**8 + 36*d**4*e**10*x**2 - 36*d**2*e**12*x**4 + 12*e**14*x**6) - 11*d**6/(-12*d**6*e**8 + 36*d**4*e**10*x**2 - 36*d**2*e**12*x**4 + 12*e**14*x**6) + 18*d**4*e**2*x**2*log(-d/e + x)/(-12*d**6*e**8 + 36*d**4*e**10*x**2 - 36*d**2*e**12*x**4 + 12*e**14*x**6) + 18*d**4*e**2*x**2*log(d/e + x)/(-12*d**6*e**8 + 36*d**4*e**10*x**2 - 36*d**2*e**12*x**4 + 12*e**14*x**6) + 27*d**4*e**2*x**2/(-12*d**6*e**8 + 36*d**4*e**10*x**2 - 36*d**2*e**12*x**4 + 12*e**14*x**6) - 18*d**2*e**4*x**4*log(-d/e + x)/(-12*d**6*e**8 + 36*d**4*e**10*x**2 - 36*d**2*e**12*x**4 + 12*e**14*x**6) - 18*d**2*e**4*x**4*log(d/e + x)/(-12*d**6*e**8 + 36*d**4*e**10*x**2 - 36*d**2*e**12*x**4 + 12*e**14*x**6) - 18*d**2*e**4*x**4/(-12*d**6*e**8 + 36*d**4*e**10*x**2 - 36*d**2*e**12*x**4 + 12*e**14*x**6) + 6*e**6*x**6*log(-d/e + x)/(-12*d**6*e**8 + 36*d**4*e**10*x**2 - 36*d**2*e**12*x**4 + 12*e**14*x**6) + 6*e**6*x**6*log(d/e + x)/(-12*d**6*e**8 + 36*d**4*e**10*x**2 - 36*d**2*e**12*x**4 + 12*e**14*x**6), Eq(p, -4)), (-6*d**6*log(-d/e + x)/(4*d**4*e**8 - 8*d**2*e**10*x**2 + 4*e**12*x**4) - 6*d**6*log(d/e + x)/(4*d**4*e**8 - 8*d**2*e**10*x**2 + 4*e**12*x**4) - 9*d**6/(4*d**4*e**8 - 8*d**2*e**10*x**2 + 4*e**12*x**4) + 12*d**4*e**2*x**2*log(-d/e + x)/(4*d**4*e**8 - 8*d**2*e**10*x**2 + 4*e**12*x**4) + 12*d**4*e**2*x**2*log(d/e + x)/(4*d**4*e**8 - 8*d**2*e**10*x**2 + 4*e**12*x**4) + 12*d**4*e**2*x**2/(4*d**4*e**8 - 8*d**2*e**10*x**2 + 4*e**12*x**4) - 6*d**2*e**4*x**4*log(-d/e + x)/(4*d**4*e**8 - 8*d**2*e**10*x**2 + 4*e**12*x**4) - 6*d**2*e**4*x**4*log(d/e + x)/(4*d**4*e**8 - 8*d**2*e**10*x**2 + 4*e**12*x**4) - 2*e**6*x**6/(4*d**4*e**8 - 8*d**2*e**10*x**2 + 4*e**12*x**4), Eq(p, -3)), (-6*d**6*log(-d/e + x)/(-4*d**2*e**8 + 4*e**10*x**2) - 6*d**6*log(d/e + x)/(-4*d**2*e**8 + 4*e**10*x**2) - 6*d**6/(-4*d**2*e**8 + 4*e**10*x**2) + 6*d**4*e**2*x**2*log(-d/e + x)/(-4*d**2*e**8 + 4*e**10*x**2) + 6*d**4*e**2*x**2*log(d/e + x)/(-4*d**2*e**8 + 4*e**10*x**2) + 3*d**2*e**4*x**4/(-4*d**2*e**8 + 4*e**10*x**2) + e**6*x**6/(-4*d**2*e**8 + 4*e**10*x**2), Eq(p, -2)), (-d**6*log(-d/e + x)/(2*e**8) - d**6*log(d/e + x)/(2*e**8) - d**4*x**2/(2*e**6) - d**2*x**4/(4*e**4) - x**6/(6*e**2), Eq(p, -1)), (-6*d**8*(d**2 - e**2*x**2)**p/(2*e**8*p**4 + 20*e**8*p**3 + 70*e**8*p**2 + 100*e**8*p + 48*e**8) - 6*d**6*e**2*p*x**2*(d**2 - e**2*x**2)**p/(2*e**8*p**4 + 20*e**8*p**3 + 70*e**8*p**2 + 100*e**8*p + 48*e**8) - 3*d**4*e**4*p**2*x**4*(d**2 - e**2*x**2)**p/(2*e**8*p**4 + 20*e**8*p**3 + 70*e**8*p**2 + 100*e**8*p + 48*e**8) - 3*d**4*e**4*p*x**4*(d**2 - e**2*x**2)**p/(2*e**8*p**4 + 20*e**8*p**3 + 70*e**8*p**2 + 100*e**8*p + 48*e**8) - d**2*e**6*p**3*x**6*(d**2 - e**2*x**2)**p/(2*e**8*p**4 + 20*e**8*p**3 + 70*e**8*p**2 + 100*e**8*p + 48*e**8) - 3*d**2*e**6*p**2*x**6*(d**2 - e**2*x**2)**p/(2*e**8*p**4 + 20*e**8*p**3 + 70*e**8*p**2 + 100*e**8*p + 48*e**8) - 2*d**2*e**6*p*x**6*(d**2 - e**2*x**2)**p/(2*e**8*p**4 + 20*e**8*p**3 + 70*e**8*p**2 + 100*e**8*p + 48*e**8) + e**8*p**3*x**8*(d**2 - e**2*x**2)**p/(2*e**8*p**4 + 20*e**8*p**3 + 70*e**8*p**2 + 100*e**8*p + 48*e**8) + 6*e**8*p**2*x**8*(d**2 - e**2*x**2)**p/(2*e**8*p**4 + 20*e**8*p**3 + 70*e**8*p**2 + 100*e**8*p + 48*e**8) + 11*e**8*p*x**8*(d**2 - e**2*x**2)**p/(2*e**8*p**4 + 20*e**8*p**3 + 70*e**8*p**2 + 100*e**8*p + 48*e**8) + 6*e**8*x**8*(d**2 - e**2*x**2)**p/(2*e**8*p**4 + 20*e**8*p**3 + 70*e**8*p**2 + 100*e**8*p + 48*e**8), True))","B",0
260,1,1370,0,11.264945," ","integrate(x**3*(e*x+d)**3*(-e**2*x**2+d**2)**p,x)","d^{3} \left(\begin{cases} \frac{x^{4} \left(d^{2}\right)^{p}}{4} & \text{for}\: e = 0 \\- \frac{d^{2} \log{\left(- \frac{d}{e} + x \right)}}{- 2 d^{2} e^{4} + 2 e^{6} x^{2}} - \frac{d^{2} \log{\left(\frac{d}{e} + x \right)}}{- 2 d^{2} e^{4} + 2 e^{6} x^{2}} - \frac{d^{2}}{- 2 d^{2} e^{4} + 2 e^{6} x^{2}} + \frac{e^{2} x^{2} \log{\left(- \frac{d}{e} + x \right)}}{- 2 d^{2} e^{4} + 2 e^{6} x^{2}} + \frac{e^{2} x^{2} \log{\left(\frac{d}{e} + x \right)}}{- 2 d^{2} e^{4} + 2 e^{6} x^{2}} & \text{for}\: p = -2 \\- \frac{d^{2} \log{\left(- \frac{d}{e} + x \right)}}{2 e^{4}} - \frac{d^{2} \log{\left(\frac{d}{e} + x \right)}}{2 e^{4}} - \frac{x^{2}}{2 e^{2}} & \text{for}\: p = -1 \\- \frac{d^{4} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{4} p^{2} + 6 e^{4} p + 4 e^{4}} - \frac{d^{2} e^{2} p x^{2} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{4} p^{2} + 6 e^{4} p + 4 e^{4}} + \frac{e^{4} p x^{4} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{4} p^{2} + 6 e^{4} p + 4 e^{4}} + \frac{e^{4} x^{4} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{4} p^{2} + 6 e^{4} p + 4 e^{4}} & \text{otherwise} \end{cases}\right) + \frac{3 d^{2} d^{2 p} e x^{5} {{}_{2}F_{1}\left(\begin{matrix} \frac{5}{2}, - p \\ \frac{7}{2} \end{matrix}\middle| {\frac{e^{2} x^{2} e^{2 i \pi}}{d^{2}}} \right)}}{5} + 3 d e^{2} \left(\begin{cases} \frac{x^{6} \left(d^{2}\right)^{p}}{6} & \text{for}\: e = 0 \\- \frac{2 d^{4} \log{\left(- \frac{d}{e} + x \right)}}{4 d^{4} e^{6} - 8 d^{2} e^{8} x^{2} + 4 e^{10} x^{4}} - \frac{2 d^{4} \log{\left(\frac{d}{e} + x \right)}}{4 d^{4} e^{6} - 8 d^{2} e^{8} x^{2} + 4 e^{10} x^{4}} - \frac{3 d^{4}}{4 d^{4} e^{6} - 8 d^{2} e^{8} x^{2} + 4 e^{10} x^{4}} + \frac{4 d^{2} e^{2} x^{2} \log{\left(- \frac{d}{e} + x \right)}}{4 d^{4} e^{6} - 8 d^{2} e^{8} x^{2} + 4 e^{10} x^{4}} + \frac{4 d^{2} e^{2} x^{2} \log{\left(\frac{d}{e} + x \right)}}{4 d^{4} e^{6} - 8 d^{2} e^{8} x^{2} + 4 e^{10} x^{4}} + \frac{4 d^{2} e^{2} x^{2}}{4 d^{4} e^{6} - 8 d^{2} e^{8} x^{2} + 4 e^{10} x^{4}} - \frac{2 e^{4} x^{4} \log{\left(- \frac{d}{e} + x \right)}}{4 d^{4} e^{6} - 8 d^{2} e^{8} x^{2} + 4 e^{10} x^{4}} - \frac{2 e^{4} x^{4} \log{\left(\frac{d}{e} + x \right)}}{4 d^{4} e^{6} - 8 d^{2} e^{8} x^{2} + 4 e^{10} x^{4}} & \text{for}\: p = -3 \\- \frac{2 d^{4} \log{\left(- \frac{d}{e} + x \right)}}{- 2 d^{2} e^{6} + 2 e^{8} x^{2}} - \frac{2 d^{4} \log{\left(\frac{d}{e} + x \right)}}{- 2 d^{2} e^{6} + 2 e^{8} x^{2}} - \frac{2 d^{4}}{- 2 d^{2} e^{6} + 2 e^{8} x^{2}} + \frac{2 d^{2} e^{2} x^{2} \log{\left(- \frac{d}{e} + x \right)}}{- 2 d^{2} e^{6} + 2 e^{8} x^{2}} + \frac{2 d^{2} e^{2} x^{2} \log{\left(\frac{d}{e} + x \right)}}{- 2 d^{2} e^{6} + 2 e^{8} x^{2}} + \frac{e^{4} x^{4}}{- 2 d^{2} e^{6} + 2 e^{8} x^{2}} & \text{for}\: p = -2 \\- \frac{d^{4} \log{\left(- \frac{d}{e} + x \right)}}{2 e^{6}} - \frac{d^{4} \log{\left(\frac{d}{e} + x \right)}}{2 e^{6}} - \frac{d^{2} x^{2}}{2 e^{4}} - \frac{x^{4}}{4 e^{2}} & \text{for}\: p = -1 \\- \frac{2 d^{6} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{6} p^{3} + 12 e^{6} p^{2} + 22 e^{6} p + 12 e^{6}} - \frac{2 d^{4} e^{2} p x^{2} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{6} p^{3} + 12 e^{6} p^{2} + 22 e^{6} p + 12 e^{6}} - \frac{d^{2} e^{4} p^{2} x^{4} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{6} p^{3} + 12 e^{6} p^{2} + 22 e^{6} p + 12 e^{6}} - \frac{d^{2} e^{4} p x^{4} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{6} p^{3} + 12 e^{6} p^{2} + 22 e^{6} p + 12 e^{6}} + \frac{e^{6} p^{2} x^{6} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{6} p^{3} + 12 e^{6} p^{2} + 22 e^{6} p + 12 e^{6}} + \frac{3 e^{6} p x^{6} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{6} p^{3} + 12 e^{6} p^{2} + 22 e^{6} p + 12 e^{6}} + \frac{2 e^{6} x^{6} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{6} p^{3} + 12 e^{6} p^{2} + 22 e^{6} p + 12 e^{6}} & \text{otherwise} \end{cases}\right) + \frac{d^{2 p} e^{3} x^{7} {{}_{2}F_{1}\left(\begin{matrix} \frac{7}{2}, - p \\ \frac{9}{2} \end{matrix}\middle| {\frac{e^{2} x^{2} e^{2 i \pi}}{d^{2}}} \right)}}{7}"," ",0,"d**3*Piecewise((x**4*(d**2)**p/4, Eq(e, 0)), (-d**2*log(-d/e + x)/(-2*d**2*e**4 + 2*e**6*x**2) - d**2*log(d/e + x)/(-2*d**2*e**4 + 2*e**6*x**2) - d**2/(-2*d**2*e**4 + 2*e**6*x**2) + e**2*x**2*log(-d/e + x)/(-2*d**2*e**4 + 2*e**6*x**2) + e**2*x**2*log(d/e + x)/(-2*d**2*e**4 + 2*e**6*x**2), Eq(p, -2)), (-d**2*log(-d/e + x)/(2*e**4) - d**2*log(d/e + x)/(2*e**4) - x**2/(2*e**2), Eq(p, -1)), (-d**4*(d**2 - e**2*x**2)**p/(2*e**4*p**2 + 6*e**4*p + 4*e**4) - d**2*e**2*p*x**2*(d**2 - e**2*x**2)**p/(2*e**4*p**2 + 6*e**4*p + 4*e**4) + e**4*p*x**4*(d**2 - e**2*x**2)**p/(2*e**4*p**2 + 6*e**4*p + 4*e**4) + e**4*x**4*(d**2 - e**2*x**2)**p/(2*e**4*p**2 + 6*e**4*p + 4*e**4), True)) + 3*d**2*d**(2*p)*e*x**5*hyper((5/2, -p), (7/2,), e**2*x**2*exp_polar(2*I*pi)/d**2)/5 + 3*d*e**2*Piecewise((x**6*(d**2)**p/6, Eq(e, 0)), (-2*d**4*log(-d/e + x)/(4*d**4*e**6 - 8*d**2*e**8*x**2 + 4*e**10*x**4) - 2*d**4*log(d/e + x)/(4*d**4*e**6 - 8*d**2*e**8*x**2 + 4*e**10*x**4) - 3*d**4/(4*d**4*e**6 - 8*d**2*e**8*x**2 + 4*e**10*x**4) + 4*d**2*e**2*x**2*log(-d/e + x)/(4*d**4*e**6 - 8*d**2*e**8*x**2 + 4*e**10*x**4) + 4*d**2*e**2*x**2*log(d/e + x)/(4*d**4*e**6 - 8*d**2*e**8*x**2 + 4*e**10*x**4) + 4*d**2*e**2*x**2/(4*d**4*e**6 - 8*d**2*e**8*x**2 + 4*e**10*x**4) - 2*e**4*x**4*log(-d/e + x)/(4*d**4*e**6 - 8*d**2*e**8*x**2 + 4*e**10*x**4) - 2*e**4*x**4*log(d/e + x)/(4*d**4*e**6 - 8*d**2*e**8*x**2 + 4*e**10*x**4), Eq(p, -3)), (-2*d**4*log(-d/e + x)/(-2*d**2*e**6 + 2*e**8*x**2) - 2*d**4*log(d/e + x)/(-2*d**2*e**6 + 2*e**8*x**2) - 2*d**4/(-2*d**2*e**6 + 2*e**8*x**2) + 2*d**2*e**2*x**2*log(-d/e + x)/(-2*d**2*e**6 + 2*e**8*x**2) + 2*d**2*e**2*x**2*log(d/e + x)/(-2*d**2*e**6 + 2*e**8*x**2) + e**4*x**4/(-2*d**2*e**6 + 2*e**8*x**2), Eq(p, -2)), (-d**4*log(-d/e + x)/(2*e**6) - d**4*log(d/e + x)/(2*e**6) - d**2*x**2/(2*e**4) - x**4/(4*e**2), Eq(p, -1)), (-2*d**6*(d**2 - e**2*x**2)**p/(2*e**6*p**3 + 12*e**6*p**2 + 22*e**6*p + 12*e**6) - 2*d**4*e**2*p*x**2*(d**2 - e**2*x**2)**p/(2*e**6*p**3 + 12*e**6*p**2 + 22*e**6*p + 12*e**6) - d**2*e**4*p**2*x**4*(d**2 - e**2*x**2)**p/(2*e**6*p**3 + 12*e**6*p**2 + 22*e**6*p + 12*e**6) - d**2*e**4*p*x**4*(d**2 - e**2*x**2)**p/(2*e**6*p**3 + 12*e**6*p**2 + 22*e**6*p + 12*e**6) + e**6*p**2*x**6*(d**2 - e**2*x**2)**p/(2*e**6*p**3 + 12*e**6*p**2 + 22*e**6*p + 12*e**6) + 3*e**6*p*x**6*(d**2 - e**2*x**2)**p/(2*e**6*p**3 + 12*e**6*p**2 + 22*e**6*p + 12*e**6) + 2*e**6*x**6*(d**2 - e**2*x**2)**p/(2*e**6*p**3 + 12*e**6*p**2 + 22*e**6*p + 12*e**6), True)) + d**(2*p)*e**3*x**7*hyper((7/2, -p), (9/2,), e**2*x**2*exp_polar(2*I*pi)/d**2)/7","B",0
261,1,1370,0,10.461868," ","integrate(x**2*(e*x+d)**3*(-e**2*x**2+d**2)**p,x)","\frac{d^{3} d^{2 p} x^{3} {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{2}, - p \\ \frac{5}{2} \end{matrix}\middle| {\frac{e^{2} x^{2} e^{2 i \pi}}{d^{2}}} \right)}}{3} + 3 d^{2} e \left(\begin{cases} \frac{x^{4} \left(d^{2}\right)^{p}}{4} & \text{for}\: e = 0 \\- \frac{d^{2} \log{\left(- \frac{d}{e} + x \right)}}{- 2 d^{2} e^{4} + 2 e^{6} x^{2}} - \frac{d^{2} \log{\left(\frac{d}{e} + x \right)}}{- 2 d^{2} e^{4} + 2 e^{6} x^{2}} - \frac{d^{2}}{- 2 d^{2} e^{4} + 2 e^{6} x^{2}} + \frac{e^{2} x^{2} \log{\left(- \frac{d}{e} + x \right)}}{- 2 d^{2} e^{4} + 2 e^{6} x^{2}} + \frac{e^{2} x^{2} \log{\left(\frac{d}{e} + x \right)}}{- 2 d^{2} e^{4} + 2 e^{6} x^{2}} & \text{for}\: p = -2 \\- \frac{d^{2} \log{\left(- \frac{d}{e} + x \right)}}{2 e^{4}} - \frac{d^{2} \log{\left(\frac{d}{e} + x \right)}}{2 e^{4}} - \frac{x^{2}}{2 e^{2}} & \text{for}\: p = -1 \\- \frac{d^{4} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{4} p^{2} + 6 e^{4} p + 4 e^{4}} - \frac{d^{2} e^{2} p x^{2} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{4} p^{2} + 6 e^{4} p + 4 e^{4}} + \frac{e^{4} p x^{4} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{4} p^{2} + 6 e^{4} p + 4 e^{4}} + \frac{e^{4} x^{4} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{4} p^{2} + 6 e^{4} p + 4 e^{4}} & \text{otherwise} \end{cases}\right) + \frac{3 d d^{2 p} e^{2} x^{5} {{}_{2}F_{1}\left(\begin{matrix} \frac{5}{2}, - p \\ \frac{7}{2} \end{matrix}\middle| {\frac{e^{2} x^{2} e^{2 i \pi}}{d^{2}}} \right)}}{5} + e^{3} \left(\begin{cases} \frac{x^{6} \left(d^{2}\right)^{p}}{6} & \text{for}\: e = 0 \\- \frac{2 d^{4} \log{\left(- \frac{d}{e} + x \right)}}{4 d^{4} e^{6} - 8 d^{2} e^{8} x^{2} + 4 e^{10} x^{4}} - \frac{2 d^{4} \log{\left(\frac{d}{e} + x \right)}}{4 d^{4} e^{6} - 8 d^{2} e^{8} x^{2} + 4 e^{10} x^{4}} - \frac{3 d^{4}}{4 d^{4} e^{6} - 8 d^{2} e^{8} x^{2} + 4 e^{10} x^{4}} + \frac{4 d^{2} e^{2} x^{2} \log{\left(- \frac{d}{e} + x \right)}}{4 d^{4} e^{6} - 8 d^{2} e^{8} x^{2} + 4 e^{10} x^{4}} + \frac{4 d^{2} e^{2} x^{2} \log{\left(\frac{d}{e} + x \right)}}{4 d^{4} e^{6} - 8 d^{2} e^{8} x^{2} + 4 e^{10} x^{4}} + \frac{4 d^{2} e^{2} x^{2}}{4 d^{4} e^{6} - 8 d^{2} e^{8} x^{2} + 4 e^{10} x^{4}} - \frac{2 e^{4} x^{4} \log{\left(- \frac{d}{e} + x \right)}}{4 d^{4} e^{6} - 8 d^{2} e^{8} x^{2} + 4 e^{10} x^{4}} - \frac{2 e^{4} x^{4} \log{\left(\frac{d}{e} + x \right)}}{4 d^{4} e^{6} - 8 d^{2} e^{8} x^{2} + 4 e^{10} x^{4}} & \text{for}\: p = -3 \\- \frac{2 d^{4} \log{\left(- \frac{d}{e} + x \right)}}{- 2 d^{2} e^{6} + 2 e^{8} x^{2}} - \frac{2 d^{4} \log{\left(\frac{d}{e} + x \right)}}{- 2 d^{2} e^{6} + 2 e^{8} x^{2}} - \frac{2 d^{4}}{- 2 d^{2} e^{6} + 2 e^{8} x^{2}} + \frac{2 d^{2} e^{2} x^{2} \log{\left(- \frac{d}{e} + x \right)}}{- 2 d^{2} e^{6} + 2 e^{8} x^{2}} + \frac{2 d^{2} e^{2} x^{2} \log{\left(\frac{d}{e} + x \right)}}{- 2 d^{2} e^{6} + 2 e^{8} x^{2}} + \frac{e^{4} x^{4}}{- 2 d^{2} e^{6} + 2 e^{8} x^{2}} & \text{for}\: p = -2 \\- \frac{d^{4} \log{\left(- \frac{d}{e} + x \right)}}{2 e^{6}} - \frac{d^{4} \log{\left(\frac{d}{e} + x \right)}}{2 e^{6}} - \frac{d^{2} x^{2}}{2 e^{4}} - \frac{x^{4}}{4 e^{2}} & \text{for}\: p = -1 \\- \frac{2 d^{6} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{6} p^{3} + 12 e^{6} p^{2} + 22 e^{6} p + 12 e^{6}} - \frac{2 d^{4} e^{2} p x^{2} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{6} p^{3} + 12 e^{6} p^{2} + 22 e^{6} p + 12 e^{6}} - \frac{d^{2} e^{4} p^{2} x^{4} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{6} p^{3} + 12 e^{6} p^{2} + 22 e^{6} p + 12 e^{6}} - \frac{d^{2} e^{4} p x^{4} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{6} p^{3} + 12 e^{6} p^{2} + 22 e^{6} p + 12 e^{6}} + \frac{e^{6} p^{2} x^{6} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{6} p^{3} + 12 e^{6} p^{2} + 22 e^{6} p + 12 e^{6}} + \frac{3 e^{6} p x^{6} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{6} p^{3} + 12 e^{6} p^{2} + 22 e^{6} p + 12 e^{6}} + \frac{2 e^{6} x^{6} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{6} p^{3} + 12 e^{6} p^{2} + 22 e^{6} p + 12 e^{6}} & \text{otherwise} \end{cases}\right)"," ",0,"d**3*d**(2*p)*x**3*hyper((3/2, -p), (5/2,), e**2*x**2*exp_polar(2*I*pi)/d**2)/3 + 3*d**2*e*Piecewise((x**4*(d**2)**p/4, Eq(e, 0)), (-d**2*log(-d/e + x)/(-2*d**2*e**4 + 2*e**6*x**2) - d**2*log(d/e + x)/(-2*d**2*e**4 + 2*e**6*x**2) - d**2/(-2*d**2*e**4 + 2*e**6*x**2) + e**2*x**2*log(-d/e + x)/(-2*d**2*e**4 + 2*e**6*x**2) + e**2*x**2*log(d/e + x)/(-2*d**2*e**4 + 2*e**6*x**2), Eq(p, -2)), (-d**2*log(-d/e + x)/(2*e**4) - d**2*log(d/e + x)/(2*e**4) - x**2/(2*e**2), Eq(p, -1)), (-d**4*(d**2 - e**2*x**2)**p/(2*e**4*p**2 + 6*e**4*p + 4*e**4) - d**2*e**2*p*x**2*(d**2 - e**2*x**2)**p/(2*e**4*p**2 + 6*e**4*p + 4*e**4) + e**4*p*x**4*(d**2 - e**2*x**2)**p/(2*e**4*p**2 + 6*e**4*p + 4*e**4) + e**4*x**4*(d**2 - e**2*x**2)**p/(2*e**4*p**2 + 6*e**4*p + 4*e**4), True)) + 3*d*d**(2*p)*e**2*x**5*hyper((5/2, -p), (7/2,), e**2*x**2*exp_polar(2*I*pi)/d**2)/5 + e**3*Piecewise((x**6*(d**2)**p/6, Eq(e, 0)), (-2*d**4*log(-d/e + x)/(4*d**4*e**6 - 8*d**2*e**8*x**2 + 4*e**10*x**4) - 2*d**4*log(d/e + x)/(4*d**4*e**6 - 8*d**2*e**8*x**2 + 4*e**10*x**4) - 3*d**4/(4*d**4*e**6 - 8*d**2*e**8*x**2 + 4*e**10*x**4) + 4*d**2*e**2*x**2*log(-d/e + x)/(4*d**4*e**6 - 8*d**2*e**8*x**2 + 4*e**10*x**4) + 4*d**2*e**2*x**2*log(d/e + x)/(4*d**4*e**6 - 8*d**2*e**8*x**2 + 4*e**10*x**4) + 4*d**2*e**2*x**2/(4*d**4*e**6 - 8*d**2*e**8*x**2 + 4*e**10*x**4) - 2*e**4*x**4*log(-d/e + x)/(4*d**4*e**6 - 8*d**2*e**8*x**2 + 4*e**10*x**4) - 2*e**4*x**4*log(d/e + x)/(4*d**4*e**6 - 8*d**2*e**8*x**2 + 4*e**10*x**4), Eq(p, -3)), (-2*d**4*log(-d/e + x)/(-2*d**2*e**6 + 2*e**8*x**2) - 2*d**4*log(d/e + x)/(-2*d**2*e**6 + 2*e**8*x**2) - 2*d**4/(-2*d**2*e**6 + 2*e**8*x**2) + 2*d**2*e**2*x**2*log(-d/e + x)/(-2*d**2*e**6 + 2*e**8*x**2) + 2*d**2*e**2*x**2*log(d/e + x)/(-2*d**2*e**6 + 2*e**8*x**2) + e**4*x**4/(-2*d**2*e**6 + 2*e**8*x**2), Eq(p, -2)), (-d**4*log(-d/e + x)/(2*e**6) - d**4*log(d/e + x)/(2*e**6) - d**2*x**2/(2*e**4) - x**4/(4*e**2), Eq(p, -1)), (-2*d**6*(d**2 - e**2*x**2)**p/(2*e**6*p**3 + 12*e**6*p**2 + 22*e**6*p + 12*e**6) - 2*d**4*e**2*p*x**2*(d**2 - e**2*x**2)**p/(2*e**6*p**3 + 12*e**6*p**2 + 22*e**6*p + 12*e**6) - d**2*e**4*p**2*x**4*(d**2 - e**2*x**2)**p/(2*e**6*p**3 + 12*e**6*p**2 + 22*e**6*p + 12*e**6) - d**2*e**4*p*x**4*(d**2 - e**2*x**2)**p/(2*e**6*p**3 + 12*e**6*p**2 + 22*e**6*p + 12*e**6) + e**6*p**2*x**6*(d**2 - e**2*x**2)**p/(2*e**6*p**3 + 12*e**6*p**2 + 22*e**6*p + 12*e**6) + 3*e**6*p*x**6*(d**2 - e**2*x**2)**p/(2*e**6*p**3 + 12*e**6*p**2 + 22*e**6*p + 12*e**6) + 2*e**6*x**6*(d**2 - e**2*x**2)**p/(2*e**6*p**3 + 12*e**6*p**2 + 22*e**6*p + 12*e**6), True))","B",0
262,1,479,0,7.578914," ","integrate(x*(e*x+d)**3*(-e**2*x**2+d**2)**p,x)","d^{3} \left(\begin{cases} \frac{x^{2} \left(d^{2}\right)^{p}}{2} & \text{for}\: e^{2} = 0 \\- \frac{\begin{cases} \frac{\left(d^{2} - e^{2} x^{2}\right)^{p + 1}}{p + 1} & \text{for}\: p \neq -1 \\\log{\left(d^{2} - e^{2} x^{2} \right)} & \text{otherwise} \end{cases}}{2 e^{2}} & \text{otherwise} \end{cases}\right) + d^{2} d^{2 p} e x^{3} {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{2}, - p \\ \frac{5}{2} \end{matrix}\middle| {\frac{e^{2} x^{2} e^{2 i \pi}}{d^{2}}} \right)} + 3 d e^{2} \left(\begin{cases} \frac{x^{4} \left(d^{2}\right)^{p}}{4} & \text{for}\: e = 0 \\- \frac{d^{2} \log{\left(- \frac{d}{e} + x \right)}}{- 2 d^{2} e^{4} + 2 e^{6} x^{2}} - \frac{d^{2} \log{\left(\frac{d}{e} + x \right)}}{- 2 d^{2} e^{4} + 2 e^{6} x^{2}} - \frac{d^{2}}{- 2 d^{2} e^{4} + 2 e^{6} x^{2}} + \frac{e^{2} x^{2} \log{\left(- \frac{d}{e} + x \right)}}{- 2 d^{2} e^{4} + 2 e^{6} x^{2}} + \frac{e^{2} x^{2} \log{\left(\frac{d}{e} + x \right)}}{- 2 d^{2} e^{4} + 2 e^{6} x^{2}} & \text{for}\: p = -2 \\- \frac{d^{2} \log{\left(- \frac{d}{e} + x \right)}}{2 e^{4}} - \frac{d^{2} \log{\left(\frac{d}{e} + x \right)}}{2 e^{4}} - \frac{x^{2}}{2 e^{2}} & \text{for}\: p = -1 \\- \frac{d^{4} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{4} p^{2} + 6 e^{4} p + 4 e^{4}} - \frac{d^{2} e^{2} p x^{2} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{4} p^{2} + 6 e^{4} p + 4 e^{4}} + \frac{e^{4} p x^{4} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{4} p^{2} + 6 e^{4} p + 4 e^{4}} + \frac{e^{4} x^{4} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{4} p^{2} + 6 e^{4} p + 4 e^{4}} & \text{otherwise} \end{cases}\right) + \frac{d^{2 p} e^{3} x^{5} {{}_{2}F_{1}\left(\begin{matrix} \frac{5}{2}, - p \\ \frac{7}{2} \end{matrix}\middle| {\frac{e^{2} x^{2} e^{2 i \pi}}{d^{2}}} \right)}}{5}"," ",0,"d**3*Piecewise((x**2*(d**2)**p/2, Eq(e**2, 0)), (-Piecewise(((d**2 - e**2*x**2)**(p + 1)/(p + 1), Ne(p, -1)), (log(d**2 - e**2*x**2), True))/(2*e**2), True)) + d**2*d**(2*p)*e*x**3*hyper((3/2, -p), (5/2,), e**2*x**2*exp_polar(2*I*pi)/d**2) + 3*d*e**2*Piecewise((x**4*(d**2)**p/4, Eq(e, 0)), (-d**2*log(-d/e + x)/(-2*d**2*e**4 + 2*e**6*x**2) - d**2*log(d/e + x)/(-2*d**2*e**4 + 2*e**6*x**2) - d**2/(-2*d**2*e**4 + 2*e**6*x**2) + e**2*x**2*log(-d/e + x)/(-2*d**2*e**4 + 2*e**6*x**2) + e**2*x**2*log(d/e + x)/(-2*d**2*e**4 + 2*e**6*x**2), Eq(p, -2)), (-d**2*log(-d/e + x)/(2*e**4) - d**2*log(d/e + x)/(2*e**4) - x**2/(2*e**2), Eq(p, -1)), (-d**4*(d**2 - e**2*x**2)**p/(2*e**4*p**2 + 6*e**4*p + 4*e**4) - d**2*e**2*p*x**2*(d**2 - e**2*x**2)**p/(2*e**4*p**2 + 6*e**4*p + 4*e**4) + e**4*p*x**4*(d**2 - e**2*x**2)**p/(2*e**4*p**2 + 6*e**4*p + 4*e**4) + e**4*x**4*(d**2 - e**2*x**2)**p/(2*e**4*p**2 + 6*e**4*p + 4*e**4), True)) + d**(2*p)*e**3*x**5*hyper((5/2, -p), (7/2,), e**2*x**2*exp_polar(2*I*pi)/d**2)/5","A",0
263,1,476,0,6.578827," ","integrate((e*x+d)**3*(-e**2*x**2+d**2)**p,x)","d^{3} d^{2 p} x {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, - p \\ \frac{3}{2} \end{matrix}\middle| {\frac{e^{2} x^{2} e^{2 i \pi}}{d^{2}}} \right)} + 3 d^{2} e \left(\begin{cases} \frac{x^{2} \left(d^{2}\right)^{p}}{2} & \text{for}\: e^{2} = 0 \\- \frac{\begin{cases} \frac{\left(d^{2} - e^{2} x^{2}\right)^{p + 1}}{p + 1} & \text{for}\: p \neq -1 \\\log{\left(d^{2} - e^{2} x^{2} \right)} & \text{otherwise} \end{cases}}{2 e^{2}} & \text{otherwise} \end{cases}\right) + d d^{2 p} e^{2} x^{3} {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{2}, - p \\ \frac{5}{2} \end{matrix}\middle| {\frac{e^{2} x^{2} e^{2 i \pi}}{d^{2}}} \right)} + e^{3} \left(\begin{cases} \frac{x^{4} \left(d^{2}\right)^{p}}{4} & \text{for}\: e = 0 \\- \frac{d^{2} \log{\left(- \frac{d}{e} + x \right)}}{- 2 d^{2} e^{4} + 2 e^{6} x^{2}} - \frac{d^{2} \log{\left(\frac{d}{e} + x \right)}}{- 2 d^{2} e^{4} + 2 e^{6} x^{2}} - \frac{d^{2}}{- 2 d^{2} e^{4} + 2 e^{6} x^{2}} + \frac{e^{2} x^{2} \log{\left(- \frac{d}{e} + x \right)}}{- 2 d^{2} e^{4} + 2 e^{6} x^{2}} + \frac{e^{2} x^{2} \log{\left(\frac{d}{e} + x \right)}}{- 2 d^{2} e^{4} + 2 e^{6} x^{2}} & \text{for}\: p = -2 \\- \frac{d^{2} \log{\left(- \frac{d}{e} + x \right)}}{2 e^{4}} - \frac{d^{2} \log{\left(\frac{d}{e} + x \right)}}{2 e^{4}} - \frac{x^{2}}{2 e^{2}} & \text{for}\: p = -1 \\- \frac{d^{4} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{4} p^{2} + 6 e^{4} p + 4 e^{4}} - \frac{d^{2} e^{2} p x^{2} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{4} p^{2} + 6 e^{4} p + 4 e^{4}} + \frac{e^{4} p x^{4} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{4} p^{2} + 6 e^{4} p + 4 e^{4}} + \frac{e^{4} x^{4} \left(d^{2} - e^{2} x^{2}\right)^{p}}{2 e^{4} p^{2} + 6 e^{4} p + 4 e^{4}} & \text{otherwise} \end{cases}\right)"," ",0,"d**3*d**(2*p)*x*hyper((1/2, -p), (3/2,), e**2*x**2*exp_polar(2*I*pi)/d**2) + 3*d**2*e*Piecewise((x**2*(d**2)**p/2, Eq(e**2, 0)), (-Piecewise(((d**2 - e**2*x**2)**(p + 1)/(p + 1), Ne(p, -1)), (log(d**2 - e**2*x**2), True))/(2*e**2), True)) + d*d**(2*p)*e**2*x**3*hyper((3/2, -p), (5/2,), e**2*x**2*exp_polar(2*I*pi)/d**2) + e**3*Piecewise((x**4*(d**2)**p/4, Eq(e, 0)), (-d**2*log(-d/e + x)/(-2*d**2*e**4 + 2*e**6*x**2) - d**2*log(d/e + x)/(-2*d**2*e**4 + 2*e**6*x**2) - d**2/(-2*d**2*e**4 + 2*e**6*x**2) + e**2*x**2*log(-d/e + x)/(-2*d**2*e**4 + 2*e**6*x**2) + e**2*x**2*log(d/e + x)/(-2*d**2*e**4 + 2*e**6*x**2), Eq(p, -2)), (-d**2*log(-d/e + x)/(2*e**4) - d**2*log(d/e + x)/(2*e**4) - x**2/(2*e**2), Eq(p, -1)), (-d**4*(d**2 - e**2*x**2)**p/(2*e**4*p**2 + 6*e**4*p + 4*e**4) - d**2*e**2*p*x**2*(d**2 - e**2*x**2)**p/(2*e**4*p**2 + 6*e**4*p + 4*e**4) + e**4*p*x**4*(d**2 - e**2*x**2)**p/(2*e**4*p**2 + 6*e**4*p + 4*e**4) + e**4*x**4*(d**2 - e**2*x**2)**p/(2*e**4*p**2 + 6*e**4*p + 4*e**4), True))","B",0
264,1,178,0,12.288644," ","integrate((e*x+d)**3*(-e**2*x**2+d**2)**p/x,x)","- \frac{d^{3} e^{2 p} x^{2 p} e^{i \pi p} \Gamma\left(- p\right) {{}_{2}F_{1}\left(\begin{matrix} - p, - p \\ 1 - p \end{matrix}\middle| {\frac{d^{2}}{e^{2} x^{2}}} \right)}}{2 \Gamma\left(1 - p\right)} + 3 d^{2} d^{2 p} e x {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, - p \\ \frac{3}{2} \end{matrix}\middle| {\frac{e^{2} x^{2} e^{2 i \pi}}{d^{2}}} \right)} + 3 d e^{2} \left(\begin{cases} \frac{x^{2} \left(d^{2}\right)^{p}}{2} & \text{for}\: e^{2} = 0 \\- \frac{\begin{cases} \frac{\left(d^{2} - e^{2} x^{2}\right)^{p + 1}}{p + 1} & \text{for}\: p \neq -1 \\\log{\left(d^{2} - e^{2} x^{2} \right)} & \text{otherwise} \end{cases}}{2 e^{2}} & \text{otherwise} \end{cases}\right) + \frac{d^{2 p} e^{3} x^{3} {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{2}, - p \\ \frac{5}{2} \end{matrix}\middle| {\frac{e^{2} x^{2} e^{2 i \pi}}{d^{2}}} \right)}}{3}"," ",0,"-d**3*e**(2*p)*x**(2*p)*exp(I*pi*p)*gamma(-p)*hyper((-p, -p), (1 - p,), d**2/(e**2*x**2))/(2*gamma(1 - p)) + 3*d**2*d**(2*p)*e*x*hyper((1/2, -p), (3/2,), e**2*x**2*exp_polar(2*I*pi)/d**2) + 3*d*e**2*Piecewise((x**2*(d**2)**p/2, Eq(e**2, 0)), (-Piecewise(((d**2 - e**2*x**2)**(p + 1)/(p + 1), Ne(p, -1)), (log(d**2 - e**2*x**2), True))/(2*e**2), True)) + d**(2*p)*e**3*x**3*hyper((3/2, -p), (5/2,), e**2*x**2*exp_polar(2*I*pi)/d**2)/3","A",0
265,1,177,0,7.450184," ","integrate((e*x+d)**3*(-e**2*x**2+d**2)**p/x**2,x)","- \frac{d^{3} d^{2 p} {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, - p \\ \frac{1}{2} \end{matrix}\middle| {\frac{e^{2} x^{2} e^{2 i \pi}}{d^{2}}} \right)}}{x} - \frac{3 d^{2} e e^{2 p} x^{2 p} e^{i \pi p} \Gamma\left(- p\right) {{}_{2}F_{1}\left(\begin{matrix} - p, - p \\ 1 - p \end{matrix}\middle| {\frac{d^{2}}{e^{2} x^{2}}} \right)}}{2 \Gamma\left(1 - p\right)} + 3 d d^{2 p} e^{2} x {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, - p \\ \frac{3}{2} \end{matrix}\middle| {\frac{e^{2} x^{2} e^{2 i \pi}}{d^{2}}} \right)} + e^{3} \left(\begin{cases} \frac{x^{2} \left(d^{2}\right)^{p}}{2} & \text{for}\: e^{2} = 0 \\- \frac{\begin{cases} \frac{\left(d^{2} - e^{2} x^{2}\right)^{p + 1}}{p + 1} & \text{for}\: p \neq -1 \\\log{\left(d^{2} - e^{2} x^{2} \right)} & \text{otherwise} \end{cases}}{2 e^{2}} & \text{otherwise} \end{cases}\right)"," ",0,"-d**3*d**(2*p)*hyper((-1/2, -p), (1/2,), e**2*x**2*exp_polar(2*I*pi)/d**2)/x - 3*d**2*e*e**(2*p)*x**(2*p)*exp(I*pi*p)*gamma(-p)*hyper((-p, -p), (1 - p,), d**2/(e**2*x**2))/(2*gamma(1 - p)) + 3*d*d**(2*p)*e**2*x*hyper((1/2, -p), (3/2,), e**2*x**2*exp_polar(2*I*pi)/d**2) + e**3*Piecewise((x**2*(d**2)**p/2, Eq(e**2, 0)), (-Piecewise(((d**2 - e**2*x**2)**(p + 1)/(p + 1), Ne(p, -1)), (log(d**2 - e**2*x**2), True))/(2*e**2), True))","A",0
266,1,177,0,8.367336," ","integrate((e*x+d)**3*(-e**2*x**2+d**2)**p/x**3,x)","- \frac{d^{3} e^{2 p} x^{2 p} e^{i \pi p} \Gamma\left(1 - p\right) {{}_{2}F_{1}\left(\begin{matrix} - p, 1 - p \\ 2 - p \end{matrix}\middle| {\frac{d^{2}}{e^{2} x^{2}}} \right)}}{2 x^{2} \Gamma\left(2 - p\right)} - \frac{3 d^{2} d^{2 p} e {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, - p \\ \frac{1}{2} \end{matrix}\middle| {\frac{e^{2} x^{2} e^{2 i \pi}}{d^{2}}} \right)}}{x} - \frac{3 d e^{2} e^{2 p} x^{2 p} e^{i \pi p} \Gamma\left(- p\right) {{}_{2}F_{1}\left(\begin{matrix} - p, - p \\ 1 - p \end{matrix}\middle| {\frac{d^{2}}{e^{2} x^{2}}} \right)}}{2 \Gamma\left(1 - p\right)} + d^{2 p} e^{3} x {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, - p \\ \frac{3}{2} \end{matrix}\middle| {\frac{e^{2} x^{2} e^{2 i \pi}}{d^{2}}} \right)}"," ",0,"-d**3*e**(2*p)*x**(2*p)*exp(I*pi*p)*gamma(1 - p)*hyper((-p, 1 - p), (2 - p,), d**2/(e**2*x**2))/(2*x**2*gamma(2 - p)) - 3*d**2*d**(2*p)*e*hyper((-1/2, -p), (1/2,), e**2*x**2*exp_polar(2*I*pi)/d**2)/x - 3*d*e**2*e**(2*p)*x**(2*p)*exp(I*pi*p)*gamma(-p)*hyper((-p, -p), (1 - p,), d**2/(e**2*x**2))/(2*gamma(1 - p)) + d**(2*p)*e**3*x*hyper((1/2, -p), (3/2,), e**2*x**2*exp_polar(2*I*pi)/d**2)","C",0
267,1,4442,0,16.535254," ","integrate(x**4*(-e**2*x**2+d**2)**p/(e*x+d),x)","\begin{cases} - \frac{6 \cdot 0^{p} d^{4} d^{2 p} p \log{\left(\frac{d^{2}}{e^{2} x^{2}} \right)} \Gamma\left(- p\right) \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) \Gamma\left(p + 3\right)}{12 e^{5} p \Gamma\left(- p\right) \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) \Gamma\left(p + 3\right) + 12 e^{5} \Gamma\left(- p\right) \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) \Gamma\left(p + 3\right)} + \frac{6 \cdot 0^{p} d^{4} d^{2 p} p \log{\left(\frac{d^{2}}{e^{2} x^{2}} - 1 \right)} \Gamma\left(- p\right) \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) \Gamma\left(p + 3\right)}{12 e^{5} p \Gamma\left(- p\right) \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) \Gamma\left(p + 3\right) + 12 e^{5} \Gamma\left(- p\right) \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) \Gamma\left(p + 3\right)} + \frac{12 \cdot 0^{p} d^{4} d^{2 p} p \operatorname{acoth}{\left(\frac{d}{e x} \right)} \Gamma\left(- p\right) \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) \Gamma\left(p + 3\right)}{12 e^{5} p \Gamma\left(- p\right) \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) \Gamma\left(p + 3\right) + 12 e^{5} \Gamma\left(- p\right) \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) \Gamma\left(p + 3\right)} - \frac{6 \cdot 0^{p} d^{4} d^{2 p} \log{\left(\frac{d^{2}}{e^{2} x^{2}} \right)} \Gamma\left(- p\right) \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) \Gamma\left(p + 3\right)}{12 e^{5} p \Gamma\left(- p\right) \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) \Gamma\left(p + 3\right) + 12 e^{5} \Gamma\left(- p\right) \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) \Gamma\left(p + 3\right)} + \frac{6 \cdot 0^{p} d^{4} d^{2 p} \log{\left(\frac{d^{2}}{e^{2} x^{2}} - 1 \right)} \Gamma\left(- p\right) \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) \Gamma\left(p + 3\right)}{12 e^{5} p \Gamma\left(- p\right) \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) \Gamma\left(p + 3\right) + 12 e^{5} \Gamma\left(- p\right) \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) \Gamma\left(p + 3\right)} + \frac{12 \cdot 0^{p} d^{4} d^{2 p} \operatorname{acoth}{\left(\frac{d}{e x} \right)} \Gamma\left(- p\right) \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) \Gamma\left(p + 3\right)}{12 e^{5} p \Gamma\left(- p\right) \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) \Gamma\left(p + 3\right) + 12 e^{5} \Gamma\left(- p\right) \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) \Gamma\left(p + 3\right)} - \frac{12 \cdot 0^{p} d^{3} d^{2 p} e p x \Gamma\left(- p\right) \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) \Gamma\left(p + 3\right)}{12 e^{5} p \Gamma\left(- p\right) \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) \Gamma\left(p + 3\right) + 12 e^{5} \Gamma\left(- p\right) \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) \Gamma\left(p + 3\right)} - \frac{12 \cdot 0^{p} d^{3} d^{2 p} e x \Gamma\left(- p\right) \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) \Gamma\left(p + 3\right)}{12 e^{5} p \Gamma\left(- p\right) \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) \Gamma\left(p + 3\right) + 12 e^{5} \Gamma\left(- p\right) \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) \Gamma\left(p + 3\right)} + \frac{6 \cdot 0^{p} d^{2} d^{2 p} e^{2} p x^{2} \Gamma\left(- p\right) \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) \Gamma\left(p + 3\right)}{12 e^{5} p \Gamma\left(- p\right) \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) \Gamma\left(p + 3\right) + 12 e^{5} \Gamma\left(- p\right) \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) \Gamma\left(p + 3\right)} + \frac{6 \cdot 0^{p} d^{2} d^{2 p} e^{2} x^{2} \Gamma\left(- p\right) \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) \Gamma\left(p + 3\right)}{12 e^{5} p \Gamma\left(- p\right) \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) \Gamma\left(p + 3\right) + 12 e^{5} \Gamma\left(- p\right) \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) \Gamma\left(p + 3\right)} - \frac{4 \cdot 0^{p} d d^{2 p} e^{3} p x^{3} \Gamma\left(- p\right) \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) \Gamma\left(p + 3\right)}{12 e^{5} p \Gamma\left(- p\right) \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) \Gamma\left(p + 3\right) + 12 e^{5} \Gamma\left(- p\right) \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) \Gamma\left(p + 3\right)} - \frac{4 \cdot 0^{p} d d^{2 p} e^{3} x^{3} \Gamma\left(- p\right) \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) \Gamma\left(p + 3\right)}{12 e^{5} p \Gamma\left(- p\right) \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) \Gamma\left(p + 3\right) + 12 e^{5} \Gamma\left(- p\right) \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) \Gamma\left(p + 3\right)} + \frac{3 \cdot 0^{p} d^{2 p} e^{4} p x^{4} \Gamma\left(- p\right) \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) \Gamma\left(p + 3\right)}{12 e^{5} p \Gamma\left(- p\right) \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) \Gamma\left(p + 3\right) + 12 e^{5} \Gamma\left(- p\right) \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) \Gamma\left(p + 3\right)} + \frac{3 \cdot 0^{p} d^{2 p} e^{4} x^{4} \Gamma\left(- p\right) \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) \Gamma\left(p + 3\right)}{12 e^{5} p \Gamma\left(- p\right) \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) \Gamma\left(p + 3\right) + 12 e^{5} \Gamma\left(- p\right) \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) \Gamma\left(p + 3\right)} + \frac{12 d^{4} e^{2 p} x^{2 p} \left(\frac{d^{2}}{e^{2} x^{2}} - 1\right)^{p} \Gamma\left(- p\right) \Gamma\left(p\right) \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 2\right)}{12 e^{5} p \Gamma\left(- p\right) \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) \Gamma\left(p + 3\right) + 12 e^{5} \Gamma\left(- p\right) \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) \Gamma\left(p + 3\right)} + \frac{12 d^{2} e^{2} e^{2 p} p x^{2} x^{2 p} \left(\frac{d^{2}}{e^{2} x^{2}} - 1\right)^{p} \Gamma\left(- p\right) \Gamma\left(p\right) \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 2\right)}{12 e^{5} p \Gamma\left(- p\right) \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) \Gamma\left(p + 3\right) + 12 e^{5} \Gamma\left(- p\right) \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) \Gamma\left(p + 3\right)} + \frac{6 d e^{3} e^{2 p} p^{2} x^{3} x^{2 p} e^{i \pi p} \Gamma\left(- p\right) \Gamma\left(p\right) \Gamma\left(- p - \frac{3}{2}\right) \Gamma\left(p + 3\right) {{}_{2}F_{1}\left(\begin{matrix} 1 - p, - p - \frac{3}{2} \\ - p - \frac{1}{2} \end{matrix}\middle| {\frac{d^{2}}{e^{2} x^{2}}} \right)}}{12 e^{5} p \Gamma\left(- p\right) \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) \Gamma\left(p + 3\right) + 12 e^{5} \Gamma\left(- p\right) \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) \Gamma\left(p + 3\right)} + \frac{6 d e^{3} e^{2 p} p x^{3} x^{2 p} e^{i \pi p} \Gamma\left(- p\right) \Gamma\left(p\right) \Gamma\left(- p - \frac{3}{2}\right) \Gamma\left(p + 3\right) {{}_{2}F_{1}\left(\begin{matrix} 1 - p, - p - \frac{3}{2} \\ - p - \frac{1}{2} \end{matrix}\middle| {\frac{d^{2}}{e^{2} x^{2}}} \right)}}{12 e^{5} p \Gamma\left(- p\right) \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) \Gamma\left(p + 3\right) + 12 e^{5} \Gamma\left(- p\right) \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) \Gamma\left(p + 3\right)} + \frac{6 e^{4} e^{2 p} p^{2} x^{4} x^{2 p} \left(\frac{d^{2}}{e^{2} x^{2}} - 1\right)^{p} \Gamma\left(- p\right) \Gamma\left(p\right) \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 2\right)}{12 e^{5} p \Gamma\left(- p\right) \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) \Gamma\left(p + 3\right) + 12 e^{5} \Gamma\left(- p\right) \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) \Gamma\left(p + 3\right)} + \frac{6 e^{4} e^{2 p} p x^{4} x^{2 p} \left(\frac{d^{2}}{e^{2} x^{2}} - 1\right)^{p} \Gamma\left(- p\right) \Gamma\left(p\right) \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 2\right)}{12 e^{5} p \Gamma\left(- p\right) \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) \Gamma\left(p + 3\right) + 12 e^{5} \Gamma\left(- p\right) \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) \Gamma\left(p + 3\right)} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\- \frac{6 \cdot 0^{p} d^{4} d^{2 p} p \log{\left(\frac{d^{2}}{e^{2} x^{2}} \right)} \Gamma\left(- p\right) \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) \Gamma\left(p + 3\right)}{12 e^{5} p \Gamma\left(- p\right) \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) \Gamma\left(p + 3\right) + 12 e^{5} \Gamma\left(- p\right) \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) \Gamma\left(p + 3\right)} + \frac{6 \cdot 0^{p} d^{4} d^{2 p} p \log{\left(- \frac{d^{2}}{e^{2} x^{2}} + 1 \right)} \Gamma\left(- p\right) \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) \Gamma\left(p + 3\right)}{12 e^{5} p \Gamma\left(- p\right) \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) \Gamma\left(p + 3\right) + 12 e^{5} \Gamma\left(- p\right) \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) \Gamma\left(p + 3\right)} + \frac{12 \cdot 0^{p} d^{4} d^{2 p} p \operatorname{atanh}{\left(\frac{d}{e x} \right)} \Gamma\left(- p\right) \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) \Gamma\left(p + 3\right)}{12 e^{5} p \Gamma\left(- p\right) \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) \Gamma\left(p + 3\right) + 12 e^{5} \Gamma\left(- p\right) \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) \Gamma\left(p + 3\right)} - \frac{6 \cdot 0^{p} d^{4} d^{2 p} \log{\left(\frac{d^{2}}{e^{2} x^{2}} \right)} \Gamma\left(- p\right) \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) \Gamma\left(p + 3\right)}{12 e^{5} p \Gamma\left(- p\right) \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) \Gamma\left(p + 3\right) + 12 e^{5} \Gamma\left(- p\right) \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) \Gamma\left(p + 3\right)} + \frac{6 \cdot 0^{p} d^{4} d^{2 p} \log{\left(- \frac{d^{2}}{e^{2} x^{2}} + 1 \right)} \Gamma\left(- p\right) \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) \Gamma\left(p + 3\right)}{12 e^{5} p \Gamma\left(- p\right) \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) \Gamma\left(p + 3\right) + 12 e^{5} \Gamma\left(- p\right) \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) \Gamma\left(p + 3\right)} + \frac{12 \cdot 0^{p} d^{4} d^{2 p} \operatorname{atanh}{\left(\frac{d}{e x} \right)} \Gamma\left(- p\right) \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) \Gamma\left(p + 3\right)}{12 e^{5} p \Gamma\left(- p\right) \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) \Gamma\left(p + 3\right) + 12 e^{5} \Gamma\left(- p\right) \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) \Gamma\left(p + 3\right)} - \frac{12 \cdot 0^{p} d^{3} d^{2 p} e p x \Gamma\left(- p\right) \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) \Gamma\left(p + 3\right)}{12 e^{5} p \Gamma\left(- p\right) \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) \Gamma\left(p + 3\right) + 12 e^{5} \Gamma\left(- p\right) \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) \Gamma\left(p + 3\right)} - \frac{12 \cdot 0^{p} d^{3} d^{2 p} e x \Gamma\left(- p\right) \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) \Gamma\left(p + 3\right)}{12 e^{5} p \Gamma\left(- p\right) \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) \Gamma\left(p + 3\right) + 12 e^{5} \Gamma\left(- p\right) \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) \Gamma\left(p + 3\right)} + \frac{6 \cdot 0^{p} d^{2} d^{2 p} e^{2} p x^{2} \Gamma\left(- p\right) \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) \Gamma\left(p + 3\right)}{12 e^{5} p \Gamma\left(- p\right) \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) \Gamma\left(p + 3\right) + 12 e^{5} \Gamma\left(- p\right) \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) \Gamma\left(p + 3\right)} + \frac{6 \cdot 0^{p} d^{2} d^{2 p} e^{2} x^{2} \Gamma\left(- p\right) \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) \Gamma\left(p + 3\right)}{12 e^{5} p \Gamma\left(- p\right) \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) \Gamma\left(p + 3\right) + 12 e^{5} \Gamma\left(- p\right) \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) \Gamma\left(p + 3\right)} - \frac{4 \cdot 0^{p} d d^{2 p} e^{3} p x^{3} \Gamma\left(- p\right) \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) \Gamma\left(p + 3\right)}{12 e^{5} p \Gamma\left(- p\right) \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) \Gamma\left(p + 3\right) + 12 e^{5} \Gamma\left(- p\right) \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) \Gamma\left(p + 3\right)} - \frac{4 \cdot 0^{p} d d^{2 p} e^{3} x^{3} \Gamma\left(- p\right) \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) \Gamma\left(p + 3\right)}{12 e^{5} p \Gamma\left(- p\right) \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) \Gamma\left(p + 3\right) + 12 e^{5} \Gamma\left(- p\right) \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) \Gamma\left(p + 3\right)} + \frac{3 \cdot 0^{p} d^{2 p} e^{4} p x^{4} \Gamma\left(- p\right) \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) \Gamma\left(p + 3\right)}{12 e^{5} p \Gamma\left(- p\right) \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) \Gamma\left(p + 3\right) + 12 e^{5} \Gamma\left(- p\right) \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) \Gamma\left(p + 3\right)} + \frac{3 \cdot 0^{p} d^{2 p} e^{4} x^{4} \Gamma\left(- p\right) \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) \Gamma\left(p + 3\right)}{12 e^{5} p \Gamma\left(- p\right) \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) \Gamma\left(p + 3\right) + 12 e^{5} \Gamma\left(- p\right) \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) \Gamma\left(p + 3\right)} + \frac{12 d^{4} e^{2 p} x^{2 p} \left(- \frac{d^{2}}{e^{2} x^{2}} + 1\right)^{p} e^{i \pi p} \Gamma\left(- p\right) \Gamma\left(p\right) \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 2\right)}{12 e^{5} p \Gamma\left(- p\right) \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) \Gamma\left(p + 3\right) + 12 e^{5} \Gamma\left(- p\right) \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) \Gamma\left(p + 3\right)} + \frac{12 d^{2} e^{2} e^{2 p} p x^{2} x^{2 p} \left(- \frac{d^{2}}{e^{2} x^{2}} + 1\right)^{p} e^{i \pi p} \Gamma\left(- p\right) \Gamma\left(p\right) \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 2\right)}{12 e^{5} p \Gamma\left(- p\right) \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) \Gamma\left(p + 3\right) + 12 e^{5} \Gamma\left(- p\right) \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) \Gamma\left(p + 3\right)} + \frac{6 d e^{3} e^{2 p} p^{2} x^{3} x^{2 p} e^{i \pi p} \Gamma\left(- p\right) \Gamma\left(p\right) \Gamma\left(- p - \frac{3}{2}\right) \Gamma\left(p + 3\right) {{}_{2}F_{1}\left(\begin{matrix} 1 - p, - p - \frac{3}{2} \\ - p - \frac{1}{2} \end{matrix}\middle| {\frac{d^{2}}{e^{2} x^{2}}} \right)}}{12 e^{5} p \Gamma\left(- p\right) \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) \Gamma\left(p + 3\right) + 12 e^{5} \Gamma\left(- p\right) \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) \Gamma\left(p + 3\right)} + \frac{6 d e^{3} e^{2 p} p x^{3} x^{2 p} e^{i \pi p} \Gamma\left(- p\right) \Gamma\left(p\right) \Gamma\left(- p - \frac{3}{2}\right) \Gamma\left(p + 3\right) {{}_{2}F_{1}\left(\begin{matrix} 1 - p, - p - \frac{3}{2} \\ - p - \frac{1}{2} \end{matrix}\middle| {\frac{d^{2}}{e^{2} x^{2}}} \right)}}{12 e^{5} p \Gamma\left(- p\right) \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) \Gamma\left(p + 3\right) + 12 e^{5} \Gamma\left(- p\right) \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) \Gamma\left(p + 3\right)} + \frac{6 e^{4} e^{2 p} p^{2} x^{4} x^{2 p} \left(- \frac{d^{2}}{e^{2} x^{2}} + 1\right)^{p} e^{i \pi p} \Gamma\left(- p\right) \Gamma\left(p\right) \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 2\right)}{12 e^{5} p \Gamma\left(- p\right) \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) \Gamma\left(p + 3\right) + 12 e^{5} \Gamma\left(- p\right) \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) \Gamma\left(p + 3\right)} + \frac{6 e^{4} e^{2 p} p x^{4} x^{2 p} \left(- \frac{d^{2}}{e^{2} x^{2}} + 1\right)^{p} e^{i \pi p} \Gamma\left(- p\right) \Gamma\left(p\right) \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 2\right)}{12 e^{5} p \Gamma\left(- p\right) \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) \Gamma\left(p + 3\right) + 12 e^{5} \Gamma\left(- p\right) \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) \Gamma\left(p + 3\right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-6*0**p*d**4*d**(2*p)*p*log(d**2/(e**2*x**2))*gamma(-p)*gamma(-p - 1/2)*gamma(p + 1)*gamma(p + 3)/(12*e**5*p*gamma(-p)*gamma(-p - 1/2)*gamma(p + 1)*gamma(p + 3) + 12*e**5*gamma(-p)*gamma(-p - 1/2)*gamma(p + 1)*gamma(p + 3)) + 6*0**p*d**4*d**(2*p)*p*log(d**2/(e**2*x**2) - 1)*gamma(-p)*gamma(-p - 1/2)*gamma(p + 1)*gamma(p + 3)/(12*e**5*p*gamma(-p)*gamma(-p - 1/2)*gamma(p + 1)*gamma(p + 3) + 12*e**5*gamma(-p)*gamma(-p - 1/2)*gamma(p + 1)*gamma(p + 3)) + 12*0**p*d**4*d**(2*p)*p*acoth(d/(e*x))*gamma(-p)*gamma(-p - 1/2)*gamma(p + 1)*gamma(p + 3)/(12*e**5*p*gamma(-p)*gamma(-p - 1/2)*gamma(p + 1)*gamma(p + 3) + 12*e**5*gamma(-p)*gamma(-p - 1/2)*gamma(p + 1)*gamma(p + 3)) - 6*0**p*d**4*d**(2*p)*log(d**2/(e**2*x**2))*gamma(-p)*gamma(-p - 1/2)*gamma(p + 1)*gamma(p + 3)/(12*e**5*p*gamma(-p)*gamma(-p - 1/2)*gamma(p + 1)*gamma(p + 3) + 12*e**5*gamma(-p)*gamma(-p - 1/2)*gamma(p + 1)*gamma(p + 3)) + 6*0**p*d**4*d**(2*p)*log(d**2/(e**2*x**2) - 1)*gamma(-p)*gamma(-p - 1/2)*gamma(p + 1)*gamma(p + 3)/(12*e**5*p*gamma(-p)*gamma(-p - 1/2)*gamma(p + 1)*gamma(p + 3) + 12*e**5*gamma(-p)*gamma(-p - 1/2)*gamma(p + 1)*gamma(p + 3)) + 12*0**p*d**4*d**(2*p)*acoth(d/(e*x))*gamma(-p)*gamma(-p - 1/2)*gamma(p + 1)*gamma(p + 3)/(12*e**5*p*gamma(-p)*gamma(-p - 1/2)*gamma(p + 1)*gamma(p + 3) + 12*e**5*gamma(-p)*gamma(-p - 1/2)*gamma(p + 1)*gamma(p + 3)) - 12*0**p*d**3*d**(2*p)*e*p*x*gamma(-p)*gamma(-p - 1/2)*gamma(p + 1)*gamma(p + 3)/(12*e**5*p*gamma(-p)*gamma(-p - 1/2)*gamma(p + 1)*gamma(p + 3) + 12*e**5*gamma(-p)*gamma(-p - 1/2)*gamma(p + 1)*gamma(p + 3)) - 12*0**p*d**3*d**(2*p)*e*x*gamma(-p)*gamma(-p - 1/2)*gamma(p + 1)*gamma(p + 3)/(12*e**5*p*gamma(-p)*gamma(-p - 1/2)*gamma(p + 1)*gamma(p + 3) + 12*e**5*gamma(-p)*gamma(-p - 1/2)*gamma(p + 1)*gamma(p + 3)) + 6*0**p*d**2*d**(2*p)*e**2*p*x**2*gamma(-p)*gamma(-p - 1/2)*gamma(p + 1)*gamma(p + 3)/(12*e**5*p*gamma(-p)*gamma(-p - 1/2)*gamma(p + 1)*gamma(p + 3) + 12*e**5*gamma(-p)*gamma(-p - 1/2)*gamma(p + 1)*gamma(p + 3)) + 6*0**p*d**2*d**(2*p)*e**2*x**2*gamma(-p)*gamma(-p - 1/2)*gamma(p + 1)*gamma(p + 3)/(12*e**5*p*gamma(-p)*gamma(-p - 1/2)*gamma(p + 1)*gamma(p + 3) + 12*e**5*gamma(-p)*gamma(-p - 1/2)*gamma(p + 1)*gamma(p + 3)) - 4*0**p*d*d**(2*p)*e**3*p*x**3*gamma(-p)*gamma(-p - 1/2)*gamma(p + 1)*gamma(p + 3)/(12*e**5*p*gamma(-p)*gamma(-p - 1/2)*gamma(p + 1)*gamma(p + 3) + 12*e**5*gamma(-p)*gamma(-p - 1/2)*gamma(p + 1)*gamma(p + 3)) - 4*0**p*d*d**(2*p)*e**3*x**3*gamma(-p)*gamma(-p - 1/2)*gamma(p + 1)*gamma(p + 3)/(12*e**5*p*gamma(-p)*gamma(-p - 1/2)*gamma(p + 1)*gamma(p + 3) + 12*e**5*gamma(-p)*gamma(-p - 1/2)*gamma(p + 1)*gamma(p + 3)) + 3*0**p*d**(2*p)*e**4*p*x**4*gamma(-p)*gamma(-p - 1/2)*gamma(p + 1)*gamma(p + 3)/(12*e**5*p*gamma(-p)*gamma(-p - 1/2)*gamma(p + 1)*gamma(p + 3) + 12*e**5*gamma(-p)*gamma(-p - 1/2)*gamma(p + 1)*gamma(p + 3)) + 3*0**p*d**(2*p)*e**4*x**4*gamma(-p)*gamma(-p - 1/2)*gamma(p + 1)*gamma(p + 3)/(12*e**5*p*gamma(-p)*gamma(-p - 1/2)*gamma(p + 1)*gamma(p + 3) + 12*e**5*gamma(-p)*gamma(-p - 1/2)*gamma(p + 1)*gamma(p + 3)) + 12*d**4*e**(2*p)*x**(2*p)*(d**2/(e**2*x**2) - 1)**p*gamma(-p)*gamma(p)*gamma(-p - 1/2)*gamma(p + 2)/(12*e**5*p*gamma(-p)*gamma(-p - 1/2)*gamma(p + 1)*gamma(p + 3) + 12*e**5*gamma(-p)*gamma(-p - 1/2)*gamma(p + 1)*gamma(p + 3)) + 12*d**2*e**2*e**(2*p)*p*x**2*x**(2*p)*(d**2/(e**2*x**2) - 1)**p*gamma(-p)*gamma(p)*gamma(-p - 1/2)*gamma(p + 2)/(12*e**5*p*gamma(-p)*gamma(-p - 1/2)*gamma(p + 1)*gamma(p + 3) + 12*e**5*gamma(-p)*gamma(-p - 1/2)*gamma(p + 1)*gamma(p + 3)) + 6*d*e**3*e**(2*p)*p**2*x**3*x**(2*p)*exp(I*pi*p)*gamma(-p)*gamma(p)*gamma(-p - 3/2)*gamma(p + 3)*hyper((1 - p, -p - 3/2), (-p - 1/2,), d**2/(e**2*x**2))/(12*e**5*p*gamma(-p)*gamma(-p - 1/2)*gamma(p + 1)*gamma(p + 3) + 12*e**5*gamma(-p)*gamma(-p - 1/2)*gamma(p + 1)*gamma(p + 3)) + 6*d*e**3*e**(2*p)*p*x**3*x**(2*p)*exp(I*pi*p)*gamma(-p)*gamma(p)*gamma(-p - 3/2)*gamma(p + 3)*hyper((1 - p, -p - 3/2), (-p - 1/2,), d**2/(e**2*x**2))/(12*e**5*p*gamma(-p)*gamma(-p - 1/2)*gamma(p + 1)*gamma(p + 3) + 12*e**5*gamma(-p)*gamma(-p - 1/2)*gamma(p + 1)*gamma(p + 3)) + 6*e**4*e**(2*p)*p**2*x**4*x**(2*p)*(d**2/(e**2*x**2) - 1)**p*gamma(-p)*gamma(p)*gamma(-p - 1/2)*gamma(p + 2)/(12*e**5*p*gamma(-p)*gamma(-p - 1/2)*gamma(p + 1)*gamma(p + 3) + 12*e**5*gamma(-p)*gamma(-p - 1/2)*gamma(p + 1)*gamma(p + 3)) + 6*e**4*e**(2*p)*p*x**4*x**(2*p)*(d**2/(e**2*x**2) - 1)**p*gamma(-p)*gamma(p)*gamma(-p - 1/2)*gamma(p + 2)/(12*e**5*p*gamma(-p)*gamma(-p - 1/2)*gamma(p + 1)*gamma(p + 3) + 12*e**5*gamma(-p)*gamma(-p - 1/2)*gamma(p + 1)*gamma(p + 3)), Abs(d**2/(e**2*x**2)) > 1), (-6*0**p*d**4*d**(2*p)*p*log(d**2/(e**2*x**2))*gamma(-p)*gamma(-p - 1/2)*gamma(p + 1)*gamma(p + 3)/(12*e**5*p*gamma(-p)*gamma(-p - 1/2)*gamma(p + 1)*gamma(p + 3) + 12*e**5*gamma(-p)*gamma(-p - 1/2)*gamma(p + 1)*gamma(p + 3)) + 6*0**p*d**4*d**(2*p)*p*log(-d**2/(e**2*x**2) + 1)*gamma(-p)*gamma(-p - 1/2)*gamma(p + 1)*gamma(p + 3)/(12*e**5*p*gamma(-p)*gamma(-p - 1/2)*gamma(p + 1)*gamma(p + 3) + 12*e**5*gamma(-p)*gamma(-p - 1/2)*gamma(p + 1)*gamma(p + 3)) + 12*0**p*d**4*d**(2*p)*p*atanh(d/(e*x))*gamma(-p)*gamma(-p - 1/2)*gamma(p + 1)*gamma(p + 3)/(12*e**5*p*gamma(-p)*gamma(-p - 1/2)*gamma(p + 1)*gamma(p + 3) + 12*e**5*gamma(-p)*gamma(-p - 1/2)*gamma(p + 1)*gamma(p + 3)) - 6*0**p*d**4*d**(2*p)*log(d**2/(e**2*x**2))*gamma(-p)*gamma(-p - 1/2)*gamma(p + 1)*gamma(p + 3)/(12*e**5*p*gamma(-p)*gamma(-p - 1/2)*gamma(p + 1)*gamma(p + 3) + 12*e**5*gamma(-p)*gamma(-p - 1/2)*gamma(p + 1)*gamma(p + 3)) + 6*0**p*d**4*d**(2*p)*log(-d**2/(e**2*x**2) + 1)*gamma(-p)*gamma(-p - 1/2)*gamma(p + 1)*gamma(p + 3)/(12*e**5*p*gamma(-p)*gamma(-p - 1/2)*gamma(p + 1)*gamma(p + 3) + 12*e**5*gamma(-p)*gamma(-p - 1/2)*gamma(p + 1)*gamma(p + 3)) + 12*0**p*d**4*d**(2*p)*atanh(d/(e*x))*gamma(-p)*gamma(-p - 1/2)*gamma(p + 1)*gamma(p + 3)/(12*e**5*p*gamma(-p)*gamma(-p - 1/2)*gamma(p + 1)*gamma(p + 3) + 12*e**5*gamma(-p)*gamma(-p - 1/2)*gamma(p + 1)*gamma(p + 3)) - 12*0**p*d**3*d**(2*p)*e*p*x*gamma(-p)*gamma(-p - 1/2)*gamma(p + 1)*gamma(p + 3)/(12*e**5*p*gamma(-p)*gamma(-p - 1/2)*gamma(p + 1)*gamma(p + 3) + 12*e**5*gamma(-p)*gamma(-p - 1/2)*gamma(p + 1)*gamma(p + 3)) - 12*0**p*d**3*d**(2*p)*e*x*gamma(-p)*gamma(-p - 1/2)*gamma(p + 1)*gamma(p + 3)/(12*e**5*p*gamma(-p)*gamma(-p - 1/2)*gamma(p + 1)*gamma(p + 3) + 12*e**5*gamma(-p)*gamma(-p - 1/2)*gamma(p + 1)*gamma(p + 3)) + 6*0**p*d**2*d**(2*p)*e**2*p*x**2*gamma(-p)*gamma(-p - 1/2)*gamma(p + 1)*gamma(p + 3)/(12*e**5*p*gamma(-p)*gamma(-p - 1/2)*gamma(p + 1)*gamma(p + 3) + 12*e**5*gamma(-p)*gamma(-p - 1/2)*gamma(p + 1)*gamma(p + 3)) + 6*0**p*d**2*d**(2*p)*e**2*x**2*gamma(-p)*gamma(-p - 1/2)*gamma(p + 1)*gamma(p + 3)/(12*e**5*p*gamma(-p)*gamma(-p - 1/2)*gamma(p + 1)*gamma(p + 3) + 12*e**5*gamma(-p)*gamma(-p - 1/2)*gamma(p + 1)*gamma(p + 3)) - 4*0**p*d*d**(2*p)*e**3*p*x**3*gamma(-p)*gamma(-p - 1/2)*gamma(p + 1)*gamma(p + 3)/(12*e**5*p*gamma(-p)*gamma(-p - 1/2)*gamma(p + 1)*gamma(p + 3) + 12*e**5*gamma(-p)*gamma(-p - 1/2)*gamma(p + 1)*gamma(p + 3)) - 4*0**p*d*d**(2*p)*e**3*x**3*gamma(-p)*gamma(-p - 1/2)*gamma(p + 1)*gamma(p + 3)/(12*e**5*p*gamma(-p)*gamma(-p - 1/2)*gamma(p + 1)*gamma(p + 3) + 12*e**5*gamma(-p)*gamma(-p - 1/2)*gamma(p + 1)*gamma(p + 3)) + 3*0**p*d**(2*p)*e**4*p*x**4*gamma(-p)*gamma(-p - 1/2)*gamma(p + 1)*gamma(p + 3)/(12*e**5*p*gamma(-p)*gamma(-p - 1/2)*gamma(p + 1)*gamma(p + 3) + 12*e**5*gamma(-p)*gamma(-p - 1/2)*gamma(p + 1)*gamma(p + 3)) + 3*0**p*d**(2*p)*e**4*x**4*gamma(-p)*gamma(-p - 1/2)*gamma(p + 1)*gamma(p + 3)/(12*e**5*p*gamma(-p)*gamma(-p - 1/2)*gamma(p + 1)*gamma(p + 3) + 12*e**5*gamma(-p)*gamma(-p - 1/2)*gamma(p + 1)*gamma(p + 3)) + 12*d**4*e**(2*p)*x**(2*p)*(-d**2/(e**2*x**2) + 1)**p*exp(I*pi*p)*gamma(-p)*gamma(p)*gamma(-p - 1/2)*gamma(p + 2)/(12*e**5*p*gamma(-p)*gamma(-p - 1/2)*gamma(p + 1)*gamma(p + 3) + 12*e**5*gamma(-p)*gamma(-p - 1/2)*gamma(p + 1)*gamma(p + 3)) + 12*d**2*e**2*e**(2*p)*p*x**2*x**(2*p)*(-d**2/(e**2*x**2) + 1)**p*exp(I*pi*p)*gamma(-p)*gamma(p)*gamma(-p - 1/2)*gamma(p + 2)/(12*e**5*p*gamma(-p)*gamma(-p - 1/2)*gamma(p + 1)*gamma(p + 3) + 12*e**5*gamma(-p)*gamma(-p - 1/2)*gamma(p + 1)*gamma(p + 3)) + 6*d*e**3*e**(2*p)*p**2*x**3*x**(2*p)*exp(I*pi*p)*gamma(-p)*gamma(p)*gamma(-p - 3/2)*gamma(p + 3)*hyper((1 - p, -p - 3/2), (-p - 1/2,), d**2/(e**2*x**2))/(12*e**5*p*gamma(-p)*gamma(-p - 1/2)*gamma(p + 1)*gamma(p + 3) + 12*e**5*gamma(-p)*gamma(-p - 1/2)*gamma(p + 1)*gamma(p + 3)) + 6*d*e**3*e**(2*p)*p*x**3*x**(2*p)*exp(I*pi*p)*gamma(-p)*gamma(p)*gamma(-p - 3/2)*gamma(p + 3)*hyper((1 - p, -p - 3/2), (-p - 1/2,), d**2/(e**2*x**2))/(12*e**5*p*gamma(-p)*gamma(-p - 1/2)*gamma(p + 1)*gamma(p + 3) + 12*e**5*gamma(-p)*gamma(-p - 1/2)*gamma(p + 1)*gamma(p + 3)) + 6*e**4*e**(2*p)*p**2*x**4*x**(2*p)*(-d**2/(e**2*x**2) + 1)**p*exp(I*pi*p)*gamma(-p)*gamma(p)*gamma(-p - 1/2)*gamma(p + 2)/(12*e**5*p*gamma(-p)*gamma(-p - 1/2)*gamma(p + 1)*gamma(p + 3) + 12*e**5*gamma(-p)*gamma(-p - 1/2)*gamma(p + 1)*gamma(p + 3)) + 6*e**4*e**(2*p)*p*x**4*x**(2*p)*(-d**2/(e**2*x**2) + 1)**p*exp(I*pi*p)*gamma(-p)*gamma(p)*gamma(-p - 1/2)*gamma(p + 2)/(12*e**5*p*gamma(-p)*gamma(-p - 1/2)*gamma(p + 1)*gamma(p + 3) + 12*e**5*gamma(-p)*gamma(-p - 1/2)*gamma(p + 1)*gamma(p + 3)), True))","C",0
268,1,5090,0,10.516623," ","integrate(x**3*(-e**2*x**2+d**2)**p/(e*x+d),x)","\begin{cases} \frac{3 \cdot 0^{p} d^{3} d^{2 p} p \log{\left(\frac{d^{2}}{e^{2} x^{2}} \right)} \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right)}{6 e^{4} p \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) + 6 e^{4} \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right)} - \frac{3 \cdot 0^{p} d^{3} d^{2 p} p \log{\left(\frac{d^{2}}{e^{2} x^{2}} - 1 \right)} \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right)}{6 e^{4} p \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) + 6 e^{4} \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right)} - \frac{6 \cdot 0^{p} d^{3} d^{2 p} p \operatorname{acoth}{\left(\frac{d}{e x} \right)} \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right)}{6 e^{4} p \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) + 6 e^{4} \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right)} + \frac{3 \cdot 0^{p} d^{3} d^{2 p} \log{\left(\frac{d^{2}}{e^{2} x^{2}} \right)} \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right)}{6 e^{4} p \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) + 6 e^{4} \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right)} - \frac{3 \cdot 0^{p} d^{3} d^{2 p} \log{\left(\frac{d^{2}}{e^{2} x^{2}} - 1 \right)} \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right)}{6 e^{4} p \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) + 6 e^{4} \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right)} - \frac{6 \cdot 0^{p} d^{3} d^{2 p} \operatorname{acoth}{\left(\frac{d}{e x} \right)} \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right)}{6 e^{4} p \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) + 6 e^{4} \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right)} + \frac{6 \cdot 0^{p} d^{2} d^{2 p} e p x \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right)}{6 e^{4} p \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) + 6 e^{4} \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right)} + \frac{6 \cdot 0^{p} d^{2} d^{2 p} e x \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right)}{6 e^{4} p \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) + 6 e^{4} \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right)} - \frac{3 \cdot 0^{p} d d^{2 p} e^{2} p x^{2} \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right)}{6 e^{4} p \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) + 6 e^{4} \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right)} - \frac{3 \cdot 0^{p} d d^{2 p} e^{2} x^{2} \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right)}{6 e^{4} p \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) + 6 e^{4} \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right)} + \frac{2 \cdot 0^{p} d^{2 p} e^{3} p x^{3} \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right)}{6 e^{4} p \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) + 6 e^{4} \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right)} + \frac{2 \cdot 0^{p} d^{2 p} e^{3} x^{3} \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right)}{6 e^{4} p \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) + 6 e^{4} \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right)} - \frac{3 d^{3} d^{2 p} \left(-1 + \frac{e^{2} x^{2}}{d^{2}}\right)^{p} e^{i \pi p} \Gamma\left(p\right) \Gamma\left(- p - \frac{1}{2}\right)}{6 e^{4} p \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) + 6 e^{4} \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right)} - \frac{3 d d^{2 p} e^{2} p x^{2} \left(-1 + \frac{e^{2} x^{2}}{d^{2}}\right)^{p} e^{i \pi p} \Gamma\left(p\right) \Gamma\left(- p - \frac{1}{2}\right)}{6 e^{4} p \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) + 6 e^{4} \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right)} - \frac{3 e^{3} e^{2 p} p^{2} x^{3} x^{2 p} e^{i \pi p} \Gamma\left(p\right) \Gamma\left(- p - \frac{3}{2}\right) {{}_{2}F_{1}\left(\begin{matrix} 1 - p, - p - \frac{3}{2} \\ - p - \frac{1}{2} \end{matrix}\middle| {\frac{d^{2}}{e^{2} x^{2}}} \right)}}{6 e^{4} p \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) + 6 e^{4} \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right)} - \frac{3 e^{3} e^{2 p} p x^{3} x^{2 p} e^{i \pi p} \Gamma\left(p\right) \Gamma\left(- p - \frac{3}{2}\right) {{}_{2}F_{1}\left(\begin{matrix} 1 - p, - p - \frac{3}{2} \\ - p - \frac{1}{2} \end{matrix}\middle| {\frac{d^{2}}{e^{2} x^{2}}} \right)}}{6 e^{4} p \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) + 6 e^{4} \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right)} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \wedge \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\\frac{3 \cdot 0^{p} d^{3} d^{2 p} p \log{\left(\frac{d^{2}}{e^{2} x^{2}} \right)} \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right)}{6 e^{4} p \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) + 6 e^{4} \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right)} - \frac{3 \cdot 0^{p} d^{3} d^{2 p} p \log{\left(- \frac{d^{2}}{e^{2} x^{2}} + 1 \right)} \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right)}{6 e^{4} p \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) + 6 e^{4} \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right)} - \frac{6 \cdot 0^{p} d^{3} d^{2 p} p \operatorname{atanh}{\left(\frac{d}{e x} \right)} \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right)}{6 e^{4} p \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) + 6 e^{4} \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right)} + \frac{3 \cdot 0^{p} d^{3} d^{2 p} \log{\left(\frac{d^{2}}{e^{2} x^{2}} \right)} \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right)}{6 e^{4} p \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) + 6 e^{4} \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right)} - \frac{3 \cdot 0^{p} d^{3} d^{2 p} \log{\left(- \frac{d^{2}}{e^{2} x^{2}} + 1 \right)} \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right)}{6 e^{4} p \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) + 6 e^{4} \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right)} - \frac{6 \cdot 0^{p} d^{3} d^{2 p} \operatorname{atanh}{\left(\frac{d}{e x} \right)} \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right)}{6 e^{4} p \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) + 6 e^{4} \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right)} + \frac{6 \cdot 0^{p} d^{2} d^{2 p} e p x \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right)}{6 e^{4} p \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) + 6 e^{4} \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right)} + \frac{6 \cdot 0^{p} d^{2} d^{2 p} e x \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right)}{6 e^{4} p \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) + 6 e^{4} \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right)} - \frac{3 \cdot 0^{p} d d^{2 p} e^{2} p x^{2} \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right)}{6 e^{4} p \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) + 6 e^{4} \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right)} - \frac{3 \cdot 0^{p} d d^{2 p} e^{2} x^{2} \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right)}{6 e^{4} p \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) + 6 e^{4} \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right)} + \frac{2 \cdot 0^{p} d^{2 p} e^{3} p x^{3} \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right)}{6 e^{4} p \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) + 6 e^{4} \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right)} + \frac{2 \cdot 0^{p} d^{2 p} e^{3} x^{3} \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right)}{6 e^{4} p \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) + 6 e^{4} \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right)} - \frac{3 d^{3} d^{2 p} \left(-1 + \frac{e^{2} x^{2}}{d^{2}}\right)^{p} e^{i \pi p} \Gamma\left(p\right) \Gamma\left(- p - \frac{1}{2}\right)}{6 e^{4} p \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) + 6 e^{4} \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right)} - \frac{3 d d^{2 p} e^{2} p x^{2} \left(-1 + \frac{e^{2} x^{2}}{d^{2}}\right)^{p} e^{i \pi p} \Gamma\left(p\right) \Gamma\left(- p - \frac{1}{2}\right)}{6 e^{4} p \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) + 6 e^{4} \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right)} - \frac{3 e^{3} e^{2 p} p^{2} x^{3} x^{2 p} e^{i \pi p} \Gamma\left(p\right) \Gamma\left(- p - \frac{3}{2}\right) {{}_{2}F_{1}\left(\begin{matrix} 1 - p, - p - \frac{3}{2} \\ - p - \frac{1}{2} \end{matrix}\middle| {\frac{d^{2}}{e^{2} x^{2}}} \right)}}{6 e^{4} p \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) + 6 e^{4} \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right)} - \frac{3 e^{3} e^{2 p} p x^{3} x^{2 p} e^{i \pi p} \Gamma\left(p\right) \Gamma\left(- p - \frac{3}{2}\right) {{}_{2}F_{1}\left(\begin{matrix} 1 - p, - p - \frac{3}{2} \\ - p - \frac{1}{2} \end{matrix}\middle| {\frac{d^{2}}{e^{2} x^{2}}} \right)}}{6 e^{4} p \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) + 6 e^{4} \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right)} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{3 \cdot 0^{p} d^{3} d^{2 p} p \log{\left(\frac{d^{2}}{e^{2} x^{2}} \right)} \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right)}{6 e^{4} p \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) + 6 e^{4} \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right)} - \frac{3 \cdot 0^{p} d^{3} d^{2 p} p \log{\left(\frac{d^{2}}{e^{2} x^{2}} - 1 \right)} \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right)}{6 e^{4} p \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) + 6 e^{4} \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right)} - \frac{6 \cdot 0^{p} d^{3} d^{2 p} p \operatorname{acoth}{\left(\frac{d}{e x} \right)} \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right)}{6 e^{4} p \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) + 6 e^{4} \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right)} + \frac{3 \cdot 0^{p} d^{3} d^{2 p} \log{\left(\frac{d^{2}}{e^{2} x^{2}} \right)} \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right)}{6 e^{4} p \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) + 6 e^{4} \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right)} - \frac{3 \cdot 0^{p} d^{3} d^{2 p} \log{\left(\frac{d^{2}}{e^{2} x^{2}} - 1 \right)} \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right)}{6 e^{4} p \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) + 6 e^{4} \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right)} - \frac{6 \cdot 0^{p} d^{3} d^{2 p} \operatorname{acoth}{\left(\frac{d}{e x} \right)} \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right)}{6 e^{4} p \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) + 6 e^{4} \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right)} + \frac{6 \cdot 0^{p} d^{2} d^{2 p} e p x \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right)}{6 e^{4} p \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) + 6 e^{4} \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right)} + \frac{6 \cdot 0^{p} d^{2} d^{2 p} e x \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right)}{6 e^{4} p \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) + 6 e^{4} \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right)} - \frac{3 \cdot 0^{p} d d^{2 p} e^{2} p x^{2} \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right)}{6 e^{4} p \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) + 6 e^{4} \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right)} - \frac{3 \cdot 0^{p} d d^{2 p} e^{2} x^{2} \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right)}{6 e^{4} p \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) + 6 e^{4} \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right)} + \frac{2 \cdot 0^{p} d^{2 p} e^{3} p x^{3} \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right)}{6 e^{4} p \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) + 6 e^{4} \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right)} + \frac{2 \cdot 0^{p} d^{2 p} e^{3} x^{3} \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right)}{6 e^{4} p \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) + 6 e^{4} \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right)} - \frac{3 d^{3} d^{2 p} \left(1 - \frac{e^{2} x^{2}}{d^{2}}\right)^{p} \Gamma\left(p\right) \Gamma\left(- p - \frac{1}{2}\right)}{6 e^{4} p \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) + 6 e^{4} \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right)} - \frac{3 d d^{2 p} e^{2} p x^{2} \left(1 - \frac{e^{2} x^{2}}{d^{2}}\right)^{p} \Gamma\left(p\right) \Gamma\left(- p - \frac{1}{2}\right)}{6 e^{4} p \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) + 6 e^{4} \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right)} - \frac{3 e^{3} e^{2 p} p^{2} x^{3} x^{2 p} e^{i \pi p} \Gamma\left(p\right) \Gamma\left(- p - \frac{3}{2}\right) {{}_{2}F_{1}\left(\begin{matrix} 1 - p, - p - \frac{3}{2} \\ - p - \frac{1}{2} \end{matrix}\middle| {\frac{d^{2}}{e^{2} x^{2}}} \right)}}{6 e^{4} p \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) + 6 e^{4} \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right)} - \frac{3 e^{3} e^{2 p} p x^{3} x^{2 p} e^{i \pi p} \Gamma\left(p\right) \Gamma\left(- p - \frac{3}{2}\right) {{}_{2}F_{1}\left(\begin{matrix} 1 - p, - p - \frac{3}{2} \\ - p - \frac{1}{2} \end{matrix}\middle| {\frac{d^{2}}{e^{2} x^{2}}} \right)}}{6 e^{4} p \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) + 6 e^{4} \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right)} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\\frac{3 \cdot 0^{p} d^{3} d^{2 p} p \log{\left(\frac{d^{2}}{e^{2} x^{2}} \right)} \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right)}{6 e^{4} p \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) + 6 e^{4} \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right)} - \frac{3 \cdot 0^{p} d^{3} d^{2 p} p \log{\left(- \frac{d^{2}}{e^{2} x^{2}} + 1 \right)} \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right)}{6 e^{4} p \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) + 6 e^{4} \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right)} - \frac{6 \cdot 0^{p} d^{3} d^{2 p} p \operatorname{atanh}{\left(\frac{d}{e x} \right)} \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right)}{6 e^{4} p \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) + 6 e^{4} \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right)} + \frac{3 \cdot 0^{p} d^{3} d^{2 p} \log{\left(\frac{d^{2}}{e^{2} x^{2}} \right)} \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right)}{6 e^{4} p \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) + 6 e^{4} \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right)} - \frac{3 \cdot 0^{p} d^{3} d^{2 p} \log{\left(- \frac{d^{2}}{e^{2} x^{2}} + 1 \right)} \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right)}{6 e^{4} p \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) + 6 e^{4} \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right)} - \frac{6 \cdot 0^{p} d^{3} d^{2 p} \operatorname{atanh}{\left(\frac{d}{e x} \right)} \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right)}{6 e^{4} p \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) + 6 e^{4} \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right)} + \frac{6 \cdot 0^{p} d^{2} d^{2 p} e p x \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right)}{6 e^{4} p \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) + 6 e^{4} \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right)} + \frac{6 \cdot 0^{p} d^{2} d^{2 p} e x \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right)}{6 e^{4} p \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) + 6 e^{4} \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right)} - \frac{3 \cdot 0^{p} d d^{2 p} e^{2} p x^{2} \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right)}{6 e^{4} p \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) + 6 e^{4} \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right)} - \frac{3 \cdot 0^{p} d d^{2 p} e^{2} x^{2} \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right)}{6 e^{4} p \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) + 6 e^{4} \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right)} + \frac{2 \cdot 0^{p} d^{2 p} e^{3} p x^{3} \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right)}{6 e^{4} p \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) + 6 e^{4} \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right)} + \frac{2 \cdot 0^{p} d^{2 p} e^{3} x^{3} \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right)}{6 e^{4} p \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) + 6 e^{4} \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right)} - \frac{3 d^{3} d^{2 p} \left(1 - \frac{e^{2} x^{2}}{d^{2}}\right)^{p} \Gamma\left(p\right) \Gamma\left(- p - \frac{1}{2}\right)}{6 e^{4} p \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) + 6 e^{4} \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right)} - \frac{3 d d^{2 p} e^{2} p x^{2} \left(1 - \frac{e^{2} x^{2}}{d^{2}}\right)^{p} \Gamma\left(p\right) \Gamma\left(- p - \frac{1}{2}\right)}{6 e^{4} p \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) + 6 e^{4} \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right)} - \frac{3 e^{3} e^{2 p} p^{2} x^{3} x^{2 p} e^{i \pi p} \Gamma\left(p\right) \Gamma\left(- p - \frac{3}{2}\right) {{}_{2}F_{1}\left(\begin{matrix} 1 - p, - p - \frac{3}{2} \\ - p - \frac{1}{2} \end{matrix}\middle| {\frac{d^{2}}{e^{2} x^{2}}} \right)}}{6 e^{4} p \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) + 6 e^{4} \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right)} - \frac{3 e^{3} e^{2 p} p x^{3} x^{2 p} e^{i \pi p} \Gamma\left(p\right) \Gamma\left(- p - \frac{3}{2}\right) {{}_{2}F_{1}\left(\begin{matrix} 1 - p, - p - \frac{3}{2} \\ - p - \frac{1}{2} \end{matrix}\middle| {\frac{d^{2}}{e^{2} x^{2}}} \right)}}{6 e^{4} p \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right) + 6 e^{4} \Gamma\left(- p - \frac{1}{2}\right) \Gamma\left(p + 1\right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((3*0**p*d**3*d**(2*p)*p*log(d**2/(e**2*x**2))*gamma(-p - 1/2)*gamma(p + 1)/(6*e**4*p*gamma(-p - 1/2)*gamma(p + 1) + 6*e**4*gamma(-p - 1/2)*gamma(p + 1)) - 3*0**p*d**3*d**(2*p)*p*log(d**2/(e**2*x**2) - 1)*gamma(-p - 1/2)*gamma(p + 1)/(6*e**4*p*gamma(-p - 1/2)*gamma(p + 1) + 6*e**4*gamma(-p - 1/2)*gamma(p + 1)) - 6*0**p*d**3*d**(2*p)*p*acoth(d/(e*x))*gamma(-p - 1/2)*gamma(p + 1)/(6*e**4*p*gamma(-p - 1/2)*gamma(p + 1) + 6*e**4*gamma(-p - 1/2)*gamma(p + 1)) + 3*0**p*d**3*d**(2*p)*log(d**2/(e**2*x**2))*gamma(-p - 1/2)*gamma(p + 1)/(6*e**4*p*gamma(-p - 1/2)*gamma(p + 1) + 6*e**4*gamma(-p - 1/2)*gamma(p + 1)) - 3*0**p*d**3*d**(2*p)*log(d**2/(e**2*x**2) - 1)*gamma(-p - 1/2)*gamma(p + 1)/(6*e**4*p*gamma(-p - 1/2)*gamma(p + 1) + 6*e**4*gamma(-p - 1/2)*gamma(p + 1)) - 6*0**p*d**3*d**(2*p)*acoth(d/(e*x))*gamma(-p - 1/2)*gamma(p + 1)/(6*e**4*p*gamma(-p - 1/2)*gamma(p + 1) + 6*e**4*gamma(-p - 1/2)*gamma(p + 1)) + 6*0**p*d**2*d**(2*p)*e*p*x*gamma(-p - 1/2)*gamma(p + 1)/(6*e**4*p*gamma(-p - 1/2)*gamma(p + 1) + 6*e**4*gamma(-p - 1/2)*gamma(p + 1)) + 6*0**p*d**2*d**(2*p)*e*x*gamma(-p - 1/2)*gamma(p + 1)/(6*e**4*p*gamma(-p - 1/2)*gamma(p + 1) + 6*e**4*gamma(-p - 1/2)*gamma(p + 1)) - 3*0**p*d*d**(2*p)*e**2*p*x**2*gamma(-p - 1/2)*gamma(p + 1)/(6*e**4*p*gamma(-p - 1/2)*gamma(p + 1) + 6*e**4*gamma(-p - 1/2)*gamma(p + 1)) - 3*0**p*d*d**(2*p)*e**2*x**2*gamma(-p - 1/2)*gamma(p + 1)/(6*e**4*p*gamma(-p - 1/2)*gamma(p + 1) + 6*e**4*gamma(-p - 1/2)*gamma(p + 1)) + 2*0**p*d**(2*p)*e**3*p*x**3*gamma(-p - 1/2)*gamma(p + 1)/(6*e**4*p*gamma(-p - 1/2)*gamma(p + 1) + 6*e**4*gamma(-p - 1/2)*gamma(p + 1)) + 2*0**p*d**(2*p)*e**3*x**3*gamma(-p - 1/2)*gamma(p + 1)/(6*e**4*p*gamma(-p - 1/2)*gamma(p + 1) + 6*e**4*gamma(-p - 1/2)*gamma(p + 1)) - 3*d**3*d**(2*p)*(-1 + e**2*x**2/d**2)**p*exp(I*pi*p)*gamma(p)*gamma(-p - 1/2)/(6*e**4*p*gamma(-p - 1/2)*gamma(p + 1) + 6*e**4*gamma(-p - 1/2)*gamma(p + 1)) - 3*d*d**(2*p)*e**2*p*x**2*(-1 + e**2*x**2/d**2)**p*exp(I*pi*p)*gamma(p)*gamma(-p - 1/2)/(6*e**4*p*gamma(-p - 1/2)*gamma(p + 1) + 6*e**4*gamma(-p - 1/2)*gamma(p + 1)) - 3*e**3*e**(2*p)*p**2*x**3*x**(2*p)*exp(I*pi*p)*gamma(p)*gamma(-p - 3/2)*hyper((1 - p, -p - 3/2), (-p - 1/2,), d**2/(e**2*x**2))/(6*e**4*p*gamma(-p - 1/2)*gamma(p + 1) + 6*e**4*gamma(-p - 1/2)*gamma(p + 1)) - 3*e**3*e**(2*p)*p*x**3*x**(2*p)*exp(I*pi*p)*gamma(p)*gamma(-p - 3/2)*hyper((1 - p, -p - 3/2), (-p - 1/2,), d**2/(e**2*x**2))/(6*e**4*p*gamma(-p - 1/2)*gamma(p + 1) + 6*e**4*gamma(-p - 1/2)*gamma(p + 1)), (Abs(e**2*x**2/d**2) > 1) & (Abs(d**2/(e**2*x**2)) > 1)), (3*0**p*d**3*d**(2*p)*p*log(d**2/(e**2*x**2))*gamma(-p - 1/2)*gamma(p + 1)/(6*e**4*p*gamma(-p - 1/2)*gamma(p + 1) + 6*e**4*gamma(-p - 1/2)*gamma(p + 1)) - 3*0**p*d**3*d**(2*p)*p*log(-d**2/(e**2*x**2) + 1)*gamma(-p - 1/2)*gamma(p + 1)/(6*e**4*p*gamma(-p - 1/2)*gamma(p + 1) + 6*e**4*gamma(-p - 1/2)*gamma(p + 1)) - 6*0**p*d**3*d**(2*p)*p*atanh(d/(e*x))*gamma(-p - 1/2)*gamma(p + 1)/(6*e**4*p*gamma(-p - 1/2)*gamma(p + 1) + 6*e**4*gamma(-p - 1/2)*gamma(p + 1)) + 3*0**p*d**3*d**(2*p)*log(d**2/(e**2*x**2))*gamma(-p - 1/2)*gamma(p + 1)/(6*e**4*p*gamma(-p - 1/2)*gamma(p + 1) + 6*e**4*gamma(-p - 1/2)*gamma(p + 1)) - 3*0**p*d**3*d**(2*p)*log(-d**2/(e**2*x**2) + 1)*gamma(-p - 1/2)*gamma(p + 1)/(6*e**4*p*gamma(-p - 1/2)*gamma(p + 1) + 6*e**4*gamma(-p - 1/2)*gamma(p + 1)) - 6*0**p*d**3*d**(2*p)*atanh(d/(e*x))*gamma(-p - 1/2)*gamma(p + 1)/(6*e**4*p*gamma(-p - 1/2)*gamma(p + 1) + 6*e**4*gamma(-p - 1/2)*gamma(p + 1)) + 6*0**p*d**2*d**(2*p)*e*p*x*gamma(-p - 1/2)*gamma(p + 1)/(6*e**4*p*gamma(-p - 1/2)*gamma(p + 1) + 6*e**4*gamma(-p - 1/2)*gamma(p + 1)) + 6*0**p*d**2*d**(2*p)*e*x*gamma(-p - 1/2)*gamma(p + 1)/(6*e**4*p*gamma(-p - 1/2)*gamma(p + 1) + 6*e**4*gamma(-p - 1/2)*gamma(p + 1)) - 3*0**p*d*d**(2*p)*e**2*p*x**2*gamma(-p - 1/2)*gamma(p + 1)/(6*e**4*p*gamma(-p - 1/2)*gamma(p + 1) + 6*e**4*gamma(-p - 1/2)*gamma(p + 1)) - 3*0**p*d*d**(2*p)*e**2*x**2*gamma(-p - 1/2)*gamma(p + 1)/(6*e**4*p*gamma(-p - 1/2)*gamma(p + 1) + 6*e**4*gamma(-p - 1/2)*gamma(p + 1)) + 2*0**p*d**(2*p)*e**3*p*x**3*gamma(-p - 1/2)*gamma(p + 1)/(6*e**4*p*gamma(-p - 1/2)*gamma(p + 1) + 6*e**4*gamma(-p - 1/2)*gamma(p + 1)) + 2*0**p*d**(2*p)*e**3*x**3*gamma(-p - 1/2)*gamma(p + 1)/(6*e**4*p*gamma(-p - 1/2)*gamma(p + 1) + 6*e**4*gamma(-p - 1/2)*gamma(p + 1)) - 3*d**3*d**(2*p)*(-1 + e**2*x**2/d**2)**p*exp(I*pi*p)*gamma(p)*gamma(-p - 1/2)/(6*e**4*p*gamma(-p - 1/2)*gamma(p + 1) + 6*e**4*gamma(-p - 1/2)*gamma(p + 1)) - 3*d*d**(2*p)*e**2*p*x**2*(-1 + e**2*x**2/d**2)**p*exp(I*pi*p)*gamma(p)*gamma(-p - 1/2)/(6*e**4*p*gamma(-p - 1/2)*gamma(p + 1) + 6*e**4*gamma(-p - 1/2)*gamma(p + 1)) - 3*e**3*e**(2*p)*p**2*x**3*x**(2*p)*exp(I*pi*p)*gamma(p)*gamma(-p - 3/2)*hyper((1 - p, -p - 3/2), (-p - 1/2,), d**2/(e**2*x**2))/(6*e**4*p*gamma(-p - 1/2)*gamma(p + 1) + 6*e**4*gamma(-p - 1/2)*gamma(p + 1)) - 3*e**3*e**(2*p)*p*x**3*x**(2*p)*exp(I*pi*p)*gamma(p)*gamma(-p - 3/2)*hyper((1 - p, -p - 3/2), (-p - 1/2,), d**2/(e**2*x**2))/(6*e**4*p*gamma(-p - 1/2)*gamma(p + 1) + 6*e**4*gamma(-p - 1/2)*gamma(p + 1)), Abs(e**2*x**2/d**2) > 1), (3*0**p*d**3*d**(2*p)*p*log(d**2/(e**2*x**2))*gamma(-p - 1/2)*gamma(p + 1)/(6*e**4*p*gamma(-p - 1/2)*gamma(p + 1) + 6*e**4*gamma(-p - 1/2)*gamma(p + 1)) - 3*0**p*d**3*d**(2*p)*p*log(d**2/(e**2*x**2) - 1)*gamma(-p - 1/2)*gamma(p + 1)/(6*e**4*p*gamma(-p - 1/2)*gamma(p + 1) + 6*e**4*gamma(-p - 1/2)*gamma(p + 1)) - 6*0**p*d**3*d**(2*p)*p*acoth(d/(e*x))*gamma(-p - 1/2)*gamma(p + 1)/(6*e**4*p*gamma(-p - 1/2)*gamma(p + 1) + 6*e**4*gamma(-p - 1/2)*gamma(p + 1)) + 3*0**p*d**3*d**(2*p)*log(d**2/(e**2*x**2))*gamma(-p - 1/2)*gamma(p + 1)/(6*e**4*p*gamma(-p - 1/2)*gamma(p + 1) + 6*e**4*gamma(-p - 1/2)*gamma(p + 1)) - 3*0**p*d**3*d**(2*p)*log(d**2/(e**2*x**2) - 1)*gamma(-p - 1/2)*gamma(p + 1)/(6*e**4*p*gamma(-p - 1/2)*gamma(p + 1) + 6*e**4*gamma(-p - 1/2)*gamma(p + 1)) - 6*0**p*d**3*d**(2*p)*acoth(d/(e*x))*gamma(-p - 1/2)*gamma(p + 1)/(6*e**4*p*gamma(-p - 1/2)*gamma(p + 1) + 6*e**4*gamma(-p - 1/2)*gamma(p + 1)) + 6*0**p*d**2*d**(2*p)*e*p*x*gamma(-p - 1/2)*gamma(p + 1)/(6*e**4*p*gamma(-p - 1/2)*gamma(p + 1) + 6*e**4*gamma(-p - 1/2)*gamma(p + 1)) + 6*0**p*d**2*d**(2*p)*e*x*gamma(-p - 1/2)*gamma(p + 1)/(6*e**4*p*gamma(-p - 1/2)*gamma(p + 1) + 6*e**4*gamma(-p - 1/2)*gamma(p + 1)) - 3*0**p*d*d**(2*p)*e**2*p*x**2*gamma(-p - 1/2)*gamma(p + 1)/(6*e**4*p*gamma(-p - 1/2)*gamma(p + 1) + 6*e**4*gamma(-p - 1/2)*gamma(p + 1)) - 3*0**p*d*d**(2*p)*e**2*x**2*gamma(-p - 1/2)*gamma(p + 1)/(6*e**4*p*gamma(-p - 1/2)*gamma(p + 1) + 6*e**4*gamma(-p - 1/2)*gamma(p + 1)) + 2*0**p*d**(2*p)*e**3*p*x**3*gamma(-p - 1/2)*gamma(p + 1)/(6*e**4*p*gamma(-p - 1/2)*gamma(p + 1) + 6*e**4*gamma(-p - 1/2)*gamma(p + 1)) + 2*0**p*d**(2*p)*e**3*x**3*gamma(-p - 1/2)*gamma(p + 1)/(6*e**4*p*gamma(-p - 1/2)*gamma(p + 1) + 6*e**4*gamma(-p - 1/2)*gamma(p + 1)) - 3*d**3*d**(2*p)*(1 - e**2*x**2/d**2)**p*gamma(p)*gamma(-p - 1/2)/(6*e**4*p*gamma(-p - 1/2)*gamma(p + 1) + 6*e**4*gamma(-p - 1/2)*gamma(p + 1)) - 3*d*d**(2*p)*e**2*p*x**2*(1 - e**2*x**2/d**2)**p*gamma(p)*gamma(-p - 1/2)/(6*e**4*p*gamma(-p - 1/2)*gamma(p + 1) + 6*e**4*gamma(-p - 1/2)*gamma(p + 1)) - 3*e**3*e**(2*p)*p**2*x**3*x**(2*p)*exp(I*pi*p)*gamma(p)*gamma(-p - 3/2)*hyper((1 - p, -p - 3/2), (-p - 1/2,), d**2/(e**2*x**2))/(6*e**4*p*gamma(-p - 1/2)*gamma(p + 1) + 6*e**4*gamma(-p - 1/2)*gamma(p + 1)) - 3*e**3*e**(2*p)*p*x**3*x**(2*p)*exp(I*pi*p)*gamma(p)*gamma(-p - 3/2)*hyper((1 - p, -p - 3/2), (-p - 1/2,), d**2/(e**2*x**2))/(6*e**4*p*gamma(-p - 1/2)*gamma(p + 1) + 6*e**4*gamma(-p - 1/2)*gamma(p + 1)), Abs(d**2/(e**2*x**2)) > 1), (3*0**p*d**3*d**(2*p)*p*log(d**2/(e**2*x**2))*gamma(-p - 1/2)*gamma(p + 1)/(6*e**4*p*gamma(-p - 1/2)*gamma(p + 1) + 6*e**4*gamma(-p - 1/2)*gamma(p + 1)) - 3*0**p*d**3*d**(2*p)*p*log(-d**2/(e**2*x**2) + 1)*gamma(-p - 1/2)*gamma(p + 1)/(6*e**4*p*gamma(-p - 1/2)*gamma(p + 1) + 6*e**4*gamma(-p - 1/2)*gamma(p + 1)) - 6*0**p*d**3*d**(2*p)*p*atanh(d/(e*x))*gamma(-p - 1/2)*gamma(p + 1)/(6*e**4*p*gamma(-p - 1/2)*gamma(p + 1) + 6*e**4*gamma(-p - 1/2)*gamma(p + 1)) + 3*0**p*d**3*d**(2*p)*log(d**2/(e**2*x**2))*gamma(-p - 1/2)*gamma(p + 1)/(6*e**4*p*gamma(-p - 1/2)*gamma(p + 1) + 6*e**4*gamma(-p - 1/2)*gamma(p + 1)) - 3*0**p*d**3*d**(2*p)*log(-d**2/(e**2*x**2) + 1)*gamma(-p - 1/2)*gamma(p + 1)/(6*e**4*p*gamma(-p - 1/2)*gamma(p + 1) + 6*e**4*gamma(-p - 1/2)*gamma(p + 1)) - 6*0**p*d**3*d**(2*p)*atanh(d/(e*x))*gamma(-p - 1/2)*gamma(p + 1)/(6*e**4*p*gamma(-p - 1/2)*gamma(p + 1) + 6*e**4*gamma(-p - 1/2)*gamma(p + 1)) + 6*0**p*d**2*d**(2*p)*e*p*x*gamma(-p - 1/2)*gamma(p + 1)/(6*e**4*p*gamma(-p - 1/2)*gamma(p + 1) + 6*e**4*gamma(-p - 1/2)*gamma(p + 1)) + 6*0**p*d**2*d**(2*p)*e*x*gamma(-p - 1/2)*gamma(p + 1)/(6*e**4*p*gamma(-p - 1/2)*gamma(p + 1) + 6*e**4*gamma(-p - 1/2)*gamma(p + 1)) - 3*0**p*d*d**(2*p)*e**2*p*x**2*gamma(-p - 1/2)*gamma(p + 1)/(6*e**4*p*gamma(-p - 1/2)*gamma(p + 1) + 6*e**4*gamma(-p - 1/2)*gamma(p + 1)) - 3*0**p*d*d**(2*p)*e**2*x**2*gamma(-p - 1/2)*gamma(p + 1)/(6*e**4*p*gamma(-p - 1/2)*gamma(p + 1) + 6*e**4*gamma(-p - 1/2)*gamma(p + 1)) + 2*0**p*d**(2*p)*e**3*p*x**3*gamma(-p - 1/2)*gamma(p + 1)/(6*e**4*p*gamma(-p - 1/2)*gamma(p + 1) + 6*e**4*gamma(-p - 1/2)*gamma(p + 1)) + 2*0**p*d**(2*p)*e**3*x**3*gamma(-p - 1/2)*gamma(p + 1)/(6*e**4*p*gamma(-p - 1/2)*gamma(p + 1) + 6*e**4*gamma(-p - 1/2)*gamma(p + 1)) - 3*d**3*d**(2*p)*(1 - e**2*x**2/d**2)**p*gamma(p)*gamma(-p - 1/2)/(6*e**4*p*gamma(-p - 1/2)*gamma(p + 1) + 6*e**4*gamma(-p - 1/2)*gamma(p + 1)) - 3*d*d**(2*p)*e**2*p*x**2*(1 - e**2*x**2/d**2)**p*gamma(p)*gamma(-p - 1/2)/(6*e**4*p*gamma(-p - 1/2)*gamma(p + 1) + 6*e**4*gamma(-p - 1/2)*gamma(p + 1)) - 3*e**3*e**(2*p)*p**2*x**3*x**(2*p)*exp(I*pi*p)*gamma(p)*gamma(-p - 3/2)*hyper((1 - p, -p - 3/2), (-p - 1/2,), d**2/(e**2*x**2))/(6*e**4*p*gamma(-p - 1/2)*gamma(p + 1) + 6*e**4*gamma(-p - 1/2)*gamma(p + 1)) - 3*e**3*e**(2*p)*p*x**3*x**(2*p)*exp(I*pi*p)*gamma(p)*gamma(-p - 3/2)*hyper((1 - p, -p - 3/2), (-p - 1/2,), d**2/(e**2*x**2))/(6*e**4*p*gamma(-p - 1/2)*gamma(p + 1) + 6*e**4*gamma(-p - 1/2)*gamma(p + 1)), True))","C",0
269,1,4124,0,8.391598," ","integrate(x**2*(-e**2*x**2+d**2)**p/(e*x+d),x)","\begin{cases} - \frac{0^{p} d^{2} d^{2 p} p \log{\left(\frac{d^{2}}{e^{2} x^{2}} \right)} \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right)}{2 e^{3} p \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right) + 2 e^{3} \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right)} + \frac{0^{p} d^{2} d^{2 p} p \log{\left(\frac{d^{2}}{e^{2} x^{2}} - 1 \right)} \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right)}{2 e^{3} p \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right) + 2 e^{3} \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right)} + \frac{2 \cdot 0^{p} d^{2} d^{2 p} p \operatorname{acoth}{\left(\frac{d}{e x} \right)} \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right)}{2 e^{3} p \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right) + 2 e^{3} \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right)} - \frac{0^{p} d^{2} d^{2 p} \log{\left(\frac{d^{2}}{e^{2} x^{2}} \right)} \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right)}{2 e^{3} p \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right) + 2 e^{3} \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right)} + \frac{0^{p} d^{2} d^{2 p} \log{\left(\frac{d^{2}}{e^{2} x^{2}} - 1 \right)} \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right)}{2 e^{3} p \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right) + 2 e^{3} \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right)} + \frac{2 \cdot 0^{p} d^{2} d^{2 p} \operatorname{acoth}{\left(\frac{d}{e x} \right)} \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right)}{2 e^{3} p \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right) + 2 e^{3} \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right)} - \frac{2 \cdot 0^{p} d d^{2 p} e p x \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right)}{2 e^{3} p \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right) + 2 e^{3} \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right)} - \frac{2 \cdot 0^{p} d d^{2 p} e x \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right)}{2 e^{3} p \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right) + 2 e^{3} \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right)} + \frac{0^{p} d^{2 p} e^{2} p x^{2} \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right)}{2 e^{3} p \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right) + 2 e^{3} \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right)} + \frac{0^{p} d^{2 p} e^{2} x^{2} \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right)}{2 e^{3} p \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right) + 2 e^{3} \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right)} + \frac{d^{2} d^{2 p} \left(-1 + \frac{e^{2} x^{2}}{d^{2}}\right)^{p} e^{i \pi p} \Gamma\left(p\right) \Gamma\left(\frac{1}{2} - p\right)}{2 e^{3} p \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right) + 2 e^{3} \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right)} + \frac{d e e^{2 p} p^{2} x x^{2 p} e^{i \pi p} \Gamma\left(p\right) \Gamma\left(- p - \frac{1}{2}\right) {{}_{2}F_{1}\left(\begin{matrix} 1 - p, - p - \frac{1}{2} \\ \frac{1}{2} - p \end{matrix}\middle| {\frac{d^{2}}{e^{2} x^{2}}} \right)}}{2 e^{3} p \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right) + 2 e^{3} \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right)} + \frac{d e e^{2 p} p x x^{2 p} e^{i \pi p} \Gamma\left(p\right) \Gamma\left(- p - \frac{1}{2}\right) {{}_{2}F_{1}\left(\begin{matrix} 1 - p, - p - \frac{1}{2} \\ \frac{1}{2} - p \end{matrix}\middle| {\frac{d^{2}}{e^{2} x^{2}}} \right)}}{2 e^{3} p \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right) + 2 e^{3} \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right)} + \frac{d^{2 p} e^{2} p x^{2} \left(-1 + \frac{e^{2} x^{2}}{d^{2}}\right)^{p} e^{i \pi p} \Gamma\left(p\right) \Gamma\left(\frac{1}{2} - p\right)}{2 e^{3} p \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right) + 2 e^{3} \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right)} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \wedge \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\- \frac{0^{p} d^{2} d^{2 p} p \log{\left(\frac{d^{2}}{e^{2} x^{2}} \right)} \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right)}{2 e^{3} p \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right) + 2 e^{3} \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right)} + \frac{0^{p} d^{2} d^{2 p} p \log{\left(\frac{d^{2}}{e^{2} x^{2}} - 1 \right)} \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right)}{2 e^{3} p \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right) + 2 e^{3} \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right)} + \frac{2 \cdot 0^{p} d^{2} d^{2 p} p \operatorname{acoth}{\left(\frac{d}{e x} \right)} \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right)}{2 e^{3} p \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right) + 2 e^{3} \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right)} - \frac{0^{p} d^{2} d^{2 p} \log{\left(\frac{d^{2}}{e^{2} x^{2}} \right)} \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right)}{2 e^{3} p \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right) + 2 e^{3} \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right)} + \frac{0^{p} d^{2} d^{2 p} \log{\left(\frac{d^{2}}{e^{2} x^{2}} - 1 \right)} \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right)}{2 e^{3} p \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right) + 2 e^{3} \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right)} + \frac{2 \cdot 0^{p} d^{2} d^{2 p} \operatorname{acoth}{\left(\frac{d}{e x} \right)} \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right)}{2 e^{3} p \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right) + 2 e^{3} \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right)} - \frac{2 \cdot 0^{p} d d^{2 p} e p x \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right)}{2 e^{3} p \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right) + 2 e^{3} \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right)} - \frac{2 \cdot 0^{p} d d^{2 p} e x \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right)}{2 e^{3} p \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right) + 2 e^{3} \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right)} + \frac{0^{p} d^{2 p} e^{2} p x^{2} \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right)}{2 e^{3} p \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right) + 2 e^{3} \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right)} + \frac{0^{p} d^{2 p} e^{2} x^{2} \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right)}{2 e^{3} p \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right) + 2 e^{3} \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right)} + \frac{d^{2} d^{2 p} \left(1 - \frac{e^{2} x^{2}}{d^{2}}\right)^{p} \Gamma\left(p\right) \Gamma\left(\frac{1}{2} - p\right)}{2 e^{3} p \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right) + 2 e^{3} \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right)} + \frac{d e e^{2 p} p^{2} x x^{2 p} e^{i \pi p} \Gamma\left(p\right) \Gamma\left(- p - \frac{1}{2}\right) {{}_{2}F_{1}\left(\begin{matrix} 1 - p, - p - \frac{1}{2} \\ \frac{1}{2} - p \end{matrix}\middle| {\frac{d^{2}}{e^{2} x^{2}}} \right)}}{2 e^{3} p \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right) + 2 e^{3} \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right)} + \frac{d e e^{2 p} p x x^{2 p} e^{i \pi p} \Gamma\left(p\right) \Gamma\left(- p - \frac{1}{2}\right) {{}_{2}F_{1}\left(\begin{matrix} 1 - p, - p - \frac{1}{2} \\ \frac{1}{2} - p \end{matrix}\middle| {\frac{d^{2}}{e^{2} x^{2}}} \right)}}{2 e^{3} p \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right) + 2 e^{3} \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right)} + \frac{d^{2 p} e^{2} p x^{2} \left(1 - \frac{e^{2} x^{2}}{d^{2}}\right)^{p} \Gamma\left(p\right) \Gamma\left(\frac{1}{2} - p\right)}{2 e^{3} p \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right) + 2 e^{3} \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right)} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\- \frac{0^{p} d^{2} d^{2 p} p \log{\left(\frac{d^{2}}{e^{2} x^{2}} \right)} \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right)}{2 e^{3} p \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right) + 2 e^{3} \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right)} + \frac{0^{p} d^{2} d^{2 p} p \log{\left(- \frac{d^{2}}{e^{2} x^{2}} + 1 \right)} \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right)}{2 e^{3} p \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right) + 2 e^{3} \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right)} + \frac{2 \cdot 0^{p} d^{2} d^{2 p} p \operatorname{atanh}{\left(\frac{d}{e x} \right)} \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right)}{2 e^{3} p \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right) + 2 e^{3} \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right)} - \frac{0^{p} d^{2} d^{2 p} \log{\left(\frac{d^{2}}{e^{2} x^{2}} \right)} \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right)}{2 e^{3} p \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right) + 2 e^{3} \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right)} + \frac{0^{p} d^{2} d^{2 p} \log{\left(- \frac{d^{2}}{e^{2} x^{2}} + 1 \right)} \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right)}{2 e^{3} p \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right) + 2 e^{3} \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right)} + \frac{2 \cdot 0^{p} d^{2} d^{2 p} \operatorname{atanh}{\left(\frac{d}{e x} \right)} \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right)}{2 e^{3} p \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right) + 2 e^{3} \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right)} - \frac{2 \cdot 0^{p} d d^{2 p} e p x \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right)}{2 e^{3} p \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right) + 2 e^{3} \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right)} - \frac{2 \cdot 0^{p} d d^{2 p} e x \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right)}{2 e^{3} p \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right) + 2 e^{3} \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right)} + \frac{0^{p} d^{2 p} e^{2} p x^{2} \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right)}{2 e^{3} p \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right) + 2 e^{3} \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right)} + \frac{0^{p} d^{2 p} e^{2} x^{2} \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right)}{2 e^{3} p \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right) + 2 e^{3} \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right)} + \frac{d^{2} d^{2 p} \left(-1 + \frac{e^{2} x^{2}}{d^{2}}\right)^{p} e^{i \pi p} \Gamma\left(p\right) \Gamma\left(\frac{1}{2} - p\right)}{2 e^{3} p \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right) + 2 e^{3} \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right)} + \frac{d e e^{2 p} p^{2} x x^{2 p} e^{i \pi p} \Gamma\left(p\right) \Gamma\left(- p - \frac{1}{2}\right) {{}_{2}F_{1}\left(\begin{matrix} 1 - p, - p - \frac{1}{2} \\ \frac{1}{2} - p \end{matrix}\middle| {\frac{d^{2}}{e^{2} x^{2}}} \right)}}{2 e^{3} p \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right) + 2 e^{3} \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right)} + \frac{d e e^{2 p} p x x^{2 p} e^{i \pi p} \Gamma\left(p\right) \Gamma\left(- p - \frac{1}{2}\right) {{}_{2}F_{1}\left(\begin{matrix} 1 - p, - p - \frac{1}{2} \\ \frac{1}{2} - p \end{matrix}\middle| {\frac{d^{2}}{e^{2} x^{2}}} \right)}}{2 e^{3} p \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right) + 2 e^{3} \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right)} + \frac{d^{2 p} e^{2} p x^{2} \left(-1 + \frac{e^{2} x^{2}}{d^{2}}\right)^{p} e^{i \pi p} \Gamma\left(p\right) \Gamma\left(\frac{1}{2} - p\right)}{2 e^{3} p \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right) + 2 e^{3} \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right)} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\- \frac{0^{p} d^{2} d^{2 p} p \log{\left(\frac{d^{2}}{e^{2} x^{2}} \right)} \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right)}{2 e^{3} p \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right) + 2 e^{3} \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right)} + \frac{0^{p} d^{2} d^{2 p} p \log{\left(- \frac{d^{2}}{e^{2} x^{2}} + 1 \right)} \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right)}{2 e^{3} p \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right) + 2 e^{3} \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right)} + \frac{2 \cdot 0^{p} d^{2} d^{2 p} p \operatorname{atanh}{\left(\frac{d}{e x} \right)} \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right)}{2 e^{3} p \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right) + 2 e^{3} \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right)} - \frac{0^{p} d^{2} d^{2 p} \log{\left(\frac{d^{2}}{e^{2} x^{2}} \right)} \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right)}{2 e^{3} p \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right) + 2 e^{3} \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right)} + \frac{0^{p} d^{2} d^{2 p} \log{\left(- \frac{d^{2}}{e^{2} x^{2}} + 1 \right)} \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right)}{2 e^{3} p \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right) + 2 e^{3} \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right)} + \frac{2 \cdot 0^{p} d^{2} d^{2 p} \operatorname{atanh}{\left(\frac{d}{e x} \right)} \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right)}{2 e^{3} p \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right) + 2 e^{3} \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right)} - \frac{2 \cdot 0^{p} d d^{2 p} e p x \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right)}{2 e^{3} p \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right) + 2 e^{3} \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right)} - \frac{2 \cdot 0^{p} d d^{2 p} e x \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right)}{2 e^{3} p \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right) + 2 e^{3} \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right)} + \frac{0^{p} d^{2 p} e^{2} p x^{2} \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right)}{2 e^{3} p \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right) + 2 e^{3} \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right)} + \frac{0^{p} d^{2 p} e^{2} x^{2} \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right)}{2 e^{3} p \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right) + 2 e^{3} \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right)} + \frac{d^{2} d^{2 p} \left(1 - \frac{e^{2} x^{2}}{d^{2}}\right)^{p} \Gamma\left(p\right) \Gamma\left(\frac{1}{2} - p\right)}{2 e^{3} p \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right) + 2 e^{3} \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right)} + \frac{d e e^{2 p} p^{2} x x^{2 p} e^{i \pi p} \Gamma\left(p\right) \Gamma\left(- p - \frac{1}{2}\right) {{}_{2}F_{1}\left(\begin{matrix} 1 - p, - p - \frac{1}{2} \\ \frac{1}{2} - p \end{matrix}\middle| {\frac{d^{2}}{e^{2} x^{2}}} \right)}}{2 e^{3} p \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right) + 2 e^{3} \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right)} + \frac{d e e^{2 p} p x x^{2 p} e^{i \pi p} \Gamma\left(p\right) \Gamma\left(- p - \frac{1}{2}\right) {{}_{2}F_{1}\left(\begin{matrix} 1 - p, - p - \frac{1}{2} \\ \frac{1}{2} - p \end{matrix}\middle| {\frac{d^{2}}{e^{2} x^{2}}} \right)}}{2 e^{3} p \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right) + 2 e^{3} \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right)} + \frac{d^{2 p} e^{2} p x^{2} \left(1 - \frac{e^{2} x^{2}}{d^{2}}\right)^{p} \Gamma\left(p\right) \Gamma\left(\frac{1}{2} - p\right)}{2 e^{3} p \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right) + 2 e^{3} \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-0**p*d**2*d**(2*p)*p*log(d**2/(e**2*x**2))*gamma(1/2 - p)*gamma(p + 1)/(2*e**3*p*gamma(1/2 - p)*gamma(p + 1) + 2*e**3*gamma(1/2 - p)*gamma(p + 1)) + 0**p*d**2*d**(2*p)*p*log(d**2/(e**2*x**2) - 1)*gamma(1/2 - p)*gamma(p + 1)/(2*e**3*p*gamma(1/2 - p)*gamma(p + 1) + 2*e**3*gamma(1/2 - p)*gamma(p + 1)) + 2*0**p*d**2*d**(2*p)*p*acoth(d/(e*x))*gamma(1/2 - p)*gamma(p + 1)/(2*e**3*p*gamma(1/2 - p)*gamma(p + 1) + 2*e**3*gamma(1/2 - p)*gamma(p + 1)) - 0**p*d**2*d**(2*p)*log(d**2/(e**2*x**2))*gamma(1/2 - p)*gamma(p + 1)/(2*e**3*p*gamma(1/2 - p)*gamma(p + 1) + 2*e**3*gamma(1/2 - p)*gamma(p + 1)) + 0**p*d**2*d**(2*p)*log(d**2/(e**2*x**2) - 1)*gamma(1/2 - p)*gamma(p + 1)/(2*e**3*p*gamma(1/2 - p)*gamma(p + 1) + 2*e**3*gamma(1/2 - p)*gamma(p + 1)) + 2*0**p*d**2*d**(2*p)*acoth(d/(e*x))*gamma(1/2 - p)*gamma(p + 1)/(2*e**3*p*gamma(1/2 - p)*gamma(p + 1) + 2*e**3*gamma(1/2 - p)*gamma(p + 1)) - 2*0**p*d*d**(2*p)*e*p*x*gamma(1/2 - p)*gamma(p + 1)/(2*e**3*p*gamma(1/2 - p)*gamma(p + 1) + 2*e**3*gamma(1/2 - p)*gamma(p + 1)) - 2*0**p*d*d**(2*p)*e*x*gamma(1/2 - p)*gamma(p + 1)/(2*e**3*p*gamma(1/2 - p)*gamma(p + 1) + 2*e**3*gamma(1/2 - p)*gamma(p + 1)) + 0**p*d**(2*p)*e**2*p*x**2*gamma(1/2 - p)*gamma(p + 1)/(2*e**3*p*gamma(1/2 - p)*gamma(p + 1) + 2*e**3*gamma(1/2 - p)*gamma(p + 1)) + 0**p*d**(2*p)*e**2*x**2*gamma(1/2 - p)*gamma(p + 1)/(2*e**3*p*gamma(1/2 - p)*gamma(p + 1) + 2*e**3*gamma(1/2 - p)*gamma(p + 1)) + d**2*d**(2*p)*(-1 + e**2*x**2/d**2)**p*exp(I*pi*p)*gamma(p)*gamma(1/2 - p)/(2*e**3*p*gamma(1/2 - p)*gamma(p + 1) + 2*e**3*gamma(1/2 - p)*gamma(p + 1)) + d*e*e**(2*p)*p**2*x*x**(2*p)*exp(I*pi*p)*gamma(p)*gamma(-p - 1/2)*hyper((1 - p, -p - 1/2), (1/2 - p,), d**2/(e**2*x**2))/(2*e**3*p*gamma(1/2 - p)*gamma(p + 1) + 2*e**3*gamma(1/2 - p)*gamma(p + 1)) + d*e*e**(2*p)*p*x*x**(2*p)*exp(I*pi*p)*gamma(p)*gamma(-p - 1/2)*hyper((1 - p, -p - 1/2), (1/2 - p,), d**2/(e**2*x**2))/(2*e**3*p*gamma(1/2 - p)*gamma(p + 1) + 2*e**3*gamma(1/2 - p)*gamma(p + 1)) + d**(2*p)*e**2*p*x**2*(-1 + e**2*x**2/d**2)**p*exp(I*pi*p)*gamma(p)*gamma(1/2 - p)/(2*e**3*p*gamma(1/2 - p)*gamma(p + 1) + 2*e**3*gamma(1/2 - p)*gamma(p + 1)), (Abs(e**2*x**2/d**2) > 1) & (Abs(d**2/(e**2*x**2)) > 1)), (-0**p*d**2*d**(2*p)*p*log(d**2/(e**2*x**2))*gamma(1/2 - p)*gamma(p + 1)/(2*e**3*p*gamma(1/2 - p)*gamma(p + 1) + 2*e**3*gamma(1/2 - p)*gamma(p + 1)) + 0**p*d**2*d**(2*p)*p*log(d**2/(e**2*x**2) - 1)*gamma(1/2 - p)*gamma(p + 1)/(2*e**3*p*gamma(1/2 - p)*gamma(p + 1) + 2*e**3*gamma(1/2 - p)*gamma(p + 1)) + 2*0**p*d**2*d**(2*p)*p*acoth(d/(e*x))*gamma(1/2 - p)*gamma(p + 1)/(2*e**3*p*gamma(1/2 - p)*gamma(p + 1) + 2*e**3*gamma(1/2 - p)*gamma(p + 1)) - 0**p*d**2*d**(2*p)*log(d**2/(e**2*x**2))*gamma(1/2 - p)*gamma(p + 1)/(2*e**3*p*gamma(1/2 - p)*gamma(p + 1) + 2*e**3*gamma(1/2 - p)*gamma(p + 1)) + 0**p*d**2*d**(2*p)*log(d**2/(e**2*x**2) - 1)*gamma(1/2 - p)*gamma(p + 1)/(2*e**3*p*gamma(1/2 - p)*gamma(p + 1) + 2*e**3*gamma(1/2 - p)*gamma(p + 1)) + 2*0**p*d**2*d**(2*p)*acoth(d/(e*x))*gamma(1/2 - p)*gamma(p + 1)/(2*e**3*p*gamma(1/2 - p)*gamma(p + 1) + 2*e**3*gamma(1/2 - p)*gamma(p + 1)) - 2*0**p*d*d**(2*p)*e*p*x*gamma(1/2 - p)*gamma(p + 1)/(2*e**3*p*gamma(1/2 - p)*gamma(p + 1) + 2*e**3*gamma(1/2 - p)*gamma(p + 1)) - 2*0**p*d*d**(2*p)*e*x*gamma(1/2 - p)*gamma(p + 1)/(2*e**3*p*gamma(1/2 - p)*gamma(p + 1) + 2*e**3*gamma(1/2 - p)*gamma(p + 1)) + 0**p*d**(2*p)*e**2*p*x**2*gamma(1/2 - p)*gamma(p + 1)/(2*e**3*p*gamma(1/2 - p)*gamma(p + 1) + 2*e**3*gamma(1/2 - p)*gamma(p + 1)) + 0**p*d**(2*p)*e**2*x**2*gamma(1/2 - p)*gamma(p + 1)/(2*e**3*p*gamma(1/2 - p)*gamma(p + 1) + 2*e**3*gamma(1/2 - p)*gamma(p + 1)) + d**2*d**(2*p)*(1 - e**2*x**2/d**2)**p*gamma(p)*gamma(1/2 - p)/(2*e**3*p*gamma(1/2 - p)*gamma(p + 1) + 2*e**3*gamma(1/2 - p)*gamma(p + 1)) + d*e*e**(2*p)*p**2*x*x**(2*p)*exp(I*pi*p)*gamma(p)*gamma(-p - 1/2)*hyper((1 - p, -p - 1/2), (1/2 - p,), d**2/(e**2*x**2))/(2*e**3*p*gamma(1/2 - p)*gamma(p + 1) + 2*e**3*gamma(1/2 - p)*gamma(p + 1)) + d*e*e**(2*p)*p*x*x**(2*p)*exp(I*pi*p)*gamma(p)*gamma(-p - 1/2)*hyper((1 - p, -p - 1/2), (1/2 - p,), d**2/(e**2*x**2))/(2*e**3*p*gamma(1/2 - p)*gamma(p + 1) + 2*e**3*gamma(1/2 - p)*gamma(p + 1)) + d**(2*p)*e**2*p*x**2*(1 - e**2*x**2/d**2)**p*gamma(p)*gamma(1/2 - p)/(2*e**3*p*gamma(1/2 - p)*gamma(p + 1) + 2*e**3*gamma(1/2 - p)*gamma(p + 1)), Abs(d**2/(e**2*x**2)) > 1), (-0**p*d**2*d**(2*p)*p*log(d**2/(e**2*x**2))*gamma(1/2 - p)*gamma(p + 1)/(2*e**3*p*gamma(1/2 - p)*gamma(p + 1) + 2*e**3*gamma(1/2 - p)*gamma(p + 1)) + 0**p*d**2*d**(2*p)*p*log(-d**2/(e**2*x**2) + 1)*gamma(1/2 - p)*gamma(p + 1)/(2*e**3*p*gamma(1/2 - p)*gamma(p + 1) + 2*e**3*gamma(1/2 - p)*gamma(p + 1)) + 2*0**p*d**2*d**(2*p)*p*atanh(d/(e*x))*gamma(1/2 - p)*gamma(p + 1)/(2*e**3*p*gamma(1/2 - p)*gamma(p + 1) + 2*e**3*gamma(1/2 - p)*gamma(p + 1)) - 0**p*d**2*d**(2*p)*log(d**2/(e**2*x**2))*gamma(1/2 - p)*gamma(p + 1)/(2*e**3*p*gamma(1/2 - p)*gamma(p + 1) + 2*e**3*gamma(1/2 - p)*gamma(p + 1)) + 0**p*d**2*d**(2*p)*log(-d**2/(e**2*x**2) + 1)*gamma(1/2 - p)*gamma(p + 1)/(2*e**3*p*gamma(1/2 - p)*gamma(p + 1) + 2*e**3*gamma(1/2 - p)*gamma(p + 1)) + 2*0**p*d**2*d**(2*p)*atanh(d/(e*x))*gamma(1/2 - p)*gamma(p + 1)/(2*e**3*p*gamma(1/2 - p)*gamma(p + 1) + 2*e**3*gamma(1/2 - p)*gamma(p + 1)) - 2*0**p*d*d**(2*p)*e*p*x*gamma(1/2 - p)*gamma(p + 1)/(2*e**3*p*gamma(1/2 - p)*gamma(p + 1) + 2*e**3*gamma(1/2 - p)*gamma(p + 1)) - 2*0**p*d*d**(2*p)*e*x*gamma(1/2 - p)*gamma(p + 1)/(2*e**3*p*gamma(1/2 - p)*gamma(p + 1) + 2*e**3*gamma(1/2 - p)*gamma(p + 1)) + 0**p*d**(2*p)*e**2*p*x**2*gamma(1/2 - p)*gamma(p + 1)/(2*e**3*p*gamma(1/2 - p)*gamma(p + 1) + 2*e**3*gamma(1/2 - p)*gamma(p + 1)) + 0**p*d**(2*p)*e**2*x**2*gamma(1/2 - p)*gamma(p + 1)/(2*e**3*p*gamma(1/2 - p)*gamma(p + 1) + 2*e**3*gamma(1/2 - p)*gamma(p + 1)) + d**2*d**(2*p)*(-1 + e**2*x**2/d**2)**p*exp(I*pi*p)*gamma(p)*gamma(1/2 - p)/(2*e**3*p*gamma(1/2 - p)*gamma(p + 1) + 2*e**3*gamma(1/2 - p)*gamma(p + 1)) + d*e*e**(2*p)*p**2*x*x**(2*p)*exp(I*pi*p)*gamma(p)*gamma(-p - 1/2)*hyper((1 - p, -p - 1/2), (1/2 - p,), d**2/(e**2*x**2))/(2*e**3*p*gamma(1/2 - p)*gamma(p + 1) + 2*e**3*gamma(1/2 - p)*gamma(p + 1)) + d*e*e**(2*p)*p*x*x**(2*p)*exp(I*pi*p)*gamma(p)*gamma(-p - 1/2)*hyper((1 - p, -p - 1/2), (1/2 - p,), d**2/(e**2*x**2))/(2*e**3*p*gamma(1/2 - p)*gamma(p + 1) + 2*e**3*gamma(1/2 - p)*gamma(p + 1)) + d**(2*p)*e**2*p*x**2*(-1 + e**2*x**2/d**2)**p*exp(I*pi*p)*gamma(p)*gamma(1/2 - p)/(2*e**3*p*gamma(1/2 - p)*gamma(p + 1) + 2*e**3*gamma(1/2 - p)*gamma(p + 1)), Abs(e**2*x**2/d**2) > 1), (-0**p*d**2*d**(2*p)*p*log(d**2/(e**2*x**2))*gamma(1/2 - p)*gamma(p + 1)/(2*e**3*p*gamma(1/2 - p)*gamma(p + 1) + 2*e**3*gamma(1/2 - p)*gamma(p + 1)) + 0**p*d**2*d**(2*p)*p*log(-d**2/(e**2*x**2) + 1)*gamma(1/2 - p)*gamma(p + 1)/(2*e**3*p*gamma(1/2 - p)*gamma(p + 1) + 2*e**3*gamma(1/2 - p)*gamma(p + 1)) + 2*0**p*d**2*d**(2*p)*p*atanh(d/(e*x))*gamma(1/2 - p)*gamma(p + 1)/(2*e**3*p*gamma(1/2 - p)*gamma(p + 1) + 2*e**3*gamma(1/2 - p)*gamma(p + 1)) - 0**p*d**2*d**(2*p)*log(d**2/(e**2*x**2))*gamma(1/2 - p)*gamma(p + 1)/(2*e**3*p*gamma(1/2 - p)*gamma(p + 1) + 2*e**3*gamma(1/2 - p)*gamma(p + 1)) + 0**p*d**2*d**(2*p)*log(-d**2/(e**2*x**2) + 1)*gamma(1/2 - p)*gamma(p + 1)/(2*e**3*p*gamma(1/2 - p)*gamma(p + 1) + 2*e**3*gamma(1/2 - p)*gamma(p + 1)) + 2*0**p*d**2*d**(2*p)*atanh(d/(e*x))*gamma(1/2 - p)*gamma(p + 1)/(2*e**3*p*gamma(1/2 - p)*gamma(p + 1) + 2*e**3*gamma(1/2 - p)*gamma(p + 1)) - 2*0**p*d*d**(2*p)*e*p*x*gamma(1/2 - p)*gamma(p + 1)/(2*e**3*p*gamma(1/2 - p)*gamma(p + 1) + 2*e**3*gamma(1/2 - p)*gamma(p + 1)) - 2*0**p*d*d**(2*p)*e*x*gamma(1/2 - p)*gamma(p + 1)/(2*e**3*p*gamma(1/2 - p)*gamma(p + 1) + 2*e**3*gamma(1/2 - p)*gamma(p + 1)) + 0**p*d**(2*p)*e**2*p*x**2*gamma(1/2 - p)*gamma(p + 1)/(2*e**3*p*gamma(1/2 - p)*gamma(p + 1) + 2*e**3*gamma(1/2 - p)*gamma(p + 1)) + 0**p*d**(2*p)*e**2*x**2*gamma(1/2 - p)*gamma(p + 1)/(2*e**3*p*gamma(1/2 - p)*gamma(p + 1) + 2*e**3*gamma(1/2 - p)*gamma(p + 1)) + d**2*d**(2*p)*(1 - e**2*x**2/d**2)**p*gamma(p)*gamma(1/2 - p)/(2*e**3*p*gamma(1/2 - p)*gamma(p + 1) + 2*e**3*gamma(1/2 - p)*gamma(p + 1)) + d*e*e**(2*p)*p**2*x*x**(2*p)*exp(I*pi*p)*gamma(p)*gamma(-p - 1/2)*hyper((1 - p, -p - 1/2), (1/2 - p,), d**2/(e**2*x**2))/(2*e**3*p*gamma(1/2 - p)*gamma(p + 1) + 2*e**3*gamma(1/2 - p)*gamma(p + 1)) + d*e*e**(2*p)*p*x*x**(2*p)*exp(I*pi*p)*gamma(p)*gamma(-p - 1/2)*hyper((1 - p, -p - 1/2), (1/2 - p,), d**2/(e**2*x**2))/(2*e**3*p*gamma(1/2 - p)*gamma(p + 1) + 2*e**3*gamma(1/2 - p)*gamma(p + 1)) + d**(2*p)*e**2*p*x**2*(1 - e**2*x**2/d**2)**p*gamma(p)*gamma(1/2 - p)/(2*e**3*p*gamma(1/2 - p)*gamma(p + 1) + 2*e**3*gamma(1/2 - p)*gamma(p + 1)), True))","C",0
270,1,427,0,7.000424," ","integrate(x*(-e**2*x**2+d**2)**p/(e*x+d),x)","\begin{cases} \frac{0^{p} d d^{2 p} \log{\left(\frac{d^{2}}{e^{2} x^{2}} \right)}}{2 e^{2}} - \frac{0^{p} d d^{2 p} \log{\left(\frac{d^{2}}{e^{2} x^{2}} - 1 \right)}}{2 e^{2}} - \frac{0^{p} d d^{2 p} \operatorname{acoth}{\left(\frac{d}{e x} \right)}}{e^{2}} + \frac{0^{p} d^{2 p} x}{e} - \frac{e^{2 p} p x x^{2 p} e^{i \pi p} \Gamma\left(p\right) \Gamma\left(- p - \frac{1}{2}\right) {{}_{2}F_{1}\left(\begin{matrix} 1 - p, - p - \frac{1}{2} \\ \frac{1}{2} - p \end{matrix}\middle| {\frac{d^{2}}{e^{2} x^{2}}} \right)}}{2 e \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right)} - \frac{d^{2 p} x^{2} \Gamma\left(p\right) \Gamma\left(1 - p\right) {{}_{3}F_{2}\left(\begin{matrix} 2, 1, 1 - p \\ 2, 2 \end{matrix}\middle| {\frac{e^{2} x^{2} e^{2 i \pi}}{d^{2}}} \right)}}{2 d \Gamma\left(- p\right) \Gamma\left(p + 1\right)} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\\frac{0^{p} d d^{2 p} \log{\left(\frac{d^{2}}{e^{2} x^{2}} \right)}}{2 e^{2}} - \frac{0^{p} d d^{2 p} \log{\left(- \frac{d^{2}}{e^{2} x^{2}} + 1 \right)}}{2 e^{2}} - \frac{0^{p} d d^{2 p} \operatorname{atanh}{\left(\frac{d}{e x} \right)}}{e^{2}} + \frac{0^{p} d^{2 p} x}{e} - \frac{e^{2 p} p x x^{2 p} e^{i \pi p} \Gamma\left(p\right) \Gamma\left(- p - \frac{1}{2}\right) {{}_{2}F_{1}\left(\begin{matrix} 1 - p, - p - \frac{1}{2} \\ \frac{1}{2} - p \end{matrix}\middle| {\frac{d^{2}}{e^{2} x^{2}}} \right)}}{2 e \Gamma\left(\frac{1}{2} - p\right) \Gamma\left(p + 1\right)} - \frac{d^{2 p} x^{2} \Gamma\left(p\right) \Gamma\left(1 - p\right) {{}_{3}F_{2}\left(\begin{matrix} 2, 1, 1 - p \\ 2, 2 \end{matrix}\middle| {\frac{e^{2} x^{2} e^{2 i \pi}}{d^{2}}} \right)}}{2 d \Gamma\left(- p\right) \Gamma\left(p + 1\right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((0**p*d*d**(2*p)*log(d**2/(e**2*x**2))/(2*e**2) - 0**p*d*d**(2*p)*log(d**2/(e**2*x**2) - 1)/(2*e**2) - 0**p*d*d**(2*p)*acoth(d/(e*x))/e**2 + 0**p*d**(2*p)*x/e - e**(2*p)*p*x*x**(2*p)*exp(I*pi*p)*gamma(p)*gamma(-p - 1/2)*hyper((1 - p, -p - 1/2), (1/2 - p,), d**2/(e**2*x**2))/(2*e*gamma(1/2 - p)*gamma(p + 1)) - d**(2*p)*x**2*gamma(p)*gamma(1 - p)*hyper((2, 1, 1 - p), (2, 2), e**2*x**2*exp_polar(2*I*pi)/d**2)/(2*d*gamma(-p)*gamma(p + 1)), Abs(d**2/(e**2*x**2)) > 1), (0**p*d*d**(2*p)*log(d**2/(e**2*x**2))/(2*e**2) - 0**p*d*d**(2*p)*log(-d**2/(e**2*x**2) + 1)/(2*e**2) - 0**p*d*d**(2*p)*atanh(d/(e*x))/e**2 + 0**p*d**(2*p)*x/e - e**(2*p)*p*x*x**(2*p)*exp(I*pi*p)*gamma(p)*gamma(-p - 1/2)*hyper((1 - p, -p - 1/2), (1/2 - p,), d**2/(e**2*x**2))/(2*e*gamma(1/2 - p)*gamma(p + 1)) - d**(2*p)*x**2*gamma(p)*gamma(1 - p)*hyper((2, 1, 1 - p), (2, 2), e**2*x**2*exp_polar(2*I*pi)/d**2)/(2*d*gamma(-p)*gamma(p + 1)), True))","C",0
271,1,321,0,7.323802," ","integrate((-e**2*x**2+d**2)**p/(e*x+d),x)","\begin{cases} \frac{0^{p} \log{\left(-1 + \frac{e^{2} x^{2}}{d^{2}} \right)}}{2 e} + \frac{0^{p} \operatorname{acoth}{\left(\frac{e x}{d} \right)}}{e} + \frac{d e^{2 p} p x^{2 p} e^{i \pi p} \Gamma\left(p\right) \Gamma\left(\frac{1}{2} - p\right) {{}_{2}F_{1}\left(\begin{matrix} 1 - p, \frac{1}{2} - p \\ \frac{3}{2} - p \end{matrix}\middle| {\frac{d^{2}}{e^{2} x^{2}}} \right)}}{2 e^{2} x \Gamma\left(\frac{3}{2} - p\right) \Gamma\left(p + 1\right)} + \frac{d^{2 p} e x^{2} \Gamma\left(p\right) \Gamma\left(1 - p\right) {{}_{3}F_{2}\left(\begin{matrix} 2, 1, 1 - p \\ 2, 2 \end{matrix}\middle| {\frac{e^{2} x^{2} e^{2 i \pi}}{d^{2}}} \right)}}{2 d^{2} \Gamma\left(- p\right) \Gamma\left(p + 1\right)} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\\frac{0^{p} \log{\left(1 - \frac{e^{2} x^{2}}{d^{2}} \right)}}{2 e} + \frac{0^{p} \operatorname{atanh}{\left(\frac{e x}{d} \right)}}{e} + \frac{d e^{2 p} p x^{2 p} e^{i \pi p} \Gamma\left(p\right) \Gamma\left(\frac{1}{2} - p\right) {{}_{2}F_{1}\left(\begin{matrix} 1 - p, \frac{1}{2} - p \\ \frac{3}{2} - p \end{matrix}\middle| {\frac{d^{2}}{e^{2} x^{2}}} \right)}}{2 e^{2} x \Gamma\left(\frac{3}{2} - p\right) \Gamma\left(p + 1\right)} + \frac{d^{2 p} e x^{2} \Gamma\left(p\right) \Gamma\left(1 - p\right) {{}_{3}F_{2}\left(\begin{matrix} 2, 1, 1 - p \\ 2, 2 \end{matrix}\middle| {\frac{e^{2} x^{2} e^{2 i \pi}}{d^{2}}} \right)}}{2 d^{2} \Gamma\left(- p\right) \Gamma\left(p + 1\right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((0**p*log(-1 + e**2*x**2/d**2)/(2*e) + 0**p*acoth(e*x/d)/e + d*e**(2*p)*p*x**(2*p)*exp(I*pi*p)*gamma(p)*gamma(1/2 - p)*hyper((1 - p, 1/2 - p), (3/2 - p,), d**2/(e**2*x**2))/(2*e**2*x*gamma(3/2 - p)*gamma(p + 1)) + d**(2*p)*e*x**2*gamma(p)*gamma(1 - p)*hyper((2, 1, 1 - p), (2, 2), e**2*x**2*exp_polar(2*I*pi)/d**2)/(2*d**2*gamma(-p)*gamma(p + 1)), Abs(e**2*x**2/d**2) > 1), (0**p*log(1 - e**2*x**2/d**2)/(2*e) + 0**p*atanh(e*x/d)/e + d*e**(2*p)*p*x**(2*p)*exp(I*pi*p)*gamma(p)*gamma(1/2 - p)*hyper((1 - p, 1/2 - p), (3/2 - p,), d**2/(e**2*x**2))/(2*e**2*x*gamma(3/2 - p)*gamma(p + 1)) + d**(2*p)*e*x**2*gamma(p)*gamma(1 - p)*hyper((2, 1, 1 - p), (2, 2), e**2*x**2*exp_polar(2*I*pi)/d**2)/(2*d**2*gamma(-p)*gamma(p + 1)), True))","C",0
272,1,355,0,6.901162," ","integrate((-e**2*x**2+d**2)**p/x/(e*x+d),x)","\begin{cases} - \frac{0^{p} d^{2 p} \log{\left(\frac{d^{2}}{e^{2} x^{2}} - 1 \right)}}{2 d} - \frac{0^{p} d^{2 p} \operatorname{acoth}{\left(\frac{d}{e x} \right)}}{d} + \frac{d e^{2 p} p x^{2 p} e^{i \pi p} \Gamma\left(p\right) \Gamma\left(1 - p\right) {{}_{2}F_{1}\left(\begin{matrix} 1 - p, 1 - p \\ 2 - p \end{matrix}\middle| {\frac{d^{2}}{e^{2} x^{2}}} \right)}}{2 e^{2} x^{2} \Gamma\left(2 - p\right) \Gamma\left(p + 1\right)} - \frac{e^{2 p} p x^{2 p} e^{i \pi p} \Gamma\left(p\right) \Gamma\left(\frac{1}{2} - p\right) {{}_{2}F_{1}\left(\begin{matrix} 1 - p, \frac{1}{2} - p \\ \frac{3}{2} - p \end{matrix}\middle| {\frac{d^{2}}{e^{2} x^{2}}} \right)}}{2 e x \Gamma\left(\frac{3}{2} - p\right) \Gamma\left(p + 1\right)} & \text{for}\: \left|{\frac{d^{2}}{e^{2} x^{2}}}\right| > 1 \\- \frac{0^{p} d^{2 p} \log{\left(- \frac{d^{2}}{e^{2} x^{2}} + 1 \right)}}{2 d} - \frac{0^{p} d^{2 p} \operatorname{atanh}{\left(\frac{d}{e x} \right)}}{d} + \frac{d e^{2 p} p x^{2 p} e^{i \pi p} \Gamma\left(p\right) \Gamma\left(1 - p\right) {{}_{2}F_{1}\left(\begin{matrix} 1 - p, 1 - p \\ 2 - p \end{matrix}\middle| {\frac{d^{2}}{e^{2} x^{2}}} \right)}}{2 e^{2} x^{2} \Gamma\left(2 - p\right) \Gamma\left(p + 1\right)} - \frac{e^{2 p} p x^{2 p} e^{i \pi p} \Gamma\left(p\right) \Gamma\left(\frac{1}{2} - p\right) {{}_{2}F_{1}\left(\begin{matrix} 1 - p, \frac{1}{2} - p \\ \frac{3}{2} - p \end{matrix}\middle| {\frac{d^{2}}{e^{2} x^{2}}} \right)}}{2 e x \Gamma\left(\frac{3}{2} - p\right) \Gamma\left(p + 1\right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-0**p*d**(2*p)*log(d**2/(e**2*x**2) - 1)/(2*d) - 0**p*d**(2*p)*acoth(d/(e*x))/d + d*e**(2*p)*p*x**(2*p)*exp(I*pi*p)*gamma(p)*gamma(1 - p)*hyper((1 - p, 1 - p), (2 - p,), d**2/(e**2*x**2))/(2*e**2*x**2*gamma(2 - p)*gamma(p + 1)) - e**(2*p)*p*x**(2*p)*exp(I*pi*p)*gamma(p)*gamma(1/2 - p)*hyper((1 - p, 1/2 - p), (3/2 - p,), d**2/(e**2*x**2))/(2*e*x*gamma(3/2 - p)*gamma(p + 1)), Abs(d**2/(e**2*x**2)) > 1), (-0**p*d**(2*p)*log(-d**2/(e**2*x**2) + 1)/(2*d) - 0**p*d**(2*p)*atanh(d/(e*x))/d + d*e**(2*p)*p*x**(2*p)*exp(I*pi*p)*gamma(p)*gamma(1 - p)*hyper((1 - p, 1 - p), (2 - p,), d**2/(e**2*x**2))/(2*e**2*x**2*gamma(2 - p)*gamma(p + 1)) - e**(2*p)*p*x**(2*p)*exp(I*pi*p)*gamma(p)*gamma(1/2 - p)*hyper((1 - p, 1/2 - p), (3/2 - p,), d**2/(e**2*x**2))/(2*e*x*gamma(3/2 - p)*gamma(p + 1)), True))","C",0
273,1,450,0,7.864797," ","integrate((-e**2*x**2+d**2)**p/x**2/(e*x+d),x)","\begin{cases} - \frac{0^{p} d^{2 p}}{d x} - \frac{0^{p} d^{2 p} e \log{\left(\frac{e^{2} x^{2}}{d^{2}} \right)}}{2 d^{2}} + \frac{0^{p} d^{2 p} e \log{\left(-1 + \frac{e^{2} x^{2}}{d^{2}} \right)}}{2 d^{2}} + \frac{0^{p} d^{2 p} e \operatorname{acoth}{\left(\frac{e x}{d} \right)}}{d^{2}} + \frac{d e^{2 p} p x^{2 p} e^{i \pi p} \Gamma\left(p\right) \Gamma\left(\frac{3}{2} - p\right) {{}_{2}F_{1}\left(\begin{matrix} 1 - p, \frac{3}{2} - p \\ \frac{5}{2} - p \end{matrix}\middle| {\frac{d^{2}}{e^{2} x^{2}}} \right)}}{2 e^{2} x^{3} \Gamma\left(\frac{5}{2} - p\right) \Gamma\left(p + 1\right)} - \frac{e^{2 p} p x^{2 p} e^{i \pi p} \Gamma\left(p\right) \Gamma\left(1 - p\right) {{}_{2}F_{1}\left(\begin{matrix} 1 - p, 1 - p \\ 2 - p \end{matrix}\middle| {\frac{d^{2}}{e^{2} x^{2}}} \right)}}{2 e x^{2} \Gamma\left(2 - p\right) \Gamma\left(p + 1\right)} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\- \frac{0^{p} d^{2 p}}{d x} - \frac{0^{p} d^{2 p} e \log{\left(\frac{e^{2} x^{2}}{d^{2}} \right)}}{2 d^{2}} + \frac{0^{p} d^{2 p} e \log{\left(1 - \frac{e^{2} x^{2}}{d^{2}} \right)}}{2 d^{2}} + \frac{0^{p} d^{2 p} e \operatorname{atanh}{\left(\frac{e x}{d} \right)}}{d^{2}} + \frac{d e^{2 p} p x^{2 p} e^{i \pi p} \Gamma\left(p\right) \Gamma\left(\frac{3}{2} - p\right) {{}_{2}F_{1}\left(\begin{matrix} 1 - p, \frac{3}{2} - p \\ \frac{5}{2} - p \end{matrix}\middle| {\frac{d^{2}}{e^{2} x^{2}}} \right)}}{2 e^{2} x^{3} \Gamma\left(\frac{5}{2} - p\right) \Gamma\left(p + 1\right)} - \frac{e^{2 p} p x^{2 p} e^{i \pi p} \Gamma\left(p\right) \Gamma\left(1 - p\right) {{}_{2}F_{1}\left(\begin{matrix} 1 - p, 1 - p \\ 2 - p \end{matrix}\middle| {\frac{d^{2}}{e^{2} x^{2}}} \right)}}{2 e x^{2} \Gamma\left(2 - p\right) \Gamma\left(p + 1\right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-0**p*d**(2*p)/(d*x) - 0**p*d**(2*p)*e*log(e**2*x**2/d**2)/(2*d**2) + 0**p*d**(2*p)*e*log(-1 + e**2*x**2/d**2)/(2*d**2) + 0**p*d**(2*p)*e*acoth(e*x/d)/d**2 + d*e**(2*p)*p*x**(2*p)*exp(I*pi*p)*gamma(p)*gamma(3/2 - p)*hyper((1 - p, 3/2 - p), (5/2 - p,), d**2/(e**2*x**2))/(2*e**2*x**3*gamma(5/2 - p)*gamma(p + 1)) - e**(2*p)*p*x**(2*p)*exp(I*pi*p)*gamma(p)*gamma(1 - p)*hyper((1 - p, 1 - p), (2 - p,), d**2/(e**2*x**2))/(2*e*x**2*gamma(2 - p)*gamma(p + 1)), Abs(e**2*x**2/d**2) > 1), (-0**p*d**(2*p)/(d*x) - 0**p*d**(2*p)*e*log(e**2*x**2/d**2)/(2*d**2) + 0**p*d**(2*p)*e*log(1 - e**2*x**2/d**2)/(2*d**2) + 0**p*d**(2*p)*e*atanh(e*x/d)/d**2 + d*e**(2*p)*p*x**(2*p)*exp(I*pi*p)*gamma(p)*gamma(3/2 - p)*hyper((1 - p, 3/2 - p), (5/2 - p,), d**2/(e**2*x**2))/(2*e**2*x**3*gamma(5/2 - p)*gamma(p + 1)) - e**(2*p)*p*x**(2*p)*exp(I*pi*p)*gamma(p)*gamma(1 - p)*hyper((1 - p, 1 - p), (2 - p,), d**2/(e**2*x**2))/(2*e*x**2*gamma(2 - p)*gamma(p + 1)), True))","C",0
274,1,498,0,9.477310," ","integrate((-e**2*x**2+d**2)**p/x**3/(e*x+d),x)","\begin{cases} - \frac{0^{p} d^{2 p}}{2 d x^{2}} + \frac{0^{p} d^{2 p} e}{d^{2} x} + \frac{0^{p} d^{2 p} e^{2} \log{\left(\frac{e^{2} x^{2}}{d^{2}} \right)}}{2 d^{3}} - \frac{0^{p} d^{2 p} e^{2} \log{\left(-1 + \frac{e^{2} x^{2}}{d^{2}} \right)}}{2 d^{3}} - \frac{0^{p} d^{2 p} e^{2} \operatorname{acoth}{\left(\frac{e x}{d} \right)}}{d^{3}} + \frac{d e^{2 p} p x^{2 p} e^{i \pi p} \Gamma\left(p\right) \Gamma\left(2 - p\right) {{}_{2}F_{1}\left(\begin{matrix} 1 - p, 2 - p \\ 3 - p \end{matrix}\middle| {\frac{d^{2}}{e^{2} x^{2}}} \right)}}{2 e^{2} x^{4} \Gamma\left(3 - p\right) \Gamma\left(p + 1\right)} - \frac{e^{2 p} p x^{2 p} e^{i \pi p} \Gamma\left(p\right) \Gamma\left(\frac{3}{2} - p\right) {{}_{2}F_{1}\left(\begin{matrix} 1 - p, \frac{3}{2} - p \\ \frac{5}{2} - p \end{matrix}\middle| {\frac{d^{2}}{e^{2} x^{2}}} \right)}}{2 e x^{3} \Gamma\left(\frac{5}{2} - p\right) \Gamma\left(p + 1\right)} & \text{for}\: \left|{\frac{e^{2} x^{2}}{d^{2}}}\right| > 1 \\- \frac{0^{p} d^{2 p}}{2 d x^{2}} + \frac{0^{p} d^{2 p} e}{d^{2} x} + \frac{0^{p} d^{2 p} e^{2} \log{\left(\frac{e^{2} x^{2}}{d^{2}} \right)}}{2 d^{3}} - \frac{0^{p} d^{2 p} e^{2} \log{\left(1 - \frac{e^{2} x^{2}}{d^{2}} \right)}}{2 d^{3}} - \frac{0^{p} d^{2 p} e^{2} \operatorname{atanh}{\left(\frac{e x}{d} \right)}}{d^{3}} + \frac{d e^{2 p} p x^{2 p} e^{i \pi p} \Gamma\left(p\right) \Gamma\left(2 - p\right) {{}_{2}F_{1}\left(\begin{matrix} 1 - p, 2 - p \\ 3 - p \end{matrix}\middle| {\frac{d^{2}}{e^{2} x^{2}}} \right)}}{2 e^{2} x^{4} \Gamma\left(3 - p\right) \Gamma\left(p + 1\right)} - \frac{e^{2 p} p x^{2 p} e^{i \pi p} \Gamma\left(p\right) \Gamma\left(\frac{3}{2} - p\right) {{}_{2}F_{1}\left(\begin{matrix} 1 - p, \frac{3}{2} - p \\ \frac{5}{2} - p \end{matrix}\middle| {\frac{d^{2}}{e^{2} x^{2}}} \right)}}{2 e x^{3} \Gamma\left(\frac{5}{2} - p\right) \Gamma\left(p + 1\right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-0**p*d**(2*p)/(2*d*x**2) + 0**p*d**(2*p)*e/(d**2*x) + 0**p*d**(2*p)*e**2*log(e**2*x**2/d**2)/(2*d**3) - 0**p*d**(2*p)*e**2*log(-1 + e**2*x**2/d**2)/(2*d**3) - 0**p*d**(2*p)*e**2*acoth(e*x/d)/d**3 + d*e**(2*p)*p*x**(2*p)*exp(I*pi*p)*gamma(p)*gamma(2 - p)*hyper((1 - p, 2 - p), (3 - p,), d**2/(e**2*x**2))/(2*e**2*x**4*gamma(3 - p)*gamma(p + 1)) - e**(2*p)*p*x**(2*p)*exp(I*pi*p)*gamma(p)*gamma(3/2 - p)*hyper((1 - p, 3/2 - p), (5/2 - p,), d**2/(e**2*x**2))/(2*e*x**3*gamma(5/2 - p)*gamma(p + 1)), Abs(e**2*x**2/d**2) > 1), (-0**p*d**(2*p)/(2*d*x**2) + 0**p*d**(2*p)*e/(d**2*x) + 0**p*d**(2*p)*e**2*log(e**2*x**2/d**2)/(2*d**3) - 0**p*d**(2*p)*e**2*log(1 - e**2*x**2/d**2)/(2*d**3) - 0**p*d**(2*p)*e**2*atanh(e*x/d)/d**3 + d*e**(2*p)*p*x**(2*p)*exp(I*pi*p)*gamma(p)*gamma(2 - p)*hyper((1 - p, 2 - p), (3 - p,), d**2/(e**2*x**2))/(2*e**2*x**4*gamma(3 - p)*gamma(p + 1)) - e**(2*p)*p*x**(2*p)*exp(I*pi*p)*gamma(p)*gamma(3/2 - p)*hyper((1 - p, 3/2 - p), (5/2 - p,), d**2/(e**2*x**2))/(2*e*x**3*gamma(5/2 - p)*gamma(p + 1)), True))","C",0
275,0,0,0,0.000000," ","integrate(x**5*(-e**2*x**2+d**2)**p/(e*x+d)**2,x)","\int \frac{x^{5} \left(- \left(- d + e x\right) \left(d + e x\right)\right)^{p}}{\left(d + e x\right)^{2}}\, dx"," ",0,"Integral(x**5*(-(-d + e*x)*(d + e*x))**p/(d + e*x)**2, x)","F",0
276,0,0,0,0.000000," ","integrate(x**4*(-e**2*x**2+d**2)**p/(e*x+d)**2,x)","\int \frac{x^{4} \left(- \left(- d + e x\right) \left(d + e x\right)\right)^{p}}{\left(d + e x\right)^{2}}\, dx"," ",0,"Integral(x**4*(-(-d + e*x)*(d + e*x))**p/(d + e*x)**2, x)","F",0
277,0,0,0,0.000000," ","integrate(x**3*(-e**2*x**2+d**2)**p/(e*x+d)**2,x)","\int \frac{x^{3} \left(- \left(- d + e x\right) \left(d + e x\right)\right)^{p}}{\left(d + e x\right)^{2}}\, dx"," ",0,"Integral(x**3*(-(-d + e*x)*(d + e*x))**p/(d + e*x)**2, x)","F",0
278,0,0,0,0.000000," ","integrate(x**2*(-e**2*x**2+d**2)**p/(e*x+d)**2,x)","\int \frac{x^{2} \left(- \left(- d + e x\right) \left(d + e x\right)\right)^{p}}{\left(d + e x\right)^{2}}\, dx"," ",0,"Integral(x**2*(-(-d + e*x)*(d + e*x))**p/(d + e*x)**2, x)","F",0
279,0,0,0,0.000000," ","integrate(x*(-e**2*x**2+d**2)**p/(e*x+d)**2,x)","\int \frac{x \left(- \left(- d + e x\right) \left(d + e x\right)\right)^{p}}{\left(d + e x\right)^{2}}\, dx"," ",0,"Integral(x*(-(-d + e*x)*(d + e*x))**p/(d + e*x)**2, x)","F",0
280,0,0,0,0.000000," ","integrate((-e**2*x**2+d**2)**p/(e*x+d)**2,x)","\int \frac{\left(- \left(- d + e x\right) \left(d + e x\right)\right)^{p}}{\left(d + e x\right)^{2}}\, dx"," ",0,"Integral((-(-d + e*x)*(d + e*x))**p/(d + e*x)**2, x)","F",0
281,0,0,0,0.000000," ","integrate((-e**2*x**2+d**2)**p/x/(e*x+d)**2,x)","\int \frac{\left(- \left(- d + e x\right) \left(d + e x\right)\right)^{p}}{x \left(d + e x\right)^{2}}\, dx"," ",0,"Integral((-(-d + e*x)*(d + e*x))**p/(x*(d + e*x)**2), x)","F",0
282,0,0,0,0.000000," ","integrate((-e**2*x**2+d**2)**p/x**2/(e*x+d)**2,x)","\int \frac{\left(- \left(- d + e x\right) \left(d + e x\right)\right)^{p}}{x^{2} \left(d + e x\right)^{2}}\, dx"," ",0,"Integral((-(-d + e*x)*(d + e*x))**p/(x**2*(d + e*x)**2), x)","F",0
283,0,0,0,0.000000," ","integrate((-e**2*x**2+d**2)**p/x**3/(e*x+d)**2,x)","\int \frac{\left(- \left(- d + e x\right) \left(d + e x\right)\right)^{p}}{x^{3} \left(d + e x\right)^{2}}\, dx"," ",0,"Integral((-(-d + e*x)*(d + e*x))**p/(x**3*(d + e*x)**2), x)","F",0
284,0,0,0,0.000000," ","integrate((-e**2*x**2+d**2)**p/x**4/(e*x+d)**2,x)","\int \frac{\left(- \left(- d + e x\right) \left(d + e x\right)\right)^{p}}{x^{4} \left(d + e x\right)^{2}}\, dx"," ",0,"Integral((-(-d + e*x)*(d + e*x))**p/(x**4*(d + e*x)**2), x)","F",0
285,0,0,0,0.000000," ","integrate((-e**2*x**2+d**2)**p/x**5/(e*x+d)**2,x)","\int \frac{\left(- \left(- d + e x\right) \left(d + e x\right)\right)^{p}}{x^{5} \left(d + e x\right)^{2}}\, dx"," ",0,"Integral((-(-d + e*x)*(d + e*x))**p/(x**5*(d + e*x)**2), x)","F",0
286,0,0,0,0.000000," ","integrate(x**4*(-e**2*x**2+d**2)**p/(e*x+d)**3,x)","\int \frac{x^{4} \left(- \left(- d + e x\right) \left(d + e x\right)\right)^{p}}{\left(d + e x\right)^{3}}\, dx"," ",0,"Integral(x**4*(-(-d + e*x)*(d + e*x))**p/(d + e*x)**3, x)","F",0
287,0,0,0,0.000000," ","integrate(x**3*(-e**2*x**2+d**2)**p/(e*x+d)**3,x)","\int \frac{x^{3} \left(- \left(- d + e x\right) \left(d + e x\right)\right)^{p}}{\left(d + e x\right)^{3}}\, dx"," ",0,"Integral(x**3*(-(-d + e*x)*(d + e*x))**p/(d + e*x)**3, x)","F",0
288,0,0,0,0.000000," ","integrate(x**2*(-e**2*x**2+d**2)**p/(e*x+d)**3,x)","\int \frac{x^{2} \left(- \left(- d + e x\right) \left(d + e x\right)\right)^{p}}{\left(d + e x\right)^{3}}\, dx"," ",0,"Integral(x**2*(-(-d + e*x)*(d + e*x))**p/(d + e*x)**3, x)","F",0
289,0,0,0,0.000000," ","integrate(x*(-e**2*x**2+d**2)**p/(e*x+d)**3,x)","\int \frac{x \left(- \left(- d + e x\right) \left(d + e x\right)\right)^{p}}{\left(d + e x\right)^{3}}\, dx"," ",0,"Integral(x*(-(-d + e*x)*(d + e*x))**p/(d + e*x)**3, x)","F",0
290,0,0,0,0.000000," ","integrate((-e**2*x**2+d**2)**p/(e*x+d)**3,x)","\int \frac{\left(- \left(- d + e x\right) \left(d + e x\right)\right)^{p}}{\left(d + e x\right)^{3}}\, dx"," ",0,"Integral((-(-d + e*x)*(d + e*x))**p/(d + e*x)**3, x)","F",0
291,0,0,0,0.000000," ","integrate((-e**2*x**2+d**2)**p/x/(e*x+d)**3,x)","\int \frac{\left(- \left(- d + e x\right) \left(d + e x\right)\right)^{p}}{x \left(d + e x\right)^{3}}\, dx"," ",0,"Integral((-(-d + e*x)*(d + e*x))**p/(x*(d + e*x)**3), x)","F",0
292,0,0,0,0.000000," ","integrate((-e**2*x**2+d**2)**p/x**2/(e*x+d)**3,x)","\int \frac{\left(- \left(- d + e x\right) \left(d + e x\right)\right)^{p}}{x^{2} \left(d + e x\right)^{3}}\, dx"," ",0,"Integral((-(-d + e*x)*(d + e*x))**p/(x**2*(d + e*x)**3), x)","F",0
293,0,0,0,0.000000," ","integrate((-e**2*x**2+d**2)**p/x**3/(e*x+d)**3,x)","\int \frac{\left(- \left(- d + e x\right) \left(d + e x\right)\right)^{p}}{x^{3} \left(d + e x\right)^{3}}\, dx"," ",0,"Integral((-(-d + e*x)*(d + e*x))**p/(x**3*(d + e*x)**3), x)","F",0
294,0,0,0,0.000000," ","integrate((-e**2*x**2+d**2)**p/x**4/(e*x+d)**3,x)","\int \frac{\left(- \left(- d + e x\right) \left(d + e x\right)\right)^{p}}{x^{4} \left(d + e x\right)^{3}}\, dx"," ",0,"Integral((-(-d + e*x)*(d + e*x))**p/(x**4*(d + e*x)**3), x)","F",0
295,0,0,0,0.000000," ","integrate((-e**2*x**2+d**2)**p/x**5/(e*x+d)**3,x)","\int \frac{\left(- \left(- d + e x\right) \left(d + e x\right)\right)^{p}}{x^{5} \left(d + e x\right)^{3}}\, dx"," ",0,"Integral((-(-d + e*x)*(d + e*x))**p/(x**5*(d + e*x)**3), x)","F",0
296,0,0,0,0.000000," ","integrate(x**4*(-e**2*x**2+d**2)**p/(e*x+d)**4,x)","\int \frac{x^{4} \left(- \left(- d + e x\right) \left(d + e x\right)\right)^{p}}{\left(d + e x\right)^{4}}\, dx"," ",0,"Integral(x**4*(-(-d + e*x)*(d + e*x))**p/(d + e*x)**4, x)","F",0
297,0,0,0,0.000000," ","integrate(x**3*(-e**2*x**2+d**2)**p/(e*x+d)**4,x)","\int \frac{x^{3} \left(- \left(- d + e x\right) \left(d + e x\right)\right)^{p}}{\left(d + e x\right)^{4}}\, dx"," ",0,"Integral(x**3*(-(-d + e*x)*(d + e*x))**p/(d + e*x)**4, x)","F",0
298,0,0,0,0.000000," ","integrate(x**2*(-e**2*x**2+d**2)**p/(e*x+d)**4,x)","\int \frac{x^{2} \left(- \left(- d + e x\right) \left(d + e x\right)\right)^{p}}{\left(d + e x\right)^{4}}\, dx"," ",0,"Integral(x**2*(-(-d + e*x)*(d + e*x))**p/(d + e*x)**4, x)","F",0
299,0,0,0,0.000000," ","integrate(x*(-e**2*x**2+d**2)**p/(e*x+d)**4,x)","\int \frac{x \left(- \left(- d + e x\right) \left(d + e x\right)\right)^{p}}{\left(d + e x\right)^{4}}\, dx"," ",0,"Integral(x*(-(-d + e*x)*(d + e*x))**p/(d + e*x)**4, x)","F",0
300,0,0,0,0.000000," ","integrate((-e**2*x**2+d**2)**p/(e*x+d)**4,x)","\int \frac{\left(- \left(- d + e x\right) \left(d + e x\right)\right)^{p}}{\left(d + e x\right)^{4}}\, dx"," ",0,"Integral((-(-d + e*x)*(d + e*x))**p/(d + e*x)**4, x)","F",0
301,0,0,0,0.000000," ","integrate((-e**2*x**2+d**2)**p/x/(e*x+d)**4,x)","\int \frac{\left(- \left(- d + e x\right) \left(d + e x\right)\right)^{p}}{x \left(d + e x\right)^{4}}\, dx"," ",0,"Integral((-(-d + e*x)*(d + e*x))**p/(x*(d + e*x)**4), x)","F",0
302,0,0,0,0.000000," ","integrate((-e**2*x**2+d**2)**p/x**2/(e*x+d)**4,x)","\int \frac{\left(- \left(- d + e x\right) \left(d + e x\right)\right)^{p}}{x^{2} \left(d + e x\right)^{4}}\, dx"," ",0,"Integral((-(-d + e*x)*(d + e*x))**p/(x**2*(d + e*x)**4), x)","F",0
303,0,0,0,0.000000," ","integrate((-e**2*x**2+d**2)**p/x**3/(e*x+d)**4,x)","\int \frac{\left(- \left(- d + e x\right) \left(d + e x\right)\right)^{p}}{x^{3} \left(d + e x\right)^{4}}\, dx"," ",0,"Integral((-(-d + e*x)*(d + e*x))**p/(x**3*(d + e*x)**4), x)","F",0
304,0,0,0,0.000000," ","integrate((-e**2*x**2+d**2)**p/x**4/(e*x+d)**4,x)","\int \frac{\left(- \left(- d + e x\right) \left(d + e x\right)\right)^{p}}{x^{4} \left(d + e x\right)^{4}}\, dx"," ",0,"Integral((-(-d + e*x)*(d + e*x))**p/(x**4*(d + e*x)**4), x)","F",0
305,0,0,0,0.000000," ","integrate((-e**2*x**2+d**2)**p/x**5/(e*x+d)**4,x)","\int \frac{\left(- \left(- d + e x\right) \left(d + e x\right)\right)^{p}}{x^{5} \left(d + e x\right)^{4}}\, dx"," ",0,"Integral((-(-d + e*x)*(d + e*x))**p/(x**5*(d + e*x)**4), x)","F",0
306,1,262,0,25.294503," ","integrate((g*x)**m*(e*x+d)**3*(-e**2*x**2+d**2)**p,x)","\frac{d^{3} d^{2 p} g^{m} x x^{m} \Gamma\left(\frac{m}{2} + \frac{1}{2}\right) {{}_{2}F_{1}\left(\begin{matrix} - p, \frac{m}{2} + \frac{1}{2} \\ \frac{m}{2} + \frac{3}{2} \end{matrix}\middle| {\frac{e^{2} x^{2} e^{2 i \pi}}{d^{2}}} \right)}}{2 \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)} + \frac{3 d^{2} d^{2 p} e g^{m} x^{2} x^{m} \Gamma\left(\frac{m}{2} + 1\right) {{}_{2}F_{1}\left(\begin{matrix} - p, \frac{m}{2} + 1 \\ \frac{m}{2} + 2 \end{matrix}\middle| {\frac{e^{2} x^{2} e^{2 i \pi}}{d^{2}}} \right)}}{2 \Gamma\left(\frac{m}{2} + 2\right)} + \frac{3 d d^{2 p} e^{2} g^{m} x^{3} x^{m} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) {{}_{2}F_{1}\left(\begin{matrix} - p, \frac{m}{2} + \frac{3}{2} \\ \frac{m}{2} + \frac{5}{2} \end{matrix}\middle| {\frac{e^{2} x^{2} e^{2 i \pi}}{d^{2}}} \right)}}{2 \Gamma\left(\frac{m}{2} + \frac{5}{2}\right)} + \frac{d^{2 p} e^{3} g^{m} x^{4} x^{m} \Gamma\left(\frac{m}{2} + 2\right) {{}_{2}F_{1}\left(\begin{matrix} - p, \frac{m}{2} + 2 \\ \frac{m}{2} + 3 \end{matrix}\middle| {\frac{e^{2} x^{2} e^{2 i \pi}}{d^{2}}} \right)}}{2 \Gamma\left(\frac{m}{2} + 3\right)}"," ",0,"d**3*d**(2*p)*g**m*x*x**m*gamma(m/2 + 1/2)*hyper((-p, m/2 + 1/2), (m/2 + 3/2,), e**2*x**2*exp_polar(2*I*pi)/d**2)/(2*gamma(m/2 + 3/2)) + 3*d**2*d**(2*p)*e*g**m*x**2*x**m*gamma(m/2 + 1)*hyper((-p, m/2 + 1), (m/2 + 2,), e**2*x**2*exp_polar(2*I*pi)/d**2)/(2*gamma(m/2 + 2)) + 3*d*d**(2*p)*e**2*g**m*x**3*x**m*gamma(m/2 + 3/2)*hyper((-p, m/2 + 3/2), (m/2 + 5/2,), e**2*x**2*exp_polar(2*I*pi)/d**2)/(2*gamma(m/2 + 5/2)) + d**(2*p)*e**3*g**m*x**4*x**m*gamma(m/2 + 2)*hyper((-p, m/2 + 2), (m/2 + 3,), e**2*x**2*exp_polar(2*I*pi)/d**2)/(2*gamma(m/2 + 3))","C",0
307,1,192,0,16.857896," ","integrate((g*x)**m*(e*x+d)**2*(-e**2*x**2+d**2)**p,x)","\frac{d^{2} d^{2 p} g^{m} x x^{m} \Gamma\left(\frac{m}{2} + \frac{1}{2}\right) {{}_{2}F_{1}\left(\begin{matrix} - p, \frac{m}{2} + \frac{1}{2} \\ \frac{m}{2} + \frac{3}{2} \end{matrix}\middle| {\frac{e^{2} x^{2} e^{2 i \pi}}{d^{2}}} \right)}}{2 \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)} + \frac{d d^{2 p} e g^{m} x^{2} x^{m} \Gamma\left(\frac{m}{2} + 1\right) {{}_{2}F_{1}\left(\begin{matrix} - p, \frac{m}{2} + 1 \\ \frac{m}{2} + 2 \end{matrix}\middle| {\frac{e^{2} x^{2} e^{2 i \pi}}{d^{2}}} \right)}}{\Gamma\left(\frac{m}{2} + 2\right)} + \frac{d^{2 p} e^{2} g^{m} x^{3} x^{m} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) {{}_{2}F_{1}\left(\begin{matrix} - p, \frac{m}{2} + \frac{3}{2} \\ \frac{m}{2} + \frac{5}{2} \end{matrix}\middle| {\frac{e^{2} x^{2} e^{2 i \pi}}{d^{2}}} \right)}}{2 \Gamma\left(\frac{m}{2} + \frac{5}{2}\right)}"," ",0,"d**2*d**(2*p)*g**m*x*x**m*gamma(m/2 + 1/2)*hyper((-p, m/2 + 1/2), (m/2 + 3/2,), e**2*x**2*exp_polar(2*I*pi)/d**2)/(2*gamma(m/2 + 3/2)) + d*d**(2*p)*e*g**m*x**2*x**m*gamma(m/2 + 1)*hyper((-p, m/2 + 1), (m/2 + 2,), e**2*x**2*exp_polar(2*I*pi)/d**2)/gamma(m/2 + 2) + d**(2*p)*e**2*g**m*x**3*x**m*gamma(m/2 + 3/2)*hyper((-p, m/2 + 3/2), (m/2 + 5/2,), e**2*x**2*exp_polar(2*I*pi)/d**2)/(2*gamma(m/2 + 5/2))","C",0
308,1,122,0,9.944388," ","integrate((g*x)**m*(e*x+d)*(-e**2*x**2+d**2)**p,x)","\frac{d d^{2 p} g^{m} x x^{m} \Gamma\left(\frac{m}{2} + \frac{1}{2}\right) {{}_{2}F_{1}\left(\begin{matrix} - p, \frac{m}{2} + \frac{1}{2} \\ \frac{m}{2} + \frac{3}{2} \end{matrix}\middle| {\frac{e^{2} x^{2} e^{2 i \pi}}{d^{2}}} \right)}}{2 \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)} + \frac{d^{2 p} e g^{m} x^{2} x^{m} \Gamma\left(\frac{m}{2} + 1\right) {{}_{2}F_{1}\left(\begin{matrix} - p, \frac{m}{2} + 1 \\ \frac{m}{2} + 2 \end{matrix}\middle| {\frac{e^{2} x^{2} e^{2 i \pi}}{d^{2}}} \right)}}{2 \Gamma\left(\frac{m}{2} + 2\right)}"," ",0,"d*d**(2*p)*g**m*x*x**m*gamma(m/2 + 1/2)*hyper((-p, m/2 + 1/2), (m/2 + 3/2,), e**2*x**2*exp_polar(2*I*pi)/d**2)/(2*gamma(m/2 + 3/2)) + d**(2*p)*e*g**m*x**2*x**m*gamma(m/2 + 1)*hyper((-p, m/2 + 1), (m/2 + 2,), e**2*x**2*exp_polar(2*I*pi)/d**2)/(2*gamma(m/2 + 2))","C",0
309,1,61,0,3.586739," ","integrate((g*x)**m*(-e**2*x**2+d**2)**p,x)","\frac{d^{2 p} g^{m} x x^{m} \Gamma\left(\frac{m}{2} + \frac{1}{2}\right) {{}_{2}F_{1}\left(\begin{matrix} - p, \frac{m}{2} + \frac{1}{2} \\ \frac{m}{2} + \frac{3}{2} \end{matrix}\middle| {\frac{e^{2} x^{2} e^{2 i \pi}}{d^{2}}} \right)}}{2 \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)}"," ",0,"d**(2*p)*g**m*x*x**m*gamma(m/2 + 1/2)*hyper((-p, m/2 + 1/2), (m/2 + 3/2,), e**2*x**2*exp_polar(2*I*pi)/d**2)/(2*gamma(m/2 + 3/2))","C",0
310,1,337,0,13.152273," ","integrate((g*x)**m*(-e**2*x**2+d**2)**p/(e*x+d),x)","- \frac{0^{p} d d^{2 p} g^{m} m x^{m} \Phi\left(\frac{d^{2}}{e^{2} x^{2}}, 1, \frac{1}{2} - \frac{m}{2}\right) \Gamma\left(\frac{1}{2} - \frac{m}{2}\right)}{4 e^{2} x \Gamma\left(\frac{3}{2} - \frac{m}{2}\right)} + \frac{0^{p} d d^{2 p} g^{m} x^{m} \Phi\left(\frac{d^{2}}{e^{2} x^{2}}, 1, \frac{1}{2} - \frac{m}{2}\right) \Gamma\left(\frac{1}{2} - \frac{m}{2}\right)}{4 e^{2} x \Gamma\left(\frac{3}{2} - \frac{m}{2}\right)} + \frac{0^{p} d^{2 p} g^{m} m x^{m} \Phi\left(\frac{d^{2}}{e^{2} x^{2}}, 1, \frac{m e^{i \pi}}{2}\right) \Gamma\left(- \frac{m}{2}\right)}{4 e \Gamma\left(1 - \frac{m}{2}\right)} + \frac{d e^{2 p} g^{m} p x^{m} x^{2 p} e^{i \pi p} \Gamma\left(p\right) \Gamma\left(- \frac{m}{2} - p + \frac{1}{2}\right) {{}_{2}F_{1}\left(\begin{matrix} 1 - p, - \frac{m}{2} - p + \frac{1}{2} \\ - \frac{m}{2} - p + \frac{3}{2} \end{matrix}\middle| {\frac{d^{2}}{e^{2} x^{2}}} \right)}}{2 e^{2} x \Gamma\left(p + 1\right) \Gamma\left(- \frac{m}{2} - p + \frac{3}{2}\right)} - \frac{e^{2 p} g^{m} p x^{m} x^{2 p} e^{i \pi p} \Gamma\left(p\right) \Gamma\left(- \frac{m}{2} - p\right) {{}_{2}F_{1}\left(\begin{matrix} 1 - p, - \frac{m}{2} - p \\ - \frac{m}{2} - p + 1 \end{matrix}\middle| {\frac{d^{2}}{e^{2} x^{2}}} \right)}}{2 e \Gamma\left(p + 1\right) \Gamma\left(- \frac{m}{2} - p + 1\right)}"," ",0,"-0**p*d*d**(2*p)*g**m*m*x**m*lerchphi(d**2/(e**2*x**2), 1, 1/2 - m/2)*gamma(1/2 - m/2)/(4*e**2*x*gamma(3/2 - m/2)) + 0**p*d*d**(2*p)*g**m*x**m*lerchphi(d**2/(e**2*x**2), 1, 1/2 - m/2)*gamma(1/2 - m/2)/(4*e**2*x*gamma(3/2 - m/2)) + 0**p*d**(2*p)*g**m*m*x**m*lerchphi(d**2/(e**2*x**2), 1, m*exp_polar(I*pi)/2)*gamma(-m/2)/(4*e*gamma(1 - m/2)) + d*e**(2*p)*g**m*p*x**m*x**(2*p)*exp(I*pi*p)*gamma(p)*gamma(-m/2 - p + 1/2)*hyper((1 - p, -m/2 - p + 1/2), (-m/2 - p + 3/2,), d**2/(e**2*x**2))/(2*e**2*x*gamma(p + 1)*gamma(-m/2 - p + 3/2)) - e**(2*p)*g**m*p*x**m*x**(2*p)*exp(I*pi*p)*gamma(p)*gamma(-m/2 - p)*hyper((1 - p, -m/2 - p), (-m/2 - p + 1,), d**2/(e**2*x**2))/(2*e*gamma(p + 1)*gamma(-m/2 - p + 1))","C",0
311,0,0,0,0.000000," ","integrate((g*x)**m*(-e**2*x**2+d**2)**p/(e*x+d)**2,x)","\int \frac{\left(g x\right)^{m} \left(- \left(- d + e x\right) \left(d + e x\right)\right)^{p}}{\left(d + e x\right)^{2}}\, dx"," ",0,"Integral((g*x)**m*(-(-d + e*x)*(d + e*x))**p/(d + e*x)**2, x)","F",0
312,0,0,0,0.000000," ","integrate((g*x)**m*(-e**2*x**2+d**2)**p/(e*x+d)**3,x)","\int \frac{\left(g x\right)^{m} \left(- \left(- d + e x\right) \left(d + e x\right)\right)^{p}}{\left(d + e x\right)^{3}}\, dx"," ",0,"Integral((g*x)**m*(-(-d + e*x)*(d + e*x))**p/(d + e*x)**3, x)","F",0
313,1,308,0,10.813748," ","integrate((g*x)**m*(-a**2*x**2+1)**p/(a*x+1),x)","\frac{0^{p} g^{m} m x^{m} \Phi\left(\frac{1}{a^{2} x^{2}}, 1, \frac{m e^{i \pi}}{2}\right) \Gamma\left(- \frac{m}{2}\right)}{4 a \Gamma\left(1 - \frac{m}{2}\right)} - \frac{0^{p} g^{m} m x^{m} \Phi\left(\frac{1}{a^{2} x^{2}}, 1, \frac{1}{2} - \frac{m}{2}\right) \Gamma\left(\frac{1}{2} - \frac{m}{2}\right)}{4 a^{2} x \Gamma\left(\frac{3}{2} - \frac{m}{2}\right)} + \frac{0^{p} g^{m} x^{m} \Phi\left(\frac{1}{a^{2} x^{2}}, 1, \frac{1}{2} - \frac{m}{2}\right) \Gamma\left(\frac{1}{2} - \frac{m}{2}\right)}{4 a^{2} x \Gamma\left(\frac{3}{2} - \frac{m}{2}\right)} - \frac{a^{2 p} g^{m} p x^{m} x^{2 p} e^{i \pi p} \Gamma\left(p\right) \Gamma\left(- \frac{m}{2} - p\right) {{}_{2}F_{1}\left(\begin{matrix} 1 - p, - \frac{m}{2} - p \\ - \frac{m}{2} - p + 1 \end{matrix}\middle| {\frac{1}{a^{2} x^{2}}} \right)}}{2 a \Gamma\left(p + 1\right) \Gamma\left(- \frac{m}{2} - p + 1\right)} + \frac{a^{2 p} g^{m} p x^{m} x^{2 p} e^{i \pi p} \Gamma\left(p\right) \Gamma\left(- \frac{m}{2} - p + \frac{1}{2}\right) {{}_{2}F_{1}\left(\begin{matrix} 1 - p, - \frac{m}{2} - p + \frac{1}{2} \\ - \frac{m}{2} - p + \frac{3}{2} \end{matrix}\middle| {\frac{1}{a^{2} x^{2}}} \right)}}{2 a^{2} x \Gamma\left(p + 1\right) \Gamma\left(- \frac{m}{2} - p + \frac{3}{2}\right)}"," ",0,"0**p*g**m*m*x**m*lerchphi(1/(a**2*x**2), 1, m*exp_polar(I*pi)/2)*gamma(-m/2)/(4*a*gamma(1 - m/2)) - 0**p*g**m*m*x**m*lerchphi(1/(a**2*x**2), 1, 1/2 - m/2)*gamma(1/2 - m/2)/(4*a**2*x*gamma(3/2 - m/2)) + 0**p*g**m*x**m*lerchphi(1/(a**2*x**2), 1, 1/2 - m/2)*gamma(1/2 - m/2)/(4*a**2*x*gamma(3/2 - m/2)) - a**(2*p)*g**m*p*x**m*x**(2*p)*exp(I*pi*p)*gamma(p)*gamma(-m/2 - p)*hyper((1 - p, -m/2 - p), (-m/2 - p + 1,), 1/(a**2*x**2))/(2*a*gamma(p + 1)*gamma(-m/2 - p + 1)) + a**(2*p)*g**m*p*x**m*x**(2*p)*exp(I*pi*p)*gamma(p)*gamma(-m/2 - p + 1/2)*hyper((1 - p, -m/2 - p + 1/2), (-m/2 - p + 3/2,), 1/(a**2*x**2))/(2*a**2*x*gamma(p + 1)*gamma(-m/2 - p + 3/2))","C",0
314,0,0,0,0.000000," ","integrate((g*x)**m*(e*x+d)**n*(-e**2*x**2+d**2)**p,x)","\int \left(g x\right)^{m} \left(- \left(- d + e x\right) \left(d + e x\right)\right)^{p} \left(d + e x\right)^{n}\, dx"," ",0,"Integral((g*x)**m*(-(-d + e*x)*(d + e*x))**p*(d + e*x)**n, x)","F",0
315,1,68,0,11.157070," ","integrate(x*(1+x)**(1/2)/(x**2+1),x)","2 \sqrt{x + 1} - 4 \operatorname{RootSum} {\left(512 t^{4} + 32 t^{2} + 1, \left( t \mapsto t \log{\left(- 128 t^{3} + \sqrt{x + 1} \right)} \right)\right)} + 2 \operatorname{RootSum} {\left(128 t^{4} + 16 t^{2} + 1, \left( t \mapsto t \log{\left(64 t^{3} + 4 t + \sqrt{x + 1} \right)} \right)\right)}"," ",0,"2*sqrt(x + 1) - 4*RootSum(512*_t**4 + 32*_t**2 + 1, Lambda(_t, _t*log(-128*_t**3 + sqrt(x + 1)))) + 2*RootSum(128*_t**4 + 16*_t**2 + 1, Lambda(_t, _t*log(64*_t**3 + 4*_t + sqrt(x + 1))))","A",0
316,0,0,0,0.000000," ","integrate(x**4*(c*x**2+a)**(1/2)/(e*x+d),x)","\int \frac{x^{4} \sqrt{a + c x^{2}}}{d + e x}\, dx"," ",0,"Integral(x**4*sqrt(a + c*x**2)/(d + e*x), x)","F",0
317,0,0,0,0.000000," ","integrate(x**3*(c*x**2+a)**(1/2)/(e*x+d),x)","\int \frac{x^{3} \sqrt{a + c x^{2}}}{d + e x}\, dx"," ",0,"Integral(x**3*sqrt(a + c*x**2)/(d + e*x), x)","F",0
318,0,0,0,0.000000," ","integrate(x**2*(c*x**2+a)**(1/2)/(e*x+d),x)","\int \frac{x^{2} \sqrt{a + c x^{2}}}{d + e x}\, dx"," ",0,"Integral(x**2*sqrt(a + c*x**2)/(d + e*x), x)","F",0
319,0,0,0,0.000000," ","integrate(x*(c*x**2+a)**(1/2)/(e*x+d),x)","\int \frac{x \sqrt{a + c x^{2}}}{d + e x}\, dx"," ",0,"Integral(x*sqrt(a + c*x**2)/(d + e*x), x)","F",0
320,0,0,0,0.000000," ","integrate((c*x**2+a)**(1/2)/(e*x+d),x)","\int \frac{\sqrt{a + c x^{2}}}{d + e x}\, dx"," ",0,"Integral(sqrt(a + c*x**2)/(d + e*x), x)","F",0
321,0,0,0,0.000000," ","integrate((c*x**2+a)**(1/2)/x/(e*x+d),x)","\int \frac{\sqrt{a + c x^{2}}}{x \left(d + e x\right)}\, dx"," ",0,"Integral(sqrt(a + c*x**2)/(x*(d + e*x)), x)","F",0
322,0,0,0,0.000000," ","integrate((c*x**2+a)**(1/2)/x**2/(e*x+d),x)","\int \frac{\sqrt{a + c x^{2}}}{x^{2} \left(d + e x\right)}\, dx"," ",0,"Integral(sqrt(a + c*x**2)/(x**2*(d + e*x)), x)","F",0
323,0,0,0,0.000000," ","integrate((c*x**2+a)**(1/2)/x**3/(e*x+d),x)","\int \frac{\sqrt{a + c x^{2}}}{x^{3} \left(d + e x\right)}\, dx"," ",0,"Integral(sqrt(a + c*x**2)/(x**3*(d + e*x)), x)","F",0
324,0,0,0,0.000000," ","integrate((c*x**2+a)**(1/2)/x**4/(e*x+d),x)","\int \frac{\sqrt{a + c x^{2}}}{x^{4} \left(d + e x\right)}\, dx"," ",0,"Integral(sqrt(a + c*x**2)/(x**4*(d + e*x)), x)","F",0
325,0,0,0,0.000000," ","integrate((c*x**2+a)**(1/2)/x**5/(e*x+d),x)","\int \frac{\sqrt{a + c x^{2}}}{x^{5} \left(d + e x\right)}\, dx"," ",0,"Integral(sqrt(a + c*x**2)/(x**5*(d + e*x)), x)","F",0
326,0,0,0,0.000000," ","integrate(x**4/(e*x+d)/(c*x**2+a)**(1/2),x)","\int \frac{x^{4}}{\sqrt{a + c x^{2}} \left(d + e x\right)}\, dx"," ",0,"Integral(x**4/(sqrt(a + c*x**2)*(d + e*x)), x)","F",0
327,0,0,0,0.000000," ","integrate(x**3/(e*x+d)/(c*x**2+a)**(1/2),x)","\int \frac{x^{3}}{\sqrt{a + c x^{2}} \left(d + e x\right)}\, dx"," ",0,"Integral(x**3/(sqrt(a + c*x**2)*(d + e*x)), x)","F",0
328,0,0,0,0.000000," ","integrate(x**2/(e*x+d)/(c*x**2+a)**(1/2),x)","\int \frac{x^{2}}{\sqrt{a + c x^{2}} \left(d + e x\right)}\, dx"," ",0,"Integral(x**2/(sqrt(a + c*x**2)*(d + e*x)), x)","F",0
329,0,0,0,0.000000," ","integrate(x/(e*x+d)/(c*x**2+a)**(1/2),x)","\int \frac{x}{\sqrt{a + c x^{2}} \left(d + e x\right)}\, dx"," ",0,"Integral(x/(sqrt(a + c*x**2)*(d + e*x)), x)","F",0
330,0,0,0,0.000000," ","integrate(1/(e*x+d)/(c*x**2+a)**(1/2),x)","\int \frac{1}{\sqrt{a + c x^{2}} \left(d + e x\right)}\, dx"," ",0,"Integral(1/(sqrt(a + c*x**2)*(d + e*x)), x)","F",0
331,0,0,0,0.000000," ","integrate(1/x/(e*x+d)/(c*x**2+a)**(1/2),x)","\int \frac{1}{x \sqrt{a + c x^{2}} \left(d + e x\right)}\, dx"," ",0,"Integral(1/(x*sqrt(a + c*x**2)*(d + e*x)), x)","F",0
332,0,0,0,0.000000," ","integrate(1/x**2/(e*x+d)/(c*x**2+a)**(1/2),x)","\int \frac{1}{x^{2} \sqrt{a + c x^{2}} \left(d + e x\right)}\, dx"," ",0,"Integral(1/(x**2*sqrt(a + c*x**2)*(d + e*x)), x)","F",0
333,0,0,0,0.000000," ","integrate(1/x**3/(e*x+d)/(c*x**2+a)**(1/2),x)","\int \frac{1}{x^{3} \sqrt{a + c x^{2}} \left(d + e x\right)}\, dx"," ",0,"Integral(1/(x**3*sqrt(a + c*x**2)*(d + e*x)), x)","F",0
334,0,0,0,0.000000," ","integrate(x**4/(e*x+d)/(c*x**2+a)**(3/2),x)","\int \frac{x^{4}}{\left(a + c x^{2}\right)^{\frac{3}{2}} \left(d + e x\right)}\, dx"," ",0,"Integral(x**4/((a + c*x**2)**(3/2)*(d + e*x)), x)","F",0
335,0,0,0,0.000000," ","integrate(x**3/(e*x+d)/(c*x**2+a)**(3/2),x)","\int \frac{x^{3}}{\left(a + c x^{2}\right)^{\frac{3}{2}} \left(d + e x\right)}\, dx"," ",0,"Integral(x**3/((a + c*x**2)**(3/2)*(d + e*x)), x)","F",0
336,0,0,0,0.000000," ","integrate(x**2/(e*x+d)/(c*x**2+a)**(3/2),x)","\int \frac{x^{2}}{\left(a + c x^{2}\right)^{\frac{3}{2}} \left(d + e x\right)}\, dx"," ",0,"Integral(x**2/((a + c*x**2)**(3/2)*(d + e*x)), x)","F",0
337,0,0,0,0.000000," ","integrate(x/(e*x+d)/(c*x**2+a)**(3/2),x)","\int \frac{x}{\left(a + c x^{2}\right)^{\frac{3}{2}} \left(d + e x\right)}\, dx"," ",0,"Integral(x/((a + c*x**2)**(3/2)*(d + e*x)), x)","F",0
338,0,0,0,0.000000," ","integrate(1/(e*x+d)/(c*x**2+a)**(3/2),x)","\int \frac{1}{\left(a + c x^{2}\right)^{\frac{3}{2}} \left(d + e x\right)}\, dx"," ",0,"Integral(1/((a + c*x**2)**(3/2)*(d + e*x)), x)","F",0
339,0,0,0,0.000000," ","integrate(1/x/(e*x+d)/(c*x**2+a)**(3/2),x)","\int \frac{1}{x \left(a + c x^{2}\right)^{\frac{3}{2}} \left(d + e x\right)}\, dx"," ",0,"Integral(1/(x*(a + c*x**2)**(3/2)*(d + e*x)), x)","F",0
340,0,0,0,0.000000," ","integrate(1/x**2/(e*x+d)/(c*x**2+a)**(3/2),x)","\int \frac{1}{x^{2} \left(a + c x^{2}\right)^{\frac{3}{2}} \left(d + e x\right)}\, dx"," ",0,"Integral(1/(x**2*(a + c*x**2)**(3/2)*(d + e*x)), x)","F",0
341,0,0,0,0.000000," ","integrate(1/x**3/(e*x+d)/(c*x**2+a)**(3/2),x)","\int \frac{1}{x^{3} \left(a + c x^{2}\right)^{\frac{3}{2}} \left(d + e x\right)}\, dx"," ",0,"Integral(1/(x**3*(a + c*x**2)**(3/2)*(d + e*x)), x)","F",0
342,0,0,0,0.000000," ","integrate(x**5/(e*x+d)**2/(c*x**2+a)**(1/2),x)","\int \frac{x^{5}}{\sqrt{a + c x^{2}} \left(d + e x\right)^{2}}\, dx"," ",0,"Integral(x**5/(sqrt(a + c*x**2)*(d + e*x)**2), x)","F",0
343,0,0,0,0.000000," ","integrate(x**4/(e*x+d)**2/(c*x**2+a)**(1/2),x)","\int \frac{x^{4}}{\sqrt{a + c x^{2}} \left(d + e x\right)^{2}}\, dx"," ",0,"Integral(x**4/(sqrt(a + c*x**2)*(d + e*x)**2), x)","F",0
344,0,0,0,0.000000," ","integrate(x**3/(e*x+d)**2/(c*x**2+a)**(1/2),x)","\int \frac{x^{3}}{\sqrt{a + c x^{2}} \left(d + e x\right)^{2}}\, dx"," ",0,"Integral(x**3/(sqrt(a + c*x**2)*(d + e*x)**2), x)","F",0
345,0,0,0,0.000000," ","integrate(x**2/(e*x+d)**2/(c*x**2+a)**(1/2),x)","\int \frac{x^{2}}{\sqrt{a + c x^{2}} \left(d + e x\right)^{2}}\, dx"," ",0,"Integral(x**2/(sqrt(a + c*x**2)*(d + e*x)**2), x)","F",0
346,0,0,0,0.000000," ","integrate(x/(e*x+d)**2/(c*x**2+a)**(1/2),x)","\int \frac{x}{\sqrt{a + c x^{2}} \left(d + e x\right)^{2}}\, dx"," ",0,"Integral(x/(sqrt(a + c*x**2)*(d + e*x)**2), x)","F",0
347,0,0,0,0.000000," ","integrate(1/(e*x+d)**2/(c*x**2+a)**(1/2),x)","\int \frac{1}{\sqrt{a + c x^{2}} \left(d + e x\right)^{2}}\, dx"," ",0,"Integral(1/(sqrt(a + c*x**2)*(d + e*x)**2), x)","F",0
348,0,0,0,0.000000," ","integrate(1/x/(e*x+d)**2/(c*x**2+a)**(1/2),x)","\int \frac{1}{x \sqrt{a + c x^{2}} \left(d + e x\right)^{2}}\, dx"," ",0,"Integral(1/(x*sqrt(a + c*x**2)*(d + e*x)**2), x)","F",0
349,0,0,0,0.000000," ","integrate(1/x**2/(e*x+d)**2/(c*x**2+a)**(1/2),x)","\int \frac{1}{x^{2} \sqrt{a + c x^{2}} \left(d + e x\right)^{2}}\, dx"," ",0,"Integral(1/(x**2*sqrt(a + c*x**2)*(d + e*x)**2), x)","F",0
350,0,0,0,0.000000," ","integrate(1/x**3/(e*x+d)**2/(c*x**2+a)**(1/2),x)","\int \frac{1}{x^{3} \sqrt{a + c x^{2}} \left(d + e x\right)^{2}}\, dx"," ",0,"Integral(1/(x**3*sqrt(a + c*x**2)*(d + e*x)**2), x)","F",0
351,1,4134,0,6.697450," ","integrate(x**2*(b*x+a)**n*(d*x**2+c),x)","\begin{cases} a^{n} \left(\frac{c x^{3}}{3} + \frac{d x^{5}}{5}\right) & \text{for}\: b = 0 \\\frac{12 a^{4} d \log{\left(\frac{a}{b} + x \right)}}{12 a^{4} b^{5} + 48 a^{3} b^{6} x + 72 a^{2} b^{7} x^{2} + 48 a b^{8} x^{3} + 12 b^{9} x^{4}} + \frac{25 a^{4} d}{12 a^{4} b^{5} + 48 a^{3} b^{6} x + 72 a^{2} b^{7} x^{2} + 48 a b^{8} x^{3} + 12 b^{9} x^{4}} + \frac{48 a^{3} b d x \log{\left(\frac{a}{b} + x \right)}}{12 a^{4} b^{5} + 48 a^{3} b^{6} x + 72 a^{2} b^{7} x^{2} + 48 a b^{8} x^{3} + 12 b^{9} x^{4}} + \frac{88 a^{3} b d x}{12 a^{4} b^{5} + 48 a^{3} b^{6} x + 72 a^{2} b^{7} x^{2} + 48 a b^{8} x^{3} + 12 b^{9} x^{4}} - \frac{a^{2} b^{2} c}{12 a^{4} b^{5} + 48 a^{3} b^{6} x + 72 a^{2} b^{7} x^{2} + 48 a b^{8} x^{3} + 12 b^{9} x^{4}} + \frac{72 a^{2} b^{2} d x^{2} \log{\left(\frac{a}{b} + x \right)}}{12 a^{4} b^{5} + 48 a^{3} b^{6} x + 72 a^{2} b^{7} x^{2} + 48 a b^{8} x^{3} + 12 b^{9} x^{4}} + \frac{108 a^{2} b^{2} d x^{2}}{12 a^{4} b^{5} + 48 a^{3} b^{6} x + 72 a^{2} b^{7} x^{2} + 48 a b^{8} x^{3} + 12 b^{9} x^{4}} - \frac{4 a b^{3} c x}{12 a^{4} b^{5} + 48 a^{3} b^{6} x + 72 a^{2} b^{7} x^{2} + 48 a b^{8} x^{3} + 12 b^{9} x^{4}} + \frac{48 a b^{3} d x^{3} \log{\left(\frac{a}{b} + x \right)}}{12 a^{4} b^{5} + 48 a^{3} b^{6} x + 72 a^{2} b^{7} x^{2} + 48 a b^{8} x^{3} + 12 b^{9} x^{4}} + \frac{48 a b^{3} d x^{3}}{12 a^{4} b^{5} + 48 a^{3} b^{6} x + 72 a^{2} b^{7} x^{2} + 48 a b^{8} x^{3} + 12 b^{9} x^{4}} - \frac{6 b^{4} c x^{2}}{12 a^{4} b^{5} + 48 a^{3} b^{6} x + 72 a^{2} b^{7} x^{2} + 48 a b^{8} x^{3} + 12 b^{9} x^{4}} + \frac{12 b^{4} d x^{4} \log{\left(\frac{a}{b} + x \right)}}{12 a^{4} b^{5} + 48 a^{3} b^{6} x + 72 a^{2} b^{7} x^{2} + 48 a b^{8} x^{3} + 12 b^{9} x^{4}} & \text{for}\: n = -5 \\- \frac{12 a^{4} d \log{\left(\frac{a}{b} + x \right)}}{3 a^{3} b^{5} + 9 a^{2} b^{6} x + 9 a b^{7} x^{2} + 3 b^{8} x^{3}} - \frac{22 a^{4} d}{3 a^{3} b^{5} + 9 a^{2} b^{6} x + 9 a b^{7} x^{2} + 3 b^{8} x^{3}} - \frac{36 a^{3} b d x \log{\left(\frac{a}{b} + x \right)}}{3 a^{3} b^{5} + 9 a^{2} b^{6} x + 9 a b^{7} x^{2} + 3 b^{8} x^{3}} - \frac{54 a^{3} b d x}{3 a^{3} b^{5} + 9 a^{2} b^{6} x + 9 a b^{7} x^{2} + 3 b^{8} x^{3}} - \frac{a^{2} b^{2} c}{3 a^{3} b^{5} + 9 a^{2} b^{6} x + 9 a b^{7} x^{2} + 3 b^{8} x^{3}} - \frac{36 a^{2} b^{2} d x^{2} \log{\left(\frac{a}{b} + x \right)}}{3 a^{3} b^{5} + 9 a^{2} b^{6} x + 9 a b^{7} x^{2} + 3 b^{8} x^{3}} - \frac{36 a^{2} b^{2} d x^{2}}{3 a^{3} b^{5} + 9 a^{2} b^{6} x + 9 a b^{7} x^{2} + 3 b^{8} x^{3}} - \frac{3 a b^{3} c x}{3 a^{3} b^{5} + 9 a^{2} b^{6} x + 9 a b^{7} x^{2} + 3 b^{8} x^{3}} - \frac{12 a b^{3} d x^{3} \log{\left(\frac{a}{b} + x \right)}}{3 a^{3} b^{5} + 9 a^{2} b^{6} x + 9 a b^{7} x^{2} + 3 b^{8} x^{3}} - \frac{3 b^{4} c x^{2}}{3 a^{3} b^{5} + 9 a^{2} b^{6} x + 9 a b^{7} x^{2} + 3 b^{8} x^{3}} + \frac{3 b^{4} d x^{4}}{3 a^{3} b^{5} + 9 a^{2} b^{6} x + 9 a b^{7} x^{2} + 3 b^{8} x^{3}} & \text{for}\: n = -4 \\\frac{12 a^{4} d \log{\left(\frac{a}{b} + x \right)}}{2 a^{2} b^{5} + 4 a b^{6} x + 2 b^{7} x^{2}} + \frac{18 a^{4} d}{2 a^{2} b^{5} + 4 a b^{6} x + 2 b^{7} x^{2}} + \frac{24 a^{3} b d x \log{\left(\frac{a}{b} + x \right)}}{2 a^{2} b^{5} + 4 a b^{6} x + 2 b^{7} x^{2}} + \frac{24 a^{3} b d x}{2 a^{2} b^{5} + 4 a b^{6} x + 2 b^{7} x^{2}} + \frac{2 a^{2} b^{2} c \log{\left(\frac{a}{b} + x \right)}}{2 a^{2} b^{5} + 4 a b^{6} x + 2 b^{7} x^{2}} + \frac{3 a^{2} b^{2} c}{2 a^{2} b^{5} + 4 a b^{6} x + 2 b^{7} x^{2}} + \frac{12 a^{2} b^{2} d x^{2} \log{\left(\frac{a}{b} + x \right)}}{2 a^{2} b^{5} + 4 a b^{6} x + 2 b^{7} x^{2}} + \frac{4 a b^{3} c x \log{\left(\frac{a}{b} + x \right)}}{2 a^{2} b^{5} + 4 a b^{6} x + 2 b^{7} x^{2}} + \frac{4 a b^{3} c x}{2 a^{2} b^{5} + 4 a b^{6} x + 2 b^{7} x^{2}} - \frac{4 a b^{3} d x^{3}}{2 a^{2} b^{5} + 4 a b^{6} x + 2 b^{7} x^{2}} + \frac{2 b^{4} c x^{2} \log{\left(\frac{a}{b} + x \right)}}{2 a^{2} b^{5} + 4 a b^{6} x + 2 b^{7} x^{2}} + \frac{b^{4} d x^{4}}{2 a^{2} b^{5} + 4 a b^{6} x + 2 b^{7} x^{2}} & \text{for}\: n = -3 \\- \frac{12 a^{4} d \log{\left(\frac{a}{b} + x \right)}}{3 a b^{5} + 3 b^{6} x} - \frac{12 a^{4} d}{3 a b^{5} + 3 b^{6} x} - \frac{12 a^{3} b d x \log{\left(\frac{a}{b} + x \right)}}{3 a b^{5} + 3 b^{6} x} - \frac{6 a^{2} b^{2} c \log{\left(\frac{a}{b} + x \right)}}{3 a b^{5} + 3 b^{6} x} - \frac{6 a^{2} b^{2} c}{3 a b^{5} + 3 b^{6} x} + \frac{6 a^{2} b^{2} d x^{2}}{3 a b^{5} + 3 b^{6} x} - \frac{6 a b^{3} c x \log{\left(\frac{a}{b} + x \right)}}{3 a b^{5} + 3 b^{6} x} - \frac{2 a b^{3} d x^{3}}{3 a b^{5} + 3 b^{6} x} + \frac{3 b^{4} c x^{2}}{3 a b^{5} + 3 b^{6} x} + \frac{b^{4} d x^{4}}{3 a b^{5} + 3 b^{6} x} & \text{for}\: n = -2 \\\frac{a^{4} d \log{\left(\frac{a}{b} + x \right)}}{b^{5}} - \frac{a^{3} d x}{b^{4}} + \frac{a^{2} c \log{\left(\frac{a}{b} + x \right)}}{b^{3}} + \frac{a^{2} d x^{2}}{2 b^{3}} - \frac{a c x}{b^{2}} - \frac{a d x^{3}}{3 b^{2}} + \frac{c x^{2}}{2 b} + \frac{d x^{4}}{4 b} & \text{for}\: n = -1 \\\frac{24 a^{5} d \left(a + b x\right)^{n}}{b^{5} n^{5} + 15 b^{5} n^{4} + 85 b^{5} n^{3} + 225 b^{5} n^{2} + 274 b^{5} n + 120 b^{5}} - \frac{24 a^{4} b d n x \left(a + b x\right)^{n}}{b^{5} n^{5} + 15 b^{5} n^{4} + 85 b^{5} n^{3} + 225 b^{5} n^{2} + 274 b^{5} n + 120 b^{5}} + \frac{2 a^{3} b^{2} c n^{2} \left(a + b x\right)^{n}}{b^{5} n^{5} + 15 b^{5} n^{4} + 85 b^{5} n^{3} + 225 b^{5} n^{2} + 274 b^{5} n + 120 b^{5}} + \frac{18 a^{3} b^{2} c n \left(a + b x\right)^{n}}{b^{5} n^{5} + 15 b^{5} n^{4} + 85 b^{5} n^{3} + 225 b^{5} n^{2} + 274 b^{5} n + 120 b^{5}} + \frac{40 a^{3} b^{2} c \left(a + b x\right)^{n}}{b^{5} n^{5} + 15 b^{5} n^{4} + 85 b^{5} n^{3} + 225 b^{5} n^{2} + 274 b^{5} n + 120 b^{5}} + \frac{12 a^{3} b^{2} d n^{2} x^{2} \left(a + b x\right)^{n}}{b^{5} n^{5} + 15 b^{5} n^{4} + 85 b^{5} n^{3} + 225 b^{5} n^{2} + 274 b^{5} n + 120 b^{5}} + \frac{12 a^{3} b^{2} d n x^{2} \left(a + b x\right)^{n}}{b^{5} n^{5} + 15 b^{5} n^{4} + 85 b^{5} n^{3} + 225 b^{5} n^{2} + 274 b^{5} n + 120 b^{5}} - \frac{2 a^{2} b^{3} c n^{3} x \left(a + b x\right)^{n}}{b^{5} n^{5} + 15 b^{5} n^{4} + 85 b^{5} n^{3} + 225 b^{5} n^{2} + 274 b^{5} n + 120 b^{5}} - \frac{18 a^{2} b^{3} c n^{2} x \left(a + b x\right)^{n}}{b^{5} n^{5} + 15 b^{5} n^{4} + 85 b^{5} n^{3} + 225 b^{5} n^{2} + 274 b^{5} n + 120 b^{5}} - \frac{40 a^{2} b^{3} c n x \left(a + b x\right)^{n}}{b^{5} n^{5} + 15 b^{5} n^{4} + 85 b^{5} n^{3} + 225 b^{5} n^{2} + 274 b^{5} n + 120 b^{5}} - \frac{4 a^{2} b^{3} d n^{3} x^{3} \left(a + b x\right)^{n}}{b^{5} n^{5} + 15 b^{5} n^{4} + 85 b^{5} n^{3} + 225 b^{5} n^{2} + 274 b^{5} n + 120 b^{5}} - \frac{12 a^{2} b^{3} d n^{2} x^{3} \left(a + b x\right)^{n}}{b^{5} n^{5} + 15 b^{5} n^{4} + 85 b^{5} n^{3} + 225 b^{5} n^{2} + 274 b^{5} n + 120 b^{5}} - \frac{8 a^{2} b^{3} d n x^{3} \left(a + b x\right)^{n}}{b^{5} n^{5} + 15 b^{5} n^{4} + 85 b^{5} n^{3} + 225 b^{5} n^{2} + 274 b^{5} n + 120 b^{5}} + \frac{a b^{4} c n^{4} x^{2} \left(a + b x\right)^{n}}{b^{5} n^{5} + 15 b^{5} n^{4} + 85 b^{5} n^{3} + 225 b^{5} n^{2} + 274 b^{5} n + 120 b^{5}} + \frac{10 a b^{4} c n^{3} x^{2} \left(a + b x\right)^{n}}{b^{5} n^{5} + 15 b^{5} n^{4} + 85 b^{5} n^{3} + 225 b^{5} n^{2} + 274 b^{5} n + 120 b^{5}} + \frac{29 a b^{4} c n^{2} x^{2} \left(a + b x\right)^{n}}{b^{5} n^{5} + 15 b^{5} n^{4} + 85 b^{5} n^{3} + 225 b^{5} n^{2} + 274 b^{5} n + 120 b^{5}} + \frac{20 a b^{4} c n x^{2} \left(a + b x\right)^{n}}{b^{5} n^{5} + 15 b^{5} n^{4} + 85 b^{5} n^{3} + 225 b^{5} n^{2} + 274 b^{5} n + 120 b^{5}} + \frac{a b^{4} d n^{4} x^{4} \left(a + b x\right)^{n}}{b^{5} n^{5} + 15 b^{5} n^{4} + 85 b^{5} n^{3} + 225 b^{5} n^{2} + 274 b^{5} n + 120 b^{5}} + \frac{6 a b^{4} d n^{3} x^{4} \left(a + b x\right)^{n}}{b^{5} n^{5} + 15 b^{5} n^{4} + 85 b^{5} n^{3} + 225 b^{5} n^{2} + 274 b^{5} n + 120 b^{5}} + \frac{11 a b^{4} d n^{2} x^{4} \left(a + b x\right)^{n}}{b^{5} n^{5} + 15 b^{5} n^{4} + 85 b^{5} n^{3} + 225 b^{5} n^{2} + 274 b^{5} n + 120 b^{5}} + \frac{6 a b^{4} d n x^{4} \left(a + b x\right)^{n}}{b^{5} n^{5} + 15 b^{5} n^{4} + 85 b^{5} n^{3} + 225 b^{5} n^{2} + 274 b^{5} n + 120 b^{5}} + \frac{b^{5} c n^{4} x^{3} \left(a + b x\right)^{n}}{b^{5} n^{5} + 15 b^{5} n^{4} + 85 b^{5} n^{3} + 225 b^{5} n^{2} + 274 b^{5} n + 120 b^{5}} + \frac{12 b^{5} c n^{3} x^{3} \left(a + b x\right)^{n}}{b^{5} n^{5} + 15 b^{5} n^{4} + 85 b^{5} n^{3} + 225 b^{5} n^{2} + 274 b^{5} n + 120 b^{5}} + \frac{49 b^{5} c n^{2} x^{3} \left(a + b x\right)^{n}}{b^{5} n^{5} + 15 b^{5} n^{4} + 85 b^{5} n^{3} + 225 b^{5} n^{2} + 274 b^{5} n + 120 b^{5}} + \frac{78 b^{5} c n x^{3} \left(a + b x\right)^{n}}{b^{5} n^{5} + 15 b^{5} n^{4} + 85 b^{5} n^{3} + 225 b^{5} n^{2} + 274 b^{5} n + 120 b^{5}} + \frac{40 b^{5} c x^{3} \left(a + b x\right)^{n}}{b^{5} n^{5} + 15 b^{5} n^{4} + 85 b^{5} n^{3} + 225 b^{5} n^{2} + 274 b^{5} n + 120 b^{5}} + \frac{b^{5} d n^{4} x^{5} \left(a + b x\right)^{n}}{b^{5} n^{5} + 15 b^{5} n^{4} + 85 b^{5} n^{3} + 225 b^{5} n^{2} + 274 b^{5} n + 120 b^{5}} + \frac{10 b^{5} d n^{3} x^{5} \left(a + b x\right)^{n}}{b^{5} n^{5} + 15 b^{5} n^{4} + 85 b^{5} n^{3} + 225 b^{5} n^{2} + 274 b^{5} n + 120 b^{5}} + \frac{35 b^{5} d n^{2} x^{5} \left(a + b x\right)^{n}}{b^{5} n^{5} + 15 b^{5} n^{4} + 85 b^{5} n^{3} + 225 b^{5} n^{2} + 274 b^{5} n + 120 b^{5}} + \frac{50 b^{5} d n x^{5} \left(a + b x\right)^{n}}{b^{5} n^{5} + 15 b^{5} n^{4} + 85 b^{5} n^{3} + 225 b^{5} n^{2} + 274 b^{5} n + 120 b^{5}} + \frac{24 b^{5} d x^{5} \left(a + b x\right)^{n}}{b^{5} n^{5} + 15 b^{5} n^{4} + 85 b^{5} n^{3} + 225 b^{5} n^{2} + 274 b^{5} n + 120 b^{5}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**n*(c*x**3/3 + d*x**5/5), Eq(b, 0)), (12*a**4*d*log(a/b + x)/(12*a**4*b**5 + 48*a**3*b**6*x + 72*a**2*b**7*x**2 + 48*a*b**8*x**3 + 12*b**9*x**4) + 25*a**4*d/(12*a**4*b**5 + 48*a**3*b**6*x + 72*a**2*b**7*x**2 + 48*a*b**8*x**3 + 12*b**9*x**4) + 48*a**3*b*d*x*log(a/b + x)/(12*a**4*b**5 + 48*a**3*b**6*x + 72*a**2*b**7*x**2 + 48*a*b**8*x**3 + 12*b**9*x**4) + 88*a**3*b*d*x/(12*a**4*b**5 + 48*a**3*b**6*x + 72*a**2*b**7*x**2 + 48*a*b**8*x**3 + 12*b**9*x**4) - a**2*b**2*c/(12*a**4*b**5 + 48*a**3*b**6*x + 72*a**2*b**7*x**2 + 48*a*b**8*x**3 + 12*b**9*x**4) + 72*a**2*b**2*d*x**2*log(a/b + x)/(12*a**4*b**5 + 48*a**3*b**6*x + 72*a**2*b**7*x**2 + 48*a*b**8*x**3 + 12*b**9*x**4) + 108*a**2*b**2*d*x**2/(12*a**4*b**5 + 48*a**3*b**6*x + 72*a**2*b**7*x**2 + 48*a*b**8*x**3 + 12*b**9*x**4) - 4*a*b**3*c*x/(12*a**4*b**5 + 48*a**3*b**6*x + 72*a**2*b**7*x**2 + 48*a*b**8*x**3 + 12*b**9*x**4) + 48*a*b**3*d*x**3*log(a/b + x)/(12*a**4*b**5 + 48*a**3*b**6*x + 72*a**2*b**7*x**2 + 48*a*b**8*x**3 + 12*b**9*x**4) + 48*a*b**3*d*x**3/(12*a**4*b**5 + 48*a**3*b**6*x + 72*a**2*b**7*x**2 + 48*a*b**8*x**3 + 12*b**9*x**4) - 6*b**4*c*x**2/(12*a**4*b**5 + 48*a**3*b**6*x + 72*a**2*b**7*x**2 + 48*a*b**8*x**3 + 12*b**9*x**4) + 12*b**4*d*x**4*log(a/b + x)/(12*a**4*b**5 + 48*a**3*b**6*x + 72*a**2*b**7*x**2 + 48*a*b**8*x**3 + 12*b**9*x**4), Eq(n, -5)), (-12*a**4*d*log(a/b + x)/(3*a**3*b**5 + 9*a**2*b**6*x + 9*a*b**7*x**2 + 3*b**8*x**3) - 22*a**4*d/(3*a**3*b**5 + 9*a**2*b**6*x + 9*a*b**7*x**2 + 3*b**8*x**3) - 36*a**3*b*d*x*log(a/b + x)/(3*a**3*b**5 + 9*a**2*b**6*x + 9*a*b**7*x**2 + 3*b**8*x**3) - 54*a**3*b*d*x/(3*a**3*b**5 + 9*a**2*b**6*x + 9*a*b**7*x**2 + 3*b**8*x**3) - a**2*b**2*c/(3*a**3*b**5 + 9*a**2*b**6*x + 9*a*b**7*x**2 + 3*b**8*x**3) - 36*a**2*b**2*d*x**2*log(a/b + x)/(3*a**3*b**5 + 9*a**2*b**6*x + 9*a*b**7*x**2 + 3*b**8*x**3) - 36*a**2*b**2*d*x**2/(3*a**3*b**5 + 9*a**2*b**6*x + 9*a*b**7*x**2 + 3*b**8*x**3) - 3*a*b**3*c*x/(3*a**3*b**5 + 9*a**2*b**6*x + 9*a*b**7*x**2 + 3*b**8*x**3) - 12*a*b**3*d*x**3*log(a/b + x)/(3*a**3*b**5 + 9*a**2*b**6*x + 9*a*b**7*x**2 + 3*b**8*x**3) - 3*b**4*c*x**2/(3*a**3*b**5 + 9*a**2*b**6*x + 9*a*b**7*x**2 + 3*b**8*x**3) + 3*b**4*d*x**4/(3*a**3*b**5 + 9*a**2*b**6*x + 9*a*b**7*x**2 + 3*b**8*x**3), Eq(n, -4)), (12*a**4*d*log(a/b + x)/(2*a**2*b**5 + 4*a*b**6*x + 2*b**7*x**2) + 18*a**4*d/(2*a**2*b**5 + 4*a*b**6*x + 2*b**7*x**2) + 24*a**3*b*d*x*log(a/b + x)/(2*a**2*b**5 + 4*a*b**6*x + 2*b**7*x**2) + 24*a**3*b*d*x/(2*a**2*b**5 + 4*a*b**6*x + 2*b**7*x**2) + 2*a**2*b**2*c*log(a/b + x)/(2*a**2*b**5 + 4*a*b**6*x + 2*b**7*x**2) + 3*a**2*b**2*c/(2*a**2*b**5 + 4*a*b**6*x + 2*b**7*x**2) + 12*a**2*b**2*d*x**2*log(a/b + x)/(2*a**2*b**5 + 4*a*b**6*x + 2*b**7*x**2) + 4*a*b**3*c*x*log(a/b + x)/(2*a**2*b**5 + 4*a*b**6*x + 2*b**7*x**2) + 4*a*b**3*c*x/(2*a**2*b**5 + 4*a*b**6*x + 2*b**7*x**2) - 4*a*b**3*d*x**3/(2*a**2*b**5 + 4*a*b**6*x + 2*b**7*x**2) + 2*b**4*c*x**2*log(a/b + x)/(2*a**2*b**5 + 4*a*b**6*x + 2*b**7*x**2) + b**4*d*x**4/(2*a**2*b**5 + 4*a*b**6*x + 2*b**7*x**2), Eq(n, -3)), (-12*a**4*d*log(a/b + x)/(3*a*b**5 + 3*b**6*x) - 12*a**4*d/(3*a*b**5 + 3*b**6*x) - 12*a**3*b*d*x*log(a/b + x)/(3*a*b**5 + 3*b**6*x) - 6*a**2*b**2*c*log(a/b + x)/(3*a*b**5 + 3*b**6*x) - 6*a**2*b**2*c/(3*a*b**5 + 3*b**6*x) + 6*a**2*b**2*d*x**2/(3*a*b**5 + 3*b**6*x) - 6*a*b**3*c*x*log(a/b + x)/(3*a*b**5 + 3*b**6*x) - 2*a*b**3*d*x**3/(3*a*b**5 + 3*b**6*x) + 3*b**4*c*x**2/(3*a*b**5 + 3*b**6*x) + b**4*d*x**4/(3*a*b**5 + 3*b**6*x), Eq(n, -2)), (a**4*d*log(a/b + x)/b**5 - a**3*d*x/b**4 + a**2*c*log(a/b + x)/b**3 + a**2*d*x**2/(2*b**3) - a*c*x/b**2 - a*d*x**3/(3*b**2) + c*x**2/(2*b) + d*x**4/(4*b), Eq(n, -1)), (24*a**5*d*(a + b*x)**n/(b**5*n**5 + 15*b**5*n**4 + 85*b**5*n**3 + 225*b**5*n**2 + 274*b**5*n + 120*b**5) - 24*a**4*b*d*n*x*(a + b*x)**n/(b**5*n**5 + 15*b**5*n**4 + 85*b**5*n**3 + 225*b**5*n**2 + 274*b**5*n + 120*b**5) + 2*a**3*b**2*c*n**2*(a + b*x)**n/(b**5*n**5 + 15*b**5*n**4 + 85*b**5*n**3 + 225*b**5*n**2 + 274*b**5*n + 120*b**5) + 18*a**3*b**2*c*n*(a + b*x)**n/(b**5*n**5 + 15*b**5*n**4 + 85*b**5*n**3 + 225*b**5*n**2 + 274*b**5*n + 120*b**5) + 40*a**3*b**2*c*(a + b*x)**n/(b**5*n**5 + 15*b**5*n**4 + 85*b**5*n**3 + 225*b**5*n**2 + 274*b**5*n + 120*b**5) + 12*a**3*b**2*d*n**2*x**2*(a + b*x)**n/(b**5*n**5 + 15*b**5*n**4 + 85*b**5*n**3 + 225*b**5*n**2 + 274*b**5*n + 120*b**5) + 12*a**3*b**2*d*n*x**2*(a + b*x)**n/(b**5*n**5 + 15*b**5*n**4 + 85*b**5*n**3 + 225*b**5*n**2 + 274*b**5*n + 120*b**5) - 2*a**2*b**3*c*n**3*x*(a + b*x)**n/(b**5*n**5 + 15*b**5*n**4 + 85*b**5*n**3 + 225*b**5*n**2 + 274*b**5*n + 120*b**5) - 18*a**2*b**3*c*n**2*x*(a + b*x)**n/(b**5*n**5 + 15*b**5*n**4 + 85*b**5*n**3 + 225*b**5*n**2 + 274*b**5*n + 120*b**5) - 40*a**2*b**3*c*n*x*(a + b*x)**n/(b**5*n**5 + 15*b**5*n**4 + 85*b**5*n**3 + 225*b**5*n**2 + 274*b**5*n + 120*b**5) - 4*a**2*b**3*d*n**3*x**3*(a + b*x)**n/(b**5*n**5 + 15*b**5*n**4 + 85*b**5*n**3 + 225*b**5*n**2 + 274*b**5*n + 120*b**5) - 12*a**2*b**3*d*n**2*x**3*(a + b*x)**n/(b**5*n**5 + 15*b**5*n**4 + 85*b**5*n**3 + 225*b**5*n**2 + 274*b**5*n + 120*b**5) - 8*a**2*b**3*d*n*x**3*(a + b*x)**n/(b**5*n**5 + 15*b**5*n**4 + 85*b**5*n**3 + 225*b**5*n**2 + 274*b**5*n + 120*b**5) + a*b**4*c*n**4*x**2*(a + b*x)**n/(b**5*n**5 + 15*b**5*n**4 + 85*b**5*n**3 + 225*b**5*n**2 + 274*b**5*n + 120*b**5) + 10*a*b**4*c*n**3*x**2*(a + b*x)**n/(b**5*n**5 + 15*b**5*n**4 + 85*b**5*n**3 + 225*b**5*n**2 + 274*b**5*n + 120*b**5) + 29*a*b**4*c*n**2*x**2*(a + b*x)**n/(b**5*n**5 + 15*b**5*n**4 + 85*b**5*n**3 + 225*b**5*n**2 + 274*b**5*n + 120*b**5) + 20*a*b**4*c*n*x**2*(a + b*x)**n/(b**5*n**5 + 15*b**5*n**4 + 85*b**5*n**3 + 225*b**5*n**2 + 274*b**5*n + 120*b**5) + a*b**4*d*n**4*x**4*(a + b*x)**n/(b**5*n**5 + 15*b**5*n**4 + 85*b**5*n**3 + 225*b**5*n**2 + 274*b**5*n + 120*b**5) + 6*a*b**4*d*n**3*x**4*(a + b*x)**n/(b**5*n**5 + 15*b**5*n**4 + 85*b**5*n**3 + 225*b**5*n**2 + 274*b**5*n + 120*b**5) + 11*a*b**4*d*n**2*x**4*(a + b*x)**n/(b**5*n**5 + 15*b**5*n**4 + 85*b**5*n**3 + 225*b**5*n**2 + 274*b**5*n + 120*b**5) + 6*a*b**4*d*n*x**4*(a + b*x)**n/(b**5*n**5 + 15*b**5*n**4 + 85*b**5*n**3 + 225*b**5*n**2 + 274*b**5*n + 120*b**5) + b**5*c*n**4*x**3*(a + b*x)**n/(b**5*n**5 + 15*b**5*n**4 + 85*b**5*n**3 + 225*b**5*n**2 + 274*b**5*n + 120*b**5) + 12*b**5*c*n**3*x**3*(a + b*x)**n/(b**5*n**5 + 15*b**5*n**4 + 85*b**5*n**3 + 225*b**5*n**2 + 274*b**5*n + 120*b**5) + 49*b**5*c*n**2*x**3*(a + b*x)**n/(b**5*n**5 + 15*b**5*n**4 + 85*b**5*n**3 + 225*b**5*n**2 + 274*b**5*n + 120*b**5) + 78*b**5*c*n*x**3*(a + b*x)**n/(b**5*n**5 + 15*b**5*n**4 + 85*b**5*n**3 + 225*b**5*n**2 + 274*b**5*n + 120*b**5) + 40*b**5*c*x**3*(a + b*x)**n/(b**5*n**5 + 15*b**5*n**4 + 85*b**5*n**3 + 225*b**5*n**2 + 274*b**5*n + 120*b**5) + b**5*d*n**4*x**5*(a + b*x)**n/(b**5*n**5 + 15*b**5*n**4 + 85*b**5*n**3 + 225*b**5*n**2 + 274*b**5*n + 120*b**5) + 10*b**5*d*n**3*x**5*(a + b*x)**n/(b**5*n**5 + 15*b**5*n**4 + 85*b**5*n**3 + 225*b**5*n**2 + 274*b**5*n + 120*b**5) + 35*b**5*d*n**2*x**5*(a + b*x)**n/(b**5*n**5 + 15*b**5*n**4 + 85*b**5*n**3 + 225*b**5*n**2 + 274*b**5*n + 120*b**5) + 50*b**5*d*n*x**5*(a + b*x)**n/(b**5*n**5 + 15*b**5*n**4 + 85*b**5*n**3 + 225*b**5*n**2 + 274*b**5*n + 120*b**5) + 24*b**5*d*x**5*(a + b*x)**n/(b**5*n**5 + 15*b**5*n**4 + 85*b**5*n**3 + 225*b**5*n**2 + 274*b**5*n + 120*b**5), True))","A",0
352,1,2181,0,3.534580," ","integrate(x*(b*x+a)**n*(d*x**2+c),x)","\begin{cases} a^{n} \left(\frac{c x^{2}}{2} + \frac{d x^{4}}{4}\right) & \text{for}\: b = 0 \\\frac{6 a^{3} d \log{\left(\frac{a}{b} + x \right)}}{6 a^{3} b^{4} + 18 a^{2} b^{5} x + 18 a b^{6} x^{2} + 6 b^{7} x^{3}} + \frac{11 a^{3} d}{6 a^{3} b^{4} + 18 a^{2} b^{5} x + 18 a b^{6} x^{2} + 6 b^{7} x^{3}} + \frac{18 a^{2} b d x \log{\left(\frac{a}{b} + x \right)}}{6 a^{3} b^{4} + 18 a^{2} b^{5} x + 18 a b^{6} x^{2} + 6 b^{7} x^{3}} + \frac{27 a^{2} b d x}{6 a^{3} b^{4} + 18 a^{2} b^{5} x + 18 a b^{6} x^{2} + 6 b^{7} x^{3}} - \frac{a b^{2} c}{6 a^{3} b^{4} + 18 a^{2} b^{5} x + 18 a b^{6} x^{2} + 6 b^{7} x^{3}} + \frac{18 a b^{2} d x^{2} \log{\left(\frac{a}{b} + x \right)}}{6 a^{3} b^{4} + 18 a^{2} b^{5} x + 18 a b^{6} x^{2} + 6 b^{7} x^{3}} + \frac{18 a b^{2} d x^{2}}{6 a^{3} b^{4} + 18 a^{2} b^{5} x + 18 a b^{6} x^{2} + 6 b^{7} x^{3}} - \frac{3 b^{3} c x}{6 a^{3} b^{4} + 18 a^{2} b^{5} x + 18 a b^{6} x^{2} + 6 b^{7} x^{3}} + \frac{6 b^{3} d x^{3} \log{\left(\frac{a}{b} + x \right)}}{6 a^{3} b^{4} + 18 a^{2} b^{5} x + 18 a b^{6} x^{2} + 6 b^{7} x^{3}} & \text{for}\: n = -4 \\- \frac{6 a^{3} d \log{\left(\frac{a}{b} + x \right)}}{2 a^{2} b^{4} + 4 a b^{5} x + 2 b^{6} x^{2}} - \frac{9 a^{3} d}{2 a^{2} b^{4} + 4 a b^{5} x + 2 b^{6} x^{2}} - \frac{12 a^{2} b d x \log{\left(\frac{a}{b} + x \right)}}{2 a^{2} b^{4} + 4 a b^{5} x + 2 b^{6} x^{2}} - \frac{12 a^{2} b d x}{2 a^{2} b^{4} + 4 a b^{5} x + 2 b^{6} x^{2}} - \frac{a b^{2} c}{2 a^{2} b^{4} + 4 a b^{5} x + 2 b^{6} x^{2}} - \frac{6 a b^{2} d x^{2} \log{\left(\frac{a}{b} + x \right)}}{2 a^{2} b^{4} + 4 a b^{5} x + 2 b^{6} x^{2}} - \frac{2 b^{3} c x}{2 a^{2} b^{4} + 4 a b^{5} x + 2 b^{6} x^{2}} + \frac{2 b^{3} d x^{3}}{2 a^{2} b^{4} + 4 a b^{5} x + 2 b^{6} x^{2}} & \text{for}\: n = -3 \\\frac{6 a^{3} d \log{\left(\frac{a}{b} + x \right)}}{2 a b^{4} + 2 b^{5} x} + \frac{6 a^{3} d}{2 a b^{4} + 2 b^{5} x} + \frac{6 a^{2} b d x \log{\left(\frac{a}{b} + x \right)}}{2 a b^{4} + 2 b^{5} x} + \frac{2 a b^{2} c \log{\left(\frac{a}{b} + x \right)}}{2 a b^{4} + 2 b^{5} x} + \frac{2 a b^{2} c}{2 a b^{4} + 2 b^{5} x} - \frac{3 a b^{2} d x^{2}}{2 a b^{4} + 2 b^{5} x} + \frac{2 b^{3} c x \log{\left(\frac{a}{b} + x \right)}}{2 a b^{4} + 2 b^{5} x} + \frac{b^{3} d x^{3}}{2 a b^{4} + 2 b^{5} x} & \text{for}\: n = -2 \\- \frac{a^{3} d \log{\left(\frac{a}{b} + x \right)}}{b^{4}} + \frac{a^{2} d x}{b^{3}} - \frac{a c \log{\left(\frac{a}{b} + x \right)}}{b^{2}} - \frac{a d x^{2}}{2 b^{2}} + \frac{c x}{b} + \frac{d x^{3}}{3 b} & \text{for}\: n = -1 \\- \frac{6 a^{4} d \left(a + b x\right)^{n}}{b^{4} n^{4} + 10 b^{4} n^{3} + 35 b^{4} n^{2} + 50 b^{4} n + 24 b^{4}} + \frac{6 a^{3} b d n x \left(a + b x\right)^{n}}{b^{4} n^{4} + 10 b^{4} n^{3} + 35 b^{4} n^{2} + 50 b^{4} n + 24 b^{4}} - \frac{a^{2} b^{2} c n^{2} \left(a + b x\right)^{n}}{b^{4} n^{4} + 10 b^{4} n^{3} + 35 b^{4} n^{2} + 50 b^{4} n + 24 b^{4}} - \frac{7 a^{2} b^{2} c n \left(a + b x\right)^{n}}{b^{4} n^{4} + 10 b^{4} n^{3} + 35 b^{4} n^{2} + 50 b^{4} n + 24 b^{4}} - \frac{12 a^{2} b^{2} c \left(a + b x\right)^{n}}{b^{4} n^{4} + 10 b^{4} n^{3} + 35 b^{4} n^{2} + 50 b^{4} n + 24 b^{4}} - \frac{3 a^{2} b^{2} d n^{2} x^{2} \left(a + b x\right)^{n}}{b^{4} n^{4} + 10 b^{4} n^{3} + 35 b^{4} n^{2} + 50 b^{4} n + 24 b^{4}} - \frac{3 a^{2} b^{2} d n x^{2} \left(a + b x\right)^{n}}{b^{4} n^{4} + 10 b^{4} n^{3} + 35 b^{4} n^{2} + 50 b^{4} n + 24 b^{4}} + \frac{a b^{3} c n^{3} x \left(a + b x\right)^{n}}{b^{4} n^{4} + 10 b^{4} n^{3} + 35 b^{4} n^{2} + 50 b^{4} n + 24 b^{4}} + \frac{7 a b^{3} c n^{2} x \left(a + b x\right)^{n}}{b^{4} n^{4} + 10 b^{4} n^{3} + 35 b^{4} n^{2} + 50 b^{4} n + 24 b^{4}} + \frac{12 a b^{3} c n x \left(a + b x\right)^{n}}{b^{4} n^{4} + 10 b^{4} n^{3} + 35 b^{4} n^{2} + 50 b^{4} n + 24 b^{4}} + \frac{a b^{3} d n^{3} x^{3} \left(a + b x\right)^{n}}{b^{4} n^{4} + 10 b^{4} n^{3} + 35 b^{4} n^{2} + 50 b^{4} n + 24 b^{4}} + \frac{3 a b^{3} d n^{2} x^{3} \left(a + b x\right)^{n}}{b^{4} n^{4} + 10 b^{4} n^{3} + 35 b^{4} n^{2} + 50 b^{4} n + 24 b^{4}} + \frac{2 a b^{3} d n x^{3} \left(a + b x\right)^{n}}{b^{4} n^{4} + 10 b^{4} n^{3} + 35 b^{4} n^{2} + 50 b^{4} n + 24 b^{4}} + \frac{b^{4} c n^{3} x^{2} \left(a + b x\right)^{n}}{b^{4} n^{4} + 10 b^{4} n^{3} + 35 b^{4} n^{2} + 50 b^{4} n + 24 b^{4}} + \frac{8 b^{4} c n^{2} x^{2} \left(a + b x\right)^{n}}{b^{4} n^{4} + 10 b^{4} n^{3} + 35 b^{4} n^{2} + 50 b^{4} n + 24 b^{4}} + \frac{19 b^{4} c n x^{2} \left(a + b x\right)^{n}}{b^{4} n^{4} + 10 b^{4} n^{3} + 35 b^{4} n^{2} + 50 b^{4} n + 24 b^{4}} + \frac{12 b^{4} c x^{2} \left(a + b x\right)^{n}}{b^{4} n^{4} + 10 b^{4} n^{3} + 35 b^{4} n^{2} + 50 b^{4} n + 24 b^{4}} + \frac{b^{4} d n^{3} x^{4} \left(a + b x\right)^{n}}{b^{4} n^{4} + 10 b^{4} n^{3} + 35 b^{4} n^{2} + 50 b^{4} n + 24 b^{4}} + \frac{6 b^{4} d n^{2} x^{4} \left(a + b x\right)^{n}}{b^{4} n^{4} + 10 b^{4} n^{3} + 35 b^{4} n^{2} + 50 b^{4} n + 24 b^{4}} + \frac{11 b^{4} d n x^{4} \left(a + b x\right)^{n}}{b^{4} n^{4} + 10 b^{4} n^{3} + 35 b^{4} n^{2} + 50 b^{4} n + 24 b^{4}} + \frac{6 b^{4} d x^{4} \left(a + b x\right)^{n}}{b^{4} n^{4} + 10 b^{4} n^{3} + 35 b^{4} n^{2} + 50 b^{4} n + 24 b^{4}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**n*(c*x**2/2 + d*x**4/4), Eq(b, 0)), (6*a**3*d*log(a/b + x)/(6*a**3*b**4 + 18*a**2*b**5*x + 18*a*b**6*x**2 + 6*b**7*x**3) + 11*a**3*d/(6*a**3*b**4 + 18*a**2*b**5*x + 18*a*b**6*x**2 + 6*b**7*x**3) + 18*a**2*b*d*x*log(a/b + x)/(6*a**3*b**4 + 18*a**2*b**5*x + 18*a*b**6*x**2 + 6*b**7*x**3) + 27*a**2*b*d*x/(6*a**3*b**4 + 18*a**2*b**5*x + 18*a*b**6*x**2 + 6*b**7*x**3) - a*b**2*c/(6*a**3*b**4 + 18*a**2*b**5*x + 18*a*b**6*x**2 + 6*b**7*x**3) + 18*a*b**2*d*x**2*log(a/b + x)/(6*a**3*b**4 + 18*a**2*b**5*x + 18*a*b**6*x**2 + 6*b**7*x**3) + 18*a*b**2*d*x**2/(6*a**3*b**4 + 18*a**2*b**5*x + 18*a*b**6*x**2 + 6*b**7*x**3) - 3*b**3*c*x/(6*a**3*b**4 + 18*a**2*b**5*x + 18*a*b**6*x**2 + 6*b**7*x**3) + 6*b**3*d*x**3*log(a/b + x)/(6*a**3*b**4 + 18*a**2*b**5*x + 18*a*b**6*x**2 + 6*b**7*x**3), Eq(n, -4)), (-6*a**3*d*log(a/b + x)/(2*a**2*b**4 + 4*a*b**5*x + 2*b**6*x**2) - 9*a**3*d/(2*a**2*b**4 + 4*a*b**5*x + 2*b**6*x**2) - 12*a**2*b*d*x*log(a/b + x)/(2*a**2*b**4 + 4*a*b**5*x + 2*b**6*x**2) - 12*a**2*b*d*x/(2*a**2*b**4 + 4*a*b**5*x + 2*b**6*x**2) - a*b**2*c/(2*a**2*b**4 + 4*a*b**5*x + 2*b**6*x**2) - 6*a*b**2*d*x**2*log(a/b + x)/(2*a**2*b**4 + 4*a*b**5*x + 2*b**6*x**2) - 2*b**3*c*x/(2*a**2*b**4 + 4*a*b**5*x + 2*b**6*x**2) + 2*b**3*d*x**3/(2*a**2*b**4 + 4*a*b**5*x + 2*b**6*x**2), Eq(n, -3)), (6*a**3*d*log(a/b + x)/(2*a*b**4 + 2*b**5*x) + 6*a**3*d/(2*a*b**4 + 2*b**5*x) + 6*a**2*b*d*x*log(a/b + x)/(2*a*b**4 + 2*b**5*x) + 2*a*b**2*c*log(a/b + x)/(2*a*b**4 + 2*b**5*x) + 2*a*b**2*c/(2*a*b**4 + 2*b**5*x) - 3*a*b**2*d*x**2/(2*a*b**4 + 2*b**5*x) + 2*b**3*c*x*log(a/b + x)/(2*a*b**4 + 2*b**5*x) + b**3*d*x**3/(2*a*b**4 + 2*b**5*x), Eq(n, -2)), (-a**3*d*log(a/b + x)/b**4 + a**2*d*x/b**3 - a*c*log(a/b + x)/b**2 - a*d*x**2/(2*b**2) + c*x/b + d*x**3/(3*b), Eq(n, -1)), (-6*a**4*d*(a + b*x)**n/(b**4*n**4 + 10*b**4*n**3 + 35*b**4*n**2 + 50*b**4*n + 24*b**4) + 6*a**3*b*d*n*x*(a + b*x)**n/(b**4*n**4 + 10*b**4*n**3 + 35*b**4*n**2 + 50*b**4*n + 24*b**4) - a**2*b**2*c*n**2*(a + b*x)**n/(b**4*n**4 + 10*b**4*n**3 + 35*b**4*n**2 + 50*b**4*n + 24*b**4) - 7*a**2*b**2*c*n*(a + b*x)**n/(b**4*n**4 + 10*b**4*n**3 + 35*b**4*n**2 + 50*b**4*n + 24*b**4) - 12*a**2*b**2*c*(a + b*x)**n/(b**4*n**4 + 10*b**4*n**3 + 35*b**4*n**2 + 50*b**4*n + 24*b**4) - 3*a**2*b**2*d*n**2*x**2*(a + b*x)**n/(b**4*n**4 + 10*b**4*n**3 + 35*b**4*n**2 + 50*b**4*n + 24*b**4) - 3*a**2*b**2*d*n*x**2*(a + b*x)**n/(b**4*n**4 + 10*b**4*n**3 + 35*b**4*n**2 + 50*b**4*n + 24*b**4) + a*b**3*c*n**3*x*(a + b*x)**n/(b**4*n**4 + 10*b**4*n**3 + 35*b**4*n**2 + 50*b**4*n + 24*b**4) + 7*a*b**3*c*n**2*x*(a + b*x)**n/(b**4*n**4 + 10*b**4*n**3 + 35*b**4*n**2 + 50*b**4*n + 24*b**4) + 12*a*b**3*c*n*x*(a + b*x)**n/(b**4*n**4 + 10*b**4*n**3 + 35*b**4*n**2 + 50*b**4*n + 24*b**4) + a*b**3*d*n**3*x**3*(a + b*x)**n/(b**4*n**4 + 10*b**4*n**3 + 35*b**4*n**2 + 50*b**4*n + 24*b**4) + 3*a*b**3*d*n**2*x**3*(a + b*x)**n/(b**4*n**4 + 10*b**4*n**3 + 35*b**4*n**2 + 50*b**4*n + 24*b**4) + 2*a*b**3*d*n*x**3*(a + b*x)**n/(b**4*n**4 + 10*b**4*n**3 + 35*b**4*n**2 + 50*b**4*n + 24*b**4) + b**4*c*n**3*x**2*(a + b*x)**n/(b**4*n**4 + 10*b**4*n**3 + 35*b**4*n**2 + 50*b**4*n + 24*b**4) + 8*b**4*c*n**2*x**2*(a + b*x)**n/(b**4*n**4 + 10*b**4*n**3 + 35*b**4*n**2 + 50*b**4*n + 24*b**4) + 19*b**4*c*n*x**2*(a + b*x)**n/(b**4*n**4 + 10*b**4*n**3 + 35*b**4*n**2 + 50*b**4*n + 24*b**4) + 12*b**4*c*x**2*(a + b*x)**n/(b**4*n**4 + 10*b**4*n**3 + 35*b**4*n**2 + 50*b**4*n + 24*b**4) + b**4*d*n**3*x**4*(a + b*x)**n/(b**4*n**4 + 10*b**4*n**3 + 35*b**4*n**2 + 50*b**4*n + 24*b**4) + 6*b**4*d*n**2*x**4*(a + b*x)**n/(b**4*n**4 + 10*b**4*n**3 + 35*b**4*n**2 + 50*b**4*n + 24*b**4) + 11*b**4*d*n*x**4*(a + b*x)**n/(b**4*n**4 + 10*b**4*n**3 + 35*b**4*n**2 + 50*b**4*n + 24*b**4) + 6*b**4*d*x**4*(a + b*x)**n/(b**4*n**4 + 10*b**4*n**3 + 35*b**4*n**2 + 50*b**4*n + 24*b**4), True))","A",0
353,1,952,0,2.072687," ","integrate((b*x+a)**n*(d*x**2+c),x)","\begin{cases} a^{n} \left(c x + \frac{d x^{3}}{3}\right) & \text{for}\: b = 0 \\\frac{2 a^{2} d \log{\left(\frac{a}{b} + x \right)}}{2 a^{2} b^{3} + 4 a b^{4} x + 2 b^{5} x^{2}} + \frac{3 a^{2} d}{2 a^{2} b^{3} + 4 a b^{4} x + 2 b^{5} x^{2}} + \frac{4 a b d x \log{\left(\frac{a}{b} + x \right)}}{2 a^{2} b^{3} + 4 a b^{4} x + 2 b^{5} x^{2}} + \frac{4 a b d x}{2 a^{2} b^{3} + 4 a b^{4} x + 2 b^{5} x^{2}} - \frac{b^{2} c}{2 a^{2} b^{3} + 4 a b^{4} x + 2 b^{5} x^{2}} + \frac{2 b^{2} d x^{2} \log{\left(\frac{a}{b} + x \right)}}{2 a^{2} b^{3} + 4 a b^{4} x + 2 b^{5} x^{2}} & \text{for}\: n = -3 \\- \frac{2 a^{2} d \log{\left(\frac{a}{b} + x \right)}}{a b^{3} + b^{4} x} - \frac{2 a^{2} d}{a b^{3} + b^{4} x} - \frac{2 a b d x \log{\left(\frac{a}{b} + x \right)}}{a b^{3} + b^{4} x} - \frac{b^{2} c}{a b^{3} + b^{4} x} + \frac{b^{2} d x^{2}}{a b^{3} + b^{4} x} & \text{for}\: n = -2 \\\frac{a^{2} d \log{\left(\frac{a}{b} + x \right)}}{b^{3}} - \frac{a d x}{b^{2}} + \frac{c \log{\left(\frac{a}{b} + x \right)}}{b} + \frac{d x^{2}}{2 b} & \text{for}\: n = -1 \\\frac{2 a^{3} d \left(a + b x\right)^{n}}{b^{3} n^{3} + 6 b^{3} n^{2} + 11 b^{3} n + 6 b^{3}} - \frac{2 a^{2} b d n x \left(a + b x\right)^{n}}{b^{3} n^{3} + 6 b^{3} n^{2} + 11 b^{3} n + 6 b^{3}} + \frac{a b^{2} c n^{2} \left(a + b x\right)^{n}}{b^{3} n^{3} + 6 b^{3} n^{2} + 11 b^{3} n + 6 b^{3}} + \frac{5 a b^{2} c n \left(a + b x\right)^{n}}{b^{3} n^{3} + 6 b^{3} n^{2} + 11 b^{3} n + 6 b^{3}} + \frac{6 a b^{2} c \left(a + b x\right)^{n}}{b^{3} n^{3} + 6 b^{3} n^{2} + 11 b^{3} n + 6 b^{3}} + \frac{a b^{2} d n^{2} x^{2} \left(a + b x\right)^{n}}{b^{3} n^{3} + 6 b^{3} n^{2} + 11 b^{3} n + 6 b^{3}} + \frac{a b^{2} d n x^{2} \left(a + b x\right)^{n}}{b^{3} n^{3} + 6 b^{3} n^{2} + 11 b^{3} n + 6 b^{3}} + \frac{b^{3} c n^{2} x \left(a + b x\right)^{n}}{b^{3} n^{3} + 6 b^{3} n^{2} + 11 b^{3} n + 6 b^{3}} + \frac{5 b^{3} c n x \left(a + b x\right)^{n}}{b^{3} n^{3} + 6 b^{3} n^{2} + 11 b^{3} n + 6 b^{3}} + \frac{6 b^{3} c x \left(a + b x\right)^{n}}{b^{3} n^{3} + 6 b^{3} n^{2} + 11 b^{3} n + 6 b^{3}} + \frac{b^{3} d n^{2} x^{3} \left(a + b x\right)^{n}}{b^{3} n^{3} + 6 b^{3} n^{2} + 11 b^{3} n + 6 b^{3}} + \frac{3 b^{3} d n x^{3} \left(a + b x\right)^{n}}{b^{3} n^{3} + 6 b^{3} n^{2} + 11 b^{3} n + 6 b^{3}} + \frac{2 b^{3} d x^{3} \left(a + b x\right)^{n}}{b^{3} n^{3} + 6 b^{3} n^{2} + 11 b^{3} n + 6 b^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**n*(c*x + d*x**3/3), Eq(b, 0)), (2*a**2*d*log(a/b + x)/(2*a**2*b**3 + 4*a*b**4*x + 2*b**5*x**2) + 3*a**2*d/(2*a**2*b**3 + 4*a*b**4*x + 2*b**5*x**2) + 4*a*b*d*x*log(a/b + x)/(2*a**2*b**3 + 4*a*b**4*x + 2*b**5*x**2) + 4*a*b*d*x/(2*a**2*b**3 + 4*a*b**4*x + 2*b**5*x**2) - b**2*c/(2*a**2*b**3 + 4*a*b**4*x + 2*b**5*x**2) + 2*b**2*d*x**2*log(a/b + x)/(2*a**2*b**3 + 4*a*b**4*x + 2*b**5*x**2), Eq(n, -3)), (-2*a**2*d*log(a/b + x)/(a*b**3 + b**4*x) - 2*a**2*d/(a*b**3 + b**4*x) - 2*a*b*d*x*log(a/b + x)/(a*b**3 + b**4*x) - b**2*c/(a*b**3 + b**4*x) + b**2*d*x**2/(a*b**3 + b**4*x), Eq(n, -2)), (a**2*d*log(a/b + x)/b**3 - a*d*x/b**2 + c*log(a/b + x)/b + d*x**2/(2*b), Eq(n, -1)), (2*a**3*d*(a + b*x)**n/(b**3*n**3 + 6*b**3*n**2 + 11*b**3*n + 6*b**3) - 2*a**2*b*d*n*x*(a + b*x)**n/(b**3*n**3 + 6*b**3*n**2 + 11*b**3*n + 6*b**3) + a*b**2*c*n**2*(a + b*x)**n/(b**3*n**3 + 6*b**3*n**2 + 11*b**3*n + 6*b**3) + 5*a*b**2*c*n*(a + b*x)**n/(b**3*n**3 + 6*b**3*n**2 + 11*b**3*n + 6*b**3) + 6*a*b**2*c*(a + b*x)**n/(b**3*n**3 + 6*b**3*n**2 + 11*b**3*n + 6*b**3) + a*b**2*d*n**2*x**2*(a + b*x)**n/(b**3*n**3 + 6*b**3*n**2 + 11*b**3*n + 6*b**3) + a*b**2*d*n*x**2*(a + b*x)**n/(b**3*n**3 + 6*b**3*n**2 + 11*b**3*n + 6*b**3) + b**3*c*n**2*x*(a + b*x)**n/(b**3*n**3 + 6*b**3*n**2 + 11*b**3*n + 6*b**3) + 5*b**3*c*n*x*(a + b*x)**n/(b**3*n**3 + 6*b**3*n**2 + 11*b**3*n + 6*b**3) + 6*b**3*c*x*(a + b*x)**n/(b**3*n**3 + 6*b**3*n**2 + 11*b**3*n + 6*b**3) + b**3*d*n**2*x**3*(a + b*x)**n/(b**3*n**3 + 6*b**3*n**2 + 11*b**3*n + 6*b**3) + 3*b**3*d*n*x**3*(a + b*x)**n/(b**3*n**3 + 6*b**3*n**2 + 11*b**3*n + 6*b**3) + 2*b**3*d*x**3*(a + b*x)**n/(b**3*n**3 + 6*b**3*n**2 + 11*b**3*n + 6*b**3), True))","A",0
354,1,345,0,7.221615," ","integrate((b*x+a)**n*(d*x**2+c)/x,x)","- \frac{b^{n} c n \left(\frac{a}{b} + x\right)^{n} \Phi\left(1 + \frac{b x}{a}, 1, n + 1\right) \Gamma\left(n + 1\right)}{\Gamma\left(n + 2\right)} - \frac{b^{n} c \left(\frac{a}{b} + x\right)^{n} \Phi\left(1 + \frac{b x}{a}, 1, n + 1\right) \Gamma\left(n + 1\right)}{\Gamma\left(n + 2\right)} + d \left(\begin{cases} \frac{a^{n} x^{2}}{2} & \text{for}\: b = 0 \\\frac{a \log{\left(\frac{a}{b} + x \right)}}{a b^{2} + b^{3} x} + \frac{a}{a b^{2} + b^{3} x} + \frac{b x \log{\left(\frac{a}{b} + x \right)}}{a b^{2} + b^{3} x} & \text{for}\: n = -2 \\- \frac{a \log{\left(\frac{a}{b} + x \right)}}{b^{2}} + \frac{x}{b} & \text{for}\: n = -1 \\- \frac{a^{2} \left(a + b x\right)^{n}}{b^{2} n^{2} + 3 b^{2} n + 2 b^{2}} + \frac{a b n x \left(a + b x\right)^{n}}{b^{2} n^{2} + 3 b^{2} n + 2 b^{2}} + \frac{b^{2} n x^{2} \left(a + b x\right)^{n}}{b^{2} n^{2} + 3 b^{2} n + 2 b^{2}} + \frac{b^{2} x^{2} \left(a + b x\right)^{n}}{b^{2} n^{2} + 3 b^{2} n + 2 b^{2}} & \text{otherwise} \end{cases}\right) - \frac{b b^{n} c n x \left(\frac{a}{b} + x\right)^{n} \Phi\left(1 + \frac{b x}{a}, 1, n + 1\right) \Gamma\left(n + 1\right)}{a \Gamma\left(n + 2\right)} - \frac{b b^{n} c x \left(\frac{a}{b} + x\right)^{n} \Phi\left(1 + \frac{b x}{a}, 1, n + 1\right) \Gamma\left(n + 1\right)}{a \Gamma\left(n + 2\right)}"," ",0,"-b**n*c*n*(a/b + x)**n*lerchphi(1 + b*x/a, 1, n + 1)*gamma(n + 1)/gamma(n + 2) - b**n*c*(a/b + x)**n*lerchphi(1 + b*x/a, 1, n + 1)*gamma(n + 1)/gamma(n + 2) + d*Piecewise((a**n*x**2/2, Eq(b, 0)), (a*log(a/b + x)/(a*b**2 + b**3*x) + a/(a*b**2 + b**3*x) + b*x*log(a/b + x)/(a*b**2 + b**3*x), Eq(n, -2)), (-a*log(a/b + x)/b**2 + x/b, Eq(n, -1)), (-a**2*(a + b*x)**n/(b**2*n**2 + 3*b**2*n + 2*b**2) + a*b*n*x*(a + b*x)**n/(b**2*n**2 + 3*b**2*n + 2*b**2) + b**2*n*x**2*(a + b*x)**n/(b**2*n**2 + 3*b**2*n + 2*b**2) + b**2*x**2*(a + b*x)**n/(b**2*n**2 + 3*b**2*n + 2*b**2), True)) - b*b**n*c*n*x*(a/b + x)**n*lerchphi(1 + b*x/a, 1, n + 1)*gamma(n + 1)/(a*gamma(n + 2)) - b*b**n*c*x*(a/b + x)**n*lerchphi(1 + b*x/a, 1, n + 1)*gamma(n + 1)/(a*gamma(n + 2))","B",0
355,1,14317,0,21.586858," ","integrate(x**2*(b*x+a)**n*(d*x**2+c)**2,x)","\begin{cases} a^{n} \left(\frac{c^{2} x^{3}}{3} + \frac{2 c d x^{5}}{5} + \frac{d^{2} x^{7}}{7}\right) & \text{for}\: b = 0 \\\frac{60 a^{6} d^{2} \log{\left(\frac{a}{b} + x \right)}}{60 a^{6} b^{7} + 360 a^{5} b^{8} x + 900 a^{4} b^{9} x^{2} + 1200 a^{3} b^{10} x^{3} + 900 a^{2} b^{11} x^{4} + 360 a b^{12} x^{5} + 60 b^{13} x^{6}} + \frac{147 a^{6} d^{2}}{60 a^{6} b^{7} + 360 a^{5} b^{8} x + 900 a^{4} b^{9} x^{2} + 1200 a^{3} b^{10} x^{3} + 900 a^{2} b^{11} x^{4} + 360 a b^{12} x^{5} + 60 b^{13} x^{6}} + \frac{360 a^{5} b d^{2} x \log{\left(\frac{a}{b} + x \right)}}{60 a^{6} b^{7} + 360 a^{5} b^{8} x + 900 a^{4} b^{9} x^{2} + 1200 a^{3} b^{10} x^{3} + 900 a^{2} b^{11} x^{4} + 360 a b^{12} x^{5} + 60 b^{13} x^{6}} + \frac{822 a^{5} b d^{2} x}{60 a^{6} b^{7} + 360 a^{5} b^{8} x + 900 a^{4} b^{9} x^{2} + 1200 a^{3} b^{10} x^{3} + 900 a^{2} b^{11} x^{4} + 360 a b^{12} x^{5} + 60 b^{13} x^{6}} - \frac{4 a^{4} b^{2} c d}{60 a^{6} b^{7} + 360 a^{5} b^{8} x + 900 a^{4} b^{9} x^{2} + 1200 a^{3} b^{10} x^{3} + 900 a^{2} b^{11} x^{4} + 360 a b^{12} x^{5} + 60 b^{13} x^{6}} + \frac{900 a^{4} b^{2} d^{2} x^{2} \log{\left(\frac{a}{b} + x \right)}}{60 a^{6} b^{7} + 360 a^{5} b^{8} x + 900 a^{4} b^{9} x^{2} + 1200 a^{3} b^{10} x^{3} + 900 a^{2} b^{11} x^{4} + 360 a b^{12} x^{5} + 60 b^{13} x^{6}} + \frac{1875 a^{4} b^{2} d^{2} x^{2}}{60 a^{6} b^{7} + 360 a^{5} b^{8} x + 900 a^{4} b^{9} x^{2} + 1200 a^{3} b^{10} x^{3} + 900 a^{2} b^{11} x^{4} + 360 a b^{12} x^{5} + 60 b^{13} x^{6}} - \frac{24 a^{3} b^{3} c d x}{60 a^{6} b^{7} + 360 a^{5} b^{8} x + 900 a^{4} b^{9} x^{2} + 1200 a^{3} b^{10} x^{3} + 900 a^{2} b^{11} x^{4} + 360 a b^{12} x^{5} + 60 b^{13} x^{6}} + \frac{1200 a^{3} b^{3} d^{2} x^{3} \log{\left(\frac{a}{b} + x \right)}}{60 a^{6} b^{7} + 360 a^{5} b^{8} x + 900 a^{4} b^{9} x^{2} + 1200 a^{3} b^{10} x^{3} + 900 a^{2} b^{11} x^{4} + 360 a b^{12} x^{5} + 60 b^{13} x^{6}} + \frac{2200 a^{3} b^{3} d^{2} x^{3}}{60 a^{6} b^{7} + 360 a^{5} b^{8} x + 900 a^{4} b^{9} x^{2} + 1200 a^{3} b^{10} x^{3} + 900 a^{2} b^{11} x^{4} + 360 a b^{12} x^{5} + 60 b^{13} x^{6}} - \frac{a^{2} b^{4} c^{2}}{60 a^{6} b^{7} + 360 a^{5} b^{8} x + 900 a^{4} b^{9} x^{2} + 1200 a^{3} b^{10} x^{3} + 900 a^{2} b^{11} x^{4} + 360 a b^{12} x^{5} + 60 b^{13} x^{6}} - \frac{60 a^{2} b^{4} c d x^{2}}{60 a^{6} b^{7} + 360 a^{5} b^{8} x + 900 a^{4} b^{9} x^{2} + 1200 a^{3} b^{10} x^{3} + 900 a^{2} b^{11} x^{4} + 360 a b^{12} x^{5} + 60 b^{13} x^{6}} + \frac{900 a^{2} b^{4} d^{2} x^{4} \log{\left(\frac{a}{b} + x \right)}}{60 a^{6} b^{7} + 360 a^{5} b^{8} x + 900 a^{4} b^{9} x^{2} + 1200 a^{3} b^{10} x^{3} + 900 a^{2} b^{11} x^{4} + 360 a b^{12} x^{5} + 60 b^{13} x^{6}} + \frac{1350 a^{2} b^{4} d^{2} x^{4}}{60 a^{6} b^{7} + 360 a^{5} b^{8} x + 900 a^{4} b^{9} x^{2} + 1200 a^{3} b^{10} x^{3} + 900 a^{2} b^{11} x^{4} + 360 a b^{12} x^{5} + 60 b^{13} x^{6}} - \frac{6 a b^{5} c^{2} x}{60 a^{6} b^{7} + 360 a^{5} b^{8} x + 900 a^{4} b^{9} x^{2} + 1200 a^{3} b^{10} x^{3} + 900 a^{2} b^{11} x^{4} + 360 a b^{12} x^{5} + 60 b^{13} x^{6}} - \frac{80 a b^{5} c d x^{3}}{60 a^{6} b^{7} + 360 a^{5} b^{8} x + 900 a^{4} b^{9} x^{2} + 1200 a^{3} b^{10} x^{3} + 900 a^{2} b^{11} x^{4} + 360 a b^{12} x^{5} + 60 b^{13} x^{6}} + \frac{360 a b^{5} d^{2} x^{5} \log{\left(\frac{a}{b} + x \right)}}{60 a^{6} b^{7} + 360 a^{5} b^{8} x + 900 a^{4} b^{9} x^{2} + 1200 a^{3} b^{10} x^{3} + 900 a^{2} b^{11} x^{4} + 360 a b^{12} x^{5} + 60 b^{13} x^{6}} + \frac{360 a b^{5} d^{2} x^{5}}{60 a^{6} b^{7} + 360 a^{5} b^{8} x + 900 a^{4} b^{9} x^{2} + 1200 a^{3} b^{10} x^{3} + 900 a^{2} b^{11} x^{4} + 360 a b^{12} x^{5} + 60 b^{13} x^{6}} - \frac{15 b^{6} c^{2} x^{2}}{60 a^{6} b^{7} + 360 a^{5} b^{8} x + 900 a^{4} b^{9} x^{2} + 1200 a^{3} b^{10} x^{3} + 900 a^{2} b^{11} x^{4} + 360 a b^{12} x^{5} + 60 b^{13} x^{6}} - \frac{60 b^{6} c d x^{4}}{60 a^{6} b^{7} + 360 a^{5} b^{8} x + 900 a^{4} b^{9} x^{2} + 1200 a^{3} b^{10} x^{3} + 900 a^{2} b^{11} x^{4} + 360 a b^{12} x^{5} + 60 b^{13} x^{6}} + \frac{60 b^{6} d^{2} x^{6} \log{\left(\frac{a}{b} + x \right)}}{60 a^{6} b^{7} + 360 a^{5} b^{8} x + 900 a^{4} b^{9} x^{2} + 1200 a^{3} b^{10} x^{3} + 900 a^{2} b^{11} x^{4} + 360 a b^{12} x^{5} + 60 b^{13} x^{6}} & \text{for}\: n = -7 \\- \frac{180 a^{6} d^{2} \log{\left(\frac{a}{b} + x \right)}}{30 a^{5} b^{7} + 150 a^{4} b^{8} x + 300 a^{3} b^{9} x^{2} + 300 a^{2} b^{10} x^{3} + 150 a b^{11} x^{4} + 30 b^{12} x^{5}} - \frac{411 a^{6} d^{2}}{30 a^{5} b^{7} + 150 a^{4} b^{8} x + 300 a^{3} b^{9} x^{2} + 300 a^{2} b^{10} x^{3} + 150 a b^{11} x^{4} + 30 b^{12} x^{5}} - \frac{900 a^{5} b d^{2} x \log{\left(\frac{a}{b} + x \right)}}{30 a^{5} b^{7} + 150 a^{4} b^{8} x + 300 a^{3} b^{9} x^{2} + 300 a^{2} b^{10} x^{3} + 150 a b^{11} x^{4} + 30 b^{12} x^{5}} - \frac{1875 a^{5} b d^{2} x}{30 a^{5} b^{7} + 150 a^{4} b^{8} x + 300 a^{3} b^{9} x^{2} + 300 a^{2} b^{10} x^{3} + 150 a b^{11} x^{4} + 30 b^{12} x^{5}} - \frac{12 a^{4} b^{2} c d}{30 a^{5} b^{7} + 150 a^{4} b^{8} x + 300 a^{3} b^{9} x^{2} + 300 a^{2} b^{10} x^{3} + 150 a b^{11} x^{4} + 30 b^{12} x^{5}} - \frac{1800 a^{4} b^{2} d^{2} x^{2} \log{\left(\frac{a}{b} + x \right)}}{30 a^{5} b^{7} + 150 a^{4} b^{8} x + 300 a^{3} b^{9} x^{2} + 300 a^{2} b^{10} x^{3} + 150 a b^{11} x^{4} + 30 b^{12} x^{5}} - \frac{3300 a^{4} b^{2} d^{2} x^{2}}{30 a^{5} b^{7} + 150 a^{4} b^{8} x + 300 a^{3} b^{9} x^{2} + 300 a^{2} b^{10} x^{3} + 150 a b^{11} x^{4} + 30 b^{12} x^{5}} - \frac{60 a^{3} b^{3} c d x}{30 a^{5} b^{7} + 150 a^{4} b^{8} x + 300 a^{3} b^{9} x^{2} + 300 a^{2} b^{10} x^{3} + 150 a b^{11} x^{4} + 30 b^{12} x^{5}} - \frac{1800 a^{3} b^{3} d^{2} x^{3} \log{\left(\frac{a}{b} + x \right)}}{30 a^{5} b^{7} + 150 a^{4} b^{8} x + 300 a^{3} b^{9} x^{2} + 300 a^{2} b^{10} x^{3} + 150 a b^{11} x^{4} + 30 b^{12} x^{5}} - \frac{2700 a^{3} b^{3} d^{2} x^{3}}{30 a^{5} b^{7} + 150 a^{4} b^{8} x + 300 a^{3} b^{9} x^{2} + 300 a^{2} b^{10} x^{3} + 150 a b^{11} x^{4} + 30 b^{12} x^{5}} - \frac{a^{2} b^{4} c^{2}}{30 a^{5} b^{7} + 150 a^{4} b^{8} x + 300 a^{3} b^{9} x^{2} + 300 a^{2} b^{10} x^{3} + 150 a b^{11} x^{4} + 30 b^{12} x^{5}} - \frac{120 a^{2} b^{4} c d x^{2}}{30 a^{5} b^{7} + 150 a^{4} b^{8} x + 300 a^{3} b^{9} x^{2} + 300 a^{2} b^{10} x^{3} + 150 a b^{11} x^{4} + 30 b^{12} x^{5}} - \frac{900 a^{2} b^{4} d^{2} x^{4} \log{\left(\frac{a}{b} + x \right)}}{30 a^{5} b^{7} + 150 a^{4} b^{8} x + 300 a^{3} b^{9} x^{2} + 300 a^{2} b^{10} x^{3} + 150 a b^{11} x^{4} + 30 b^{12} x^{5}} - \frac{900 a^{2} b^{4} d^{2} x^{4}}{30 a^{5} b^{7} + 150 a^{4} b^{8} x + 300 a^{3} b^{9} x^{2} + 300 a^{2} b^{10} x^{3} + 150 a b^{11} x^{4} + 30 b^{12} x^{5}} - \frac{5 a b^{5} c^{2} x}{30 a^{5} b^{7} + 150 a^{4} b^{8} x + 300 a^{3} b^{9} x^{2} + 300 a^{2} b^{10} x^{3} + 150 a b^{11} x^{4} + 30 b^{12} x^{5}} - \frac{120 a b^{5} c d x^{3}}{30 a^{5} b^{7} + 150 a^{4} b^{8} x + 300 a^{3} b^{9} x^{2} + 300 a^{2} b^{10} x^{3} + 150 a b^{11} x^{4} + 30 b^{12} x^{5}} - \frac{180 a b^{5} d^{2} x^{5} \log{\left(\frac{a}{b} + x \right)}}{30 a^{5} b^{7} + 150 a^{4} b^{8} x + 300 a^{3} b^{9} x^{2} + 300 a^{2} b^{10} x^{3} + 150 a b^{11} x^{4} + 30 b^{12} x^{5}} - \frac{10 b^{6} c^{2} x^{2}}{30 a^{5} b^{7} + 150 a^{4} b^{8} x + 300 a^{3} b^{9} x^{2} + 300 a^{2} b^{10} x^{3} + 150 a b^{11} x^{4} + 30 b^{12} x^{5}} - \frac{60 b^{6} c d x^{4}}{30 a^{5} b^{7} + 150 a^{4} b^{8} x + 300 a^{3} b^{9} x^{2} + 300 a^{2} b^{10} x^{3} + 150 a b^{11} x^{4} + 30 b^{12} x^{5}} + \frac{30 b^{6} d^{2} x^{6}}{30 a^{5} b^{7} + 150 a^{4} b^{8} x + 300 a^{3} b^{9} x^{2} + 300 a^{2} b^{10} x^{3} + 150 a b^{11} x^{4} + 30 b^{12} x^{5}} & \text{for}\: n = -6 \\\frac{180 a^{6} d^{2} \log{\left(\frac{a}{b} + x \right)}}{12 a^{4} b^{7} + 48 a^{3} b^{8} x + 72 a^{2} b^{9} x^{2} + 48 a b^{10} x^{3} + 12 b^{11} x^{4}} + \frac{375 a^{6} d^{2}}{12 a^{4} b^{7} + 48 a^{3} b^{8} x + 72 a^{2} b^{9} x^{2} + 48 a b^{10} x^{3} + 12 b^{11} x^{4}} + \frac{720 a^{5} b d^{2} x \log{\left(\frac{a}{b} + x \right)}}{12 a^{4} b^{7} + 48 a^{3} b^{8} x + 72 a^{2} b^{9} x^{2} + 48 a b^{10} x^{3} + 12 b^{11} x^{4}} + \frac{1320 a^{5} b d^{2} x}{12 a^{4} b^{7} + 48 a^{3} b^{8} x + 72 a^{2} b^{9} x^{2} + 48 a b^{10} x^{3} + 12 b^{11} x^{4}} + \frac{24 a^{4} b^{2} c d \log{\left(\frac{a}{b} + x \right)}}{12 a^{4} b^{7} + 48 a^{3} b^{8} x + 72 a^{2} b^{9} x^{2} + 48 a b^{10} x^{3} + 12 b^{11} x^{4}} + \frac{50 a^{4} b^{2} c d}{12 a^{4} b^{7} + 48 a^{3} b^{8} x + 72 a^{2} b^{9} x^{2} + 48 a b^{10} x^{3} + 12 b^{11} x^{4}} + \frac{1080 a^{4} b^{2} d^{2} x^{2} \log{\left(\frac{a}{b} + x \right)}}{12 a^{4} b^{7} + 48 a^{3} b^{8} x + 72 a^{2} b^{9} x^{2} + 48 a b^{10} x^{3} + 12 b^{11} x^{4}} + \frac{1620 a^{4} b^{2} d^{2} x^{2}}{12 a^{4} b^{7} + 48 a^{3} b^{8} x + 72 a^{2} b^{9} x^{2} + 48 a b^{10} x^{3} + 12 b^{11} x^{4}} + \frac{96 a^{3} b^{3} c d x \log{\left(\frac{a}{b} + x \right)}}{12 a^{4} b^{7} + 48 a^{3} b^{8} x + 72 a^{2} b^{9} x^{2} + 48 a b^{10} x^{3} + 12 b^{11} x^{4}} + \frac{176 a^{3} b^{3} c d x}{12 a^{4} b^{7} + 48 a^{3} b^{8} x + 72 a^{2} b^{9} x^{2} + 48 a b^{10} x^{3} + 12 b^{11} x^{4}} + \frac{720 a^{3} b^{3} d^{2} x^{3} \log{\left(\frac{a}{b} + x \right)}}{12 a^{4} b^{7} + 48 a^{3} b^{8} x + 72 a^{2} b^{9} x^{2} + 48 a b^{10} x^{3} + 12 b^{11} x^{4}} + \frac{720 a^{3} b^{3} d^{2} x^{3}}{12 a^{4} b^{7} + 48 a^{3} b^{8} x + 72 a^{2} b^{9} x^{2} + 48 a b^{10} x^{3} + 12 b^{11} x^{4}} - \frac{a^{2} b^{4} c^{2}}{12 a^{4} b^{7} + 48 a^{3} b^{8} x + 72 a^{2} b^{9} x^{2} + 48 a b^{10} x^{3} + 12 b^{11} x^{4}} + \frac{144 a^{2} b^{4} c d x^{2} \log{\left(\frac{a}{b} + x \right)}}{12 a^{4} b^{7} + 48 a^{3} b^{8} x + 72 a^{2} b^{9} x^{2} + 48 a b^{10} x^{3} + 12 b^{11} x^{4}} + \frac{216 a^{2} b^{4} c d x^{2}}{12 a^{4} b^{7} + 48 a^{3} b^{8} x + 72 a^{2} b^{9} x^{2} + 48 a b^{10} x^{3} + 12 b^{11} x^{4}} + \frac{180 a^{2} b^{4} d^{2} x^{4} \log{\left(\frac{a}{b} + x \right)}}{12 a^{4} b^{7} + 48 a^{3} b^{8} x + 72 a^{2} b^{9} x^{2} + 48 a b^{10} x^{3} + 12 b^{11} x^{4}} - \frac{4 a b^{5} c^{2} x}{12 a^{4} b^{7} + 48 a^{3} b^{8} x + 72 a^{2} b^{9} x^{2} + 48 a b^{10} x^{3} + 12 b^{11} x^{4}} + \frac{96 a b^{5} c d x^{3} \log{\left(\frac{a}{b} + x \right)}}{12 a^{4} b^{7} + 48 a^{3} b^{8} x + 72 a^{2} b^{9} x^{2} + 48 a b^{10} x^{3} + 12 b^{11} x^{4}} + \frac{96 a b^{5} c d x^{3}}{12 a^{4} b^{7} + 48 a^{3} b^{8} x + 72 a^{2} b^{9} x^{2} + 48 a b^{10} x^{3} + 12 b^{11} x^{4}} - \frac{36 a b^{5} d^{2} x^{5}}{12 a^{4} b^{7} + 48 a^{3} b^{8} x + 72 a^{2} b^{9} x^{2} + 48 a b^{10} x^{3} + 12 b^{11} x^{4}} - \frac{6 b^{6} c^{2} x^{2}}{12 a^{4} b^{7} + 48 a^{3} b^{8} x + 72 a^{2} b^{9} x^{2} + 48 a b^{10} x^{3} + 12 b^{11} x^{4}} + \frac{24 b^{6} c d x^{4} \log{\left(\frac{a}{b} + x \right)}}{12 a^{4} b^{7} + 48 a^{3} b^{8} x + 72 a^{2} b^{9} x^{2} + 48 a b^{10} x^{3} + 12 b^{11} x^{4}} + \frac{6 b^{6} d^{2} x^{6}}{12 a^{4} b^{7} + 48 a^{3} b^{8} x + 72 a^{2} b^{9} x^{2} + 48 a b^{10} x^{3} + 12 b^{11} x^{4}} & \text{for}\: n = -5 \\- \frac{60 a^{6} d^{2} \log{\left(\frac{a}{b} + x \right)}}{3 a^{3} b^{7} + 9 a^{2} b^{8} x + 9 a b^{9} x^{2} + 3 b^{10} x^{3}} - \frac{110 a^{6} d^{2}}{3 a^{3} b^{7} + 9 a^{2} b^{8} x + 9 a b^{9} x^{2} + 3 b^{10} x^{3}} - \frac{180 a^{5} b d^{2} x \log{\left(\frac{a}{b} + x \right)}}{3 a^{3} b^{7} + 9 a^{2} b^{8} x + 9 a b^{9} x^{2} + 3 b^{10} x^{3}} - \frac{270 a^{5} b d^{2} x}{3 a^{3} b^{7} + 9 a^{2} b^{8} x + 9 a b^{9} x^{2} + 3 b^{10} x^{3}} - \frac{24 a^{4} b^{2} c d \log{\left(\frac{a}{b} + x \right)}}{3 a^{3} b^{7} + 9 a^{2} b^{8} x + 9 a b^{9} x^{2} + 3 b^{10} x^{3}} - \frac{44 a^{4} b^{2} c d}{3 a^{3} b^{7} + 9 a^{2} b^{8} x + 9 a b^{9} x^{2} + 3 b^{10} x^{3}} - \frac{180 a^{4} b^{2} d^{2} x^{2} \log{\left(\frac{a}{b} + x \right)}}{3 a^{3} b^{7} + 9 a^{2} b^{8} x + 9 a b^{9} x^{2} + 3 b^{10} x^{3}} - \frac{180 a^{4} b^{2} d^{2} x^{2}}{3 a^{3} b^{7} + 9 a^{2} b^{8} x + 9 a b^{9} x^{2} + 3 b^{10} x^{3}} - \frac{72 a^{3} b^{3} c d x \log{\left(\frac{a}{b} + x \right)}}{3 a^{3} b^{7} + 9 a^{2} b^{8} x + 9 a b^{9} x^{2} + 3 b^{10} x^{3}} - \frac{108 a^{3} b^{3} c d x}{3 a^{3} b^{7} + 9 a^{2} b^{8} x + 9 a b^{9} x^{2} + 3 b^{10} x^{3}} - \frac{60 a^{3} b^{3} d^{2} x^{3} \log{\left(\frac{a}{b} + x \right)}}{3 a^{3} b^{7} + 9 a^{2} b^{8} x + 9 a b^{9} x^{2} + 3 b^{10} x^{3}} - \frac{a^{2} b^{4} c^{2}}{3 a^{3} b^{7} + 9 a^{2} b^{8} x + 9 a b^{9} x^{2} + 3 b^{10} x^{3}} - \frac{72 a^{2} b^{4} c d x^{2} \log{\left(\frac{a}{b} + x \right)}}{3 a^{3} b^{7} + 9 a^{2} b^{8} x + 9 a b^{9} x^{2} + 3 b^{10} x^{3}} - \frac{72 a^{2} b^{4} c d x^{2}}{3 a^{3} b^{7} + 9 a^{2} b^{8} x + 9 a b^{9} x^{2} + 3 b^{10} x^{3}} + \frac{15 a^{2} b^{4} d^{2} x^{4}}{3 a^{3} b^{7} + 9 a^{2} b^{8} x + 9 a b^{9} x^{2} + 3 b^{10} x^{3}} - \frac{3 a b^{5} c^{2} x}{3 a^{3} b^{7} + 9 a^{2} b^{8} x + 9 a b^{9} x^{2} + 3 b^{10} x^{3}} - \frac{24 a b^{5} c d x^{3} \log{\left(\frac{a}{b} + x \right)}}{3 a^{3} b^{7} + 9 a^{2} b^{8} x + 9 a b^{9} x^{2} + 3 b^{10} x^{3}} - \frac{3 a b^{5} d^{2} x^{5}}{3 a^{3} b^{7} + 9 a^{2} b^{8} x + 9 a b^{9} x^{2} + 3 b^{10} x^{3}} - \frac{3 b^{6} c^{2} x^{2}}{3 a^{3} b^{7} + 9 a^{2} b^{8} x + 9 a b^{9} x^{2} + 3 b^{10} x^{3}} + \frac{6 b^{6} c d x^{4}}{3 a^{3} b^{7} + 9 a^{2} b^{8} x + 9 a b^{9} x^{2} + 3 b^{10} x^{3}} + \frac{b^{6} d^{2} x^{6}}{3 a^{3} b^{7} + 9 a^{2} b^{8} x + 9 a b^{9} x^{2} + 3 b^{10} x^{3}} & \text{for}\: n = -4 \\\frac{60 a^{6} d^{2} \log{\left(\frac{a}{b} + x \right)}}{4 a^{2} b^{7} + 8 a b^{8} x + 4 b^{9} x^{2}} + \frac{90 a^{6} d^{2}}{4 a^{2} b^{7} + 8 a b^{8} x + 4 b^{9} x^{2}} + \frac{120 a^{5} b d^{2} x \log{\left(\frac{a}{b} + x \right)}}{4 a^{2} b^{7} + 8 a b^{8} x + 4 b^{9} x^{2}} + \frac{120 a^{5} b d^{2} x}{4 a^{2} b^{7} + 8 a b^{8} x + 4 b^{9} x^{2}} + \frac{48 a^{4} b^{2} c d \log{\left(\frac{a}{b} + x \right)}}{4 a^{2} b^{7} + 8 a b^{8} x + 4 b^{9} x^{2}} + \frac{72 a^{4} b^{2} c d}{4 a^{2} b^{7} + 8 a b^{8} x + 4 b^{9} x^{2}} + \frac{60 a^{4} b^{2} d^{2} x^{2} \log{\left(\frac{a}{b} + x \right)}}{4 a^{2} b^{7} + 8 a b^{8} x + 4 b^{9} x^{2}} + \frac{96 a^{3} b^{3} c d x \log{\left(\frac{a}{b} + x \right)}}{4 a^{2} b^{7} + 8 a b^{8} x + 4 b^{9} x^{2}} + \frac{96 a^{3} b^{3} c d x}{4 a^{2} b^{7} + 8 a b^{8} x + 4 b^{9} x^{2}} - \frac{20 a^{3} b^{3} d^{2} x^{3}}{4 a^{2} b^{7} + 8 a b^{8} x + 4 b^{9} x^{2}} + \frac{4 a^{2} b^{4} c^{2} \log{\left(\frac{a}{b} + x \right)}}{4 a^{2} b^{7} + 8 a b^{8} x + 4 b^{9} x^{2}} + \frac{6 a^{2} b^{4} c^{2}}{4 a^{2} b^{7} + 8 a b^{8} x + 4 b^{9} x^{2}} + \frac{48 a^{2} b^{4} c d x^{2} \log{\left(\frac{a}{b} + x \right)}}{4 a^{2} b^{7} + 8 a b^{8} x + 4 b^{9} x^{2}} + \frac{5 a^{2} b^{4} d^{2} x^{4}}{4 a^{2} b^{7} + 8 a b^{8} x + 4 b^{9} x^{2}} + \frac{8 a b^{5} c^{2} x \log{\left(\frac{a}{b} + x \right)}}{4 a^{2} b^{7} + 8 a b^{8} x + 4 b^{9} x^{2}} + \frac{8 a b^{5} c^{2} x}{4 a^{2} b^{7} + 8 a b^{8} x + 4 b^{9} x^{2}} - \frac{16 a b^{5} c d x^{3}}{4 a^{2} b^{7} + 8 a b^{8} x + 4 b^{9} x^{2}} - \frac{2 a b^{5} d^{2} x^{5}}{4 a^{2} b^{7} + 8 a b^{8} x + 4 b^{9} x^{2}} + \frac{4 b^{6} c^{2} x^{2} \log{\left(\frac{a}{b} + x \right)}}{4 a^{2} b^{7} + 8 a b^{8} x + 4 b^{9} x^{2}} + \frac{4 b^{6} c d x^{4}}{4 a^{2} b^{7} + 8 a b^{8} x + 4 b^{9} x^{2}} + \frac{b^{6} d^{2} x^{6}}{4 a^{2} b^{7} + 8 a b^{8} x + 4 b^{9} x^{2}} & \text{for}\: n = -3 \\- \frac{180 a^{6} d^{2} \log{\left(\frac{a}{b} + x \right)}}{30 a b^{7} + 30 b^{8} x} - \frac{180 a^{6} d^{2}}{30 a b^{7} + 30 b^{8} x} - \frac{180 a^{5} b d^{2} x \log{\left(\frac{a}{b} + x \right)}}{30 a b^{7} + 30 b^{8} x} - \frac{240 a^{4} b^{2} c d \log{\left(\frac{a}{b} + x \right)}}{30 a b^{7} + 30 b^{8} x} - \frac{240 a^{4} b^{2} c d}{30 a b^{7} + 30 b^{8} x} + \frac{90 a^{4} b^{2} d^{2} x^{2}}{30 a b^{7} + 30 b^{8} x} - \frac{240 a^{3} b^{3} c d x \log{\left(\frac{a}{b} + x \right)}}{30 a b^{7} + 30 b^{8} x} - \frac{30 a^{3} b^{3} d^{2} x^{3}}{30 a b^{7} + 30 b^{8} x} - \frac{60 a^{2} b^{4} c^{2} \log{\left(\frac{a}{b} + x \right)}}{30 a b^{7} + 30 b^{8} x} - \frac{60 a^{2} b^{4} c^{2}}{30 a b^{7} + 30 b^{8} x} + \frac{120 a^{2} b^{4} c d x^{2}}{30 a b^{7} + 30 b^{8} x} + \frac{15 a^{2} b^{4} d^{2} x^{4}}{30 a b^{7} + 30 b^{8} x} - \frac{60 a b^{5} c^{2} x \log{\left(\frac{a}{b} + x \right)}}{30 a b^{7} + 30 b^{8} x} - \frac{40 a b^{5} c d x^{3}}{30 a b^{7} + 30 b^{8} x} - \frac{9 a b^{5} d^{2} x^{5}}{30 a b^{7} + 30 b^{8} x} + \frac{30 b^{6} c^{2} x^{2}}{30 a b^{7} + 30 b^{8} x} + \frac{20 b^{6} c d x^{4}}{30 a b^{7} + 30 b^{8} x} + \frac{6 b^{6} d^{2} x^{6}}{30 a b^{7} + 30 b^{8} x} & \text{for}\: n = -2 \\\frac{a^{6} d^{2} \log{\left(\frac{a}{b} + x \right)}}{b^{7}} - \frac{a^{5} d^{2} x}{b^{6}} + \frac{2 a^{4} c d \log{\left(\frac{a}{b} + x \right)}}{b^{5}} + \frac{a^{4} d^{2} x^{2}}{2 b^{5}} - \frac{2 a^{3} c d x}{b^{4}} - \frac{a^{3} d^{2} x^{3}}{3 b^{4}} + \frac{a^{2} c^{2} \log{\left(\frac{a}{b} + x \right)}}{b^{3}} + \frac{a^{2} c d x^{2}}{b^{3}} + \frac{a^{2} d^{2} x^{4}}{4 b^{3}} - \frac{a c^{2} x}{b^{2}} - \frac{2 a c d x^{3}}{3 b^{2}} - \frac{a d^{2} x^{5}}{5 b^{2}} + \frac{c^{2} x^{2}}{2 b} + \frac{c d x^{4}}{2 b} + \frac{d^{2} x^{6}}{6 b} & \text{for}\: n = -1 \\\frac{720 a^{7} d^{2} \left(a + b x\right)^{n}}{b^{7} n^{7} + 28 b^{7} n^{6} + 322 b^{7} n^{5} + 1960 b^{7} n^{4} + 6769 b^{7} n^{3} + 13132 b^{7} n^{2} + 13068 b^{7} n + 5040 b^{7}} - \frac{720 a^{6} b d^{2} n x \left(a + b x\right)^{n}}{b^{7} n^{7} + 28 b^{7} n^{6} + 322 b^{7} n^{5} + 1960 b^{7} n^{4} + 6769 b^{7} n^{3} + 13132 b^{7} n^{2} + 13068 b^{7} n + 5040 b^{7}} + \frac{48 a^{5} b^{2} c d n^{2} \left(a + b x\right)^{n}}{b^{7} n^{7} + 28 b^{7} n^{6} + 322 b^{7} n^{5} + 1960 b^{7} n^{4} + 6769 b^{7} n^{3} + 13132 b^{7} n^{2} + 13068 b^{7} n + 5040 b^{7}} + \frac{624 a^{5} b^{2} c d n \left(a + b x\right)^{n}}{b^{7} n^{7} + 28 b^{7} n^{6} + 322 b^{7} n^{5} + 1960 b^{7} n^{4} + 6769 b^{7} n^{3} + 13132 b^{7} n^{2} + 13068 b^{7} n + 5040 b^{7}} + \frac{2016 a^{5} b^{2} c d \left(a + b x\right)^{n}}{b^{7} n^{7} + 28 b^{7} n^{6} + 322 b^{7} n^{5} + 1960 b^{7} n^{4} + 6769 b^{7} n^{3} + 13132 b^{7} n^{2} + 13068 b^{7} n + 5040 b^{7}} + \frac{360 a^{5} b^{2} d^{2} n^{2} x^{2} \left(a + b x\right)^{n}}{b^{7} n^{7} + 28 b^{7} n^{6} + 322 b^{7} n^{5} + 1960 b^{7} n^{4} + 6769 b^{7} n^{3} + 13132 b^{7} n^{2} + 13068 b^{7} n + 5040 b^{7}} + \frac{360 a^{5} b^{2} d^{2} n x^{2} \left(a + b x\right)^{n}}{b^{7} n^{7} + 28 b^{7} n^{6} + 322 b^{7} n^{5} + 1960 b^{7} n^{4} + 6769 b^{7} n^{3} + 13132 b^{7} n^{2} + 13068 b^{7} n + 5040 b^{7}} - \frac{48 a^{4} b^{3} c d n^{3} x \left(a + b x\right)^{n}}{b^{7} n^{7} + 28 b^{7} n^{6} + 322 b^{7} n^{5} + 1960 b^{7} n^{4} + 6769 b^{7} n^{3} + 13132 b^{7} n^{2} + 13068 b^{7} n + 5040 b^{7}} - \frac{624 a^{4} b^{3} c d n^{2} x \left(a + b x\right)^{n}}{b^{7} n^{7} + 28 b^{7} n^{6} + 322 b^{7} n^{5} + 1960 b^{7} n^{4} + 6769 b^{7} n^{3} + 13132 b^{7} n^{2} + 13068 b^{7} n + 5040 b^{7}} - \frac{2016 a^{4} b^{3} c d n x \left(a + b x\right)^{n}}{b^{7} n^{7} + 28 b^{7} n^{6} + 322 b^{7} n^{5} + 1960 b^{7} n^{4} + 6769 b^{7} n^{3} + 13132 b^{7} n^{2} + 13068 b^{7} n + 5040 b^{7}} - \frac{120 a^{4} b^{3} d^{2} n^{3} x^{3} \left(a + b x\right)^{n}}{b^{7} n^{7} + 28 b^{7} n^{6} + 322 b^{7} n^{5} + 1960 b^{7} n^{4} + 6769 b^{7} n^{3} + 13132 b^{7} n^{2} + 13068 b^{7} n + 5040 b^{7}} - \frac{360 a^{4} b^{3} d^{2} n^{2} x^{3} \left(a + b x\right)^{n}}{b^{7} n^{7} + 28 b^{7} n^{6} + 322 b^{7} n^{5} + 1960 b^{7} n^{4} + 6769 b^{7} n^{3} + 13132 b^{7} n^{2} + 13068 b^{7} n + 5040 b^{7}} - \frac{240 a^{4} b^{3} d^{2} n x^{3} \left(a + b x\right)^{n}}{b^{7} n^{7} + 28 b^{7} n^{6} + 322 b^{7} n^{5} + 1960 b^{7} n^{4} + 6769 b^{7} n^{3} + 13132 b^{7} n^{2} + 13068 b^{7} n + 5040 b^{7}} + \frac{2 a^{3} b^{4} c^{2} n^{4} \left(a + b x\right)^{n}}{b^{7} n^{7} + 28 b^{7} n^{6} + 322 b^{7} n^{5} + 1960 b^{7} n^{4} + 6769 b^{7} n^{3} + 13132 b^{7} n^{2} + 13068 b^{7} n + 5040 b^{7}} + \frac{44 a^{3} b^{4} c^{2} n^{3} \left(a + b x\right)^{n}}{b^{7} n^{7} + 28 b^{7} n^{6} + 322 b^{7} n^{5} + 1960 b^{7} n^{4} + 6769 b^{7} n^{3} + 13132 b^{7} n^{2} + 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x\right)^{n}}{b^{7} n^{7} + 28 b^{7} n^{6} + 322 b^{7} n^{5} + 1960 b^{7} n^{4} + 6769 b^{7} n^{3} + 13132 b^{7} n^{2} + 13068 b^{7} n + 5040 b^{7}} + \frac{2 b^{7} c d n^{6} x^{5} \left(a + b x\right)^{n}}{b^{7} n^{7} + 28 b^{7} n^{6} + 322 b^{7} n^{5} + 1960 b^{7} n^{4} + 6769 b^{7} n^{3} + 13132 b^{7} n^{2} + 13068 b^{7} n + 5040 b^{7}} + \frac{46 b^{7} c d n^{5} x^{5} \left(a + b x\right)^{n}}{b^{7} n^{7} + 28 b^{7} n^{6} + 322 b^{7} n^{5} + 1960 b^{7} n^{4} + 6769 b^{7} n^{3} + 13132 b^{7} n^{2} + 13068 b^{7} n + 5040 b^{7}} + \frac{414 b^{7} c d n^{4} x^{5} \left(a + b x\right)^{n}}{b^{7} n^{7} + 28 b^{7} n^{6} + 322 b^{7} n^{5} + 1960 b^{7} n^{4} + 6769 b^{7} n^{3} + 13132 b^{7} n^{2} + 13068 b^{7} n + 5040 b^{7}} + \frac{1850 b^{7} c d n^{3} x^{5} \left(a + b x\right)^{n}}{b^{7} n^{7} + 28 b^{7} n^{6} + 322 b^{7} n^{5} + 1960 b^{7} n^{4} + 6769 b^{7} n^{3} + 13132 b^{7} n^{2} + 13068 b^{7} n + 5040 b^{7}} + \frac{4288 b^{7} c d n^{2} x^{5} \left(a + b x\right)^{n}}{b^{7} n^{7} + 28 b^{7} n^{6} + 322 b^{7} n^{5} + 1960 b^{7} n^{4} + 6769 b^{7} n^{3} + 13132 b^{7} n^{2} + 13068 b^{7} n + 5040 b^{7}} + \frac{4824 b^{7} c d n x^{5} \left(a + b x\right)^{n}}{b^{7} n^{7} + 28 b^{7} n^{6} + 322 b^{7} n^{5} + 1960 b^{7} n^{4} + 6769 b^{7} n^{3} + 13132 b^{7} n^{2} + 13068 b^{7} n + 5040 b^{7}} + \frac{2016 b^{7} c d x^{5} \left(a + b x\right)^{n}}{b^{7} n^{7} + 28 b^{7} n^{6} + 322 b^{7} n^{5} + 1960 b^{7} n^{4} + 6769 b^{7} n^{3} + 13132 b^{7} n^{2} + 13068 b^{7} n + 5040 b^{7}} + \frac{b^{7} d^{2} n^{6} x^{7} \left(a + b x\right)^{n}}{b^{7} n^{7} + 28 b^{7} n^{6} + 322 b^{7} n^{5} + 1960 b^{7} n^{4} + 6769 b^{7} n^{3} + 13132 b^{7} n^{2} + 13068 b^{7} n + 5040 b^{7}} + \frac{21 b^{7} d^{2} n^{5} x^{7} \left(a + b x\right)^{n}}{b^{7} n^{7} + 28 b^{7} n^{6} + 322 b^{7} n^{5} + 1960 b^{7} n^{4} + 6769 b^{7} n^{3} + 13132 b^{7} n^{2} + 13068 b^{7} n + 5040 b^{7}} + \frac{175 b^{7} d^{2} n^{4} x^{7} \left(a + b x\right)^{n}}{b^{7} n^{7} + 28 b^{7} n^{6} + 322 b^{7} n^{5} + 1960 b^{7} n^{4} + 6769 b^{7} n^{3} + 13132 b^{7} n^{2} + 13068 b^{7} n + 5040 b^{7}} + \frac{735 b^{7} d^{2} n^{3} x^{7} \left(a + b x\right)^{n}}{b^{7} n^{7} + 28 b^{7} n^{6} + 322 b^{7} n^{5} + 1960 b^{7} n^{4} + 6769 b^{7} n^{3} + 13132 b^{7} n^{2} + 13068 b^{7} n + 5040 b^{7}} + \frac{1624 b^{7} d^{2} n^{2} x^{7} \left(a + b x\right)^{n}}{b^{7} n^{7} + 28 b^{7} n^{6} + 322 b^{7} n^{5} + 1960 b^{7} n^{4} + 6769 b^{7} n^{3} + 13132 b^{7} n^{2} + 13068 b^{7} n + 5040 b^{7}} + \frac{1764 b^{7} d^{2} n x^{7} \left(a + b x\right)^{n}}{b^{7} n^{7} + 28 b^{7} n^{6} + 322 b^{7} n^{5} + 1960 b^{7} n^{4} + 6769 b^{7} n^{3} + 13132 b^{7} n^{2} + 13068 b^{7} n + 5040 b^{7}} + \frac{720 b^{7} d^{2} x^{7} \left(a + b x\right)^{n}}{b^{7} n^{7} + 28 b^{7} n^{6} + 322 b^{7} n^{5} + 1960 b^{7} n^{4} + 6769 b^{7} n^{3} + 13132 b^{7} n^{2} + 13068 b^{7} n + 5040 b^{7}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**n*(c**2*x**3/3 + 2*c*d*x**5/5 + d**2*x**7/7), Eq(b, 0)), (60*a**6*d**2*log(a/b + x)/(60*a**6*b**7 + 360*a**5*b**8*x + 900*a**4*b**9*x**2 + 1200*a**3*b**10*x**3 + 900*a**2*b**11*x**4 + 360*a*b**12*x**5 + 60*b**13*x**6) + 147*a**6*d**2/(60*a**6*b**7 + 360*a**5*b**8*x + 900*a**4*b**9*x**2 + 1200*a**3*b**10*x**3 + 900*a**2*b**11*x**4 + 360*a*b**12*x**5 + 60*b**13*x**6) + 360*a**5*b*d**2*x*log(a/b + x)/(60*a**6*b**7 + 360*a**5*b**8*x + 900*a**4*b**9*x**2 + 1200*a**3*b**10*x**3 + 900*a**2*b**11*x**4 + 360*a*b**12*x**5 + 60*b**13*x**6) + 822*a**5*b*d**2*x/(60*a**6*b**7 + 360*a**5*b**8*x + 900*a**4*b**9*x**2 + 1200*a**3*b**10*x**3 + 900*a**2*b**11*x**4 + 360*a*b**12*x**5 + 60*b**13*x**6) - 4*a**4*b**2*c*d/(60*a**6*b**7 + 360*a**5*b**8*x + 900*a**4*b**9*x**2 + 1200*a**3*b**10*x**3 + 900*a**2*b**11*x**4 + 360*a*b**12*x**5 + 60*b**13*x**6) + 900*a**4*b**2*d**2*x**2*log(a/b + x)/(60*a**6*b**7 + 360*a**5*b**8*x + 900*a**4*b**9*x**2 + 1200*a**3*b**10*x**3 + 900*a**2*b**11*x**4 + 360*a*b**12*x**5 + 60*b**13*x**6) + 1875*a**4*b**2*d**2*x**2/(60*a**6*b**7 + 360*a**5*b**8*x + 900*a**4*b**9*x**2 + 1200*a**3*b**10*x**3 + 900*a**2*b**11*x**4 + 360*a*b**12*x**5 + 60*b**13*x**6) - 24*a**3*b**3*c*d*x/(60*a**6*b**7 + 360*a**5*b**8*x + 900*a**4*b**9*x**2 + 1200*a**3*b**10*x**3 + 900*a**2*b**11*x**4 + 360*a*b**12*x**5 + 60*b**13*x**6) + 1200*a**3*b**3*d**2*x**3*log(a/b + x)/(60*a**6*b**7 + 360*a**5*b**8*x + 900*a**4*b**9*x**2 + 1200*a**3*b**10*x**3 + 900*a**2*b**11*x**4 + 360*a*b**12*x**5 + 60*b**13*x**6) + 2200*a**3*b**3*d**2*x**3/(60*a**6*b**7 + 360*a**5*b**8*x + 900*a**4*b**9*x**2 + 1200*a**3*b**10*x**3 + 900*a**2*b**11*x**4 + 360*a*b**12*x**5 + 60*b**13*x**6) - a**2*b**4*c**2/(60*a**6*b**7 + 360*a**5*b**8*x + 900*a**4*b**9*x**2 + 1200*a**3*b**10*x**3 + 900*a**2*b**11*x**4 + 360*a*b**12*x**5 + 60*b**13*x**6) - 60*a**2*b**4*c*d*x**2/(60*a**6*b**7 + 360*a**5*b**8*x + 900*a**4*b**9*x**2 + 1200*a**3*b**10*x**3 + 900*a**2*b**11*x**4 + 360*a*b**12*x**5 + 60*b**13*x**6) + 900*a**2*b**4*d**2*x**4*log(a/b + x)/(60*a**6*b**7 + 360*a**5*b**8*x + 900*a**4*b**9*x**2 + 1200*a**3*b**10*x**3 + 900*a**2*b**11*x**4 + 360*a*b**12*x**5 + 60*b**13*x**6) + 1350*a**2*b**4*d**2*x**4/(60*a**6*b**7 + 360*a**5*b**8*x + 900*a**4*b**9*x**2 + 1200*a**3*b**10*x**3 + 900*a**2*b**11*x**4 + 360*a*b**12*x**5 + 60*b**13*x**6) - 6*a*b**5*c**2*x/(60*a**6*b**7 + 360*a**5*b**8*x + 900*a**4*b**9*x**2 + 1200*a**3*b**10*x**3 + 900*a**2*b**11*x**4 + 360*a*b**12*x**5 + 60*b**13*x**6) - 80*a*b**5*c*d*x**3/(60*a**6*b**7 + 360*a**5*b**8*x + 900*a**4*b**9*x**2 + 1200*a**3*b**10*x**3 + 900*a**2*b**11*x**4 + 360*a*b**12*x**5 + 60*b**13*x**6) + 360*a*b**5*d**2*x**5*log(a/b + x)/(60*a**6*b**7 + 360*a**5*b**8*x + 900*a**4*b**9*x**2 + 1200*a**3*b**10*x**3 + 900*a**2*b**11*x**4 + 360*a*b**12*x**5 + 60*b**13*x**6) + 360*a*b**5*d**2*x**5/(60*a**6*b**7 + 360*a**5*b**8*x + 900*a**4*b**9*x**2 + 1200*a**3*b**10*x**3 + 900*a**2*b**11*x**4 + 360*a*b**12*x**5 + 60*b**13*x**6) - 15*b**6*c**2*x**2/(60*a**6*b**7 + 360*a**5*b**8*x + 900*a**4*b**9*x**2 + 1200*a**3*b**10*x**3 + 900*a**2*b**11*x**4 + 360*a*b**12*x**5 + 60*b**13*x**6) - 60*b**6*c*d*x**4/(60*a**6*b**7 + 360*a**5*b**8*x + 900*a**4*b**9*x**2 + 1200*a**3*b**10*x**3 + 900*a**2*b**11*x**4 + 360*a*b**12*x**5 + 60*b**13*x**6) + 60*b**6*d**2*x**6*log(a/b + x)/(60*a**6*b**7 + 360*a**5*b**8*x + 900*a**4*b**9*x**2 + 1200*a**3*b**10*x**3 + 900*a**2*b**11*x**4 + 360*a*b**12*x**5 + 60*b**13*x**6), Eq(n, -7)), (-180*a**6*d**2*log(a/b + x)/(30*a**5*b**7 + 150*a**4*b**8*x + 300*a**3*b**9*x**2 + 300*a**2*b**10*x**3 + 150*a*b**11*x**4 + 30*b**12*x**5) - 411*a**6*d**2/(30*a**5*b**7 + 150*a**4*b**8*x + 300*a**3*b**9*x**2 + 300*a**2*b**10*x**3 + 150*a*b**11*x**4 + 30*b**12*x**5) - 900*a**5*b*d**2*x*log(a/b + x)/(30*a**5*b**7 + 150*a**4*b**8*x + 300*a**3*b**9*x**2 + 300*a**2*b**10*x**3 + 150*a*b**11*x**4 + 30*b**12*x**5) - 1875*a**5*b*d**2*x/(30*a**5*b**7 + 150*a**4*b**8*x + 300*a**3*b**9*x**2 + 300*a**2*b**10*x**3 + 150*a*b**11*x**4 + 30*b**12*x**5) - 12*a**4*b**2*c*d/(30*a**5*b**7 + 150*a**4*b**8*x + 300*a**3*b**9*x**2 + 300*a**2*b**10*x**3 + 150*a*b**11*x**4 + 30*b**12*x**5) - 1800*a**4*b**2*d**2*x**2*log(a/b + x)/(30*a**5*b**7 + 150*a**4*b**8*x + 300*a**3*b**9*x**2 + 300*a**2*b**10*x**3 + 150*a*b**11*x**4 + 30*b**12*x**5) - 3300*a**4*b**2*d**2*x**2/(30*a**5*b**7 + 150*a**4*b**8*x + 300*a**3*b**9*x**2 + 300*a**2*b**10*x**3 + 150*a*b**11*x**4 + 30*b**12*x**5) - 60*a**3*b**3*c*d*x/(30*a**5*b**7 + 150*a**4*b**8*x + 300*a**3*b**9*x**2 + 300*a**2*b**10*x**3 + 150*a*b**11*x**4 + 30*b**12*x**5) - 1800*a**3*b**3*d**2*x**3*log(a/b + x)/(30*a**5*b**7 + 150*a**4*b**8*x + 300*a**3*b**9*x**2 + 300*a**2*b**10*x**3 + 150*a*b**11*x**4 + 30*b**12*x**5) - 2700*a**3*b**3*d**2*x**3/(30*a**5*b**7 + 150*a**4*b**8*x + 300*a**3*b**9*x**2 + 300*a**2*b**10*x**3 + 150*a*b**11*x**4 + 30*b**12*x**5) - a**2*b**4*c**2/(30*a**5*b**7 + 150*a**4*b**8*x + 300*a**3*b**9*x**2 + 300*a**2*b**10*x**3 + 150*a*b**11*x**4 + 30*b**12*x**5) - 120*a**2*b**4*c*d*x**2/(30*a**5*b**7 + 150*a**4*b**8*x + 300*a**3*b**9*x**2 + 300*a**2*b**10*x**3 + 150*a*b**11*x**4 + 30*b**12*x**5) - 900*a**2*b**4*d**2*x**4*log(a/b + x)/(30*a**5*b**7 + 150*a**4*b**8*x + 300*a**3*b**9*x**2 + 300*a**2*b**10*x**3 + 150*a*b**11*x**4 + 30*b**12*x**5) - 900*a**2*b**4*d**2*x**4/(30*a**5*b**7 + 150*a**4*b**8*x + 300*a**3*b**9*x**2 + 300*a**2*b**10*x**3 + 150*a*b**11*x**4 + 30*b**12*x**5) - 5*a*b**5*c**2*x/(30*a**5*b**7 + 150*a**4*b**8*x + 300*a**3*b**9*x**2 + 300*a**2*b**10*x**3 + 150*a*b**11*x**4 + 30*b**12*x**5) - 120*a*b**5*c*d*x**3/(30*a**5*b**7 + 150*a**4*b**8*x + 300*a**3*b**9*x**2 + 300*a**2*b**10*x**3 + 150*a*b**11*x**4 + 30*b**12*x**5) - 180*a*b**5*d**2*x**5*log(a/b + x)/(30*a**5*b**7 + 150*a**4*b**8*x + 300*a**3*b**9*x**2 + 300*a**2*b**10*x**3 + 150*a*b**11*x**4 + 30*b**12*x**5) - 10*b**6*c**2*x**2/(30*a**5*b**7 + 150*a**4*b**8*x + 300*a**3*b**9*x**2 + 300*a**2*b**10*x**3 + 150*a*b**11*x**4 + 30*b**12*x**5) - 60*b**6*c*d*x**4/(30*a**5*b**7 + 150*a**4*b**8*x + 300*a**3*b**9*x**2 + 300*a**2*b**10*x**3 + 150*a*b**11*x**4 + 30*b**12*x**5) + 30*b**6*d**2*x**6/(30*a**5*b**7 + 150*a**4*b**8*x + 300*a**3*b**9*x**2 + 300*a**2*b**10*x**3 + 150*a*b**11*x**4 + 30*b**12*x**5), Eq(n, -6)), (180*a**6*d**2*log(a/b + x)/(12*a**4*b**7 + 48*a**3*b**8*x + 72*a**2*b**9*x**2 + 48*a*b**10*x**3 + 12*b**11*x**4) + 375*a**6*d**2/(12*a**4*b**7 + 48*a**3*b**8*x + 72*a**2*b**9*x**2 + 48*a*b**10*x**3 + 12*b**11*x**4) + 720*a**5*b*d**2*x*log(a/b + x)/(12*a**4*b**7 + 48*a**3*b**8*x + 72*a**2*b**9*x**2 + 48*a*b**10*x**3 + 12*b**11*x**4) + 1320*a**5*b*d**2*x/(12*a**4*b**7 + 48*a**3*b**8*x + 72*a**2*b**9*x**2 + 48*a*b**10*x**3 + 12*b**11*x**4) + 24*a**4*b**2*c*d*log(a/b + x)/(12*a**4*b**7 + 48*a**3*b**8*x + 72*a**2*b**9*x**2 + 48*a*b**10*x**3 + 12*b**11*x**4) + 50*a**4*b**2*c*d/(12*a**4*b**7 + 48*a**3*b**8*x + 72*a**2*b**9*x**2 + 48*a*b**10*x**3 + 12*b**11*x**4) + 1080*a**4*b**2*d**2*x**2*log(a/b + x)/(12*a**4*b**7 + 48*a**3*b**8*x + 72*a**2*b**9*x**2 + 48*a*b**10*x**3 + 12*b**11*x**4) + 1620*a**4*b**2*d**2*x**2/(12*a**4*b**7 + 48*a**3*b**8*x + 72*a**2*b**9*x**2 + 48*a*b**10*x**3 + 12*b**11*x**4) + 96*a**3*b**3*c*d*x*log(a/b + x)/(12*a**4*b**7 + 48*a**3*b**8*x + 72*a**2*b**9*x**2 + 48*a*b**10*x**3 + 12*b**11*x**4) + 176*a**3*b**3*c*d*x/(12*a**4*b**7 + 48*a**3*b**8*x + 72*a**2*b**9*x**2 + 48*a*b**10*x**3 + 12*b**11*x**4) + 720*a**3*b**3*d**2*x**3*log(a/b + x)/(12*a**4*b**7 + 48*a**3*b**8*x + 72*a**2*b**9*x**2 + 48*a*b**10*x**3 + 12*b**11*x**4) + 720*a**3*b**3*d**2*x**3/(12*a**4*b**7 + 48*a**3*b**8*x + 72*a**2*b**9*x**2 + 48*a*b**10*x**3 + 12*b**11*x**4) - a**2*b**4*c**2/(12*a**4*b**7 + 48*a**3*b**8*x + 72*a**2*b**9*x**2 + 48*a*b**10*x**3 + 12*b**11*x**4) + 144*a**2*b**4*c*d*x**2*log(a/b + x)/(12*a**4*b**7 + 48*a**3*b**8*x + 72*a**2*b**9*x**2 + 48*a*b**10*x**3 + 12*b**11*x**4) + 216*a**2*b**4*c*d*x**2/(12*a**4*b**7 + 48*a**3*b**8*x + 72*a**2*b**9*x**2 + 48*a*b**10*x**3 + 12*b**11*x**4) + 180*a**2*b**4*d**2*x**4*log(a/b + x)/(12*a**4*b**7 + 48*a**3*b**8*x + 72*a**2*b**9*x**2 + 48*a*b**10*x**3 + 12*b**11*x**4) - 4*a*b**5*c**2*x/(12*a**4*b**7 + 48*a**3*b**8*x + 72*a**2*b**9*x**2 + 48*a*b**10*x**3 + 12*b**11*x**4) + 96*a*b**5*c*d*x**3*log(a/b + x)/(12*a**4*b**7 + 48*a**3*b**8*x + 72*a**2*b**9*x**2 + 48*a*b**10*x**3 + 12*b**11*x**4) + 96*a*b**5*c*d*x**3/(12*a**4*b**7 + 48*a**3*b**8*x + 72*a**2*b**9*x**2 + 48*a*b**10*x**3 + 12*b**11*x**4) - 36*a*b**5*d**2*x**5/(12*a**4*b**7 + 48*a**3*b**8*x + 72*a**2*b**9*x**2 + 48*a*b**10*x**3 + 12*b**11*x**4) - 6*b**6*c**2*x**2/(12*a**4*b**7 + 48*a**3*b**8*x + 72*a**2*b**9*x**2 + 48*a*b**10*x**3 + 12*b**11*x**4) + 24*b**6*c*d*x**4*log(a/b + x)/(12*a**4*b**7 + 48*a**3*b**8*x + 72*a**2*b**9*x**2 + 48*a*b**10*x**3 + 12*b**11*x**4) + 6*b**6*d**2*x**6/(12*a**4*b**7 + 48*a**3*b**8*x + 72*a**2*b**9*x**2 + 48*a*b**10*x**3 + 12*b**11*x**4), Eq(n, -5)), (-60*a**6*d**2*log(a/b + x)/(3*a**3*b**7 + 9*a**2*b**8*x + 9*a*b**9*x**2 + 3*b**10*x**3) - 110*a**6*d**2/(3*a**3*b**7 + 9*a**2*b**8*x + 9*a*b**9*x**2 + 3*b**10*x**3) - 180*a**5*b*d**2*x*log(a/b + x)/(3*a**3*b**7 + 9*a**2*b**8*x + 9*a*b**9*x**2 + 3*b**10*x**3) - 270*a**5*b*d**2*x/(3*a**3*b**7 + 9*a**2*b**8*x + 9*a*b**9*x**2 + 3*b**10*x**3) - 24*a**4*b**2*c*d*log(a/b + x)/(3*a**3*b**7 + 9*a**2*b**8*x + 9*a*b**9*x**2 + 3*b**10*x**3) - 44*a**4*b**2*c*d/(3*a**3*b**7 + 9*a**2*b**8*x + 9*a*b**9*x**2 + 3*b**10*x**3) - 180*a**4*b**2*d**2*x**2*log(a/b + x)/(3*a**3*b**7 + 9*a**2*b**8*x + 9*a*b**9*x**2 + 3*b**10*x**3) - 180*a**4*b**2*d**2*x**2/(3*a**3*b**7 + 9*a**2*b**8*x + 9*a*b**9*x**2 + 3*b**10*x**3) - 72*a**3*b**3*c*d*x*log(a/b + x)/(3*a**3*b**7 + 9*a**2*b**8*x + 9*a*b**9*x**2 + 3*b**10*x**3) - 108*a**3*b**3*c*d*x/(3*a**3*b**7 + 9*a**2*b**8*x + 9*a*b**9*x**2 + 3*b**10*x**3) - 60*a**3*b**3*d**2*x**3*log(a/b + x)/(3*a**3*b**7 + 9*a**2*b**8*x + 9*a*b**9*x**2 + 3*b**10*x**3) - a**2*b**4*c**2/(3*a**3*b**7 + 9*a**2*b**8*x + 9*a*b**9*x**2 + 3*b**10*x**3) - 72*a**2*b**4*c*d*x**2*log(a/b + x)/(3*a**3*b**7 + 9*a**2*b**8*x + 9*a*b**9*x**2 + 3*b**10*x**3) - 72*a**2*b**4*c*d*x**2/(3*a**3*b**7 + 9*a**2*b**8*x + 9*a*b**9*x**2 + 3*b**10*x**3) + 15*a**2*b**4*d**2*x**4/(3*a**3*b**7 + 9*a**2*b**8*x + 9*a*b**9*x**2 + 3*b**10*x**3) - 3*a*b**5*c**2*x/(3*a**3*b**7 + 9*a**2*b**8*x + 9*a*b**9*x**2 + 3*b**10*x**3) - 24*a*b**5*c*d*x**3*log(a/b + x)/(3*a**3*b**7 + 9*a**2*b**8*x + 9*a*b**9*x**2 + 3*b**10*x**3) - 3*a*b**5*d**2*x**5/(3*a**3*b**7 + 9*a**2*b**8*x + 9*a*b**9*x**2 + 3*b**10*x**3) - 3*b**6*c**2*x**2/(3*a**3*b**7 + 9*a**2*b**8*x + 9*a*b**9*x**2 + 3*b**10*x**3) + 6*b**6*c*d*x**4/(3*a**3*b**7 + 9*a**2*b**8*x + 9*a*b**9*x**2 + 3*b**10*x**3) + b**6*d**2*x**6/(3*a**3*b**7 + 9*a**2*b**8*x + 9*a*b**9*x**2 + 3*b**10*x**3), Eq(n, -4)), (60*a**6*d**2*log(a/b + x)/(4*a**2*b**7 + 8*a*b**8*x + 4*b**9*x**2) + 90*a**6*d**2/(4*a**2*b**7 + 8*a*b**8*x + 4*b**9*x**2) + 120*a**5*b*d**2*x*log(a/b + x)/(4*a**2*b**7 + 8*a*b**8*x + 4*b**9*x**2) + 120*a**5*b*d**2*x/(4*a**2*b**7 + 8*a*b**8*x + 4*b**9*x**2) + 48*a**4*b**2*c*d*log(a/b + x)/(4*a**2*b**7 + 8*a*b**8*x + 4*b**9*x**2) + 72*a**4*b**2*c*d/(4*a**2*b**7 + 8*a*b**8*x + 4*b**9*x**2) + 60*a**4*b**2*d**2*x**2*log(a/b + x)/(4*a**2*b**7 + 8*a*b**8*x + 4*b**9*x**2) + 96*a**3*b**3*c*d*x*log(a/b + x)/(4*a**2*b**7 + 8*a*b**8*x + 4*b**9*x**2) + 96*a**3*b**3*c*d*x/(4*a**2*b**7 + 8*a*b**8*x + 4*b**9*x**2) - 20*a**3*b**3*d**2*x**3/(4*a**2*b**7 + 8*a*b**8*x + 4*b**9*x**2) + 4*a**2*b**4*c**2*log(a/b + x)/(4*a**2*b**7 + 8*a*b**8*x + 4*b**9*x**2) + 6*a**2*b**4*c**2/(4*a**2*b**7 + 8*a*b**8*x + 4*b**9*x**2) + 48*a**2*b**4*c*d*x**2*log(a/b + x)/(4*a**2*b**7 + 8*a*b**8*x + 4*b**9*x**2) + 5*a**2*b**4*d**2*x**4/(4*a**2*b**7 + 8*a*b**8*x + 4*b**9*x**2) + 8*a*b**5*c**2*x*log(a/b + x)/(4*a**2*b**7 + 8*a*b**8*x + 4*b**9*x**2) + 8*a*b**5*c**2*x/(4*a**2*b**7 + 8*a*b**8*x + 4*b**9*x**2) - 16*a*b**5*c*d*x**3/(4*a**2*b**7 + 8*a*b**8*x + 4*b**9*x**2) - 2*a*b**5*d**2*x**5/(4*a**2*b**7 + 8*a*b**8*x + 4*b**9*x**2) + 4*b**6*c**2*x**2*log(a/b + x)/(4*a**2*b**7 + 8*a*b**8*x + 4*b**9*x**2) + 4*b**6*c*d*x**4/(4*a**2*b**7 + 8*a*b**8*x + 4*b**9*x**2) + b**6*d**2*x**6/(4*a**2*b**7 + 8*a*b**8*x + 4*b**9*x**2), Eq(n, -3)), (-180*a**6*d**2*log(a/b + x)/(30*a*b**7 + 30*b**8*x) - 180*a**6*d**2/(30*a*b**7 + 30*b**8*x) - 180*a**5*b*d**2*x*log(a/b + x)/(30*a*b**7 + 30*b**8*x) - 240*a**4*b**2*c*d*log(a/b + x)/(30*a*b**7 + 30*b**8*x) - 240*a**4*b**2*c*d/(30*a*b**7 + 30*b**8*x) + 90*a**4*b**2*d**2*x**2/(30*a*b**7 + 30*b**8*x) - 240*a**3*b**3*c*d*x*log(a/b + x)/(30*a*b**7 + 30*b**8*x) - 30*a**3*b**3*d**2*x**3/(30*a*b**7 + 30*b**8*x) - 60*a**2*b**4*c**2*log(a/b + x)/(30*a*b**7 + 30*b**8*x) - 60*a**2*b**4*c**2/(30*a*b**7 + 30*b**8*x) + 120*a**2*b**4*c*d*x**2/(30*a*b**7 + 30*b**8*x) + 15*a**2*b**4*d**2*x**4/(30*a*b**7 + 30*b**8*x) - 60*a*b**5*c**2*x*log(a/b + x)/(30*a*b**7 + 30*b**8*x) - 40*a*b**5*c*d*x**3/(30*a*b**7 + 30*b**8*x) - 9*a*b**5*d**2*x**5/(30*a*b**7 + 30*b**8*x) + 30*b**6*c**2*x**2/(30*a*b**7 + 30*b**8*x) + 20*b**6*c*d*x**4/(30*a*b**7 + 30*b**8*x) + 6*b**6*d**2*x**6/(30*a*b**7 + 30*b**8*x), Eq(n, -2)), (a**6*d**2*log(a/b + x)/b**7 - a**5*d**2*x/b**6 + 2*a**4*c*d*log(a/b + x)/b**5 + a**4*d**2*x**2/(2*b**5) - 2*a**3*c*d*x/b**4 - a**3*d**2*x**3/(3*b**4) + a**2*c**2*log(a/b + x)/b**3 + a**2*c*d*x**2/b**3 + a**2*d**2*x**4/(4*b**3) - a*c**2*x/b**2 - 2*a*c*d*x**3/(3*b**2) - a*d**2*x**5/(5*b**2) + c**2*x**2/(2*b) + c*d*x**4/(2*b) + d**2*x**6/(6*b), Eq(n, -1)), (720*a**7*d**2*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) - 720*a**6*b*d**2*n*x*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) + 48*a**5*b**2*c*d*n**2*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) + 624*a**5*b**2*c*d*n*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) + 2016*a**5*b**2*c*d*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) + 360*a**5*b**2*d**2*n**2*x**2*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) + 360*a**5*b**2*d**2*n*x**2*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) - 48*a**4*b**3*c*d*n**3*x*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) - 624*a**4*b**3*c*d*n**2*x*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) - 2016*a**4*b**3*c*d*n*x*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) - 120*a**4*b**3*d**2*n**3*x**3*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) - 360*a**4*b**3*d**2*n**2*x**3*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) - 240*a**4*b**3*d**2*n*x**3*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) + 2*a**3*b**4*c**2*n**4*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) + 44*a**3*b**4*c**2*n**3*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) + 358*a**3*b**4*c**2*n**2*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) + 1276*a**3*b**4*c**2*n*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) + 1680*a**3*b**4*c**2*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) + 24*a**3*b**4*c*d*n**4*x**2*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) + 336*a**3*b**4*c*d*n**3*x**2*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) + 1320*a**3*b**4*c*d*n**2*x**2*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) + 1008*a**3*b**4*c*d*n*x**2*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) + 30*a**3*b**4*d**2*n**4*x**4*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) + 180*a**3*b**4*d**2*n**3*x**4*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) + 330*a**3*b**4*d**2*n**2*x**4*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) + 180*a**3*b**4*d**2*n*x**4*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) - 2*a**2*b**5*c**2*n**5*x*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) - 44*a**2*b**5*c**2*n**4*x*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) - 358*a**2*b**5*c**2*n**3*x*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) - 1276*a**2*b**5*c**2*n**2*x*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) - 1680*a**2*b**5*c**2*n*x*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) - 8*a**2*b**5*c*d*n**5*x**3*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) - 128*a**2*b**5*c*d*n**4*x**3*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) - 664*a**2*b**5*c*d*n**3*x**3*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) - 1216*a**2*b**5*c*d*n**2*x**3*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) - 672*a**2*b**5*c*d*n*x**3*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) - 6*a**2*b**5*d**2*n**5*x**5*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) - 60*a**2*b**5*d**2*n**4*x**5*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) - 210*a**2*b**5*d**2*n**3*x**5*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) - 300*a**2*b**5*d**2*n**2*x**5*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) - 144*a**2*b**5*d**2*n*x**5*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) + a*b**6*c**2*n**6*x**2*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) + 23*a*b**6*c**2*n**5*x**2*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) + 201*a*b**6*c**2*n**4*x**2*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) + 817*a*b**6*c**2*n**3*x**2*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) + 1478*a*b**6*c**2*n**2*x**2*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) + 840*a*b**6*c**2*n*x**2*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) + 2*a*b**6*c*d*n**6*x**4*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) + 38*a*b**6*c*d*n**5*x**4*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) + 262*a*b**6*c*d*n**4*x**4*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) + 802*a*b**6*c*d*n**3*x**4*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) + 1080*a*b**6*c*d*n**2*x**4*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) + 504*a*b**6*c*d*n*x**4*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) + a*b**6*d**2*n**6*x**6*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) + 15*a*b**6*d**2*n**5*x**6*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) + 85*a*b**6*d**2*n**4*x**6*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) + 225*a*b**6*d**2*n**3*x**6*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) + 274*a*b**6*d**2*n**2*x**6*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) + 120*a*b**6*d**2*n*x**6*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) + b**7*c**2*n**6*x**3*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) + 25*b**7*c**2*n**5*x**3*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) + 247*b**7*c**2*n**4*x**3*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) + 1219*b**7*c**2*n**3*x**3*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) + 3112*b**7*c**2*n**2*x**3*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) + 3796*b**7*c**2*n*x**3*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) + 1680*b**7*c**2*x**3*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) + 2*b**7*c*d*n**6*x**5*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) + 46*b**7*c*d*n**5*x**5*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) + 414*b**7*c*d*n**4*x**5*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) + 1850*b**7*c*d*n**3*x**5*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) + 4288*b**7*c*d*n**2*x**5*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) + 4824*b**7*c*d*n*x**5*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) + 2016*b**7*c*d*x**5*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) + b**7*d**2*n**6*x**7*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) + 21*b**7*d**2*n**5*x**7*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) + 175*b**7*d**2*n**4*x**7*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) + 735*b**7*d**2*n**3*x**7*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) + 1624*b**7*d**2*n**2*x**7*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) + 1764*b**7*d**2*n*x**7*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7) + 720*b**7*d**2*x**7*(a + b*x)**n/(b**7*n**7 + 28*b**7*n**6 + 322*b**7*n**5 + 1960*b**7*n**4 + 6769*b**7*n**3 + 13132*b**7*n**2 + 13068*b**7*n + 5040*b**7), True))","A",0
356,1,8940,0,13.801370," ","integrate(x*(b*x+a)**n*(d*x**2+c)**2,x)","\begin{cases} a^{n} \left(\frac{c^{2} x^{2}}{2} + \frac{c d x^{4}}{2} + \frac{d^{2} x^{6}}{6}\right) & \text{for}\: b = 0 \\\frac{60 a^{5} d^{2} \log{\left(\frac{a}{b} + x \right)}}{60 a^{5} b^{6} + 300 a^{4} b^{7} x + 600 a^{3} b^{8} x^{2} + 600 a^{2} b^{9} x^{3} + 300 a b^{10} x^{4} + 60 b^{11} x^{5}} + \frac{137 a^{5} d^{2}}{60 a^{5} b^{6} + 300 a^{4} b^{7} x + 600 a^{3} b^{8} x^{2} + 600 a^{2} b^{9} x^{3} + 300 a b^{10} x^{4} + 60 b^{11} x^{5}} + \frac{300 a^{4} b d^{2} x \log{\left(\frac{a}{b} + x \right)}}{60 a^{5} b^{6} + 300 a^{4} b^{7} x + 600 a^{3} b^{8} x^{2} + 600 a^{2} b^{9} x^{3} + 300 a b^{10} x^{4} + 60 b^{11} x^{5}} + \frac{625 a^{4} b d^{2} x}{60 a^{5} b^{6} + 300 a^{4} b^{7} x + 600 a^{3} b^{8} x^{2} + 600 a^{2} b^{9} x^{3} + 300 a b^{10} x^{4} + 60 b^{11} x^{5}} - \frac{6 a^{3} b^{2} c d}{60 a^{5} b^{6} + 300 a^{4} b^{7} x + 600 a^{3} b^{8} x^{2} + 600 a^{2} b^{9} x^{3} + 300 a b^{10} x^{4} + 60 b^{11} x^{5}} + \frac{600 a^{3} b^{2} d^{2} x^{2} \log{\left(\frac{a}{b} + x \right)}}{60 a^{5} b^{6} + 300 a^{4} b^{7} x + 600 a^{3} b^{8} x^{2} + 600 a^{2} b^{9} x^{3} + 300 a b^{10} x^{4} + 60 b^{11} x^{5}} + \frac{1100 a^{3} b^{2} d^{2} x^{2}}{60 a^{5} b^{6} + 300 a^{4} b^{7} x + 600 a^{3} b^{8} x^{2} + 600 a^{2} b^{9} x^{3} + 300 a b^{10} x^{4} + 60 b^{11} x^{5}} - \frac{30 a^{2} b^{3} c d x}{60 a^{5} b^{6} + 300 a^{4} b^{7} x + 600 a^{3} b^{8} x^{2} + 600 a^{2} b^{9} x^{3} + 300 a b^{10} x^{4} + 60 b^{11} x^{5}} + \frac{600 a^{2} b^{3} d^{2} x^{3} \log{\left(\frac{a}{b} + x \right)}}{60 a^{5} b^{6} + 300 a^{4} b^{7} x + 600 a^{3} b^{8} x^{2} + 600 a^{2} b^{9} x^{3} + 300 a b^{10} x^{4} + 60 b^{11} x^{5}} + \frac{900 a^{2} b^{3} d^{2} x^{3}}{60 a^{5} b^{6} + 300 a^{4} b^{7} x + 600 a^{3} b^{8} x^{2} + 600 a^{2} b^{9} x^{3} + 300 a b^{10} x^{4} + 60 b^{11} x^{5}} - \frac{3 a b^{4} c^{2}}{60 a^{5} b^{6} + 300 a^{4} b^{7} x + 600 a^{3} b^{8} x^{2} + 600 a^{2} b^{9} x^{3} + 300 a b^{10} x^{4} + 60 b^{11} x^{5}} - \frac{60 a b^{4} c d x^{2}}{60 a^{5} b^{6} + 300 a^{4} b^{7} x + 600 a^{3} b^{8} x^{2} + 600 a^{2} b^{9} x^{3} + 300 a b^{10} x^{4} + 60 b^{11} x^{5}} + \frac{300 a b^{4} d^{2} x^{4} \log{\left(\frac{a}{b} + x \right)}}{60 a^{5} b^{6} + 300 a^{4} b^{7} x + 600 a^{3} b^{8} x^{2} + 600 a^{2} b^{9} x^{3} + 300 a b^{10} x^{4} + 60 b^{11} x^{5}} + \frac{300 a b^{4} d^{2} x^{4}}{60 a^{5} b^{6} + 300 a^{4} b^{7} x + 600 a^{3} b^{8} x^{2} + 600 a^{2} b^{9} x^{3} + 300 a b^{10} x^{4} + 60 b^{11} x^{5}} - \frac{15 b^{5} c^{2} x}{60 a^{5} b^{6} + 300 a^{4} b^{7} x + 600 a^{3} b^{8} x^{2} + 600 a^{2} b^{9} x^{3} + 300 a b^{10} x^{4} + 60 b^{11} x^{5}} - \frac{60 b^{5} c d x^{3}}{60 a^{5} b^{6} + 300 a^{4} b^{7} x + 600 a^{3} b^{8} x^{2} + 600 a^{2} b^{9} x^{3} + 300 a b^{10} x^{4} + 60 b^{11} x^{5}} + \frac{60 b^{5} d^{2} x^{5} \log{\left(\frac{a}{b} + x \right)}}{60 a^{5} b^{6} + 300 a^{4} b^{7} x + 600 a^{3} b^{8} x^{2} + 600 a^{2} b^{9} x^{3} + 300 a b^{10} x^{4} + 60 b^{11} x^{5}} & \text{for}\: n = -6 \\- \frac{60 a^{5} d^{2} \log{\left(\frac{a}{b} + x \right)}}{12 a^{4} b^{6} + 48 a^{3} b^{7} x + 72 a^{2} b^{8} x^{2} + 48 a b^{9} x^{3} + 12 b^{10} x^{4}} - \frac{125 a^{5} d^{2}}{12 a^{4} b^{6} + 48 a^{3} b^{7} x + 72 a^{2} b^{8} x^{2} + 48 a b^{9} x^{3} + 12 b^{10} x^{4}} - \frac{240 a^{4} b d^{2} x \log{\left(\frac{a}{b} + x \right)}}{12 a^{4} b^{6} + 48 a^{3} b^{7} x + 72 a^{2} b^{8} x^{2} + 48 a b^{9} x^{3} + 12 b^{10} x^{4}} - \frac{440 a^{4} b d^{2} x}{12 a^{4} b^{6} + 48 a^{3} b^{7} x + 72 a^{2} b^{8} x^{2} + 48 a b^{9} x^{3} + 12 b^{10} x^{4}} - \frac{6 a^{3} b^{2} c d}{12 a^{4} b^{6} + 48 a^{3} b^{7} x + 72 a^{2} b^{8} x^{2} + 48 a b^{9} x^{3} + 12 b^{10} x^{4}} - \frac{360 a^{3} b^{2} d^{2} x^{2} \log{\left(\frac{a}{b} + x \right)}}{12 a^{4} b^{6} + 48 a^{3} b^{7} x + 72 a^{2} b^{8} x^{2} + 48 a b^{9} x^{3} + 12 b^{10} x^{4}} - \frac{540 a^{3} b^{2} d^{2} x^{2}}{12 a^{4} b^{6} + 48 a^{3} b^{7} x + 72 a^{2} b^{8} x^{2} + 48 a b^{9} x^{3} + 12 b^{10} x^{4}} - \frac{24 a^{2} b^{3} c d x}{12 a^{4} b^{6} + 48 a^{3} b^{7} x + 72 a^{2} b^{8} x^{2} + 48 a b^{9} x^{3} + 12 b^{10} x^{4}} - \frac{240 a^{2} b^{3} d^{2} x^{3} \log{\left(\frac{a}{b} + x \right)}}{12 a^{4} b^{6} + 48 a^{3} b^{7} x + 72 a^{2} b^{8} x^{2} + 48 a b^{9} x^{3} + 12 b^{10} x^{4}} - \frac{240 a^{2} b^{3} d^{2} x^{3}}{12 a^{4} b^{6} + 48 a^{3} b^{7} x + 72 a^{2} b^{8} x^{2} + 48 a b^{9} x^{3} + 12 b^{10} x^{4}} - \frac{a b^{4} c^{2}}{12 a^{4} b^{6} + 48 a^{3} b^{7} x + 72 a^{2} b^{8} x^{2} + 48 a b^{9} x^{3} + 12 b^{10} x^{4}} - \frac{36 a b^{4} c d x^{2}}{12 a^{4} b^{6} + 48 a^{3} b^{7} x + 72 a^{2} b^{8} x^{2} + 48 a b^{9} x^{3} + 12 b^{10} x^{4}} - \frac{60 a b^{4} d^{2} x^{4} \log{\left(\frac{a}{b} + x \right)}}{12 a^{4} b^{6} + 48 a^{3} b^{7} x + 72 a^{2} b^{8} x^{2} + 48 a b^{9} x^{3} + 12 b^{10} x^{4}} - \frac{4 b^{5} c^{2} x}{12 a^{4} b^{6} + 48 a^{3} b^{7} x + 72 a^{2} b^{8} x^{2} + 48 a b^{9} x^{3} + 12 b^{10} x^{4}} - \frac{24 b^{5} c d x^{3}}{12 a^{4} b^{6} + 48 a^{3} b^{7} x + 72 a^{2} b^{8} x^{2} + 48 a b^{9} x^{3} + 12 b^{10} x^{4}} + \frac{12 b^{5} d^{2} x^{5}}{12 a^{4} b^{6} + 48 a^{3} b^{7} x + 72 a^{2} b^{8} x^{2} + 48 a b^{9} x^{3} + 12 b^{10} x^{4}} & \text{for}\: n = -5 \\\frac{60 a^{5} d^{2} \log{\left(\frac{a}{b} + x \right)}}{6 a^{3} b^{6} + 18 a^{2} b^{7} x + 18 a b^{8} x^{2} + 6 b^{9} x^{3}} + \frac{110 a^{5} d^{2}}{6 a^{3} b^{6} + 18 a^{2} b^{7} x + 18 a b^{8} x^{2} + 6 b^{9} x^{3}} + \frac{180 a^{4} b d^{2} x \log{\left(\frac{a}{b} + x \right)}}{6 a^{3} b^{6} + 18 a^{2} b^{7} x + 18 a b^{8} x^{2} + 6 b^{9} x^{3}} + \frac{270 a^{4} b d^{2} x}{6 a^{3} b^{6} + 18 a^{2} b^{7} x + 18 a b^{8} x^{2} + 6 b^{9} x^{3}} + \frac{12 a^{3} b^{2} c d \log{\left(\frac{a}{b} + x \right)}}{6 a^{3} b^{6} + 18 a^{2} b^{7} x + 18 a b^{8} x^{2} + 6 b^{9} x^{3}} + \frac{22 a^{3} b^{2} c d}{6 a^{3} b^{6} + 18 a^{2} b^{7} x + 18 a b^{8} x^{2} + 6 b^{9} x^{3}} + \frac{180 a^{3} b^{2} d^{2} x^{2} \log{\left(\frac{a}{b} + x \right)}}{6 a^{3} b^{6} + 18 a^{2} b^{7} x + 18 a b^{8} x^{2} + 6 b^{9} x^{3}} + \frac{180 a^{3} b^{2} d^{2} x^{2}}{6 a^{3} b^{6} + 18 a^{2} b^{7} x + 18 a b^{8} x^{2} + 6 b^{9} x^{3}} + \frac{36 a^{2} b^{3} c d x \log{\left(\frac{a}{b} + x \right)}}{6 a^{3} b^{6} + 18 a^{2} b^{7} x + 18 a b^{8} x^{2} + 6 b^{9} x^{3}} + \frac{54 a^{2} b^{3} c d x}{6 a^{3} b^{6} + 18 a^{2} b^{7} x + 18 a b^{8} x^{2} + 6 b^{9} x^{3}} + \frac{60 a^{2} b^{3} d^{2} x^{3} \log{\left(\frac{a}{b} + x \right)}}{6 a^{3} b^{6} + 18 a^{2} b^{7} x + 18 a b^{8} x^{2} + 6 b^{9} x^{3}} - \frac{a b^{4} c^{2}}{6 a^{3} b^{6} + 18 a^{2} b^{7} x + 18 a b^{8} x^{2} + 6 b^{9} x^{3}} + \frac{36 a b^{4} c d x^{2} \log{\left(\frac{a}{b} + x \right)}}{6 a^{3} b^{6} + 18 a^{2} b^{7} x + 18 a b^{8} x^{2} + 6 b^{9} x^{3}} + \frac{36 a b^{4} c d x^{2}}{6 a^{3} b^{6} + 18 a^{2} b^{7} x + 18 a b^{8} x^{2} + 6 b^{9} x^{3}} - \frac{15 a b^{4} d^{2} x^{4}}{6 a^{3} b^{6} + 18 a^{2} b^{7} x + 18 a b^{8} x^{2} + 6 b^{9} x^{3}} - \frac{3 b^{5} c^{2} x}{6 a^{3} b^{6} + 18 a^{2} b^{7} x + 18 a b^{8} x^{2} + 6 b^{9} x^{3}} + \frac{12 b^{5} c d x^{3} \log{\left(\frac{a}{b} + x \right)}}{6 a^{3} b^{6} + 18 a^{2} b^{7} x + 18 a b^{8} x^{2} + 6 b^{9} x^{3}} + \frac{3 b^{5} d^{2} x^{5}}{6 a^{3} b^{6} + 18 a^{2} b^{7} x + 18 a b^{8} x^{2} + 6 b^{9} x^{3}} & \text{for}\: n = -4 \\- \frac{60 a^{5} d^{2} \log{\left(\frac{a}{b} + x \right)}}{6 a^{2} b^{6} + 12 a b^{7} x + 6 b^{8} x^{2}} - \frac{90 a^{5} d^{2}}{6 a^{2} b^{6} + 12 a b^{7} x + 6 b^{8} x^{2}} - \frac{120 a^{4} b d^{2} x \log{\left(\frac{a}{b} + x \right)}}{6 a^{2} b^{6} + 12 a b^{7} x + 6 b^{8} x^{2}} - \frac{120 a^{4} b d^{2} x}{6 a^{2} b^{6} + 12 a b^{7} x + 6 b^{8} x^{2}} - \frac{36 a^{3} b^{2} c d \log{\left(\frac{a}{b} + x \right)}}{6 a^{2} b^{6} + 12 a b^{7} x + 6 b^{8} x^{2}} - \frac{54 a^{3} b^{2} c d}{6 a^{2} b^{6} + 12 a b^{7} x + 6 b^{8} x^{2}} - \frac{60 a^{3} b^{2} d^{2} x^{2} \log{\left(\frac{a}{b} + x \right)}}{6 a^{2} b^{6} + 12 a b^{7} x + 6 b^{8} x^{2}} - \frac{72 a^{2} b^{3} c d x \log{\left(\frac{a}{b} + x \right)}}{6 a^{2} b^{6} + 12 a b^{7} x + 6 b^{8} x^{2}} - \frac{72 a^{2} b^{3} c d x}{6 a^{2} b^{6} + 12 a b^{7} x + 6 b^{8} x^{2}} + \frac{20 a^{2} b^{3} d^{2} x^{3}}{6 a^{2} b^{6} + 12 a b^{7} x + 6 b^{8} x^{2}} - \frac{3 a b^{4} c^{2}}{6 a^{2} b^{6} + 12 a b^{7} x + 6 b^{8} x^{2}} - \frac{36 a b^{4} c d x^{2} \log{\left(\frac{a}{b} + x \right)}}{6 a^{2} b^{6} + 12 a b^{7} x + 6 b^{8} x^{2}} - \frac{5 a b^{4} d^{2} x^{4}}{6 a^{2} b^{6} + 12 a b^{7} x + 6 b^{8} x^{2}} - \frac{6 b^{5} c^{2} x}{6 a^{2} b^{6} + 12 a b^{7} x + 6 b^{8} x^{2}} + \frac{12 b^{5} c d x^{3}}{6 a^{2} b^{6} + 12 a b^{7} x + 6 b^{8} x^{2}} + \frac{2 b^{5} d^{2} x^{5}}{6 a^{2} b^{6} + 12 a b^{7} x + 6 b^{8} x^{2}} & \text{for}\: n = -3 \\\frac{60 a^{5} d^{2} \log{\left(\frac{a}{b} + x \right)}}{12 a b^{6} + 12 b^{7} x} + \frac{60 a^{5} d^{2}}{12 a b^{6} + 12 b^{7} x} + \frac{60 a^{4} b d^{2} x \log{\left(\frac{a}{b} + x \right)}}{12 a b^{6} + 12 b^{7} x} + \frac{72 a^{3} b^{2} c d \log{\left(\frac{a}{b} + x \right)}}{12 a b^{6} + 12 b^{7} x} + \frac{72 a^{3} b^{2} c d}{12 a b^{6} + 12 b^{7} x} - \frac{30 a^{3} b^{2} d^{2} x^{2}}{12 a b^{6} + 12 b^{7} x} + \frac{72 a^{2} b^{3} c d x \log{\left(\frac{a}{b} + x \right)}}{12 a b^{6} + 12 b^{7} x} + \frac{10 a^{2} b^{3} d^{2} x^{3}}{12 a b^{6} + 12 b^{7} x} + \frac{12 a b^{4} c^{2} \log{\left(\frac{a}{b} + x \right)}}{12 a b^{6} + 12 b^{7} x} + \frac{12 a b^{4} c^{2}}{12 a b^{6} + 12 b^{7} x} - \frac{36 a b^{4} c d x^{2}}{12 a b^{6} + 12 b^{7} x} - \frac{5 a b^{4} d^{2} x^{4}}{12 a b^{6} + 12 b^{7} x} + \frac{12 b^{5} c^{2} x \log{\left(\frac{a}{b} + x \right)}}{12 a b^{6} + 12 b^{7} x} + \frac{12 b^{5} c d x^{3}}{12 a b^{6} + 12 b^{7} x} + \frac{3 b^{5} d^{2} x^{5}}{12 a b^{6} + 12 b^{7} x} & \text{for}\: n = -2 \\- \frac{a^{5} d^{2} \log{\left(\frac{a}{b} + x \right)}}{b^{6}} + \frac{a^{4} d^{2} x}{b^{5}} - \frac{2 a^{3} c d \log{\left(\frac{a}{b} + x \right)}}{b^{4}} - \frac{a^{3} d^{2} x^{2}}{2 b^{4}} + \frac{2 a^{2} c d x}{b^{3}} + \frac{a^{2} d^{2} x^{3}}{3 b^{3}} - \frac{a c^{2} \log{\left(\frac{a}{b} + x \right)}}{b^{2}} - \frac{a c d x^{2}}{b^{2}} - \frac{a d^{2} x^{4}}{4 b^{2}} + \frac{c^{2} x}{b} + \frac{2 c d x^{3}}{3 b} + \frac{d^{2} x^{5}}{5 b} & \text{for}\: n = -1 \\- \frac{120 a^{6} d^{2} \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} + \frac{120 a^{5} b d^{2} n x \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} - \frac{12 a^{4} b^{2} c d n^{2} \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} - \frac{132 a^{4} b^{2} c d n \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} - \frac{360 a^{4} b^{2} c d \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} - \frac{60 a^{4} b^{2} d^{2} n^{2} x^{2} \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} - \frac{60 a^{4} b^{2} d^{2} n x^{2} \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} + \frac{12 a^{3} b^{3} c d n^{3} x \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} + \frac{132 a^{3} b^{3} c d n^{2} x \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} + \frac{360 a^{3} b^{3} c d n x \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} + \frac{20 a^{3} b^{3} d^{2} n^{3} x^{3} \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} + \frac{60 a^{3} b^{3} d^{2} n^{2} x^{3} \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} + \frac{40 a^{3} b^{3} d^{2} n x^{3} \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} - \frac{a^{2} b^{4} c^{2} n^{4} \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} - \frac{18 a^{2} b^{4} c^{2} n^{3} \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} - \frac{119 a^{2} b^{4} c^{2} n^{2} \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} - \frac{342 a^{2} b^{4} c^{2} n \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} - \frac{360 a^{2} b^{4} c^{2} \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} - \frac{6 a^{2} b^{4} c d n^{4} x^{2} \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} - \frac{72 a^{2} b^{4} c d n^{3} x^{2} \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} - \frac{246 a^{2} b^{4} c d n^{2} x^{2} \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} - \frac{180 a^{2} b^{4} c d n x^{2} \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} - \frac{5 a^{2} b^{4} d^{2} n^{4} x^{4} \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} - \frac{30 a^{2} b^{4} d^{2} n^{3} x^{4} \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} - \frac{55 a^{2} b^{4} d^{2} n^{2} x^{4} \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} - \frac{30 a^{2} b^{4} d^{2} n x^{4} \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} + \frac{a b^{5} c^{2} n^{5} x \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} + \frac{18 a b^{5} c^{2} n^{4} x \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} + \frac{119 a b^{5} c^{2} n^{3} x \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} + \frac{342 a b^{5} c^{2} n^{2} x \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} + \frac{360 a b^{5} c^{2} n x \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} + \frac{2 a b^{5} c d n^{5} x^{3} \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} + \frac{28 a b^{5} c d n^{4} x^{3} \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} + \frac{130 a b^{5} c d n^{3} x^{3} \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} + \frac{224 a b^{5} c d n^{2} x^{3} \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} + \frac{120 a b^{5} c d n x^{3} \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} + \frac{a b^{5} d^{2} n^{5} x^{5} \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} + \frac{10 a b^{5} d^{2} n^{4} x^{5} \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} + \frac{35 a b^{5} d^{2} n^{3} x^{5} \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} + \frac{50 a b^{5} d^{2} n^{2} x^{5} \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} + \frac{24 a b^{5} d^{2} n x^{5} \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} + \frac{b^{6} c^{2} n^{5} x^{2} \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} + \frac{19 b^{6} c^{2} n^{4} x^{2} \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} + \frac{137 b^{6} c^{2} n^{3} x^{2} \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} + \frac{461 b^{6} c^{2} n^{2} x^{2} \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} + \frac{702 b^{6} c^{2} n x^{2} \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} + \frac{360 b^{6} c^{2} x^{2} \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} + \frac{2 b^{6} c d n^{5} x^{4} \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} + \frac{34 b^{6} c d n^{4} x^{4} \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} + \frac{214 b^{6} c d n^{3} x^{4} \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} + \frac{614 b^{6} c d n^{2} x^{4} \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} + \frac{792 b^{6} c d n x^{4} \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} + \frac{360 b^{6} c d x^{4} \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} + \frac{b^{6} d^{2} n^{5} x^{6} \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} + \frac{15 b^{6} d^{2} n^{4} x^{6} \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} + \frac{85 b^{6} d^{2} n^{3} x^{6} \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} + \frac{225 b^{6} d^{2} n^{2} x^{6} \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} + \frac{274 b^{6} d^{2} n x^{6} \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} + \frac{120 b^{6} d^{2} x^{6} \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**n*(c**2*x**2/2 + c*d*x**4/2 + d**2*x**6/6), Eq(b, 0)), (60*a**5*d**2*log(a/b + x)/(60*a**5*b**6 + 300*a**4*b**7*x + 600*a**3*b**8*x**2 + 600*a**2*b**9*x**3 + 300*a*b**10*x**4 + 60*b**11*x**5) + 137*a**5*d**2/(60*a**5*b**6 + 300*a**4*b**7*x + 600*a**3*b**8*x**2 + 600*a**2*b**9*x**3 + 300*a*b**10*x**4 + 60*b**11*x**5) + 300*a**4*b*d**2*x*log(a/b + x)/(60*a**5*b**6 + 300*a**4*b**7*x + 600*a**3*b**8*x**2 + 600*a**2*b**9*x**3 + 300*a*b**10*x**4 + 60*b**11*x**5) + 625*a**4*b*d**2*x/(60*a**5*b**6 + 300*a**4*b**7*x + 600*a**3*b**8*x**2 + 600*a**2*b**9*x**3 + 300*a*b**10*x**4 + 60*b**11*x**5) - 6*a**3*b**2*c*d/(60*a**5*b**6 + 300*a**4*b**7*x + 600*a**3*b**8*x**2 + 600*a**2*b**9*x**3 + 300*a*b**10*x**4 + 60*b**11*x**5) + 600*a**3*b**2*d**2*x**2*log(a/b + x)/(60*a**5*b**6 + 300*a**4*b**7*x + 600*a**3*b**8*x**2 + 600*a**2*b**9*x**3 + 300*a*b**10*x**4 + 60*b**11*x**5) + 1100*a**3*b**2*d**2*x**2/(60*a**5*b**6 + 300*a**4*b**7*x + 600*a**3*b**8*x**2 + 600*a**2*b**9*x**3 + 300*a*b**10*x**4 + 60*b**11*x**5) - 30*a**2*b**3*c*d*x/(60*a**5*b**6 + 300*a**4*b**7*x + 600*a**3*b**8*x**2 + 600*a**2*b**9*x**3 + 300*a*b**10*x**4 + 60*b**11*x**5) + 600*a**2*b**3*d**2*x**3*log(a/b + x)/(60*a**5*b**6 + 300*a**4*b**7*x + 600*a**3*b**8*x**2 + 600*a**2*b**9*x**3 + 300*a*b**10*x**4 + 60*b**11*x**5) + 900*a**2*b**3*d**2*x**3/(60*a**5*b**6 + 300*a**4*b**7*x + 600*a**3*b**8*x**2 + 600*a**2*b**9*x**3 + 300*a*b**10*x**4 + 60*b**11*x**5) - 3*a*b**4*c**2/(60*a**5*b**6 + 300*a**4*b**7*x + 600*a**3*b**8*x**2 + 600*a**2*b**9*x**3 + 300*a*b**10*x**4 + 60*b**11*x**5) - 60*a*b**4*c*d*x**2/(60*a**5*b**6 + 300*a**4*b**7*x + 600*a**3*b**8*x**2 + 600*a**2*b**9*x**3 + 300*a*b**10*x**4 + 60*b**11*x**5) + 300*a*b**4*d**2*x**4*log(a/b + x)/(60*a**5*b**6 + 300*a**4*b**7*x + 600*a**3*b**8*x**2 + 600*a**2*b**9*x**3 + 300*a*b**10*x**4 + 60*b**11*x**5) + 300*a*b**4*d**2*x**4/(60*a**5*b**6 + 300*a**4*b**7*x + 600*a**3*b**8*x**2 + 600*a**2*b**9*x**3 + 300*a*b**10*x**4 + 60*b**11*x**5) - 15*b**5*c**2*x/(60*a**5*b**6 + 300*a**4*b**7*x + 600*a**3*b**8*x**2 + 600*a**2*b**9*x**3 + 300*a*b**10*x**4 + 60*b**11*x**5) - 60*b**5*c*d*x**3/(60*a**5*b**6 + 300*a**4*b**7*x + 600*a**3*b**8*x**2 + 600*a**2*b**9*x**3 + 300*a*b**10*x**4 + 60*b**11*x**5) + 60*b**5*d**2*x**5*log(a/b + x)/(60*a**5*b**6 + 300*a**4*b**7*x + 600*a**3*b**8*x**2 + 600*a**2*b**9*x**3 + 300*a*b**10*x**4 + 60*b**11*x**5), Eq(n, -6)), (-60*a**5*d**2*log(a/b + x)/(12*a**4*b**6 + 48*a**3*b**7*x + 72*a**2*b**8*x**2 + 48*a*b**9*x**3 + 12*b**10*x**4) - 125*a**5*d**2/(12*a**4*b**6 + 48*a**3*b**7*x + 72*a**2*b**8*x**2 + 48*a*b**9*x**3 + 12*b**10*x**4) - 240*a**4*b*d**2*x*log(a/b + x)/(12*a**4*b**6 + 48*a**3*b**7*x + 72*a**2*b**8*x**2 + 48*a*b**9*x**3 + 12*b**10*x**4) - 440*a**4*b*d**2*x/(12*a**4*b**6 + 48*a**3*b**7*x + 72*a**2*b**8*x**2 + 48*a*b**9*x**3 + 12*b**10*x**4) - 6*a**3*b**2*c*d/(12*a**4*b**6 + 48*a**3*b**7*x + 72*a**2*b**8*x**2 + 48*a*b**9*x**3 + 12*b**10*x**4) - 360*a**3*b**2*d**2*x**2*log(a/b + x)/(12*a**4*b**6 + 48*a**3*b**7*x + 72*a**2*b**8*x**2 + 48*a*b**9*x**3 + 12*b**10*x**4) - 540*a**3*b**2*d**2*x**2/(12*a**4*b**6 + 48*a**3*b**7*x + 72*a**2*b**8*x**2 + 48*a*b**9*x**3 + 12*b**10*x**4) - 24*a**2*b**3*c*d*x/(12*a**4*b**6 + 48*a**3*b**7*x + 72*a**2*b**8*x**2 + 48*a*b**9*x**3 + 12*b**10*x**4) - 240*a**2*b**3*d**2*x**3*log(a/b + x)/(12*a**4*b**6 + 48*a**3*b**7*x + 72*a**2*b**8*x**2 + 48*a*b**9*x**3 + 12*b**10*x**4) - 240*a**2*b**3*d**2*x**3/(12*a**4*b**6 + 48*a**3*b**7*x + 72*a**2*b**8*x**2 + 48*a*b**9*x**3 + 12*b**10*x**4) - a*b**4*c**2/(12*a**4*b**6 + 48*a**3*b**7*x + 72*a**2*b**8*x**2 + 48*a*b**9*x**3 + 12*b**10*x**4) - 36*a*b**4*c*d*x**2/(12*a**4*b**6 + 48*a**3*b**7*x + 72*a**2*b**8*x**2 + 48*a*b**9*x**3 + 12*b**10*x**4) - 60*a*b**4*d**2*x**4*log(a/b + x)/(12*a**4*b**6 + 48*a**3*b**7*x + 72*a**2*b**8*x**2 + 48*a*b**9*x**3 + 12*b**10*x**4) - 4*b**5*c**2*x/(12*a**4*b**6 + 48*a**3*b**7*x + 72*a**2*b**8*x**2 + 48*a*b**9*x**3 + 12*b**10*x**4) - 24*b**5*c*d*x**3/(12*a**4*b**6 + 48*a**3*b**7*x + 72*a**2*b**8*x**2 + 48*a*b**9*x**3 + 12*b**10*x**4) + 12*b**5*d**2*x**5/(12*a**4*b**6 + 48*a**3*b**7*x + 72*a**2*b**8*x**2 + 48*a*b**9*x**3 + 12*b**10*x**4), Eq(n, -5)), (60*a**5*d**2*log(a/b + x)/(6*a**3*b**6 + 18*a**2*b**7*x + 18*a*b**8*x**2 + 6*b**9*x**3) + 110*a**5*d**2/(6*a**3*b**6 + 18*a**2*b**7*x + 18*a*b**8*x**2 + 6*b**9*x**3) + 180*a**4*b*d**2*x*log(a/b + x)/(6*a**3*b**6 + 18*a**2*b**7*x + 18*a*b**8*x**2 + 6*b**9*x**3) + 270*a**4*b*d**2*x/(6*a**3*b**6 + 18*a**2*b**7*x + 18*a*b**8*x**2 + 6*b**9*x**3) + 12*a**3*b**2*c*d*log(a/b + x)/(6*a**3*b**6 + 18*a**2*b**7*x + 18*a*b**8*x**2 + 6*b**9*x**3) + 22*a**3*b**2*c*d/(6*a**3*b**6 + 18*a**2*b**7*x + 18*a*b**8*x**2 + 6*b**9*x**3) + 180*a**3*b**2*d**2*x**2*log(a/b + x)/(6*a**3*b**6 + 18*a**2*b**7*x + 18*a*b**8*x**2 + 6*b**9*x**3) + 180*a**3*b**2*d**2*x**2/(6*a**3*b**6 + 18*a**2*b**7*x + 18*a*b**8*x**2 + 6*b**9*x**3) + 36*a**2*b**3*c*d*x*log(a/b + x)/(6*a**3*b**6 + 18*a**2*b**7*x + 18*a*b**8*x**2 + 6*b**9*x**3) + 54*a**2*b**3*c*d*x/(6*a**3*b**6 + 18*a**2*b**7*x + 18*a*b**8*x**2 + 6*b**9*x**3) + 60*a**2*b**3*d**2*x**3*log(a/b + x)/(6*a**3*b**6 + 18*a**2*b**7*x + 18*a*b**8*x**2 + 6*b**9*x**3) - a*b**4*c**2/(6*a**3*b**6 + 18*a**2*b**7*x + 18*a*b**8*x**2 + 6*b**9*x**3) + 36*a*b**4*c*d*x**2*log(a/b + x)/(6*a**3*b**6 + 18*a**2*b**7*x + 18*a*b**8*x**2 + 6*b**9*x**3) + 36*a*b**4*c*d*x**2/(6*a**3*b**6 + 18*a**2*b**7*x + 18*a*b**8*x**2 + 6*b**9*x**3) - 15*a*b**4*d**2*x**4/(6*a**3*b**6 + 18*a**2*b**7*x + 18*a*b**8*x**2 + 6*b**9*x**3) - 3*b**5*c**2*x/(6*a**3*b**6 + 18*a**2*b**7*x + 18*a*b**8*x**2 + 6*b**9*x**3) + 12*b**5*c*d*x**3*log(a/b + x)/(6*a**3*b**6 + 18*a**2*b**7*x + 18*a*b**8*x**2 + 6*b**9*x**3) + 3*b**5*d**2*x**5/(6*a**3*b**6 + 18*a**2*b**7*x + 18*a*b**8*x**2 + 6*b**9*x**3), Eq(n, -4)), (-60*a**5*d**2*log(a/b + x)/(6*a**2*b**6 + 12*a*b**7*x + 6*b**8*x**2) - 90*a**5*d**2/(6*a**2*b**6 + 12*a*b**7*x + 6*b**8*x**2) - 120*a**4*b*d**2*x*log(a/b + x)/(6*a**2*b**6 + 12*a*b**7*x + 6*b**8*x**2) - 120*a**4*b*d**2*x/(6*a**2*b**6 + 12*a*b**7*x + 6*b**8*x**2) - 36*a**3*b**2*c*d*log(a/b + x)/(6*a**2*b**6 + 12*a*b**7*x + 6*b**8*x**2) - 54*a**3*b**2*c*d/(6*a**2*b**6 + 12*a*b**7*x + 6*b**8*x**2) - 60*a**3*b**2*d**2*x**2*log(a/b + x)/(6*a**2*b**6 + 12*a*b**7*x + 6*b**8*x**2) - 72*a**2*b**3*c*d*x*log(a/b + x)/(6*a**2*b**6 + 12*a*b**7*x + 6*b**8*x**2) - 72*a**2*b**3*c*d*x/(6*a**2*b**6 + 12*a*b**7*x + 6*b**8*x**2) + 20*a**2*b**3*d**2*x**3/(6*a**2*b**6 + 12*a*b**7*x + 6*b**8*x**2) - 3*a*b**4*c**2/(6*a**2*b**6 + 12*a*b**7*x + 6*b**8*x**2) - 36*a*b**4*c*d*x**2*log(a/b + x)/(6*a**2*b**6 + 12*a*b**7*x + 6*b**8*x**2) - 5*a*b**4*d**2*x**4/(6*a**2*b**6 + 12*a*b**7*x + 6*b**8*x**2) - 6*b**5*c**2*x/(6*a**2*b**6 + 12*a*b**7*x + 6*b**8*x**2) + 12*b**5*c*d*x**3/(6*a**2*b**6 + 12*a*b**7*x + 6*b**8*x**2) + 2*b**5*d**2*x**5/(6*a**2*b**6 + 12*a*b**7*x + 6*b**8*x**2), Eq(n, -3)), (60*a**5*d**2*log(a/b + x)/(12*a*b**6 + 12*b**7*x) + 60*a**5*d**2/(12*a*b**6 + 12*b**7*x) + 60*a**4*b*d**2*x*log(a/b + x)/(12*a*b**6 + 12*b**7*x) + 72*a**3*b**2*c*d*log(a/b + x)/(12*a*b**6 + 12*b**7*x) + 72*a**3*b**2*c*d/(12*a*b**6 + 12*b**7*x) - 30*a**3*b**2*d**2*x**2/(12*a*b**6 + 12*b**7*x) + 72*a**2*b**3*c*d*x*log(a/b + x)/(12*a*b**6 + 12*b**7*x) + 10*a**2*b**3*d**2*x**3/(12*a*b**6 + 12*b**7*x) + 12*a*b**4*c**2*log(a/b + x)/(12*a*b**6 + 12*b**7*x) + 12*a*b**4*c**2/(12*a*b**6 + 12*b**7*x) - 36*a*b**4*c*d*x**2/(12*a*b**6 + 12*b**7*x) - 5*a*b**4*d**2*x**4/(12*a*b**6 + 12*b**7*x) + 12*b**5*c**2*x*log(a/b + x)/(12*a*b**6 + 12*b**7*x) + 12*b**5*c*d*x**3/(12*a*b**6 + 12*b**7*x) + 3*b**5*d**2*x**5/(12*a*b**6 + 12*b**7*x), Eq(n, -2)), (-a**5*d**2*log(a/b + x)/b**6 + a**4*d**2*x/b**5 - 2*a**3*c*d*log(a/b + x)/b**4 - a**3*d**2*x**2/(2*b**4) + 2*a**2*c*d*x/b**3 + a**2*d**2*x**3/(3*b**3) - a*c**2*log(a/b + x)/b**2 - a*c*d*x**2/b**2 - a*d**2*x**4/(4*b**2) + c**2*x/b + 2*c*d*x**3/(3*b) + d**2*x**5/(5*b), Eq(n, -1)), (-120*a**6*d**2*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) + 120*a**5*b*d**2*n*x*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) - 12*a**4*b**2*c*d*n**2*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) - 132*a**4*b**2*c*d*n*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) - 360*a**4*b**2*c*d*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) - 60*a**4*b**2*d**2*n**2*x**2*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) - 60*a**4*b**2*d**2*n*x**2*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) + 12*a**3*b**3*c*d*n**3*x*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) + 132*a**3*b**3*c*d*n**2*x*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) + 360*a**3*b**3*c*d*n*x*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) + 20*a**3*b**3*d**2*n**3*x**3*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) + 60*a**3*b**3*d**2*n**2*x**3*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) + 40*a**3*b**3*d**2*n*x**3*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) - a**2*b**4*c**2*n**4*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) - 18*a**2*b**4*c**2*n**3*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) - 119*a**2*b**4*c**2*n**2*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) - 342*a**2*b**4*c**2*n*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) - 360*a**2*b**4*c**2*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) - 6*a**2*b**4*c*d*n**4*x**2*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) - 72*a**2*b**4*c*d*n**3*x**2*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) - 246*a**2*b**4*c*d*n**2*x**2*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) - 180*a**2*b**4*c*d*n*x**2*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) - 5*a**2*b**4*d**2*n**4*x**4*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) - 30*a**2*b**4*d**2*n**3*x**4*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) - 55*a**2*b**4*d**2*n**2*x**4*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) - 30*a**2*b**4*d**2*n*x**4*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) + a*b**5*c**2*n**5*x*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) + 18*a*b**5*c**2*n**4*x*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) + 119*a*b**5*c**2*n**3*x*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) + 342*a*b**5*c**2*n**2*x*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) + 360*a*b**5*c**2*n*x*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) + 2*a*b**5*c*d*n**5*x**3*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) + 28*a*b**5*c*d*n**4*x**3*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) + 130*a*b**5*c*d*n**3*x**3*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) + 224*a*b**5*c*d*n**2*x**3*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) + 120*a*b**5*c*d*n*x**3*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) + a*b**5*d**2*n**5*x**5*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) + 10*a*b**5*d**2*n**4*x**5*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) + 35*a*b**5*d**2*n**3*x**5*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) + 50*a*b**5*d**2*n**2*x**5*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) + 24*a*b**5*d**2*n*x**5*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) + b**6*c**2*n**5*x**2*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) + 19*b**6*c**2*n**4*x**2*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) + 137*b**6*c**2*n**3*x**2*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) + 461*b**6*c**2*n**2*x**2*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) + 702*b**6*c**2*n*x**2*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) + 360*b**6*c**2*x**2*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) + 2*b**6*c*d*n**5*x**4*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) + 34*b**6*c*d*n**4*x**4*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) + 214*b**6*c*d*n**3*x**4*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) + 614*b**6*c*d*n**2*x**4*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) + 792*b**6*c*d*n*x**4*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) + 360*b**6*c*d*x**4*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) + b**6*d**2*n**5*x**6*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) + 15*b**6*d**2*n**4*x**6*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) + 85*b**6*d**2*n**3*x**6*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) + 225*b**6*d**2*n**2*x**6*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) + 274*b**6*d**2*n*x**6*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) + 120*b**6*d**2*x**6*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6), True))","A",0
357,1,5097,0,7.127888," ","integrate((b*x+a)**n*(d*x**2+c)**2,x)","\begin{cases} a^{n} \left(c^{2} x + \frac{2 c d x^{3}}{3} + \frac{d^{2} x^{5}}{5}\right) & \text{for}\: b = 0 \\\frac{12 a^{4} d^{2} \log{\left(\frac{a}{b} + x \right)}}{12 a^{4} b^{5} + 48 a^{3} b^{6} x + 72 a^{2} b^{7} x^{2} + 48 a b^{8} x^{3} + 12 b^{9} x^{4}} + \frac{25 a^{4} d^{2}}{12 a^{4} b^{5} + 48 a^{3} b^{6} x + 72 a^{2} b^{7} x^{2} + 48 a b^{8} x^{3} + 12 b^{9} x^{4}} + \frac{48 a^{3} b d^{2} x \log{\left(\frac{a}{b} + x \right)}}{12 a^{4} b^{5} + 48 a^{3} b^{6} x + 72 a^{2} b^{7} x^{2} + 48 a b^{8} x^{3} + 12 b^{9} x^{4}} + \frac{88 a^{3} b d^{2} x}{12 a^{4} b^{5} + 48 a^{3} b^{6} x + 72 a^{2} b^{7} x^{2} + 48 a b^{8} x^{3} + 12 b^{9} x^{4}} - \frac{2 a^{2} b^{2} c d}{12 a^{4} b^{5} + 48 a^{3} b^{6} x + 72 a^{2} b^{7} x^{2} + 48 a b^{8} x^{3} + 12 b^{9} x^{4}} + \frac{72 a^{2} b^{2} d^{2} x^{2} \log{\left(\frac{a}{b} + x \right)}}{12 a^{4} b^{5} + 48 a^{3} b^{6} x + 72 a^{2} b^{7} x^{2} + 48 a b^{8} x^{3} + 12 b^{9} x^{4}} + \frac{108 a^{2} b^{2} d^{2} x^{2}}{12 a^{4} b^{5} + 48 a^{3} b^{6} x + 72 a^{2} b^{7} x^{2} + 48 a b^{8} x^{3} + 12 b^{9} x^{4}} - \frac{8 a b^{3} c d x}{12 a^{4} b^{5} + 48 a^{3} b^{6} x + 72 a^{2} b^{7} x^{2} + 48 a b^{8} x^{3} + 12 b^{9} x^{4}} + \frac{48 a b^{3} d^{2} x^{3} \log{\left(\frac{a}{b} + x \right)}}{12 a^{4} b^{5} + 48 a^{3} b^{6} x + 72 a^{2} b^{7} x^{2} + 48 a b^{8} x^{3} + 12 b^{9} x^{4}} + \frac{48 a b^{3} d^{2} x^{3}}{12 a^{4} b^{5} + 48 a^{3} b^{6} x + 72 a^{2} b^{7} x^{2} + 48 a b^{8} x^{3} + 12 b^{9} x^{4}} - \frac{3 b^{4} c^{2}}{12 a^{4} b^{5} + 48 a^{3} b^{6} x + 72 a^{2} b^{7} x^{2} + 48 a b^{8} x^{3} + 12 b^{9} x^{4}} - \frac{12 b^{4} c d x^{2}}{12 a^{4} b^{5} + 48 a^{3} b^{6} x + 72 a^{2} b^{7} x^{2} + 48 a b^{8} x^{3} + 12 b^{9} x^{4}} + \frac{12 b^{4} d^{2} x^{4} \log{\left(\frac{a}{b} + x \right)}}{12 a^{4} b^{5} + 48 a^{3} b^{6} x + 72 a^{2} b^{7} x^{2} + 48 a b^{8} x^{3} + 12 b^{9} x^{4}} & \text{for}\: n = -5 \\- \frac{12 a^{4} d^{2} \log{\left(\frac{a}{b} + x \right)}}{3 a^{3} b^{5} + 9 a^{2} b^{6} x + 9 a b^{7} x^{2} + 3 b^{8} x^{3}} - \frac{22 a^{4} d^{2}}{3 a^{3} b^{5} + 9 a^{2} b^{6} x + 9 a b^{7} x^{2} + 3 b^{8} x^{3}} - \frac{36 a^{3} b d^{2} x \log{\left(\frac{a}{b} + x \right)}}{3 a^{3} b^{5} + 9 a^{2} b^{6} x + 9 a b^{7} x^{2} + 3 b^{8} x^{3}} - \frac{54 a^{3} b d^{2} x}{3 a^{3} b^{5} + 9 a^{2} b^{6} x + 9 a b^{7} x^{2} + 3 b^{8} x^{3}} - \frac{2 a^{2} b^{2} c d}{3 a^{3} b^{5} + 9 a^{2} b^{6} x + 9 a b^{7} x^{2} + 3 b^{8} x^{3}} - \frac{36 a^{2} b^{2} d^{2} x^{2} \log{\left(\frac{a}{b} + x \right)}}{3 a^{3} b^{5} + 9 a^{2} b^{6} x + 9 a b^{7} x^{2} + 3 b^{8} x^{3}} - \frac{36 a^{2} b^{2} d^{2} x^{2}}{3 a^{3} b^{5} + 9 a^{2} b^{6} x + 9 a b^{7} x^{2} + 3 b^{8} x^{3}} - \frac{6 a b^{3} c d x}{3 a^{3} b^{5} + 9 a^{2} b^{6} x + 9 a b^{7} x^{2} + 3 b^{8} x^{3}} - \frac{12 a b^{3} d^{2} x^{3} \log{\left(\frac{a}{b} + x \right)}}{3 a^{3} b^{5} + 9 a^{2} b^{6} x + 9 a b^{7} x^{2} + 3 b^{8} x^{3}} - \frac{b^{4} c^{2}}{3 a^{3} b^{5} + 9 a^{2} b^{6} x + 9 a b^{7} x^{2} + 3 b^{8} x^{3}} - \frac{6 b^{4} c d x^{2}}{3 a^{3} b^{5} + 9 a^{2} b^{6} x + 9 a b^{7} x^{2} + 3 b^{8} x^{3}} + \frac{3 b^{4} d^{2} x^{4}}{3 a^{3} b^{5} + 9 a^{2} b^{6} x + 9 a b^{7} x^{2} + 3 b^{8} x^{3}} & \text{for}\: n = -4 \\\frac{12 a^{4} d^{2} \log{\left(\frac{a}{b} + x \right)}}{2 a^{2} b^{5} + 4 a b^{6} x + 2 b^{7} x^{2}} + \frac{18 a^{4} d^{2}}{2 a^{2} b^{5} + 4 a b^{6} x + 2 b^{7} x^{2}} + \frac{24 a^{3} b d^{2} x \log{\left(\frac{a}{b} + x \right)}}{2 a^{2} b^{5} + 4 a b^{6} x + 2 b^{7} x^{2}} + \frac{24 a^{3} b d^{2} x}{2 a^{2} b^{5} + 4 a b^{6} x + 2 b^{7} x^{2}} + \frac{4 a^{2} b^{2} c d \log{\left(\frac{a}{b} + x \right)}}{2 a^{2} b^{5} + 4 a b^{6} x + 2 b^{7} x^{2}} + \frac{6 a^{2} b^{2} c d}{2 a^{2} b^{5} + 4 a b^{6} x + 2 b^{7} x^{2}} + \frac{12 a^{2} b^{2} d^{2} x^{2} \log{\left(\frac{a}{b} + x \right)}}{2 a^{2} b^{5} + 4 a b^{6} x + 2 b^{7} x^{2}} + \frac{8 a b^{3} c d x \log{\left(\frac{a}{b} + x \right)}}{2 a^{2} b^{5} + 4 a b^{6} x + 2 b^{7} x^{2}} + \frac{8 a b^{3} c d x}{2 a^{2} b^{5} + 4 a b^{6} x + 2 b^{7} x^{2}} - \frac{4 a b^{3} d^{2} x^{3}}{2 a^{2} b^{5} + 4 a b^{6} x + 2 b^{7} x^{2}} - \frac{b^{4} c^{2}}{2 a^{2} b^{5} + 4 a b^{6} x + 2 b^{7} x^{2}} + \frac{4 b^{4} c d x^{2} \log{\left(\frac{a}{b} + x \right)}}{2 a^{2} b^{5} + 4 a b^{6} x + 2 b^{7} x^{2}} + \frac{b^{4} d^{2} x^{4}}{2 a^{2} b^{5} + 4 a b^{6} x + 2 b^{7} x^{2}} & \text{for}\: n = -3 \\- \frac{12 a^{4} d^{2} \log{\left(\frac{a}{b} + x \right)}}{3 a b^{5} + 3 b^{6} x} - \frac{12 a^{4} d^{2}}{3 a b^{5} + 3 b^{6} x} - \frac{12 a^{3} b d^{2} x \log{\left(\frac{a}{b} + x \right)}}{3 a b^{5} + 3 b^{6} x} - \frac{12 a^{2} b^{2} c d \log{\left(\frac{a}{b} + x \right)}}{3 a b^{5} + 3 b^{6} x} - \frac{12 a^{2} b^{2} c d}{3 a b^{5} + 3 b^{6} x} + \frac{6 a^{2} b^{2} d^{2} x^{2}}{3 a b^{5} + 3 b^{6} x} - \frac{12 a b^{3} c d x \log{\left(\frac{a}{b} + x \right)}}{3 a b^{5} + 3 b^{6} x} - \frac{2 a b^{3} d^{2} x^{3}}{3 a b^{5} + 3 b^{6} x} - \frac{3 b^{4} c^{2}}{3 a b^{5} + 3 b^{6} x} + \frac{6 b^{4} c d x^{2}}{3 a b^{5} + 3 b^{6} x} + \frac{b^{4} d^{2} x^{4}}{3 a b^{5} + 3 b^{6} x} & \text{for}\: n = -2 \\\frac{a^{4} d^{2} \log{\left(\frac{a}{b} + x \right)}}{b^{5}} - \frac{a^{3} d^{2} x}{b^{4}} + \frac{2 a^{2} c d \log{\left(\frac{a}{b} + x \right)}}{b^{3}} + \frac{a^{2} d^{2} x^{2}}{2 b^{3}} - \frac{2 a c d x}{b^{2}} - \frac{a d^{2} x^{3}}{3 b^{2}} + \frac{c^{2} \log{\left(\frac{a}{b} + x \right)}}{b} + \frac{c d x^{2}}{b} + \frac{d^{2} x^{4}}{4 b} & \text{for}\: n = -1 \\\frac{24 a^{5} d^{2} \left(a + b x\right)^{n}}{b^{5} n^{5} + 15 b^{5} n^{4} + 85 b^{5} n^{3} + 225 b^{5} n^{2} + 274 b^{5} n + 120 b^{5}} - \frac{24 a^{4} b d^{2} n x \left(a + b x\right)^{n}}{b^{5} n^{5} + 15 b^{5} n^{4} + 85 b^{5} n^{3} + 225 b^{5} n^{2} + 274 b^{5} n + 120 b^{5}} + \frac{4 a^{3} b^{2} c d n^{2} \left(a + b x\right)^{n}}{b^{5} n^{5} + 15 b^{5} n^{4} + 85 b^{5} n^{3} + 225 b^{5} n^{2} + 274 b^{5} n + 120 b^{5}} + \frac{36 a^{3} b^{2} c d n \left(a + b x\right)^{n}}{b^{5} n^{5} + 15 b^{5} n^{4} + 85 b^{5} n^{3} + 225 b^{5} n^{2} + 274 b^{5} n + 120 b^{5}} + \frac{80 a^{3} b^{2} c d \left(a + b x\right)^{n}}{b^{5} n^{5} + 15 b^{5} n^{4} + 85 b^{5} n^{3} + 225 b^{5} n^{2} + 274 b^{5} n + 120 b^{5}} + \frac{12 a^{3} b^{2} d^{2} n^{2} x^{2} \left(a + b x\right)^{n}}{b^{5} n^{5} + 15 b^{5} n^{4} + 85 b^{5} n^{3} + 225 b^{5} n^{2} + 274 b^{5} n + 120 b^{5}} + \frac{12 a^{3} b^{2} d^{2} n x^{2} \left(a + b x\right)^{n}}{b^{5} n^{5} + 15 b^{5} n^{4} + 85 b^{5} n^{3} + 225 b^{5} n^{2} + 274 b^{5} n + 120 b^{5}} - \frac{4 a^{2} b^{3} c d n^{3} x \left(a + b x\right)^{n}}{b^{5} n^{5} + 15 b^{5} n^{4} + 85 b^{5} n^{3} + 225 b^{5} n^{2} + 274 b^{5} n + 120 b^{5}} - \frac{36 a^{2} b^{3} c d n^{2} x \left(a + b x\right)^{n}}{b^{5} n^{5} + 15 b^{5} n^{4} + 85 b^{5} n^{3} + 225 b^{5} n^{2} + 274 b^{5} n + 120 b^{5}} - \frac{80 a^{2} b^{3} c d n x \left(a + b x\right)^{n}}{b^{5} n^{5} + 15 b^{5} n^{4} + 85 b^{5} n^{3} + 225 b^{5} n^{2} + 274 b^{5} n + 120 b^{5}} - \frac{4 a^{2} b^{3} d^{2} n^{3} x^{3} \left(a + b x\right)^{n}}{b^{5} n^{5} + 15 b^{5} n^{4} + 85 b^{5} n^{3} + 225 b^{5} n^{2} + 274 b^{5} n + 120 b^{5}} - \frac{12 a^{2} b^{3} d^{2} n^{2} x^{3} \left(a + b x\right)^{n}}{b^{5} n^{5} + 15 b^{5} n^{4} + 85 b^{5} n^{3} + 225 b^{5} n^{2} + 274 b^{5} n + 120 b^{5}} - \frac{8 a^{2} b^{3} d^{2} n x^{3} \left(a + b x\right)^{n}}{b^{5} n^{5} + 15 b^{5} n^{4} + 85 b^{5} n^{3} + 225 b^{5} n^{2} + 274 b^{5} n + 120 b^{5}} + \frac{a b^{4} c^{2} n^{4} \left(a + b x\right)^{n}}{b^{5} n^{5} + 15 b^{5} n^{4} + 85 b^{5} n^{3} + 225 b^{5} n^{2} + 274 b^{5} n + 120 b^{5}} + \frac{14 a b^{4} c^{2} n^{3} \left(a + b x\right)^{n}}{b^{5} n^{5} + 15 b^{5} n^{4} + 85 b^{5} n^{3} + 225 b^{5} n^{2} + 274 b^{5} n + 120 b^{5}} + \frac{71 a b^{4} c^{2} n^{2} \left(a + b x\right)^{n}}{b^{5} n^{5} + 15 b^{5} n^{4} + 85 b^{5} n^{3} + 225 b^{5} n^{2} + 274 b^{5} n + 120 b^{5}} + \frac{154 a b^{4} c^{2} n \left(a + b x\right)^{n}}{b^{5} n^{5} + 15 b^{5} n^{4} + 85 b^{5} n^{3} + 225 b^{5} n^{2} + 274 b^{5} n + 120 b^{5}} + \frac{120 a b^{4} c^{2} \left(a + b x\right)^{n}}{b^{5} n^{5} + 15 b^{5} n^{4} + 85 b^{5} n^{3} + 225 b^{5} n^{2} + 274 b^{5} n + 120 b^{5}} + \frac{2 a b^{4} c d n^{4} x^{2} \left(a + b x\right)^{n}}{b^{5} n^{5} + 15 b^{5} n^{4} + 85 b^{5} n^{3} + 225 b^{5} n^{2} + 274 b^{5} n + 120 b^{5}} + \frac{20 a b^{4} c d n^{3} x^{2} \left(a + b x\right)^{n}}{b^{5} n^{5} + 15 b^{5} n^{4} + 85 b^{5} n^{3} + 225 b^{5} n^{2} + 274 b^{5} n + 120 b^{5}} + \frac{58 a b^{4} c d n^{2} x^{2} \left(a + b x\right)^{n}}{b^{5} n^{5} + 15 b^{5} n^{4} + 85 b^{5} n^{3} + 225 b^{5} n^{2} + 274 b^{5} n + 120 b^{5}} + \frac{40 a b^{4} c d n x^{2} \left(a + b x\right)^{n}}{b^{5} n^{5} + 15 b^{5} n^{4} + 85 b^{5} n^{3} + 225 b^{5} n^{2} + 274 b^{5} n + 120 b^{5}} + \frac{a b^{4} d^{2} n^{4} x^{4} \left(a + b x\right)^{n}}{b^{5} n^{5} + 15 b^{5} n^{4} + 85 b^{5} n^{3} + 225 b^{5} n^{2} + 274 b^{5} n + 120 b^{5}} + \frac{6 a b^{4} d^{2} n^{3} x^{4} \left(a + b x\right)^{n}}{b^{5} n^{5} + 15 b^{5} n^{4} + 85 b^{5} n^{3} + 225 b^{5} n^{2} + 274 b^{5} n + 120 b^{5}} + \frac{11 a b^{4} d^{2} n^{2} x^{4} \left(a + b x\right)^{n}}{b^{5} n^{5} + 15 b^{5} n^{4} + 85 b^{5} n^{3} + 225 b^{5} n^{2} + 274 b^{5} n + 120 b^{5}} + \frac{6 a b^{4} d^{2} n x^{4} \left(a + b x\right)^{n}}{b^{5} n^{5} + 15 b^{5} n^{4} + 85 b^{5} n^{3} + 225 b^{5} n^{2} + 274 b^{5} n + 120 b^{5}} + \frac{b^{5} c^{2} n^{4} x \left(a + b x\right)^{n}}{b^{5} n^{5} + 15 b^{5} n^{4} + 85 b^{5} n^{3} + 225 b^{5} n^{2} + 274 b^{5} n + 120 b^{5}} + \frac{14 b^{5} c^{2} n^{3} x \left(a + b x\right)^{n}}{b^{5} n^{5} + 15 b^{5} n^{4} + 85 b^{5} n^{3} + 225 b^{5} n^{2} + 274 b^{5} n + 120 b^{5}} + \frac{71 b^{5} c^{2} n^{2} x \left(a + b x\right)^{n}}{b^{5} n^{5} + 15 b^{5} n^{4} + 85 b^{5} n^{3} + 225 b^{5} n^{2} + 274 b^{5} n + 120 b^{5}} + \frac{154 b^{5} c^{2} n x \left(a + b x\right)^{n}}{b^{5} n^{5} + 15 b^{5} n^{4} + 85 b^{5} n^{3} + 225 b^{5} n^{2} + 274 b^{5} n + 120 b^{5}} + \frac{120 b^{5} c^{2} x \left(a + b x\right)^{n}}{b^{5} n^{5} + 15 b^{5} n^{4} + 85 b^{5} n^{3} + 225 b^{5} n^{2} + 274 b^{5} n + 120 b^{5}} + \frac{2 b^{5} c d n^{4} x^{3} \left(a + b x\right)^{n}}{b^{5} n^{5} + 15 b^{5} n^{4} + 85 b^{5} n^{3} + 225 b^{5} n^{2} + 274 b^{5} n + 120 b^{5}} + \frac{24 b^{5} c d n^{3} x^{3} \left(a + b x\right)^{n}}{b^{5} n^{5} + 15 b^{5} n^{4} + 85 b^{5} n^{3} + 225 b^{5} n^{2} + 274 b^{5} n + 120 b^{5}} + \frac{98 b^{5} c d n^{2} x^{3} \left(a + b x\right)^{n}}{b^{5} n^{5} + 15 b^{5} n^{4} + 85 b^{5} n^{3} + 225 b^{5} n^{2} + 274 b^{5} n + 120 b^{5}} + \frac{156 b^{5} c d n x^{3} \left(a + b x\right)^{n}}{b^{5} n^{5} + 15 b^{5} n^{4} + 85 b^{5} n^{3} + 225 b^{5} n^{2} + 274 b^{5} n + 120 b^{5}} + \frac{80 b^{5} c d x^{3} \left(a + b x\right)^{n}}{b^{5} n^{5} + 15 b^{5} n^{4} + 85 b^{5} n^{3} + 225 b^{5} n^{2} + 274 b^{5} n + 120 b^{5}} + \frac{b^{5} d^{2} n^{4} x^{5} \left(a + b x\right)^{n}}{b^{5} n^{5} + 15 b^{5} n^{4} + 85 b^{5} n^{3} + 225 b^{5} n^{2} + 274 b^{5} n + 120 b^{5}} + \frac{10 b^{5} d^{2} n^{3} x^{5} \left(a + b x\right)^{n}}{b^{5} n^{5} + 15 b^{5} n^{4} + 85 b^{5} n^{3} + 225 b^{5} n^{2} + 274 b^{5} n + 120 b^{5}} + \frac{35 b^{5} d^{2} n^{2} x^{5} \left(a + b x\right)^{n}}{b^{5} n^{5} + 15 b^{5} n^{4} + 85 b^{5} n^{3} + 225 b^{5} n^{2} + 274 b^{5} n + 120 b^{5}} + \frac{50 b^{5} d^{2} n x^{5} \left(a + b x\right)^{n}}{b^{5} n^{5} + 15 b^{5} n^{4} + 85 b^{5} n^{3} + 225 b^{5} n^{2} + 274 b^{5} n + 120 b^{5}} + \frac{24 b^{5} d^{2} x^{5} \left(a + b x\right)^{n}}{b^{5} n^{5} + 15 b^{5} n^{4} + 85 b^{5} n^{3} + 225 b^{5} n^{2} + 274 b^{5} n + 120 b^{5}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**n*(c**2*x + 2*c*d*x**3/3 + d**2*x**5/5), Eq(b, 0)), (12*a**4*d**2*log(a/b + x)/(12*a**4*b**5 + 48*a**3*b**6*x + 72*a**2*b**7*x**2 + 48*a*b**8*x**3 + 12*b**9*x**4) + 25*a**4*d**2/(12*a**4*b**5 + 48*a**3*b**6*x + 72*a**2*b**7*x**2 + 48*a*b**8*x**3 + 12*b**9*x**4) + 48*a**3*b*d**2*x*log(a/b + x)/(12*a**4*b**5 + 48*a**3*b**6*x + 72*a**2*b**7*x**2 + 48*a*b**8*x**3 + 12*b**9*x**4) + 88*a**3*b*d**2*x/(12*a**4*b**5 + 48*a**3*b**6*x + 72*a**2*b**7*x**2 + 48*a*b**8*x**3 + 12*b**9*x**4) - 2*a**2*b**2*c*d/(12*a**4*b**5 + 48*a**3*b**6*x + 72*a**2*b**7*x**2 + 48*a*b**8*x**3 + 12*b**9*x**4) + 72*a**2*b**2*d**2*x**2*log(a/b + x)/(12*a**4*b**5 + 48*a**3*b**6*x + 72*a**2*b**7*x**2 + 48*a*b**8*x**3 + 12*b**9*x**4) + 108*a**2*b**2*d**2*x**2/(12*a**4*b**5 + 48*a**3*b**6*x + 72*a**2*b**7*x**2 + 48*a*b**8*x**3 + 12*b**9*x**4) - 8*a*b**3*c*d*x/(12*a**4*b**5 + 48*a**3*b**6*x + 72*a**2*b**7*x**2 + 48*a*b**8*x**3 + 12*b**9*x**4) + 48*a*b**3*d**2*x**3*log(a/b + x)/(12*a**4*b**5 + 48*a**3*b**6*x + 72*a**2*b**7*x**2 + 48*a*b**8*x**3 + 12*b**9*x**4) + 48*a*b**3*d**2*x**3/(12*a**4*b**5 + 48*a**3*b**6*x + 72*a**2*b**7*x**2 + 48*a*b**8*x**3 + 12*b**9*x**4) - 3*b**4*c**2/(12*a**4*b**5 + 48*a**3*b**6*x + 72*a**2*b**7*x**2 + 48*a*b**8*x**3 + 12*b**9*x**4) - 12*b**4*c*d*x**2/(12*a**4*b**5 + 48*a**3*b**6*x + 72*a**2*b**7*x**2 + 48*a*b**8*x**3 + 12*b**9*x**4) + 12*b**4*d**2*x**4*log(a/b + x)/(12*a**4*b**5 + 48*a**3*b**6*x + 72*a**2*b**7*x**2 + 48*a*b**8*x**3 + 12*b**9*x**4), Eq(n, -5)), (-12*a**4*d**2*log(a/b + x)/(3*a**3*b**5 + 9*a**2*b**6*x + 9*a*b**7*x**2 + 3*b**8*x**3) - 22*a**4*d**2/(3*a**3*b**5 + 9*a**2*b**6*x + 9*a*b**7*x**2 + 3*b**8*x**3) - 36*a**3*b*d**2*x*log(a/b + x)/(3*a**3*b**5 + 9*a**2*b**6*x + 9*a*b**7*x**2 + 3*b**8*x**3) - 54*a**3*b*d**2*x/(3*a**3*b**5 + 9*a**2*b**6*x + 9*a*b**7*x**2 + 3*b**8*x**3) - 2*a**2*b**2*c*d/(3*a**3*b**5 + 9*a**2*b**6*x + 9*a*b**7*x**2 + 3*b**8*x**3) - 36*a**2*b**2*d**2*x**2*log(a/b + x)/(3*a**3*b**5 + 9*a**2*b**6*x + 9*a*b**7*x**2 + 3*b**8*x**3) - 36*a**2*b**2*d**2*x**2/(3*a**3*b**5 + 9*a**2*b**6*x + 9*a*b**7*x**2 + 3*b**8*x**3) - 6*a*b**3*c*d*x/(3*a**3*b**5 + 9*a**2*b**6*x + 9*a*b**7*x**2 + 3*b**8*x**3) - 12*a*b**3*d**2*x**3*log(a/b + x)/(3*a**3*b**5 + 9*a**2*b**6*x + 9*a*b**7*x**2 + 3*b**8*x**3) - b**4*c**2/(3*a**3*b**5 + 9*a**2*b**6*x + 9*a*b**7*x**2 + 3*b**8*x**3) - 6*b**4*c*d*x**2/(3*a**3*b**5 + 9*a**2*b**6*x + 9*a*b**7*x**2 + 3*b**8*x**3) + 3*b**4*d**2*x**4/(3*a**3*b**5 + 9*a**2*b**6*x + 9*a*b**7*x**2 + 3*b**8*x**3), Eq(n, -4)), (12*a**4*d**2*log(a/b + x)/(2*a**2*b**5 + 4*a*b**6*x + 2*b**7*x**2) + 18*a**4*d**2/(2*a**2*b**5 + 4*a*b**6*x + 2*b**7*x**2) + 24*a**3*b*d**2*x*log(a/b + x)/(2*a**2*b**5 + 4*a*b**6*x + 2*b**7*x**2) + 24*a**3*b*d**2*x/(2*a**2*b**5 + 4*a*b**6*x + 2*b**7*x**2) + 4*a**2*b**2*c*d*log(a/b + x)/(2*a**2*b**5 + 4*a*b**6*x + 2*b**7*x**2) + 6*a**2*b**2*c*d/(2*a**2*b**5 + 4*a*b**6*x + 2*b**7*x**2) + 12*a**2*b**2*d**2*x**2*log(a/b + x)/(2*a**2*b**5 + 4*a*b**6*x + 2*b**7*x**2) + 8*a*b**3*c*d*x*log(a/b + x)/(2*a**2*b**5 + 4*a*b**6*x + 2*b**7*x**2) + 8*a*b**3*c*d*x/(2*a**2*b**5 + 4*a*b**6*x + 2*b**7*x**2) - 4*a*b**3*d**2*x**3/(2*a**2*b**5 + 4*a*b**6*x + 2*b**7*x**2) - b**4*c**2/(2*a**2*b**5 + 4*a*b**6*x + 2*b**7*x**2) + 4*b**4*c*d*x**2*log(a/b + x)/(2*a**2*b**5 + 4*a*b**6*x + 2*b**7*x**2) + b**4*d**2*x**4/(2*a**2*b**5 + 4*a*b**6*x + 2*b**7*x**2), Eq(n, -3)), (-12*a**4*d**2*log(a/b + x)/(3*a*b**5 + 3*b**6*x) - 12*a**4*d**2/(3*a*b**5 + 3*b**6*x) - 12*a**3*b*d**2*x*log(a/b + x)/(3*a*b**5 + 3*b**6*x) - 12*a**2*b**2*c*d*log(a/b + x)/(3*a*b**5 + 3*b**6*x) - 12*a**2*b**2*c*d/(3*a*b**5 + 3*b**6*x) + 6*a**2*b**2*d**2*x**2/(3*a*b**5 + 3*b**6*x) - 12*a*b**3*c*d*x*log(a/b + x)/(3*a*b**5 + 3*b**6*x) - 2*a*b**3*d**2*x**3/(3*a*b**5 + 3*b**6*x) - 3*b**4*c**2/(3*a*b**5 + 3*b**6*x) + 6*b**4*c*d*x**2/(3*a*b**5 + 3*b**6*x) + b**4*d**2*x**4/(3*a*b**5 + 3*b**6*x), Eq(n, -2)), (a**4*d**2*log(a/b + x)/b**5 - a**3*d**2*x/b**4 + 2*a**2*c*d*log(a/b + x)/b**3 + a**2*d**2*x**2/(2*b**3) - 2*a*c*d*x/b**2 - a*d**2*x**3/(3*b**2) + c**2*log(a/b + x)/b + c*d*x**2/b + d**2*x**4/(4*b), Eq(n, -1)), (24*a**5*d**2*(a + b*x)**n/(b**5*n**5 + 15*b**5*n**4 + 85*b**5*n**3 + 225*b**5*n**2 + 274*b**5*n + 120*b**5) - 24*a**4*b*d**2*n*x*(a + b*x)**n/(b**5*n**5 + 15*b**5*n**4 + 85*b**5*n**3 + 225*b**5*n**2 + 274*b**5*n + 120*b**5) + 4*a**3*b**2*c*d*n**2*(a + b*x)**n/(b**5*n**5 + 15*b**5*n**4 + 85*b**5*n**3 + 225*b**5*n**2 + 274*b**5*n + 120*b**5) + 36*a**3*b**2*c*d*n*(a + b*x)**n/(b**5*n**5 + 15*b**5*n**4 + 85*b**5*n**3 + 225*b**5*n**2 + 274*b**5*n + 120*b**5) + 80*a**3*b**2*c*d*(a + b*x)**n/(b**5*n**5 + 15*b**5*n**4 + 85*b**5*n**3 + 225*b**5*n**2 + 274*b**5*n + 120*b**5) + 12*a**3*b**2*d**2*n**2*x**2*(a + b*x)**n/(b**5*n**5 + 15*b**5*n**4 + 85*b**5*n**3 + 225*b**5*n**2 + 274*b**5*n + 120*b**5) + 12*a**3*b**2*d**2*n*x**2*(a + b*x)**n/(b**5*n**5 + 15*b**5*n**4 + 85*b**5*n**3 + 225*b**5*n**2 + 274*b**5*n + 120*b**5) - 4*a**2*b**3*c*d*n**3*x*(a + b*x)**n/(b**5*n**5 + 15*b**5*n**4 + 85*b**5*n**3 + 225*b**5*n**2 + 274*b**5*n + 120*b**5) - 36*a**2*b**3*c*d*n**2*x*(a + b*x)**n/(b**5*n**5 + 15*b**5*n**4 + 85*b**5*n**3 + 225*b**5*n**2 + 274*b**5*n + 120*b**5) - 80*a**2*b**3*c*d*n*x*(a + b*x)**n/(b**5*n**5 + 15*b**5*n**4 + 85*b**5*n**3 + 225*b**5*n**2 + 274*b**5*n + 120*b**5) - 4*a**2*b**3*d**2*n**3*x**3*(a + b*x)**n/(b**5*n**5 + 15*b**5*n**4 + 85*b**5*n**3 + 225*b**5*n**2 + 274*b**5*n + 120*b**5) - 12*a**2*b**3*d**2*n**2*x**3*(a + b*x)**n/(b**5*n**5 + 15*b**5*n**4 + 85*b**5*n**3 + 225*b**5*n**2 + 274*b**5*n + 120*b**5) - 8*a**2*b**3*d**2*n*x**3*(a + b*x)**n/(b**5*n**5 + 15*b**5*n**4 + 85*b**5*n**3 + 225*b**5*n**2 + 274*b**5*n + 120*b**5) + a*b**4*c**2*n**4*(a + b*x)**n/(b**5*n**5 + 15*b**5*n**4 + 85*b**5*n**3 + 225*b**5*n**2 + 274*b**5*n + 120*b**5) + 14*a*b**4*c**2*n**3*(a + b*x)**n/(b**5*n**5 + 15*b**5*n**4 + 85*b**5*n**3 + 225*b**5*n**2 + 274*b**5*n + 120*b**5) + 71*a*b**4*c**2*n**2*(a + b*x)**n/(b**5*n**5 + 15*b**5*n**4 + 85*b**5*n**3 + 225*b**5*n**2 + 274*b**5*n + 120*b**5) + 154*a*b**4*c**2*n*(a + b*x)**n/(b**5*n**5 + 15*b**5*n**4 + 85*b**5*n**3 + 225*b**5*n**2 + 274*b**5*n + 120*b**5) + 120*a*b**4*c**2*(a + b*x)**n/(b**5*n**5 + 15*b**5*n**4 + 85*b**5*n**3 + 225*b**5*n**2 + 274*b**5*n + 120*b**5) + 2*a*b**4*c*d*n**4*x**2*(a + b*x)**n/(b**5*n**5 + 15*b**5*n**4 + 85*b**5*n**3 + 225*b**5*n**2 + 274*b**5*n + 120*b**5) + 20*a*b**4*c*d*n**3*x**2*(a + b*x)**n/(b**5*n**5 + 15*b**5*n**4 + 85*b**5*n**3 + 225*b**5*n**2 + 274*b**5*n + 120*b**5) + 58*a*b**4*c*d*n**2*x**2*(a + b*x)**n/(b**5*n**5 + 15*b**5*n**4 + 85*b**5*n**3 + 225*b**5*n**2 + 274*b**5*n + 120*b**5) + 40*a*b**4*c*d*n*x**2*(a + b*x)**n/(b**5*n**5 + 15*b**5*n**4 + 85*b**5*n**3 + 225*b**5*n**2 + 274*b**5*n + 120*b**5) + a*b**4*d**2*n**4*x**4*(a + b*x)**n/(b**5*n**5 + 15*b**5*n**4 + 85*b**5*n**3 + 225*b**5*n**2 + 274*b**5*n + 120*b**5) + 6*a*b**4*d**2*n**3*x**4*(a + b*x)**n/(b**5*n**5 + 15*b**5*n**4 + 85*b**5*n**3 + 225*b**5*n**2 + 274*b**5*n + 120*b**5) + 11*a*b**4*d**2*n**2*x**4*(a + b*x)**n/(b**5*n**5 + 15*b**5*n**4 + 85*b**5*n**3 + 225*b**5*n**2 + 274*b**5*n + 120*b**5) + 6*a*b**4*d**2*n*x**4*(a + b*x)**n/(b**5*n**5 + 15*b**5*n**4 + 85*b**5*n**3 + 225*b**5*n**2 + 274*b**5*n + 120*b**5) + b**5*c**2*n**4*x*(a + b*x)**n/(b**5*n**5 + 15*b**5*n**4 + 85*b**5*n**3 + 225*b**5*n**2 + 274*b**5*n + 120*b**5) + 14*b**5*c**2*n**3*x*(a + b*x)**n/(b**5*n**5 + 15*b**5*n**4 + 85*b**5*n**3 + 225*b**5*n**2 + 274*b**5*n + 120*b**5) + 71*b**5*c**2*n**2*x*(a + b*x)**n/(b**5*n**5 + 15*b**5*n**4 + 85*b**5*n**3 + 225*b**5*n**2 + 274*b**5*n + 120*b**5) + 154*b**5*c**2*n*x*(a + b*x)**n/(b**5*n**5 + 15*b**5*n**4 + 85*b**5*n**3 + 225*b**5*n**2 + 274*b**5*n + 120*b**5) + 120*b**5*c**2*x*(a + b*x)**n/(b**5*n**5 + 15*b**5*n**4 + 85*b**5*n**3 + 225*b**5*n**2 + 274*b**5*n + 120*b**5) + 2*b**5*c*d*n**4*x**3*(a + b*x)**n/(b**5*n**5 + 15*b**5*n**4 + 85*b**5*n**3 + 225*b**5*n**2 + 274*b**5*n + 120*b**5) + 24*b**5*c*d*n**3*x**3*(a + b*x)**n/(b**5*n**5 + 15*b**5*n**4 + 85*b**5*n**3 + 225*b**5*n**2 + 274*b**5*n + 120*b**5) + 98*b**5*c*d*n**2*x**3*(a + b*x)**n/(b**5*n**5 + 15*b**5*n**4 + 85*b**5*n**3 + 225*b**5*n**2 + 274*b**5*n + 120*b**5) + 156*b**5*c*d*n*x**3*(a + b*x)**n/(b**5*n**5 + 15*b**5*n**4 + 85*b**5*n**3 + 225*b**5*n**2 + 274*b**5*n + 120*b**5) + 80*b**5*c*d*x**3*(a + b*x)**n/(b**5*n**5 + 15*b**5*n**4 + 85*b**5*n**3 + 225*b**5*n**2 + 274*b**5*n + 120*b**5) + b**5*d**2*n**4*x**5*(a + b*x)**n/(b**5*n**5 + 15*b**5*n**4 + 85*b**5*n**3 + 225*b**5*n**2 + 274*b**5*n + 120*b**5) + 10*b**5*d**2*n**3*x**5*(a + b*x)**n/(b**5*n**5 + 15*b**5*n**4 + 85*b**5*n**3 + 225*b**5*n**2 + 274*b**5*n + 120*b**5) + 35*b**5*d**2*n**2*x**5*(a + b*x)**n/(b**5*n**5 + 15*b**5*n**4 + 85*b**5*n**3 + 225*b**5*n**2 + 274*b**5*n + 120*b**5) + 50*b**5*d**2*n*x**5*(a + b*x)**n/(b**5*n**5 + 15*b**5*n**4 + 85*b**5*n**3 + 225*b**5*n**2 + 274*b**5*n + 120*b**5) + 24*b**5*d**2*x**5*(a + b*x)**n/(b**5*n**5 + 15*b**5*n**4 + 85*b**5*n**3 + 225*b**5*n**2 + 274*b**5*n + 120*b**5), True))","A",0
358,1,1678,0,11.189408," ","integrate((b*x+a)**n*(d*x**2+c)**2/x,x)","- \frac{b^{n} c^{2} n \left(\frac{a}{b} + x\right)^{n} \Phi\left(1 + \frac{b x}{a}, 1, n + 1\right) \Gamma\left(n + 1\right)}{\Gamma\left(n + 2\right)} - \frac{b^{n} c^{2} \left(\frac{a}{b} + x\right)^{n} \Phi\left(1 + \frac{b x}{a}, 1, n + 1\right) \Gamma\left(n + 1\right)}{\Gamma\left(n + 2\right)} + 2 c d \left(\begin{cases} \frac{a^{n} x^{2}}{2} & \text{for}\: b = 0 \\\frac{a \log{\left(\frac{a}{b} + x \right)}}{a b^{2} + b^{3} x} + \frac{a}{a b^{2} + b^{3} x} + \frac{b x \log{\left(\frac{a}{b} + x \right)}}{a b^{2} + b^{3} x} & \text{for}\: n = -2 \\- \frac{a \log{\left(\frac{a}{b} + x \right)}}{b^{2}} + \frac{x}{b} & \text{for}\: n = -1 \\- \frac{a^{2} \left(a + b x\right)^{n}}{b^{2} n^{2} + 3 b^{2} n + 2 b^{2}} + \frac{a b n x \left(a + b x\right)^{n}}{b^{2} n^{2} + 3 b^{2} n + 2 b^{2}} + \frac{b^{2} n x^{2} \left(a + b x\right)^{n}}{b^{2} n^{2} + 3 b^{2} n + 2 b^{2}} + \frac{b^{2} x^{2} \left(a + b x\right)^{n}}{b^{2} n^{2} + 3 b^{2} n + 2 b^{2}} & \text{otherwise} \end{cases}\right) + d^{2} \left(\begin{cases} \frac{a^{n} x^{4}}{4} & \text{for}\: b = 0 \\\frac{6 a^{3} \log{\left(\frac{a}{b} + x \right)}}{6 a^{3} b^{4} + 18 a^{2} b^{5} x + 18 a b^{6} x^{2} + 6 b^{7} x^{3}} + \frac{11 a^{3}}{6 a^{3} b^{4} + 18 a^{2} b^{5} x + 18 a b^{6} x^{2} + 6 b^{7} x^{3}} + \frac{18 a^{2} b x \log{\left(\frac{a}{b} + x \right)}}{6 a^{3} b^{4} + 18 a^{2} b^{5} x + 18 a b^{6} x^{2} + 6 b^{7} x^{3}} + \frac{27 a^{2} b x}{6 a^{3} b^{4} + 18 a^{2} b^{5} x + 18 a b^{6} x^{2} + 6 b^{7} x^{3}} + \frac{18 a b^{2} x^{2} \log{\left(\frac{a}{b} + x \right)}}{6 a^{3} b^{4} + 18 a^{2} b^{5} x + 18 a b^{6} x^{2} + 6 b^{7} x^{3}} + \frac{18 a b^{2} x^{2}}{6 a^{3} b^{4} + 18 a^{2} b^{5} x + 18 a b^{6} x^{2} + 6 b^{7} x^{3}} + \frac{6 b^{3} x^{3} \log{\left(\frac{a}{b} + x \right)}}{6 a^{3} b^{4} + 18 a^{2} b^{5} x + 18 a b^{6} x^{2} + 6 b^{7} x^{3}} & \text{for}\: n = -4 \\- \frac{6 a^{3} \log{\left(\frac{a}{b} + x \right)}}{2 a^{2} b^{4} + 4 a b^{5} x + 2 b^{6} x^{2}} - \frac{9 a^{3}}{2 a^{2} b^{4} + 4 a b^{5} x + 2 b^{6} x^{2}} - \frac{12 a^{2} b x \log{\left(\frac{a}{b} + x \right)}}{2 a^{2} b^{4} + 4 a b^{5} x + 2 b^{6} x^{2}} - \frac{12 a^{2} b x}{2 a^{2} b^{4} + 4 a b^{5} x + 2 b^{6} x^{2}} - \frac{6 a b^{2} x^{2} \log{\left(\frac{a}{b} + x \right)}}{2 a^{2} b^{4} + 4 a b^{5} x + 2 b^{6} x^{2}} + \frac{2 b^{3} x^{3}}{2 a^{2} b^{4} + 4 a b^{5} x + 2 b^{6} x^{2}} & \text{for}\: n = -3 \\\frac{6 a^{3} \log{\left(\frac{a}{b} + x \right)}}{2 a b^{4} + 2 b^{5} x} + \frac{6 a^{3}}{2 a b^{4} + 2 b^{5} x} + \frac{6 a^{2} b x \log{\left(\frac{a}{b} + x \right)}}{2 a b^{4} + 2 b^{5} x} - \frac{3 a b^{2} x^{2}}{2 a b^{4} + 2 b^{5} x} + \frac{b^{3} x^{3}}{2 a b^{4} + 2 b^{5} x} & \text{for}\: n = -2 \\- \frac{a^{3} \log{\left(\frac{a}{b} + x \right)}}{b^{4}} + \frac{a^{2} x}{b^{3}} - \frac{a x^{2}}{2 b^{2}} + \frac{x^{3}}{3 b} & \text{for}\: n = -1 \\- \frac{6 a^{4} \left(a + b x\right)^{n}}{b^{4} n^{4} + 10 b^{4} n^{3} + 35 b^{4} n^{2} + 50 b^{4} n + 24 b^{4}} + \frac{6 a^{3} b n x \left(a + b x\right)^{n}}{b^{4} n^{4} + 10 b^{4} n^{3} + 35 b^{4} n^{2} + 50 b^{4} n + 24 b^{4}} - \frac{3 a^{2} b^{2} n^{2} x^{2} \left(a + b x\right)^{n}}{b^{4} n^{4} + 10 b^{4} n^{3} + 35 b^{4} n^{2} + 50 b^{4} n + 24 b^{4}} - \frac{3 a^{2} b^{2} n x^{2} \left(a + b x\right)^{n}}{b^{4} n^{4} + 10 b^{4} n^{3} + 35 b^{4} n^{2} + 50 b^{4} n + 24 b^{4}} + \frac{a b^{3} n^{3} x^{3} \left(a + b x\right)^{n}}{b^{4} n^{4} + 10 b^{4} n^{3} + 35 b^{4} n^{2} + 50 b^{4} n + 24 b^{4}} + \frac{3 a b^{3} n^{2} x^{3} \left(a + b x\right)^{n}}{b^{4} n^{4} + 10 b^{4} n^{3} + 35 b^{4} n^{2} + 50 b^{4} n + 24 b^{4}} + \frac{2 a b^{3} n x^{3} \left(a + b x\right)^{n}}{b^{4} n^{4} + 10 b^{4} n^{3} + 35 b^{4} n^{2} + 50 b^{4} n + 24 b^{4}} + \frac{b^{4} n^{3} x^{4} \left(a + b x\right)^{n}}{b^{4} n^{4} + 10 b^{4} n^{3} + 35 b^{4} n^{2} + 50 b^{4} n + 24 b^{4}} + \frac{6 b^{4} n^{2} x^{4} \left(a + b x\right)^{n}}{b^{4} n^{4} + 10 b^{4} n^{3} + 35 b^{4} n^{2} + 50 b^{4} n + 24 b^{4}} + \frac{11 b^{4} n x^{4} \left(a + b x\right)^{n}}{b^{4} n^{4} + 10 b^{4} n^{3} + 35 b^{4} n^{2} + 50 b^{4} n + 24 b^{4}} + \frac{6 b^{4} x^{4} \left(a + b x\right)^{n}}{b^{4} n^{4} + 10 b^{4} n^{3} + 35 b^{4} n^{2} + 50 b^{4} n + 24 b^{4}} & \text{otherwise} \end{cases}\right) - \frac{b b^{n} c^{2} n x \left(\frac{a}{b} + x\right)^{n} \Phi\left(1 + \frac{b x}{a}, 1, n + 1\right) \Gamma\left(n + 1\right)}{a \Gamma\left(n + 2\right)} - \frac{b b^{n} c^{2} x \left(\frac{a}{b} + x\right)^{n} \Phi\left(1 + \frac{b x}{a}, 1, n + 1\right) \Gamma\left(n + 1\right)}{a \Gamma\left(n + 2\right)}"," ",0,"-b**n*c**2*n*(a/b + x)**n*lerchphi(1 + b*x/a, 1, n + 1)*gamma(n + 1)/gamma(n + 2) - b**n*c**2*(a/b + x)**n*lerchphi(1 + b*x/a, 1, n + 1)*gamma(n + 1)/gamma(n + 2) + 2*c*d*Piecewise((a**n*x**2/2, Eq(b, 0)), (a*log(a/b + x)/(a*b**2 + b**3*x) + a/(a*b**2 + b**3*x) + b*x*log(a/b + x)/(a*b**2 + b**3*x), Eq(n, -2)), (-a*log(a/b + x)/b**2 + x/b, Eq(n, -1)), (-a**2*(a + b*x)**n/(b**2*n**2 + 3*b**2*n + 2*b**2) + a*b*n*x*(a + b*x)**n/(b**2*n**2 + 3*b**2*n + 2*b**2) + b**2*n*x**2*(a + b*x)**n/(b**2*n**2 + 3*b**2*n + 2*b**2) + b**2*x**2*(a + b*x)**n/(b**2*n**2 + 3*b**2*n + 2*b**2), True)) + d**2*Piecewise((a**n*x**4/4, Eq(b, 0)), (6*a**3*log(a/b + x)/(6*a**3*b**4 + 18*a**2*b**5*x + 18*a*b**6*x**2 + 6*b**7*x**3) + 11*a**3/(6*a**3*b**4 + 18*a**2*b**5*x + 18*a*b**6*x**2 + 6*b**7*x**3) + 18*a**2*b*x*log(a/b + x)/(6*a**3*b**4 + 18*a**2*b**5*x + 18*a*b**6*x**2 + 6*b**7*x**3) + 27*a**2*b*x/(6*a**3*b**4 + 18*a**2*b**5*x + 18*a*b**6*x**2 + 6*b**7*x**3) + 18*a*b**2*x**2*log(a/b + x)/(6*a**3*b**4 + 18*a**2*b**5*x + 18*a*b**6*x**2 + 6*b**7*x**3) + 18*a*b**2*x**2/(6*a**3*b**4 + 18*a**2*b**5*x + 18*a*b**6*x**2 + 6*b**7*x**3) + 6*b**3*x**3*log(a/b + x)/(6*a**3*b**4 + 18*a**2*b**5*x + 18*a*b**6*x**2 + 6*b**7*x**3), Eq(n, -4)), (-6*a**3*log(a/b + x)/(2*a**2*b**4 + 4*a*b**5*x + 2*b**6*x**2) - 9*a**3/(2*a**2*b**4 + 4*a*b**5*x + 2*b**6*x**2) - 12*a**2*b*x*log(a/b + x)/(2*a**2*b**4 + 4*a*b**5*x + 2*b**6*x**2) - 12*a**2*b*x/(2*a**2*b**4 + 4*a*b**5*x + 2*b**6*x**2) - 6*a*b**2*x**2*log(a/b + x)/(2*a**2*b**4 + 4*a*b**5*x + 2*b**6*x**2) + 2*b**3*x**3/(2*a**2*b**4 + 4*a*b**5*x + 2*b**6*x**2), Eq(n, -3)), (6*a**3*log(a/b + x)/(2*a*b**4 + 2*b**5*x) + 6*a**3/(2*a*b**4 + 2*b**5*x) + 6*a**2*b*x*log(a/b + x)/(2*a*b**4 + 2*b**5*x) - 3*a*b**2*x**2/(2*a*b**4 + 2*b**5*x) + b**3*x**3/(2*a*b**4 + 2*b**5*x), Eq(n, -2)), (-a**3*log(a/b + x)/b**4 + a**2*x/b**3 - a*x**2/(2*b**2) + x**3/(3*b), Eq(n, -1)), (-6*a**4*(a + b*x)**n/(b**4*n**4 + 10*b**4*n**3 + 35*b**4*n**2 + 50*b**4*n + 24*b**4) + 6*a**3*b*n*x*(a + b*x)**n/(b**4*n**4 + 10*b**4*n**3 + 35*b**4*n**2 + 50*b**4*n + 24*b**4) - 3*a**2*b**2*n**2*x**2*(a + b*x)**n/(b**4*n**4 + 10*b**4*n**3 + 35*b**4*n**2 + 50*b**4*n + 24*b**4) - 3*a**2*b**2*n*x**2*(a + b*x)**n/(b**4*n**4 + 10*b**4*n**3 + 35*b**4*n**2 + 50*b**4*n + 24*b**4) + a*b**3*n**3*x**3*(a + b*x)**n/(b**4*n**4 + 10*b**4*n**3 + 35*b**4*n**2 + 50*b**4*n + 24*b**4) + 3*a*b**3*n**2*x**3*(a + b*x)**n/(b**4*n**4 + 10*b**4*n**3 + 35*b**4*n**2 + 50*b**4*n + 24*b**4) + 2*a*b**3*n*x**3*(a + b*x)**n/(b**4*n**4 + 10*b**4*n**3 + 35*b**4*n**2 + 50*b**4*n + 24*b**4) + b**4*n**3*x**4*(a + b*x)**n/(b**4*n**4 + 10*b**4*n**3 + 35*b**4*n**2 + 50*b**4*n + 24*b**4) + 6*b**4*n**2*x**4*(a + b*x)**n/(b**4*n**4 + 10*b**4*n**3 + 35*b**4*n**2 + 50*b**4*n + 24*b**4) + 11*b**4*n*x**4*(a + b*x)**n/(b**4*n**4 + 10*b**4*n**3 + 35*b**4*n**2 + 50*b**4*n + 24*b**4) + 6*b**4*x**4*(a + b*x)**n/(b**4*n**4 + 10*b**4*n**3 + 35*b**4*n**2 + 50*b**4*n + 24*b**4), True)) - b*b**n*c**2*n*x*(a/b + x)**n*lerchphi(1 + b*x/a, 1, n + 1)*gamma(n + 1)/(a*gamma(n + 2)) - b*b**n*c**2*x*(a/b + x)**n*lerchphi(1 + b*x/a, 1, n + 1)*gamma(n + 1)/(a*gamma(n + 2))","B",0
359,-1,0,0,0.000000," ","integrate(x**2*(b*x+a)**n*(d*x**2+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
360,-1,0,0,0.000000," ","integrate(x*(b*x+a)**n*(d*x**2+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
361,-1,0,0,0.000000," ","integrate((b*x+a)**n*(d*x**2+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
362,1,5692,0,17.733119," ","integrate((b*x+a)**n*(d*x**2+c)**3/x,x)","- \frac{b^{n} c^{3} n \left(\frac{a}{b} + x\right)^{n} \Phi\left(1 + \frac{b x}{a}, 1, n + 1\right) \Gamma\left(n + 1\right)}{\Gamma\left(n + 2\right)} - \frac{b^{n} c^{3} \left(\frac{a}{b} + x\right)^{n} \Phi\left(1 + \frac{b x}{a}, 1, n + 1\right) \Gamma\left(n + 1\right)}{\Gamma\left(n + 2\right)} + 3 c^{2} d \left(\begin{cases} \frac{a^{n} x^{2}}{2} & \text{for}\: b = 0 \\\frac{a \log{\left(\frac{a}{b} + x \right)}}{a b^{2} + b^{3} x} + \frac{a}{a b^{2} + b^{3} x} + \frac{b x \log{\left(\frac{a}{b} + x \right)}}{a b^{2} + b^{3} x} & \text{for}\: n = -2 \\- \frac{a \log{\left(\frac{a}{b} + x \right)}}{b^{2}} + \frac{x}{b} & \text{for}\: n = -1 \\- \frac{a^{2} \left(a + b x\right)^{n}}{b^{2} n^{2} + 3 b^{2} n + 2 b^{2}} + \frac{a b n x \left(a + b x\right)^{n}}{b^{2} n^{2} + 3 b^{2} n + 2 b^{2}} + \frac{b^{2} n x^{2} \left(a + b x\right)^{n}}{b^{2} n^{2} + 3 b^{2} n + 2 b^{2}} + \frac{b^{2} x^{2} \left(a + b x\right)^{n}}{b^{2} n^{2} + 3 b^{2} n + 2 b^{2}} & \text{otherwise} \end{cases}\right) + 3 c d^{2} \left(\begin{cases} \frac{a^{n} x^{4}}{4} & \text{for}\: b = 0 \\\frac{6 a^{3} \log{\left(\frac{a}{b} + x \right)}}{6 a^{3} b^{4} + 18 a^{2} b^{5} x + 18 a b^{6} x^{2} + 6 b^{7} x^{3}} + \frac{11 a^{3}}{6 a^{3} b^{4} + 18 a^{2} b^{5} x + 18 a b^{6} x^{2} + 6 b^{7} x^{3}} + \frac{18 a^{2} b x \log{\left(\frac{a}{b} + x \right)}}{6 a^{3} b^{4} + 18 a^{2} b^{5} x + 18 a b^{6} x^{2} + 6 b^{7} x^{3}} + \frac{27 a^{2} b x}{6 a^{3} b^{4} + 18 a^{2} b^{5} x + 18 a b^{6} x^{2} + 6 b^{7} x^{3}} + \frac{18 a b^{2} x^{2} \log{\left(\frac{a}{b} + x \right)}}{6 a^{3} b^{4} + 18 a^{2} b^{5} x + 18 a b^{6} x^{2} + 6 b^{7} x^{3}} + \frac{18 a b^{2} x^{2}}{6 a^{3} b^{4} + 18 a^{2} b^{5} x + 18 a b^{6} x^{2} + 6 b^{7} x^{3}} + \frac{6 b^{3} x^{3} \log{\left(\frac{a}{b} + x \right)}}{6 a^{3} b^{4} + 18 a^{2} b^{5} x + 18 a b^{6} x^{2} + 6 b^{7} x^{3}} & \text{for}\: n = -4 \\- \frac{6 a^{3} \log{\left(\frac{a}{b} + x \right)}}{2 a^{2} b^{4} + 4 a b^{5} x + 2 b^{6} x^{2}} - \frac{9 a^{3}}{2 a^{2} b^{4} + 4 a b^{5} x + 2 b^{6} x^{2}} - \frac{12 a^{2} b x \log{\left(\frac{a}{b} + x \right)}}{2 a^{2} b^{4} + 4 a b^{5} x + 2 b^{6} x^{2}} - \frac{12 a^{2} b x}{2 a^{2} b^{4} + 4 a b^{5} x + 2 b^{6} x^{2}} - \frac{6 a b^{2} x^{2} \log{\left(\frac{a}{b} + x \right)}}{2 a^{2} b^{4} + 4 a b^{5} x + 2 b^{6} x^{2}} + \frac{2 b^{3} x^{3}}{2 a^{2} b^{4} + 4 a b^{5} x + 2 b^{6} x^{2}} & \text{for}\: n = -3 \\\frac{6 a^{3} \log{\left(\frac{a}{b} + x \right)}}{2 a b^{4} + 2 b^{5} x} + \frac{6 a^{3}}{2 a b^{4} + 2 b^{5} x} + \frac{6 a^{2} b x \log{\left(\frac{a}{b} + x \right)}}{2 a b^{4} + 2 b^{5} x} - \frac{3 a b^{2} x^{2}}{2 a b^{4} + 2 b^{5} x} + \frac{b^{3} x^{3}}{2 a b^{4} + 2 b^{5} x} & \text{for}\: n = -2 \\- \frac{a^{3} \log{\left(\frac{a}{b} + x \right)}}{b^{4}} + \frac{a^{2} x}{b^{3}} - \frac{a x^{2}}{2 b^{2}} + \frac{x^{3}}{3 b} & \text{for}\: n = -1 \\- \frac{6 a^{4} \left(a + b x\right)^{n}}{b^{4} n^{4} + 10 b^{4} n^{3} + 35 b^{4} n^{2} + 50 b^{4} n + 24 b^{4}} + \frac{6 a^{3} b n x \left(a + b x\right)^{n}}{b^{4} n^{4} + 10 b^{4} n^{3} + 35 b^{4} n^{2} + 50 b^{4} n + 24 b^{4}} - \frac{3 a^{2} b^{2} n^{2} x^{2} \left(a + b x\right)^{n}}{b^{4} n^{4} + 10 b^{4} n^{3} + 35 b^{4} n^{2} + 50 b^{4} n + 24 b^{4}} - \frac{3 a^{2} b^{2} n x^{2} \left(a + b x\right)^{n}}{b^{4} n^{4} + 10 b^{4} n^{3} + 35 b^{4} n^{2} + 50 b^{4} n + 24 b^{4}} + \frac{a b^{3} n^{3} x^{3} \left(a + b x\right)^{n}}{b^{4} n^{4} + 10 b^{4} n^{3} + 35 b^{4} n^{2} + 50 b^{4} n + 24 b^{4}} + \frac{3 a b^{3} n^{2} x^{3} \left(a + b x\right)^{n}}{b^{4} n^{4} + 10 b^{4} n^{3} + 35 b^{4} n^{2} + 50 b^{4} n + 24 b^{4}} + \frac{2 a b^{3} n x^{3} \left(a + b x\right)^{n}}{b^{4} n^{4} + 10 b^{4} n^{3} + 35 b^{4} n^{2} + 50 b^{4} n + 24 b^{4}} + \frac{b^{4} n^{3} x^{4} \left(a + b x\right)^{n}}{b^{4} n^{4} + 10 b^{4} n^{3} + 35 b^{4} n^{2} + 50 b^{4} n + 24 b^{4}} + \frac{6 b^{4} n^{2} x^{4} \left(a + b x\right)^{n}}{b^{4} n^{4} + 10 b^{4} n^{3} + 35 b^{4} n^{2} + 50 b^{4} n + 24 b^{4}} + \frac{11 b^{4} n x^{4} \left(a + b x\right)^{n}}{b^{4} n^{4} + 10 b^{4} n^{3} + 35 b^{4} n^{2} + 50 b^{4} n + 24 b^{4}} + \frac{6 b^{4} x^{4} \left(a + b x\right)^{n}}{b^{4} n^{4} + 10 b^{4} n^{3} + 35 b^{4} n^{2} + 50 b^{4} n + 24 b^{4}} & \text{otherwise} \end{cases}\right) + d^{3} \left(\begin{cases} \frac{a^{n} x^{6}}{6} & \text{for}\: b = 0 \\\frac{60 a^{5} \log{\left(\frac{a}{b} + x \right)}}{60 a^{5} b^{6} + 300 a^{4} b^{7} x + 600 a^{3} b^{8} x^{2} + 600 a^{2} b^{9} x^{3} + 300 a b^{10} x^{4} + 60 b^{11} x^{5}} + \frac{137 a^{5}}{60 a^{5} b^{6} + 300 a^{4} b^{7} x + 600 a^{3} b^{8} x^{2} + 600 a^{2} b^{9} x^{3} + 300 a b^{10} x^{4} + 60 b^{11} x^{5}} + \frac{300 a^{4} b x \log{\left(\frac{a}{b} + x \right)}}{60 a^{5} b^{6} + 300 a^{4} b^{7} x + 600 a^{3} b^{8} x^{2} + 600 a^{2} b^{9} x^{3} + 300 a b^{10} x^{4} + 60 b^{11} x^{5}} + \frac{625 a^{4} b x}{60 a^{5} b^{6} + 300 a^{4} b^{7} x + 600 a^{3} b^{8} x^{2} + 600 a^{2} b^{9} x^{3} + 300 a b^{10} x^{4} + 60 b^{11} x^{5}} + \frac{600 a^{3} b^{2} x^{2} \log{\left(\frac{a}{b} + x \right)}}{60 a^{5} b^{6} + 300 a^{4} b^{7} x + 600 a^{3} b^{8} x^{2} + 600 a^{2} b^{9} x^{3} + 300 a b^{10} x^{4} + 60 b^{11} x^{5}} + \frac{1100 a^{3} b^{2} x^{2}}{60 a^{5} b^{6} + 300 a^{4} b^{7} x + 600 a^{3} b^{8} x^{2} + 600 a^{2} b^{9} x^{3} + 300 a b^{10} x^{4} + 60 b^{11} x^{5}} + \frac{600 a^{2} b^{3} x^{3} \log{\left(\frac{a}{b} + x \right)}}{60 a^{5} b^{6} + 300 a^{4} b^{7} x + 600 a^{3} b^{8} x^{2} + 600 a^{2} b^{9} x^{3} + 300 a b^{10} x^{4} + 60 b^{11} x^{5}} + \frac{900 a^{2} b^{3} x^{3}}{60 a^{5} b^{6} + 300 a^{4} b^{7} x + 600 a^{3} b^{8} x^{2} + 600 a^{2} b^{9} x^{3} + 300 a b^{10} x^{4} + 60 b^{11} x^{5}} + \frac{300 a b^{4} x^{4} \log{\left(\frac{a}{b} + x \right)}}{60 a^{5} b^{6} + 300 a^{4} b^{7} x + 600 a^{3} b^{8} x^{2} + 600 a^{2} b^{9} x^{3} + 300 a b^{10} x^{4} + 60 b^{11} x^{5}} + \frac{300 a b^{4} x^{4}}{60 a^{5} b^{6} + 300 a^{4} b^{7} x + 600 a^{3} b^{8} x^{2} + 600 a^{2} b^{9} x^{3} + 300 a b^{10} x^{4} + 60 b^{11} x^{5}} + \frac{60 b^{5} x^{5} \log{\left(\frac{a}{b} + x \right)}}{60 a^{5} b^{6} + 300 a^{4} b^{7} x + 600 a^{3} b^{8} x^{2} + 600 a^{2} b^{9} x^{3} + 300 a b^{10} x^{4} + 60 b^{11} x^{5}} & \text{for}\: n = -6 \\- \frac{60 a^{5} \log{\left(\frac{a}{b} + x \right)}}{12 a^{4} b^{6} + 48 a^{3} b^{7} x + 72 a^{2} b^{8} x^{2} + 48 a b^{9} x^{3} + 12 b^{10} x^{4}} - \frac{125 a^{5}}{12 a^{4} b^{6} + 48 a^{3} b^{7} x + 72 a^{2} b^{8} x^{2} + 48 a b^{9} x^{3} + 12 b^{10} x^{4}} - \frac{240 a^{4} b x \log{\left(\frac{a}{b} + x \right)}}{12 a^{4} b^{6} + 48 a^{3} b^{7} x + 72 a^{2} b^{8} x^{2} + 48 a b^{9} x^{3} + 12 b^{10} x^{4}} - \frac{440 a^{4} b x}{12 a^{4} b^{6} + 48 a^{3} b^{7} x + 72 a^{2} b^{8} x^{2} + 48 a b^{9} x^{3} + 12 b^{10} x^{4}} - \frac{360 a^{3} b^{2} x^{2} \log{\left(\frac{a}{b} + x \right)}}{12 a^{4} b^{6} + 48 a^{3} b^{7} x + 72 a^{2} b^{8} x^{2} + 48 a b^{9} x^{3} + 12 b^{10} x^{4}} - \frac{540 a^{3} b^{2} x^{2}}{12 a^{4} b^{6} + 48 a^{3} b^{7} x + 72 a^{2} b^{8} x^{2} + 48 a b^{9} x^{3} + 12 b^{10} x^{4}} - \frac{240 a^{2} b^{3} x^{3} \log{\left(\frac{a}{b} + x \right)}}{12 a^{4} b^{6} + 48 a^{3} b^{7} x + 72 a^{2} b^{8} x^{2} + 48 a b^{9} x^{3} + 12 b^{10} x^{4}} - \frac{240 a^{2} b^{3} x^{3}}{12 a^{4} b^{6} + 48 a^{3} b^{7} x + 72 a^{2} b^{8} x^{2} + 48 a b^{9} x^{3} + 12 b^{10} x^{4}} - \frac{60 a b^{4} x^{4} \log{\left(\frac{a}{b} + x \right)}}{12 a^{4} b^{6} + 48 a^{3} b^{7} x + 72 a^{2} b^{8} x^{2} + 48 a b^{9} x^{3} + 12 b^{10} x^{4}} + \frac{12 b^{5} x^{5}}{12 a^{4} b^{6} + 48 a^{3} b^{7} x + 72 a^{2} b^{8} x^{2} + 48 a b^{9} x^{3} + 12 b^{10} x^{4}} & \text{for}\: n = -5 \\\frac{60 a^{5} \log{\left(\frac{a}{b} + x \right)}}{6 a^{3} b^{6} + 18 a^{2} b^{7} x + 18 a b^{8} x^{2} + 6 b^{9} x^{3}} + \frac{110 a^{5}}{6 a^{3} b^{6} + 18 a^{2} b^{7} x + 18 a b^{8} x^{2} + 6 b^{9} x^{3}} + \frac{180 a^{4} b x \log{\left(\frac{a}{b} + x \right)}}{6 a^{3} b^{6} + 18 a^{2} b^{7} x + 18 a b^{8} x^{2} + 6 b^{9} x^{3}} + \frac{270 a^{4} b x}{6 a^{3} b^{6} + 18 a^{2} b^{7} x + 18 a b^{8} x^{2} + 6 b^{9} x^{3}} + \frac{180 a^{3} b^{2} x^{2} \log{\left(\frac{a}{b} + x \right)}}{6 a^{3} b^{6} + 18 a^{2} b^{7} x + 18 a b^{8} x^{2} + 6 b^{9} x^{3}} + \frac{180 a^{3} b^{2} x^{2}}{6 a^{3} b^{6} + 18 a^{2} b^{7} x + 18 a b^{8} x^{2} + 6 b^{9} x^{3}} + \frac{60 a^{2} b^{3} x^{3} \log{\left(\frac{a}{b} + x \right)}}{6 a^{3} b^{6} + 18 a^{2} b^{7} x + 18 a b^{8} x^{2} + 6 b^{9} x^{3}} - \frac{15 a b^{4} x^{4}}{6 a^{3} b^{6} + 18 a^{2} b^{7} x + 18 a b^{8} x^{2} + 6 b^{9} x^{3}} + \frac{3 b^{5} x^{5}}{6 a^{3} b^{6} + 18 a^{2} b^{7} x + 18 a b^{8} x^{2} + 6 b^{9} x^{3}} & \text{for}\: n = -4 \\- \frac{60 a^{5} \log{\left(\frac{a}{b} + x \right)}}{6 a^{2} b^{6} + 12 a b^{7} x + 6 b^{8} x^{2}} - \frac{90 a^{5}}{6 a^{2} b^{6} + 12 a b^{7} x + 6 b^{8} x^{2}} - \frac{120 a^{4} b x \log{\left(\frac{a}{b} + x \right)}}{6 a^{2} b^{6} + 12 a b^{7} x + 6 b^{8} x^{2}} - \frac{120 a^{4} b x}{6 a^{2} b^{6} + 12 a b^{7} x + 6 b^{8} x^{2}} - \frac{60 a^{3} b^{2} x^{2} \log{\left(\frac{a}{b} + x \right)}}{6 a^{2} b^{6} + 12 a b^{7} x + 6 b^{8} x^{2}} + \frac{20 a^{2} b^{3} x^{3}}{6 a^{2} b^{6} + 12 a b^{7} x + 6 b^{8} x^{2}} - \frac{5 a b^{4} x^{4}}{6 a^{2} b^{6} + 12 a b^{7} x + 6 b^{8} x^{2}} + \frac{2 b^{5} x^{5}}{6 a^{2} b^{6} + 12 a b^{7} x + 6 b^{8} x^{2}} & \text{for}\: n = -3 \\\frac{60 a^{5} \log{\left(\frac{a}{b} + x \right)}}{12 a b^{6} + 12 b^{7} x} + \frac{60 a^{5}}{12 a b^{6} + 12 b^{7} x} + \frac{60 a^{4} b x \log{\left(\frac{a}{b} + x \right)}}{12 a b^{6} + 12 b^{7} x} - \frac{30 a^{3} b^{2} x^{2}}{12 a b^{6} + 12 b^{7} x} + \frac{10 a^{2} b^{3} x^{3}}{12 a b^{6} + 12 b^{7} x} - \frac{5 a b^{4} x^{4}}{12 a b^{6} + 12 b^{7} x} + \frac{3 b^{5} x^{5}}{12 a b^{6} + 12 b^{7} x} & \text{for}\: n = -2 \\- \frac{a^{5} \log{\left(\frac{a}{b} + x \right)}}{b^{6}} + \frac{a^{4} x}{b^{5}} - \frac{a^{3} x^{2}}{2 b^{4}} + \frac{a^{2} x^{3}}{3 b^{3}} - \frac{a x^{4}}{4 b^{2}} + \frac{x^{5}}{5 b} & \text{for}\: n = -1 \\- \frac{120 a^{6} \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} + \frac{120 a^{5} b n x \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} - \frac{60 a^{4} b^{2} n^{2} x^{2} \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} - \frac{60 a^{4} b^{2} n x^{2} \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} + \frac{20 a^{3} b^{3} n^{3} x^{3} \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} + \frac{60 a^{3} b^{3} n^{2} x^{3} \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} + \frac{40 a^{3} b^{3} n x^{3} \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} - \frac{5 a^{2} b^{4} n^{4} x^{4} \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} - \frac{30 a^{2} b^{4} n^{3} x^{4} \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} - \frac{55 a^{2} b^{4} n^{2} x^{4} \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} - \frac{30 a^{2} b^{4} n x^{4} \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} + \frac{a b^{5} n^{5} x^{5} \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} + \frac{10 a b^{5} n^{4} x^{5} \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} + \frac{35 a b^{5} n^{3} x^{5} \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} + \frac{50 a b^{5} n^{2} x^{5} \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} + \frac{24 a b^{5} n x^{5} \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} + \frac{b^{6} n^{5} x^{6} \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} + \frac{15 b^{6} n^{4} x^{6} \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} + \frac{85 b^{6} n^{3} x^{6} \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} + \frac{225 b^{6} n^{2} x^{6} \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} + \frac{274 b^{6} n x^{6} \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} + \frac{120 b^{6} x^{6} \left(a + b x\right)^{n}}{b^{6} n^{6} + 21 b^{6} n^{5} + 175 b^{6} n^{4} + 735 b^{6} n^{3} + 1624 b^{6} n^{2} + 1764 b^{6} n + 720 b^{6}} & \text{otherwise} \end{cases}\right) - \frac{b b^{n} c^{3} n x \left(\frac{a}{b} + x\right)^{n} \Phi\left(1 + \frac{b x}{a}, 1, n + 1\right) \Gamma\left(n + 1\right)}{a \Gamma\left(n + 2\right)} - \frac{b b^{n} c^{3} x \left(\frac{a}{b} + x\right)^{n} \Phi\left(1 + \frac{b x}{a}, 1, n + 1\right) \Gamma\left(n + 1\right)}{a \Gamma\left(n + 2\right)}"," ",0,"-b**n*c**3*n*(a/b + x)**n*lerchphi(1 + b*x/a, 1, n + 1)*gamma(n + 1)/gamma(n + 2) - b**n*c**3*(a/b + x)**n*lerchphi(1 + b*x/a, 1, n + 1)*gamma(n + 1)/gamma(n + 2) + 3*c**2*d*Piecewise((a**n*x**2/2, Eq(b, 0)), (a*log(a/b + x)/(a*b**2 + b**3*x) + a/(a*b**2 + b**3*x) + b*x*log(a/b + x)/(a*b**2 + b**3*x), Eq(n, -2)), (-a*log(a/b + x)/b**2 + x/b, Eq(n, -1)), (-a**2*(a + b*x)**n/(b**2*n**2 + 3*b**2*n + 2*b**2) + a*b*n*x*(a + b*x)**n/(b**2*n**2 + 3*b**2*n + 2*b**2) + b**2*n*x**2*(a + b*x)**n/(b**2*n**2 + 3*b**2*n + 2*b**2) + b**2*x**2*(a + b*x)**n/(b**2*n**2 + 3*b**2*n + 2*b**2), True)) + 3*c*d**2*Piecewise((a**n*x**4/4, Eq(b, 0)), (6*a**3*log(a/b + x)/(6*a**3*b**4 + 18*a**2*b**5*x + 18*a*b**6*x**2 + 6*b**7*x**3) + 11*a**3/(6*a**3*b**4 + 18*a**2*b**5*x + 18*a*b**6*x**2 + 6*b**7*x**3) + 18*a**2*b*x*log(a/b + x)/(6*a**3*b**4 + 18*a**2*b**5*x + 18*a*b**6*x**2 + 6*b**7*x**3) + 27*a**2*b*x/(6*a**3*b**4 + 18*a**2*b**5*x + 18*a*b**6*x**2 + 6*b**7*x**3) + 18*a*b**2*x**2*log(a/b + x)/(6*a**3*b**4 + 18*a**2*b**5*x + 18*a*b**6*x**2 + 6*b**7*x**3) + 18*a*b**2*x**2/(6*a**3*b**4 + 18*a**2*b**5*x + 18*a*b**6*x**2 + 6*b**7*x**3) + 6*b**3*x**3*log(a/b + x)/(6*a**3*b**4 + 18*a**2*b**5*x + 18*a*b**6*x**2 + 6*b**7*x**3), Eq(n, -4)), (-6*a**3*log(a/b + x)/(2*a**2*b**4 + 4*a*b**5*x + 2*b**6*x**2) - 9*a**3/(2*a**2*b**4 + 4*a*b**5*x + 2*b**6*x**2) - 12*a**2*b*x*log(a/b + x)/(2*a**2*b**4 + 4*a*b**5*x + 2*b**6*x**2) - 12*a**2*b*x/(2*a**2*b**4 + 4*a*b**5*x + 2*b**6*x**2) - 6*a*b**2*x**2*log(a/b + x)/(2*a**2*b**4 + 4*a*b**5*x + 2*b**6*x**2) + 2*b**3*x**3/(2*a**2*b**4 + 4*a*b**5*x + 2*b**6*x**2), Eq(n, -3)), (6*a**3*log(a/b + x)/(2*a*b**4 + 2*b**5*x) + 6*a**3/(2*a*b**4 + 2*b**5*x) + 6*a**2*b*x*log(a/b + x)/(2*a*b**4 + 2*b**5*x) - 3*a*b**2*x**2/(2*a*b**4 + 2*b**5*x) + b**3*x**3/(2*a*b**4 + 2*b**5*x), Eq(n, -2)), (-a**3*log(a/b + x)/b**4 + a**2*x/b**3 - a*x**2/(2*b**2) + x**3/(3*b), Eq(n, -1)), (-6*a**4*(a + b*x)**n/(b**4*n**4 + 10*b**4*n**3 + 35*b**4*n**2 + 50*b**4*n + 24*b**4) + 6*a**3*b*n*x*(a + b*x)**n/(b**4*n**4 + 10*b**4*n**3 + 35*b**4*n**2 + 50*b**4*n + 24*b**4) - 3*a**2*b**2*n**2*x**2*(a + b*x)**n/(b**4*n**4 + 10*b**4*n**3 + 35*b**4*n**2 + 50*b**4*n + 24*b**4) - 3*a**2*b**2*n*x**2*(a + b*x)**n/(b**4*n**4 + 10*b**4*n**3 + 35*b**4*n**2 + 50*b**4*n + 24*b**4) + a*b**3*n**3*x**3*(a + b*x)**n/(b**4*n**4 + 10*b**4*n**3 + 35*b**4*n**2 + 50*b**4*n + 24*b**4) + 3*a*b**3*n**2*x**3*(a + b*x)**n/(b**4*n**4 + 10*b**4*n**3 + 35*b**4*n**2 + 50*b**4*n + 24*b**4) + 2*a*b**3*n*x**3*(a + b*x)**n/(b**4*n**4 + 10*b**4*n**3 + 35*b**4*n**2 + 50*b**4*n + 24*b**4) + b**4*n**3*x**4*(a + b*x)**n/(b**4*n**4 + 10*b**4*n**3 + 35*b**4*n**2 + 50*b**4*n + 24*b**4) + 6*b**4*n**2*x**4*(a + b*x)**n/(b**4*n**4 + 10*b**4*n**3 + 35*b**4*n**2 + 50*b**4*n + 24*b**4) + 11*b**4*n*x**4*(a + b*x)**n/(b**4*n**4 + 10*b**4*n**3 + 35*b**4*n**2 + 50*b**4*n + 24*b**4) + 6*b**4*x**4*(a + b*x)**n/(b**4*n**4 + 10*b**4*n**3 + 35*b**4*n**2 + 50*b**4*n + 24*b**4), True)) + d**3*Piecewise((a**n*x**6/6, Eq(b, 0)), (60*a**5*log(a/b + x)/(60*a**5*b**6 + 300*a**4*b**7*x + 600*a**3*b**8*x**2 + 600*a**2*b**9*x**3 + 300*a*b**10*x**4 + 60*b**11*x**5) + 137*a**5/(60*a**5*b**6 + 300*a**4*b**7*x + 600*a**3*b**8*x**2 + 600*a**2*b**9*x**3 + 300*a*b**10*x**4 + 60*b**11*x**5) + 300*a**4*b*x*log(a/b + x)/(60*a**5*b**6 + 300*a**4*b**7*x + 600*a**3*b**8*x**2 + 600*a**2*b**9*x**3 + 300*a*b**10*x**4 + 60*b**11*x**5) + 625*a**4*b*x/(60*a**5*b**6 + 300*a**4*b**7*x + 600*a**3*b**8*x**2 + 600*a**2*b**9*x**3 + 300*a*b**10*x**4 + 60*b**11*x**5) + 600*a**3*b**2*x**2*log(a/b + x)/(60*a**5*b**6 + 300*a**4*b**7*x + 600*a**3*b**8*x**2 + 600*a**2*b**9*x**3 + 300*a*b**10*x**4 + 60*b**11*x**5) + 1100*a**3*b**2*x**2/(60*a**5*b**6 + 300*a**4*b**7*x + 600*a**3*b**8*x**2 + 600*a**2*b**9*x**3 + 300*a*b**10*x**4 + 60*b**11*x**5) + 600*a**2*b**3*x**3*log(a/b + x)/(60*a**5*b**6 + 300*a**4*b**7*x + 600*a**3*b**8*x**2 + 600*a**2*b**9*x**3 + 300*a*b**10*x**4 + 60*b**11*x**5) + 900*a**2*b**3*x**3/(60*a**5*b**6 + 300*a**4*b**7*x + 600*a**3*b**8*x**2 + 600*a**2*b**9*x**3 + 300*a*b**10*x**4 + 60*b**11*x**5) + 300*a*b**4*x**4*log(a/b + x)/(60*a**5*b**6 + 300*a**4*b**7*x + 600*a**3*b**8*x**2 + 600*a**2*b**9*x**3 + 300*a*b**10*x**4 + 60*b**11*x**5) + 300*a*b**4*x**4/(60*a**5*b**6 + 300*a**4*b**7*x + 600*a**3*b**8*x**2 + 600*a**2*b**9*x**3 + 300*a*b**10*x**4 + 60*b**11*x**5) + 60*b**5*x**5*log(a/b + x)/(60*a**5*b**6 + 300*a**4*b**7*x + 600*a**3*b**8*x**2 + 600*a**2*b**9*x**3 + 300*a*b**10*x**4 + 60*b**11*x**5), Eq(n, -6)), (-60*a**5*log(a/b + x)/(12*a**4*b**6 + 48*a**3*b**7*x + 72*a**2*b**8*x**2 + 48*a*b**9*x**3 + 12*b**10*x**4) - 125*a**5/(12*a**4*b**6 + 48*a**3*b**7*x + 72*a**2*b**8*x**2 + 48*a*b**9*x**3 + 12*b**10*x**4) - 240*a**4*b*x*log(a/b + x)/(12*a**4*b**6 + 48*a**3*b**7*x + 72*a**2*b**8*x**2 + 48*a*b**9*x**3 + 12*b**10*x**4) - 440*a**4*b*x/(12*a**4*b**6 + 48*a**3*b**7*x + 72*a**2*b**8*x**2 + 48*a*b**9*x**3 + 12*b**10*x**4) - 360*a**3*b**2*x**2*log(a/b + x)/(12*a**4*b**6 + 48*a**3*b**7*x + 72*a**2*b**8*x**2 + 48*a*b**9*x**3 + 12*b**10*x**4) - 540*a**3*b**2*x**2/(12*a**4*b**6 + 48*a**3*b**7*x + 72*a**2*b**8*x**2 + 48*a*b**9*x**3 + 12*b**10*x**4) - 240*a**2*b**3*x**3*log(a/b + x)/(12*a**4*b**6 + 48*a**3*b**7*x + 72*a**2*b**8*x**2 + 48*a*b**9*x**3 + 12*b**10*x**4) - 240*a**2*b**3*x**3/(12*a**4*b**6 + 48*a**3*b**7*x + 72*a**2*b**8*x**2 + 48*a*b**9*x**3 + 12*b**10*x**4) - 60*a*b**4*x**4*log(a/b + x)/(12*a**4*b**6 + 48*a**3*b**7*x + 72*a**2*b**8*x**2 + 48*a*b**9*x**3 + 12*b**10*x**4) + 12*b**5*x**5/(12*a**4*b**6 + 48*a**3*b**7*x + 72*a**2*b**8*x**2 + 48*a*b**9*x**3 + 12*b**10*x**4), Eq(n, -5)), (60*a**5*log(a/b + x)/(6*a**3*b**6 + 18*a**2*b**7*x + 18*a*b**8*x**2 + 6*b**9*x**3) + 110*a**5/(6*a**3*b**6 + 18*a**2*b**7*x + 18*a*b**8*x**2 + 6*b**9*x**3) + 180*a**4*b*x*log(a/b + x)/(6*a**3*b**6 + 18*a**2*b**7*x + 18*a*b**8*x**2 + 6*b**9*x**3) + 270*a**4*b*x/(6*a**3*b**6 + 18*a**2*b**7*x + 18*a*b**8*x**2 + 6*b**9*x**3) + 180*a**3*b**2*x**2*log(a/b + x)/(6*a**3*b**6 + 18*a**2*b**7*x + 18*a*b**8*x**2 + 6*b**9*x**3) + 180*a**3*b**2*x**2/(6*a**3*b**6 + 18*a**2*b**7*x + 18*a*b**8*x**2 + 6*b**9*x**3) + 60*a**2*b**3*x**3*log(a/b + x)/(6*a**3*b**6 + 18*a**2*b**7*x + 18*a*b**8*x**2 + 6*b**9*x**3) - 15*a*b**4*x**4/(6*a**3*b**6 + 18*a**2*b**7*x + 18*a*b**8*x**2 + 6*b**9*x**3) + 3*b**5*x**5/(6*a**3*b**6 + 18*a**2*b**7*x + 18*a*b**8*x**2 + 6*b**9*x**3), Eq(n, -4)), (-60*a**5*log(a/b + x)/(6*a**2*b**6 + 12*a*b**7*x + 6*b**8*x**2) - 90*a**5/(6*a**2*b**6 + 12*a*b**7*x + 6*b**8*x**2) - 120*a**4*b*x*log(a/b + x)/(6*a**2*b**6 + 12*a*b**7*x + 6*b**8*x**2) - 120*a**4*b*x/(6*a**2*b**6 + 12*a*b**7*x + 6*b**8*x**2) - 60*a**3*b**2*x**2*log(a/b + x)/(6*a**2*b**6 + 12*a*b**7*x + 6*b**8*x**2) + 20*a**2*b**3*x**3/(6*a**2*b**6 + 12*a*b**7*x + 6*b**8*x**2) - 5*a*b**4*x**4/(6*a**2*b**6 + 12*a*b**7*x + 6*b**8*x**2) + 2*b**5*x**5/(6*a**2*b**6 + 12*a*b**7*x + 6*b**8*x**2), Eq(n, -3)), (60*a**5*log(a/b + x)/(12*a*b**6 + 12*b**7*x) + 60*a**5/(12*a*b**6 + 12*b**7*x) + 60*a**4*b*x*log(a/b + x)/(12*a*b**6 + 12*b**7*x) - 30*a**3*b**2*x**2/(12*a*b**6 + 12*b**7*x) + 10*a**2*b**3*x**3/(12*a*b**6 + 12*b**7*x) - 5*a*b**4*x**4/(12*a*b**6 + 12*b**7*x) + 3*b**5*x**5/(12*a*b**6 + 12*b**7*x), Eq(n, -2)), (-a**5*log(a/b + x)/b**6 + a**4*x/b**5 - a**3*x**2/(2*b**4) + a**2*x**3/(3*b**3) - a*x**4/(4*b**2) + x**5/(5*b), Eq(n, -1)), (-120*a**6*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) + 120*a**5*b*n*x*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) - 60*a**4*b**2*n**2*x**2*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) - 60*a**4*b**2*n*x**2*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) + 20*a**3*b**3*n**3*x**3*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) + 60*a**3*b**3*n**2*x**3*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) + 40*a**3*b**3*n*x**3*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) - 5*a**2*b**4*n**4*x**4*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) - 30*a**2*b**4*n**3*x**4*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) - 55*a**2*b**4*n**2*x**4*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) - 30*a**2*b**4*n*x**4*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) + a*b**5*n**5*x**5*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) + 10*a*b**5*n**4*x**5*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) + 35*a*b**5*n**3*x**5*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) + 50*a*b**5*n**2*x**5*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) + 24*a*b**5*n*x**5*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) + b**6*n**5*x**6*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) + 15*b**6*n**4*x**6*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) + 85*b**6*n**3*x**6*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) + 225*b**6*n**2*x**6*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) + 274*b**6*n*x**6*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6) + 120*b**6*x**6*(a + b*x)**n/(b**6*n**6 + 21*b**6*n**5 + 175*b**6*n**4 + 735*b**6*n**3 + 1624*b**6*n**2 + 1764*b**6*n + 720*b**6), True)) - b*b**n*c**3*n*x*(a/b + x)**n*lerchphi(1 + b*x/a, 1, n + 1)*gamma(n + 1)/(a*gamma(n + 2)) - b*b**n*c**3*x*(a/b + x)**n*lerchphi(1 + b*x/a, 1, n + 1)*gamma(n + 1)/(a*gamma(n + 2))","B",0
363,0,0,0,0.000000," ","integrate(x**4*(e*x+d)**n/(c*x**2+a),x)","\int \frac{x^{4} \left(d + e x\right)^{n}}{a + c x^{2}}\, dx"," ",0,"Integral(x**4*(d + e*x)**n/(a + c*x**2), x)","F",0
364,0,0,0,0.000000," ","integrate(x**3*(e*x+d)**n/(c*x**2+a),x)","\int \frac{x^{3} \left(d + e x\right)^{n}}{a + c x^{2}}\, dx"," ",0,"Integral(x**3*(d + e*x)**n/(a + c*x**2), x)","F",0
365,0,0,0,0.000000," ","integrate(x**2*(e*x+d)**n/(c*x**2+a),x)","\int \frac{x^{2} \left(d + e x\right)^{n}}{a + c x^{2}}\, dx"," ",0,"Integral(x**2*(d + e*x)**n/(a + c*x**2), x)","F",0
366,0,0,0,0.000000," ","integrate(x*(e*x+d)**n/(c*x**2+a),x)","\int \frac{x \left(d + e x\right)^{n}}{a + c x^{2}}\, dx"," ",0,"Integral(x*(d + e*x)**n/(a + c*x**2), x)","F",0
367,0,0,0,0.000000," ","integrate((e*x+d)**n/(c*x**2+a),x)","\int \frac{\left(d + e x\right)^{n}}{a + c x^{2}}\, dx"," ",0,"Integral((d + e*x)**n/(a + c*x**2), x)","F",0
368,0,0,0,0.000000," ","integrate((e*x+d)**n/x/(c*x**2+a),x)","\int \frac{\left(d + e x\right)^{n}}{x \left(a + c x^{2}\right)}\, dx"," ",0,"Integral((d + e*x)**n/(x*(a + c*x**2)), x)","F",0
369,-1,0,0,0.000000," ","integrate((e*x+d)**n/x**2/(c*x**2+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
370,-1,0,0,0.000000," ","integrate(x**4*(e*x+d)**n/(c*x**2+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
371,-1,0,0,0.000000," ","integrate(x**3*(e*x+d)**n/(c*x**2+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
372,-1,0,0,0.000000," ","integrate(x**2*(e*x+d)**n/(c*x**2+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
373,-1,0,0,0.000000," ","integrate(x*(e*x+d)**n/(c*x**2+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
374,-1,0,0,0.000000," ","integrate((e*x+d)**n/(c*x**2+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
375,0,0,0,0.000000," ","integrate((e*x+d)**n/x/(c*x**2+a)**2,x)","\int \frac{\left(d + e x\right)^{n}}{x \left(a + c x^{2}\right)^{2}}\, dx"," ",0,"Integral((d + e*x)**n/(x*(a + c*x**2)**2), x)","F",0
376,-1,0,0,0.000000," ","integrate((e*x+d)**n/x**2/(c*x**2+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
377,1,131,0,38.734456," ","integrate((g*x)**m*(e*x+d)**n*(c*x**2+a)**2,x)","\frac{a^{2} d^{n} g^{m} x x^{m} \Gamma\left(m + 1\right) {{}_{2}F_{1}\left(\begin{matrix} - n, m + 1 \\ m + 2 \end{matrix}\middle| {\frac{e x e^{i \pi}}{d}} \right)}}{\Gamma\left(m + 2\right)} + \frac{2 a c d^{n} g^{m} x^{3} x^{m} \Gamma\left(m + 3\right) {{}_{2}F_{1}\left(\begin{matrix} - n, m + 3 \\ m + 4 \end{matrix}\middle| {\frac{e x e^{i \pi}}{d}} \right)}}{\Gamma\left(m + 4\right)} + \frac{c^{2} d^{n} g^{m} x^{5} x^{m} \Gamma\left(m + 5\right) {{}_{2}F_{1}\left(\begin{matrix} - n, m + 5 \\ m + 6 \end{matrix}\middle| {\frac{e x e^{i \pi}}{d}} \right)}}{\Gamma\left(m + 6\right)}"," ",0,"a**2*d**n*g**m*x*x**m*gamma(m + 1)*hyper((-n, m + 1), (m + 2,), e*x*exp_polar(I*pi)/d)/gamma(m + 2) + 2*a*c*d**n*g**m*x**3*x**m*gamma(m + 3)*hyper((-n, m + 3), (m + 4,), e*x*exp_polar(I*pi)/d)/gamma(m + 4) + c**2*d**n*g**m*x**5*x**m*gamma(m + 5)*hyper((-n, m + 5), (m + 6,), e*x*exp_polar(I*pi)/d)/gamma(m + 6)","C",0
378,1,82,0,15.753728," ","integrate((g*x)**m*(e*x+d)**n*(c*x**2+a),x)","\frac{a d^{n} g^{m} x x^{m} \Gamma\left(m + 1\right) {{}_{2}F_{1}\left(\begin{matrix} - n, m + 1 \\ m + 2 \end{matrix}\middle| {\frac{e x e^{i \pi}}{d}} \right)}}{\Gamma\left(m + 2\right)} + \frac{c d^{n} g^{m} x^{3} x^{m} \Gamma\left(m + 3\right) {{}_{2}F_{1}\left(\begin{matrix} - n, m + 3 \\ m + 4 \end{matrix}\middle| {\frac{e x e^{i \pi}}{d}} \right)}}{\Gamma\left(m + 4\right)}"," ",0,"a*d**n*g**m*x*x**m*gamma(m + 1)*hyper((-n, m + 1), (m + 2,), e*x*exp_polar(I*pi)/d)/gamma(m + 2) + c*d**n*g**m*x**3*x**m*gamma(m + 3)*hyper((-n, m + 3), (m + 4,), e*x*exp_polar(I*pi)/d)/gamma(m + 4)","C",0
379,-2,0,0,0.000000," ","integrate((g*x)**m*(e*x+d)**n/(c*x**2+a),x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
380,-1,0,0,0.000000," ","integrate((g*x)**m*(e*x+d)**n/(c*x**2+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
381,1,1012,0,29.683567," ","integrate(x**5*(e*x+d)*(b*x**2+a)**p,x)","\frac{a^{p} e x^{7} {{}_{2}F_{1}\left(\begin{matrix} \frac{7}{2}, - p \\ \frac{9}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{7} + d \left(\begin{cases} \frac{a^{p} x^{6}}{6} & \text{for}\: b = 0 \\\frac{2 a^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{4 a^{2} b^{3} + 8 a b^{4} x^{2} + 4 b^{5} x^{4}} + \frac{2 a^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{4 a^{2} b^{3} + 8 a b^{4} x^{2} + 4 b^{5} x^{4}} + \frac{3 a^{2}}{4 a^{2} b^{3} + 8 a b^{4} x^{2} + 4 b^{5} x^{4}} + \frac{4 a b x^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{4 a^{2} b^{3} + 8 a b^{4} x^{2} + 4 b^{5} x^{4}} + \frac{4 a b x^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{4 a^{2} b^{3} + 8 a b^{4} x^{2} + 4 b^{5} x^{4}} + \frac{4 a b x^{2}}{4 a^{2} b^{3} + 8 a b^{4} x^{2} + 4 b^{5} x^{4}} + \frac{2 b^{2} x^{4} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{4 a^{2} b^{3} + 8 a b^{4} x^{2} + 4 b^{5} x^{4}} + \frac{2 b^{2} x^{4} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{4 a^{2} b^{3} + 8 a b^{4} x^{2} + 4 b^{5} x^{4}} & \text{for}\: p = -3 \\- \frac{2 a^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 a b^{3} + 2 b^{4} x^{2}} - \frac{2 a^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 a b^{3} + 2 b^{4} x^{2}} - \frac{2 a^{2}}{2 a b^{3} + 2 b^{4} x^{2}} - \frac{2 a b x^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 a b^{3} + 2 b^{4} x^{2}} - \frac{2 a b x^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 a b^{3} + 2 b^{4} x^{2}} + \frac{b^{2} x^{4}}{2 a b^{3} + 2 b^{4} x^{2}} & \text{for}\: p = -2 \\\frac{a^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 b^{3}} + \frac{a^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 b^{3}} - \frac{a x^{2}}{2 b^{2}} + \frac{x^{4}}{4 b} & \text{for}\: p = -1 \\\frac{2 a^{3} \left(a + b x^{2}\right)^{p}}{2 b^{3} p^{3} + 12 b^{3} p^{2} + 22 b^{3} p + 12 b^{3}} - \frac{2 a^{2} b p x^{2} \left(a + b x^{2}\right)^{p}}{2 b^{3} p^{3} + 12 b^{3} p^{2} + 22 b^{3} p + 12 b^{3}} + \frac{a b^{2} p^{2} x^{4} \left(a + b x^{2}\right)^{p}}{2 b^{3} p^{3} + 12 b^{3} p^{2} + 22 b^{3} p + 12 b^{3}} + \frac{a b^{2} p x^{4} \left(a + b x^{2}\right)^{p}}{2 b^{3} p^{3} + 12 b^{3} p^{2} + 22 b^{3} p + 12 b^{3}} + \frac{b^{3} p^{2} x^{6} \left(a + b x^{2}\right)^{p}}{2 b^{3} p^{3} + 12 b^{3} p^{2} + 22 b^{3} p + 12 b^{3}} + \frac{3 b^{3} p x^{6} \left(a + b x^{2}\right)^{p}}{2 b^{3} p^{3} + 12 b^{3} p^{2} + 22 b^{3} p + 12 b^{3}} + \frac{2 b^{3} x^{6} \left(a + b x^{2}\right)^{p}}{2 b^{3} p^{3} + 12 b^{3} p^{2} + 22 b^{3} p + 12 b^{3}} & \text{otherwise} \end{cases}\right)"," ",0,"a**p*e*x**7*hyper((7/2, -p), (9/2,), b*x**2*exp_polar(I*pi)/a)/7 + d*Piecewise((a**p*x**6/6, Eq(b, 0)), (2*a**2*log(-I*sqrt(a)*sqrt(1/b) + x)/(4*a**2*b**3 + 8*a*b**4*x**2 + 4*b**5*x**4) + 2*a**2*log(I*sqrt(a)*sqrt(1/b) + x)/(4*a**2*b**3 + 8*a*b**4*x**2 + 4*b**5*x**4) + 3*a**2/(4*a**2*b**3 + 8*a*b**4*x**2 + 4*b**5*x**4) + 4*a*b*x**2*log(-I*sqrt(a)*sqrt(1/b) + x)/(4*a**2*b**3 + 8*a*b**4*x**2 + 4*b**5*x**4) + 4*a*b*x**2*log(I*sqrt(a)*sqrt(1/b) + x)/(4*a**2*b**3 + 8*a*b**4*x**2 + 4*b**5*x**4) + 4*a*b*x**2/(4*a**2*b**3 + 8*a*b**4*x**2 + 4*b**5*x**4) + 2*b**2*x**4*log(-I*sqrt(a)*sqrt(1/b) + x)/(4*a**2*b**3 + 8*a*b**4*x**2 + 4*b**5*x**4) + 2*b**2*x**4*log(I*sqrt(a)*sqrt(1/b) + x)/(4*a**2*b**3 + 8*a*b**4*x**2 + 4*b**5*x**4), Eq(p, -3)), (-2*a**2*log(-I*sqrt(a)*sqrt(1/b) + x)/(2*a*b**3 + 2*b**4*x**2) - 2*a**2*log(I*sqrt(a)*sqrt(1/b) + x)/(2*a*b**3 + 2*b**4*x**2) - 2*a**2/(2*a*b**3 + 2*b**4*x**2) - 2*a*b*x**2*log(-I*sqrt(a)*sqrt(1/b) + x)/(2*a*b**3 + 2*b**4*x**2) - 2*a*b*x**2*log(I*sqrt(a)*sqrt(1/b) + x)/(2*a*b**3 + 2*b**4*x**2) + b**2*x**4/(2*a*b**3 + 2*b**4*x**2), Eq(p, -2)), (a**2*log(-I*sqrt(a)*sqrt(1/b) + x)/(2*b**3) + a**2*log(I*sqrt(a)*sqrt(1/b) + x)/(2*b**3) - a*x**2/(2*b**2) + x**4/(4*b), Eq(p, -1)), (2*a**3*(a + b*x**2)**p/(2*b**3*p**3 + 12*b**3*p**2 + 22*b**3*p + 12*b**3) - 2*a**2*b*p*x**2*(a + b*x**2)**p/(2*b**3*p**3 + 12*b**3*p**2 + 22*b**3*p + 12*b**3) + a*b**2*p**2*x**4*(a + b*x**2)**p/(2*b**3*p**3 + 12*b**3*p**2 + 22*b**3*p + 12*b**3) + a*b**2*p*x**4*(a + b*x**2)**p/(2*b**3*p**3 + 12*b**3*p**2 + 22*b**3*p + 12*b**3) + b**3*p**2*x**6*(a + b*x**2)**p/(2*b**3*p**3 + 12*b**3*p**2 + 22*b**3*p + 12*b**3) + 3*b**3*p*x**6*(a + b*x**2)**p/(2*b**3*p**3 + 12*b**3*p**2 + 22*b**3*p + 12*b**3) + 2*b**3*x**6*(a + b*x**2)**p/(2*b**3*p**3 + 12*b**3*p**2 + 22*b**3*p + 12*b**3), True))","C",0
382,1,1012,0,21.959456," ","integrate(x**4*(e*x+d)*(b*x**2+a)**p,x)","\frac{a^{p} d x^{5} {{}_{2}F_{1}\left(\begin{matrix} \frac{5}{2}, - p \\ \frac{7}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{5} + e \left(\begin{cases} \frac{a^{p} x^{6}}{6} & \text{for}\: b = 0 \\\frac{2 a^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{4 a^{2} b^{3} + 8 a b^{4} x^{2} + 4 b^{5} x^{4}} + \frac{2 a^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{4 a^{2} b^{3} + 8 a b^{4} x^{2} + 4 b^{5} x^{4}} + \frac{3 a^{2}}{4 a^{2} b^{3} + 8 a b^{4} x^{2} + 4 b^{5} x^{4}} + \frac{4 a b x^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{4 a^{2} b^{3} + 8 a b^{4} x^{2} + 4 b^{5} x^{4}} + \frac{4 a b x^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{4 a^{2} b^{3} + 8 a b^{4} x^{2} + 4 b^{5} x^{4}} + \frac{4 a b x^{2}}{4 a^{2} b^{3} + 8 a b^{4} x^{2} + 4 b^{5} x^{4}} + \frac{2 b^{2} x^{4} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{4 a^{2} b^{3} + 8 a b^{4} x^{2} + 4 b^{5} x^{4}} + \frac{2 b^{2} x^{4} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{4 a^{2} b^{3} + 8 a b^{4} x^{2} + 4 b^{5} x^{4}} & \text{for}\: p = -3 \\- \frac{2 a^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 a b^{3} + 2 b^{4} x^{2}} - \frac{2 a^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 a b^{3} + 2 b^{4} x^{2}} - \frac{2 a^{2}}{2 a b^{3} + 2 b^{4} x^{2}} - \frac{2 a b x^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 a b^{3} + 2 b^{4} x^{2}} - \frac{2 a b x^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 a b^{3} + 2 b^{4} x^{2}} + \frac{b^{2} x^{4}}{2 a b^{3} + 2 b^{4} x^{2}} & \text{for}\: p = -2 \\\frac{a^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 b^{3}} + \frac{a^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 b^{3}} - \frac{a x^{2}}{2 b^{2}} + \frac{x^{4}}{4 b} & \text{for}\: p = -1 \\\frac{2 a^{3} \left(a + b x^{2}\right)^{p}}{2 b^{3} p^{3} + 12 b^{3} p^{2} + 22 b^{3} p + 12 b^{3}} - \frac{2 a^{2} b p x^{2} \left(a + b x^{2}\right)^{p}}{2 b^{3} p^{3} + 12 b^{3} p^{2} + 22 b^{3} p + 12 b^{3}} + \frac{a b^{2} p^{2} x^{4} \left(a + b x^{2}\right)^{p}}{2 b^{3} p^{3} + 12 b^{3} p^{2} + 22 b^{3} p + 12 b^{3}} + \frac{a b^{2} p x^{4} \left(a + b x^{2}\right)^{p}}{2 b^{3} p^{3} + 12 b^{3} p^{2} + 22 b^{3} p + 12 b^{3}} + \frac{b^{3} p^{2} x^{6} \left(a + b x^{2}\right)^{p}}{2 b^{3} p^{3} + 12 b^{3} p^{2} + 22 b^{3} p + 12 b^{3}} + \frac{3 b^{3} p x^{6} \left(a + b x^{2}\right)^{p}}{2 b^{3} p^{3} + 12 b^{3} p^{2} + 22 b^{3} p + 12 b^{3}} + \frac{2 b^{3} x^{6} \left(a + b x^{2}\right)^{p}}{2 b^{3} p^{3} + 12 b^{3} p^{2} + 22 b^{3} p + 12 b^{3}} & \text{otherwise} \end{cases}\right)"," ",0,"a**p*d*x**5*hyper((5/2, -p), (7/2,), b*x**2*exp_polar(I*pi)/a)/5 + e*Piecewise((a**p*x**6/6, Eq(b, 0)), (2*a**2*log(-I*sqrt(a)*sqrt(1/b) + x)/(4*a**2*b**3 + 8*a*b**4*x**2 + 4*b**5*x**4) + 2*a**2*log(I*sqrt(a)*sqrt(1/b) + x)/(4*a**2*b**3 + 8*a*b**4*x**2 + 4*b**5*x**4) + 3*a**2/(4*a**2*b**3 + 8*a*b**4*x**2 + 4*b**5*x**4) + 4*a*b*x**2*log(-I*sqrt(a)*sqrt(1/b) + x)/(4*a**2*b**3 + 8*a*b**4*x**2 + 4*b**5*x**4) + 4*a*b*x**2*log(I*sqrt(a)*sqrt(1/b) + x)/(4*a**2*b**3 + 8*a*b**4*x**2 + 4*b**5*x**4) + 4*a*b*x**2/(4*a**2*b**3 + 8*a*b**4*x**2 + 4*b**5*x**4) + 2*b**2*x**4*log(-I*sqrt(a)*sqrt(1/b) + x)/(4*a**2*b**3 + 8*a*b**4*x**2 + 4*b**5*x**4) + 2*b**2*x**4*log(I*sqrt(a)*sqrt(1/b) + x)/(4*a**2*b**3 + 8*a*b**4*x**2 + 4*b**5*x**4), Eq(p, -3)), (-2*a**2*log(-I*sqrt(a)*sqrt(1/b) + x)/(2*a*b**3 + 2*b**4*x**2) - 2*a**2*log(I*sqrt(a)*sqrt(1/b) + x)/(2*a*b**3 + 2*b**4*x**2) - 2*a**2/(2*a*b**3 + 2*b**4*x**2) - 2*a*b*x**2*log(-I*sqrt(a)*sqrt(1/b) + x)/(2*a*b**3 + 2*b**4*x**2) - 2*a*b*x**2*log(I*sqrt(a)*sqrt(1/b) + x)/(2*a*b**3 + 2*b**4*x**2) + b**2*x**4/(2*a*b**3 + 2*b**4*x**2), Eq(p, -2)), (a**2*log(-I*sqrt(a)*sqrt(1/b) + x)/(2*b**3) + a**2*log(I*sqrt(a)*sqrt(1/b) + x)/(2*b**3) - a*x**2/(2*b**2) + x**4/(4*b), Eq(p, -1)), (2*a**3*(a + b*x**2)**p/(2*b**3*p**3 + 12*b**3*p**2 + 22*b**3*p + 12*b**3) - 2*a**2*b*p*x**2*(a + b*x**2)**p/(2*b**3*p**3 + 12*b**3*p**2 + 22*b**3*p + 12*b**3) + a*b**2*p**2*x**4*(a + b*x**2)**p/(2*b**3*p**3 + 12*b**3*p**2 + 22*b**3*p + 12*b**3) + a*b**2*p*x**4*(a + b*x**2)**p/(2*b**3*p**3 + 12*b**3*p**2 + 22*b**3*p + 12*b**3) + b**3*p**2*x**6*(a + b*x**2)**p/(2*b**3*p**3 + 12*b**3*p**2 + 22*b**3*p + 12*b**3) + 3*b**3*p*x**6*(a + b*x**2)**p/(2*b**3*p**3 + 12*b**3*p**2 + 22*b**3*p + 12*b**3) + 2*b**3*x**6*(a + b*x**2)**p/(2*b**3*p**3 + 12*b**3*p**2 + 22*b**3*p + 12*b**3), True))","C",0
383,1,394,0,16.782459," ","integrate(x**3*(e*x+d)*(b*x**2+a)**p,x)","\frac{a^{p} e x^{5} {{}_{2}F_{1}\left(\begin{matrix} \frac{5}{2}, - p \\ \frac{7}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{5} + d \left(\begin{cases} \frac{a^{p} x^{4}}{4} & \text{for}\: b = 0 \\\frac{a \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 a b^{2} + 2 b^{3} x^{2}} + \frac{a \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 a b^{2} + 2 b^{3} x^{2}} + \frac{a}{2 a b^{2} + 2 b^{3} x^{2}} + \frac{b x^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 a b^{2} + 2 b^{3} x^{2}} + \frac{b x^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 a b^{2} + 2 b^{3} x^{2}} & \text{for}\: p = -2 \\- \frac{a \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 b^{2}} - \frac{a \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 b^{2}} + \frac{x^{2}}{2 b} & \text{for}\: p = -1 \\- \frac{a^{2} \left(a + b x^{2}\right)^{p}}{2 b^{2} p^{2} + 6 b^{2} p + 4 b^{2}} + \frac{a b p x^{2} \left(a + b x^{2}\right)^{p}}{2 b^{2} p^{2} + 6 b^{2} p + 4 b^{2}} + \frac{b^{2} p x^{4} \left(a + b x^{2}\right)^{p}}{2 b^{2} p^{2} + 6 b^{2} p + 4 b^{2}} + \frac{b^{2} x^{4} \left(a + b x^{2}\right)^{p}}{2 b^{2} p^{2} + 6 b^{2} p + 4 b^{2}} & \text{otherwise} \end{cases}\right)"," ",0,"a**p*e*x**5*hyper((5/2, -p), (7/2,), b*x**2*exp_polar(I*pi)/a)/5 + d*Piecewise((a**p*x**4/4, Eq(b, 0)), (a*log(-I*sqrt(a)*sqrt(1/b) + x)/(2*a*b**2 + 2*b**3*x**2) + a*log(I*sqrt(a)*sqrt(1/b) + x)/(2*a*b**2 + 2*b**3*x**2) + a/(2*a*b**2 + 2*b**3*x**2) + b*x**2*log(-I*sqrt(a)*sqrt(1/b) + x)/(2*a*b**2 + 2*b**3*x**2) + b*x**2*log(I*sqrt(a)*sqrt(1/b) + x)/(2*a*b**2 + 2*b**3*x**2), Eq(p, -2)), (-a*log(-I*sqrt(a)*sqrt(1/b) + x)/(2*b**2) - a*log(I*sqrt(a)*sqrt(1/b) + x)/(2*b**2) + x**2/(2*b), Eq(p, -1)), (-a**2*(a + b*x**2)**p/(2*b**2*p**2 + 6*b**2*p + 4*b**2) + a*b*p*x**2*(a + b*x**2)**p/(2*b**2*p**2 + 6*b**2*p + 4*b**2) + b**2*p*x**4*(a + b*x**2)**p/(2*b**2*p**2 + 6*b**2*p + 4*b**2) + b**2*x**4*(a + b*x**2)**p/(2*b**2*p**2 + 6*b**2*p + 4*b**2), True))","C",0
384,1,394,0,11.876698," ","integrate(x**2*(e*x+d)*(b*x**2+a)**p,x)","\frac{a^{p} d x^{3} {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{2}, - p \\ \frac{5}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{3} + e \left(\begin{cases} \frac{a^{p} x^{4}}{4} & \text{for}\: b = 0 \\\frac{a \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 a b^{2} + 2 b^{3} x^{2}} + \frac{a \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 a b^{2} + 2 b^{3} x^{2}} + \frac{a}{2 a b^{2} + 2 b^{3} x^{2}} + \frac{b x^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 a b^{2} + 2 b^{3} x^{2}} + \frac{b x^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 a b^{2} + 2 b^{3} x^{2}} & \text{for}\: p = -2 \\- \frac{a \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 b^{2}} - \frac{a \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 b^{2}} + \frac{x^{2}}{2 b} & \text{for}\: p = -1 \\- \frac{a^{2} \left(a + b x^{2}\right)^{p}}{2 b^{2} p^{2} + 6 b^{2} p + 4 b^{2}} + \frac{a b p x^{2} \left(a + b x^{2}\right)^{p}}{2 b^{2} p^{2} + 6 b^{2} p + 4 b^{2}} + \frac{b^{2} p x^{4} \left(a + b x^{2}\right)^{p}}{2 b^{2} p^{2} + 6 b^{2} p + 4 b^{2}} + \frac{b^{2} x^{4} \left(a + b x^{2}\right)^{p}}{2 b^{2} p^{2} + 6 b^{2} p + 4 b^{2}} & \text{otherwise} \end{cases}\right)"," ",0,"a**p*d*x**3*hyper((3/2, -p), (5/2,), b*x**2*exp_polar(I*pi)/a)/3 + e*Piecewise((a**p*x**4/4, Eq(b, 0)), (a*log(-I*sqrt(a)*sqrt(1/b) + x)/(2*a*b**2 + 2*b**3*x**2) + a*log(I*sqrt(a)*sqrt(1/b) + x)/(2*a*b**2 + 2*b**3*x**2) + a/(2*a*b**2 + 2*b**3*x**2) + b*x**2*log(-I*sqrt(a)*sqrt(1/b) + x)/(2*a*b**2 + 2*b**3*x**2) + b*x**2*log(I*sqrt(a)*sqrt(1/b) + x)/(2*a*b**2 + 2*b**3*x**2), Eq(p, -2)), (-a*log(-I*sqrt(a)*sqrt(1/b) + x)/(2*b**2) - a*log(I*sqrt(a)*sqrt(1/b) + x)/(2*b**2) + x**2/(2*b), Eq(p, -1)), (-a**2*(a + b*x**2)**p/(2*b**2*p**2 + 6*b**2*p + 4*b**2) + a*b*p*x**2*(a + b*x**2)**p/(2*b**2*p**2 + 6*b**2*p + 4*b**2) + b**2*p*x**4*(a + b*x**2)**p/(2*b**2*p**2 + 6*b**2*p + 4*b**2) + b**2*x**4*(a + b*x**2)**p/(2*b**2*p**2 + 6*b**2*p + 4*b**2), True))","C",0
385,1,65,0,9.007940," ","integrate(x*(e*x+d)*(b*x**2+a)**p,x)","\frac{a^{p} e x^{3} {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{2}, - p \\ \frac{5}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{3} + d \left(\begin{cases} \frac{a^{p} x^{2}}{2} & \text{for}\: b = 0 \\\frac{\begin{cases} \frac{\left(a + b x^{2}\right)^{p + 1}}{p + 1} & \text{for}\: p \neq -1 \\\log{\left(a + b x^{2} \right)} & \text{otherwise} \end{cases}}{2 b} & \text{otherwise} \end{cases}\right)"," ",0,"a**p*e*x**3*hyper((3/2, -p), (5/2,), b*x**2*exp_polar(I*pi)/a)/3 + d*Piecewise((a**p*x**2/2, Eq(b, 0)), (Piecewise(((a + b*x**2)**(p + 1)/(p + 1), Ne(p, -1)), (log(a + b*x**2), True))/(2*b), True))","A",0
386,1,61,0,6.414111," ","integrate((e*x+d)*(b*x**2+a)**p,x)","a^{p} d x {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, - p \\ \frac{3}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)} + e \left(\begin{cases} \frac{a^{p} x^{2}}{2} & \text{for}\: b = 0 \\\frac{\begin{cases} \frac{\left(a + b x^{2}\right)^{p + 1}}{p + 1} & \text{for}\: p \neq -1 \\\log{\left(a + b x^{2} \right)} & \text{otherwise} \end{cases}}{2 b} & \text{otherwise} \end{cases}\right)"," ",0,"a**p*d*x*hyper((1/2, -p), (3/2,), b*x**2*exp_polar(I*pi)/a) + e*Piecewise((a**p*x**2/2, Eq(b, 0)), (Piecewise(((a + b*x**2)**(p + 1)/(p + 1), Ne(p, -1)), (log(a + b*x**2), True))/(2*b), True))","A",0
387,1,65,0,9.672525," ","integrate((e*x+d)*(b*x**2+a)**p/x,x)","a^{p} e x {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, - p \\ \frac{3}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)} - \frac{b^{p} d x^{2 p} \Gamma\left(- p\right) {{}_{2}F_{1}\left(\begin{matrix} - p, - p \\ 1 - p \end{matrix}\middle| {\frac{a e^{i \pi}}{b x^{2}}} \right)}}{2 \Gamma\left(1 - p\right)}"," ",0,"a**p*e*x*hyper((1/2, -p), (3/2,), b*x**2*exp_polar(I*pi)/a) - b**p*d*x**(2*p)*gamma(-p)*hyper((-p, -p), (1 - p,), a*exp_polar(I*pi)/(b*x**2))/(2*gamma(1 - p))","C",0
388,1,68,0,10.866820," ","integrate((e*x+d)*(b*x**2+a)**p/x**2,x)","- \frac{a^{p} d {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, - p \\ \frac{1}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{x} - \frac{b^{p} e x^{2 p} \Gamma\left(- p\right) {{}_{2}F_{1}\left(\begin{matrix} - p, - p \\ 1 - p \end{matrix}\middle| {\frac{a e^{i \pi}}{b x^{2}}} \right)}}{2 \Gamma\left(1 - p\right)}"," ",0,"-a**p*d*hyper((-1/2, -p), (1/2,), b*x**2*exp_polar(I*pi)/a)/x - b**p*e*x**(2*p)*gamma(-p)*hyper((-p, -p), (1 - p,), a*exp_polar(I*pi)/(b*x**2))/(2*gamma(1 - p))","C",0
389,1,71,0,13.917423," ","integrate((e*x+d)*(b*x**2+a)**p/x**3,x)","- \frac{a^{p} e {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, - p \\ \frac{1}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{x} - \frac{b^{p} d x^{2 p} \Gamma\left(1 - p\right) {{}_{2}F_{1}\left(\begin{matrix} - p, 1 - p \\ 2 - p \end{matrix}\middle| {\frac{a e^{i \pi}}{b x^{2}}} \right)}}{2 x^{2} \Gamma\left(2 - p\right)}"," ",0,"-a**p*e*hyper((-1/2, -p), (1/2,), b*x**2*exp_polar(I*pi)/a)/x - b**p*d*x**(2*p)*gamma(1 - p)*hyper((-p, 1 - p), (2 - p,), a*exp_polar(I*pi)/(b*x**2))/(2*x**2*gamma(2 - p))","C",0
390,1,3046,0,46.588881," ","integrate(x**5*(e*x+d)**2*(b*x**2+a)**p,x)","\frac{2 a^{p} d e x^{7} {{}_{2}F_{1}\left(\begin{matrix} \frac{7}{2}, - p \\ \frac{9}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{7} + d^{2} \left(\begin{cases} \frac{a^{p} x^{6}}{6} & \text{for}\: b = 0 \\\frac{2 a^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{4 a^{2} b^{3} + 8 a b^{4} x^{2} + 4 b^{5} x^{4}} + \frac{2 a^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{4 a^{2} b^{3} + 8 a b^{4} x^{2} + 4 b^{5} x^{4}} + \frac{3 a^{2}}{4 a^{2} b^{3} + 8 a b^{4} x^{2} + 4 b^{5} x^{4}} + \frac{4 a b x^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{4 a^{2} b^{3} + 8 a b^{4} x^{2} + 4 b^{5} x^{4}} + \frac{4 a b x^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{4 a^{2} b^{3} + 8 a b^{4} x^{2} + 4 b^{5} x^{4}} + \frac{4 a b x^{2}}{4 a^{2} b^{3} + 8 a b^{4} x^{2} + 4 b^{5} x^{4}} + \frac{2 b^{2} x^{4} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{4 a^{2} b^{3} + 8 a b^{4} x^{2} + 4 b^{5} x^{4}} + \frac{2 b^{2} x^{4} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{4 a^{2} b^{3} + 8 a b^{4} x^{2} + 4 b^{5} x^{4}} & \text{for}\: p = -3 \\- \frac{2 a^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 a b^{3} + 2 b^{4} x^{2}} - \frac{2 a^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 a b^{3} + 2 b^{4} x^{2}} - \frac{2 a^{2}}{2 a b^{3} + 2 b^{4} x^{2}} - \frac{2 a b x^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 a b^{3} + 2 b^{4} x^{2}} - \frac{2 a b x^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 a b^{3} + 2 b^{4} x^{2}} + \frac{b^{2} x^{4}}{2 a b^{3} + 2 b^{4} x^{2}} & \text{for}\: p = -2 \\\frac{a^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 b^{3}} + \frac{a^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 b^{3}} - \frac{a x^{2}}{2 b^{2}} + \frac{x^{4}}{4 b} & \text{for}\: p = -1 \\\frac{2 a^{3} \left(a + b x^{2}\right)^{p}}{2 b^{3} p^{3} + 12 b^{3} p^{2} + 22 b^{3} p + 12 b^{3}} - \frac{2 a^{2} b p x^{2} \left(a + b x^{2}\right)^{p}}{2 b^{3} p^{3} + 12 b^{3} p^{2} + 22 b^{3} p + 12 b^{3}} + \frac{a b^{2} p^{2} x^{4} \left(a + b x^{2}\right)^{p}}{2 b^{3} p^{3} + 12 b^{3} p^{2} + 22 b^{3} p + 12 b^{3}} + \frac{a b^{2} p x^{4} \left(a + b x^{2}\right)^{p}}{2 b^{3} p^{3} + 12 b^{3} p^{2} + 22 b^{3} p + 12 b^{3}} + \frac{b^{3} p^{2} x^{6} \left(a + b x^{2}\right)^{p}}{2 b^{3} p^{3} + 12 b^{3} p^{2} + 22 b^{3} p + 12 b^{3}} + \frac{3 b^{3} p x^{6} \left(a + b x^{2}\right)^{p}}{2 b^{3} p^{3} + 12 b^{3} p^{2} + 22 b^{3} p + 12 b^{3}} + \frac{2 b^{3} x^{6} \left(a + b x^{2}\right)^{p}}{2 b^{3} p^{3} + 12 b^{3} p^{2} + 22 b^{3} p + 12 b^{3}} & \text{otherwise} \end{cases}\right) + e^{2} \left(\begin{cases} \frac{a^{p} x^{8}}{8} & \text{for}\: b = 0 \\\frac{6 a^{3} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{12 a^{3} b^{4} + 36 a^{2} b^{5} x^{2} + 36 a b^{6} x^{4} + 12 b^{7} x^{6}} + \frac{6 a^{3} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{12 a^{3} b^{4} + 36 a^{2} b^{5} x^{2} + 36 a b^{6} x^{4} + 12 b^{7} x^{6}} + \frac{11 a^{3}}{12 a^{3} b^{4} + 36 a^{2} b^{5} x^{2} + 36 a b^{6} x^{4} + 12 b^{7} x^{6}} + \frac{18 a^{2} b x^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{12 a^{3} b^{4} + 36 a^{2} b^{5} x^{2} + 36 a b^{6} x^{4} + 12 b^{7} x^{6}} + \frac{18 a^{2} b x^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{12 a^{3} b^{4} + 36 a^{2} b^{5} x^{2} + 36 a b^{6} x^{4} + 12 b^{7} x^{6}} + \frac{27 a^{2} b x^{2}}{12 a^{3} b^{4} + 36 a^{2} b^{5} x^{2} + 36 a b^{6} x^{4} + 12 b^{7} x^{6}} + \frac{18 a b^{2} x^{4} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{12 a^{3} b^{4} + 36 a^{2} b^{5} x^{2} + 36 a b^{6} x^{4} + 12 b^{7} x^{6}} + \frac{18 a b^{2} x^{4} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{12 a^{3} b^{4} + 36 a^{2} b^{5} x^{2} + 36 a b^{6} x^{4} + 12 b^{7} x^{6}} + \frac{18 a b^{2} x^{4}}{12 a^{3} b^{4} + 36 a^{2} b^{5} x^{2} + 36 a b^{6} x^{4} + 12 b^{7} x^{6}} + \frac{6 b^{3} x^{6} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{12 a^{3} b^{4} + 36 a^{2} b^{5} x^{2} + 36 a b^{6} x^{4} + 12 b^{7} x^{6}} + \frac{6 b^{3} x^{6} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{12 a^{3} b^{4} + 36 a^{2} b^{5} x^{2} + 36 a b^{6} x^{4} + 12 b^{7} x^{6}} & \text{for}\: p = -4 \\- \frac{6 a^{3} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{4 a^{2} b^{4} + 8 a b^{5} x^{2} + 4 b^{6} x^{4}} - \frac{6 a^{3} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{4 a^{2} b^{4} + 8 a b^{5} x^{2} + 4 b^{6} x^{4}} - \frac{9 a^{3}}{4 a^{2} b^{4} + 8 a b^{5} x^{2} + 4 b^{6} x^{4}} - \frac{12 a^{2} b x^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{4 a^{2} b^{4} + 8 a b^{5} x^{2} + 4 b^{6} x^{4}} - \frac{12 a^{2} b x^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{4 a^{2} b^{4} + 8 a b^{5} x^{2} + 4 b^{6} x^{4}} - \frac{12 a^{2} b x^{2}}{4 a^{2} b^{4} + 8 a b^{5} x^{2} + 4 b^{6} x^{4}} - \frac{6 a b^{2} x^{4} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{4 a^{2} b^{4} + 8 a b^{5} x^{2} + 4 b^{6} x^{4}} - \frac{6 a b^{2} x^{4} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{4 a^{2} b^{4} + 8 a b^{5} x^{2} + 4 b^{6} x^{4}} + \frac{2 b^{3} x^{6}}{4 a^{2} b^{4} + 8 a b^{5} x^{2} + 4 b^{6} x^{4}} & \text{for}\: p = -3 \\\frac{6 a^{3} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{4 a b^{4} + 4 b^{5} x^{2}} + \frac{6 a^{3} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{4 a b^{4} + 4 b^{5} x^{2}} + \frac{6 a^{3}}{4 a b^{4} + 4 b^{5} x^{2}} + \frac{6 a^{2} b x^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{4 a b^{4} + 4 b^{5} x^{2}} + \frac{6 a^{2} b x^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{4 a b^{4} + 4 b^{5} x^{2}} - \frac{3 a b^{2} x^{4}}{4 a b^{4} + 4 b^{5} x^{2}} + \frac{b^{3} x^{6}}{4 a b^{4} + 4 b^{5} x^{2}} & \text{for}\: p = -2 \\- \frac{a^{3} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 b^{4}} - \frac{a^{3} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 b^{4}} + \frac{a^{2} x^{2}}{2 b^{3}} - \frac{a x^{4}}{4 b^{2}} + \frac{x^{6}}{6 b} & \text{for}\: p = -1 \\- \frac{6 a^{4} \left(a + b x^{2}\right)^{p}}{2 b^{4} p^{4} + 20 b^{4} p^{3} + 70 b^{4} p^{2} + 100 b^{4} p + 48 b^{4}} + \frac{6 a^{3} b p x^{2} \left(a + b x^{2}\right)^{p}}{2 b^{4} p^{4} + 20 b^{4} p^{3} + 70 b^{4} p^{2} + 100 b^{4} p + 48 b^{4}} - \frac{3 a^{2} b^{2} p^{2} x^{4} \left(a + b x^{2}\right)^{p}}{2 b^{4} p^{4} + 20 b^{4} p^{3} + 70 b^{4} p^{2} + 100 b^{4} p + 48 b^{4}} - \frac{3 a^{2} b^{2} p x^{4} \left(a + b x^{2}\right)^{p}}{2 b^{4} p^{4} + 20 b^{4} p^{3} + 70 b^{4} p^{2} + 100 b^{4} p + 48 b^{4}} + \frac{a b^{3} p^{3} x^{6} \left(a + b x^{2}\right)^{p}}{2 b^{4} p^{4} + 20 b^{4} p^{3} + 70 b^{4} p^{2} + 100 b^{4} p + 48 b^{4}} + \frac{3 a b^{3} p^{2} x^{6} \left(a + b x^{2}\right)^{p}}{2 b^{4} p^{4} + 20 b^{4} p^{3} + 70 b^{4} p^{2} + 100 b^{4} p + 48 b^{4}} + \frac{2 a b^{3} p x^{6} \left(a + b x^{2}\right)^{p}}{2 b^{4} p^{4} + 20 b^{4} p^{3} + 70 b^{4} p^{2} + 100 b^{4} p + 48 b^{4}} + \frac{b^{4} p^{3} x^{8} \left(a + b x^{2}\right)^{p}}{2 b^{4} p^{4} + 20 b^{4} p^{3} + 70 b^{4} p^{2} + 100 b^{4} p + 48 b^{4}} + \frac{6 b^{4} p^{2} x^{8} \left(a + b x^{2}\right)^{p}}{2 b^{4} p^{4} + 20 b^{4} p^{3} + 70 b^{4} p^{2} + 100 b^{4} p + 48 b^{4}} + \frac{11 b^{4} p x^{8} \left(a + b x^{2}\right)^{p}}{2 b^{4} p^{4} + 20 b^{4} p^{3} + 70 b^{4} p^{2} + 100 b^{4} p + 48 b^{4}} + \frac{6 b^{4} x^{8} \left(a + b x^{2}\right)^{p}}{2 b^{4} p^{4} + 20 b^{4} p^{3} + 70 b^{4} p^{2} + 100 b^{4} p + 48 b^{4}} & \text{otherwise} \end{cases}\right)"," ",0,"2*a**p*d*e*x**7*hyper((7/2, -p), (9/2,), b*x**2*exp_polar(I*pi)/a)/7 + d**2*Piecewise((a**p*x**6/6, Eq(b, 0)), (2*a**2*log(-I*sqrt(a)*sqrt(1/b) + x)/(4*a**2*b**3 + 8*a*b**4*x**2 + 4*b**5*x**4) + 2*a**2*log(I*sqrt(a)*sqrt(1/b) + x)/(4*a**2*b**3 + 8*a*b**4*x**2 + 4*b**5*x**4) + 3*a**2/(4*a**2*b**3 + 8*a*b**4*x**2 + 4*b**5*x**4) + 4*a*b*x**2*log(-I*sqrt(a)*sqrt(1/b) + x)/(4*a**2*b**3 + 8*a*b**4*x**2 + 4*b**5*x**4) + 4*a*b*x**2*log(I*sqrt(a)*sqrt(1/b) + x)/(4*a**2*b**3 + 8*a*b**4*x**2 + 4*b**5*x**4) + 4*a*b*x**2/(4*a**2*b**3 + 8*a*b**4*x**2 + 4*b**5*x**4) + 2*b**2*x**4*log(-I*sqrt(a)*sqrt(1/b) + x)/(4*a**2*b**3 + 8*a*b**4*x**2 + 4*b**5*x**4) + 2*b**2*x**4*log(I*sqrt(a)*sqrt(1/b) + x)/(4*a**2*b**3 + 8*a*b**4*x**2 + 4*b**5*x**4), Eq(p, -3)), (-2*a**2*log(-I*sqrt(a)*sqrt(1/b) + x)/(2*a*b**3 + 2*b**4*x**2) - 2*a**2*log(I*sqrt(a)*sqrt(1/b) + x)/(2*a*b**3 + 2*b**4*x**2) - 2*a**2/(2*a*b**3 + 2*b**4*x**2) - 2*a*b*x**2*log(-I*sqrt(a)*sqrt(1/b) + x)/(2*a*b**3 + 2*b**4*x**2) - 2*a*b*x**2*log(I*sqrt(a)*sqrt(1/b) + x)/(2*a*b**3 + 2*b**4*x**2) + b**2*x**4/(2*a*b**3 + 2*b**4*x**2), Eq(p, -2)), (a**2*log(-I*sqrt(a)*sqrt(1/b) + x)/(2*b**3) + a**2*log(I*sqrt(a)*sqrt(1/b) + x)/(2*b**3) - a*x**2/(2*b**2) + x**4/(4*b), Eq(p, -1)), (2*a**3*(a + b*x**2)**p/(2*b**3*p**3 + 12*b**3*p**2 + 22*b**3*p + 12*b**3) - 2*a**2*b*p*x**2*(a + b*x**2)**p/(2*b**3*p**3 + 12*b**3*p**2 + 22*b**3*p + 12*b**3) + a*b**2*p**2*x**4*(a + b*x**2)**p/(2*b**3*p**3 + 12*b**3*p**2 + 22*b**3*p + 12*b**3) + a*b**2*p*x**4*(a + b*x**2)**p/(2*b**3*p**3 + 12*b**3*p**2 + 22*b**3*p + 12*b**3) + b**3*p**2*x**6*(a + b*x**2)**p/(2*b**3*p**3 + 12*b**3*p**2 + 22*b**3*p + 12*b**3) + 3*b**3*p*x**6*(a + b*x**2)**p/(2*b**3*p**3 + 12*b**3*p**2 + 22*b**3*p + 12*b**3) + 2*b**3*x**6*(a + b*x**2)**p/(2*b**3*p**3 + 12*b**3*p**2 + 22*b**3*p + 12*b**3), True)) + e**2*Piecewise((a**p*x**8/8, Eq(b, 0)), (6*a**3*log(-I*sqrt(a)*sqrt(1/b) + x)/(12*a**3*b**4 + 36*a**2*b**5*x**2 + 36*a*b**6*x**4 + 12*b**7*x**6) + 6*a**3*log(I*sqrt(a)*sqrt(1/b) + x)/(12*a**3*b**4 + 36*a**2*b**5*x**2 + 36*a*b**6*x**4 + 12*b**7*x**6) + 11*a**3/(12*a**3*b**4 + 36*a**2*b**5*x**2 + 36*a*b**6*x**4 + 12*b**7*x**6) + 18*a**2*b*x**2*log(-I*sqrt(a)*sqrt(1/b) + x)/(12*a**3*b**4 + 36*a**2*b**5*x**2 + 36*a*b**6*x**4 + 12*b**7*x**6) + 18*a**2*b*x**2*log(I*sqrt(a)*sqrt(1/b) + x)/(12*a**3*b**4 + 36*a**2*b**5*x**2 + 36*a*b**6*x**4 + 12*b**7*x**6) + 27*a**2*b*x**2/(12*a**3*b**4 + 36*a**2*b**5*x**2 + 36*a*b**6*x**4 + 12*b**7*x**6) + 18*a*b**2*x**4*log(-I*sqrt(a)*sqrt(1/b) + x)/(12*a**3*b**4 + 36*a**2*b**5*x**2 + 36*a*b**6*x**4 + 12*b**7*x**6) + 18*a*b**2*x**4*log(I*sqrt(a)*sqrt(1/b) + x)/(12*a**3*b**4 + 36*a**2*b**5*x**2 + 36*a*b**6*x**4 + 12*b**7*x**6) + 18*a*b**2*x**4/(12*a**3*b**4 + 36*a**2*b**5*x**2 + 36*a*b**6*x**4 + 12*b**7*x**6) + 6*b**3*x**6*log(-I*sqrt(a)*sqrt(1/b) + x)/(12*a**3*b**4 + 36*a**2*b**5*x**2 + 36*a*b**6*x**4 + 12*b**7*x**6) + 6*b**3*x**6*log(I*sqrt(a)*sqrt(1/b) + x)/(12*a**3*b**4 + 36*a**2*b**5*x**2 + 36*a*b**6*x**4 + 12*b**7*x**6), Eq(p, -4)), (-6*a**3*log(-I*sqrt(a)*sqrt(1/b) + x)/(4*a**2*b**4 + 8*a*b**5*x**2 + 4*b**6*x**4) - 6*a**3*log(I*sqrt(a)*sqrt(1/b) + x)/(4*a**2*b**4 + 8*a*b**5*x**2 + 4*b**6*x**4) - 9*a**3/(4*a**2*b**4 + 8*a*b**5*x**2 + 4*b**6*x**4) - 12*a**2*b*x**2*log(-I*sqrt(a)*sqrt(1/b) + x)/(4*a**2*b**4 + 8*a*b**5*x**2 + 4*b**6*x**4) - 12*a**2*b*x**2*log(I*sqrt(a)*sqrt(1/b) + x)/(4*a**2*b**4 + 8*a*b**5*x**2 + 4*b**6*x**4) - 12*a**2*b*x**2/(4*a**2*b**4 + 8*a*b**5*x**2 + 4*b**6*x**4) - 6*a*b**2*x**4*log(-I*sqrt(a)*sqrt(1/b) + x)/(4*a**2*b**4 + 8*a*b**5*x**2 + 4*b**6*x**4) - 6*a*b**2*x**4*log(I*sqrt(a)*sqrt(1/b) + x)/(4*a**2*b**4 + 8*a*b**5*x**2 + 4*b**6*x**4) + 2*b**3*x**6/(4*a**2*b**4 + 8*a*b**5*x**2 + 4*b**6*x**4), Eq(p, -3)), (6*a**3*log(-I*sqrt(a)*sqrt(1/b) + x)/(4*a*b**4 + 4*b**5*x**2) + 6*a**3*log(I*sqrt(a)*sqrt(1/b) + x)/(4*a*b**4 + 4*b**5*x**2) + 6*a**3/(4*a*b**4 + 4*b**5*x**2) + 6*a**2*b*x**2*log(-I*sqrt(a)*sqrt(1/b) + x)/(4*a*b**4 + 4*b**5*x**2) + 6*a**2*b*x**2*log(I*sqrt(a)*sqrt(1/b) + x)/(4*a*b**4 + 4*b**5*x**2) - 3*a*b**2*x**4/(4*a*b**4 + 4*b**5*x**2) + b**3*x**6/(4*a*b**4 + 4*b**5*x**2), Eq(p, -2)), (-a**3*log(-I*sqrt(a)*sqrt(1/b) + x)/(2*b**4) - a**3*log(I*sqrt(a)*sqrt(1/b) + x)/(2*b**4) + a**2*x**2/(2*b**3) - a*x**4/(4*b**2) + x**6/(6*b), Eq(p, -1)), (-6*a**4*(a + b*x**2)**p/(2*b**4*p**4 + 20*b**4*p**3 + 70*b**4*p**2 + 100*b**4*p + 48*b**4) + 6*a**3*b*p*x**2*(a + b*x**2)**p/(2*b**4*p**4 + 20*b**4*p**3 + 70*b**4*p**2 + 100*b**4*p + 48*b**4) - 3*a**2*b**2*p**2*x**4*(a + b*x**2)**p/(2*b**4*p**4 + 20*b**4*p**3 + 70*b**4*p**2 + 100*b**4*p + 48*b**4) - 3*a**2*b**2*p*x**4*(a + b*x**2)**p/(2*b**4*p**4 + 20*b**4*p**3 + 70*b**4*p**2 + 100*b**4*p + 48*b**4) + a*b**3*p**3*x**6*(a + b*x**2)**p/(2*b**4*p**4 + 20*b**4*p**3 + 70*b**4*p**2 + 100*b**4*p + 48*b**4) + 3*a*b**3*p**2*x**6*(a + b*x**2)**p/(2*b**4*p**4 + 20*b**4*p**3 + 70*b**4*p**2 + 100*b**4*p + 48*b**4) + 2*a*b**3*p*x**6*(a + b*x**2)**p/(2*b**4*p**4 + 20*b**4*p**3 + 70*b**4*p**2 + 100*b**4*p + 48*b**4) + b**4*p**3*x**8*(a + b*x**2)**p/(2*b**4*p**4 + 20*b**4*p**3 + 70*b**4*p**2 + 100*b**4*p + 48*b**4) + 6*b**4*p**2*x**8*(a + b*x**2)**p/(2*b**4*p**4 + 20*b**4*p**3 + 70*b**4*p**2 + 100*b**4*p + 48*b**4) + 11*b**4*p*x**8*(a + b*x**2)**p/(2*b**4*p**4 + 20*b**4*p**3 + 70*b**4*p**2 + 100*b**4*p + 48*b**4) + 6*b**4*x**8*(a + b*x**2)**p/(2*b**4*p**4 + 20*b**4*p**3 + 70*b**4*p**2 + 100*b**4*p + 48*b**4), True))","C",0
391,1,1047,0,38.893372," ","integrate(x**4*(e*x+d)**2*(b*x**2+a)**p,x)","\frac{a^{p} d^{2} x^{5} {{}_{2}F_{1}\left(\begin{matrix} \frac{5}{2}, - p \\ \frac{7}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{5} + \frac{a^{p} e^{2} x^{7} {{}_{2}F_{1}\left(\begin{matrix} \frac{7}{2}, - p \\ \frac{9}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{7} + 2 d e \left(\begin{cases} \frac{a^{p} x^{6}}{6} & \text{for}\: b = 0 \\\frac{2 a^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{4 a^{2} b^{3} + 8 a b^{4} x^{2} + 4 b^{5} x^{4}} + \frac{2 a^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{4 a^{2} b^{3} + 8 a b^{4} x^{2} + 4 b^{5} x^{4}} + \frac{3 a^{2}}{4 a^{2} b^{3} + 8 a b^{4} x^{2} + 4 b^{5} x^{4}} + \frac{4 a b x^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{4 a^{2} b^{3} + 8 a b^{4} x^{2} + 4 b^{5} x^{4}} + \frac{4 a b x^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{4 a^{2} b^{3} + 8 a b^{4} x^{2} + 4 b^{5} x^{4}} + \frac{4 a b x^{2}}{4 a^{2} b^{3} + 8 a b^{4} x^{2} + 4 b^{5} x^{4}} + \frac{2 b^{2} x^{4} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{4 a^{2} b^{3} + 8 a b^{4} x^{2} + 4 b^{5} x^{4}} + \frac{2 b^{2} x^{4} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{4 a^{2} b^{3} + 8 a b^{4} x^{2} + 4 b^{5} x^{4}} & \text{for}\: p = -3 \\- \frac{2 a^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 a b^{3} + 2 b^{4} x^{2}} - \frac{2 a^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 a b^{3} + 2 b^{4} x^{2}} - \frac{2 a^{2}}{2 a b^{3} + 2 b^{4} x^{2}} - \frac{2 a b x^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 a b^{3} + 2 b^{4} x^{2}} - \frac{2 a b x^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 a b^{3} + 2 b^{4} x^{2}} + \frac{b^{2} x^{4}}{2 a b^{3} + 2 b^{4} x^{2}} & \text{for}\: p = -2 \\\frac{a^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 b^{3}} + \frac{a^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 b^{3}} - \frac{a x^{2}}{2 b^{2}} + \frac{x^{4}}{4 b} & \text{for}\: p = -1 \\\frac{2 a^{3} \left(a + b x^{2}\right)^{p}}{2 b^{3} p^{3} + 12 b^{3} p^{2} + 22 b^{3} p + 12 b^{3}} - \frac{2 a^{2} b p x^{2} \left(a + b x^{2}\right)^{p}}{2 b^{3} p^{3} + 12 b^{3} p^{2} + 22 b^{3} p + 12 b^{3}} + \frac{a b^{2} p^{2} x^{4} \left(a + b x^{2}\right)^{p}}{2 b^{3} p^{3} + 12 b^{3} p^{2} + 22 b^{3} p + 12 b^{3}} + \frac{a b^{2} p x^{4} \left(a + b x^{2}\right)^{p}}{2 b^{3} p^{3} + 12 b^{3} p^{2} + 22 b^{3} p + 12 b^{3}} + \frac{b^{3} p^{2} x^{6} \left(a + b x^{2}\right)^{p}}{2 b^{3} p^{3} + 12 b^{3} p^{2} + 22 b^{3} p + 12 b^{3}} + \frac{3 b^{3} p x^{6} \left(a + b x^{2}\right)^{p}}{2 b^{3} p^{3} + 12 b^{3} p^{2} + 22 b^{3} p + 12 b^{3}} + \frac{2 b^{3} x^{6} \left(a + b x^{2}\right)^{p}}{2 b^{3} p^{3} + 12 b^{3} p^{2} + 22 b^{3} p + 12 b^{3}} & \text{otherwise} \end{cases}\right)"," ",0,"a**p*d**2*x**5*hyper((5/2, -p), (7/2,), b*x**2*exp_polar(I*pi)/a)/5 + a**p*e**2*x**7*hyper((7/2, -p), (9/2,), b*x**2*exp_polar(I*pi)/a)/7 + 2*d*e*Piecewise((a**p*x**6/6, Eq(b, 0)), (2*a**2*log(-I*sqrt(a)*sqrt(1/b) + x)/(4*a**2*b**3 + 8*a*b**4*x**2 + 4*b**5*x**4) + 2*a**2*log(I*sqrt(a)*sqrt(1/b) + x)/(4*a**2*b**3 + 8*a*b**4*x**2 + 4*b**5*x**4) + 3*a**2/(4*a**2*b**3 + 8*a*b**4*x**2 + 4*b**5*x**4) + 4*a*b*x**2*log(-I*sqrt(a)*sqrt(1/b) + x)/(4*a**2*b**3 + 8*a*b**4*x**2 + 4*b**5*x**4) + 4*a*b*x**2*log(I*sqrt(a)*sqrt(1/b) + x)/(4*a**2*b**3 + 8*a*b**4*x**2 + 4*b**5*x**4) + 4*a*b*x**2/(4*a**2*b**3 + 8*a*b**4*x**2 + 4*b**5*x**4) + 2*b**2*x**4*log(-I*sqrt(a)*sqrt(1/b) + x)/(4*a**2*b**3 + 8*a*b**4*x**2 + 4*b**5*x**4) + 2*b**2*x**4*log(I*sqrt(a)*sqrt(1/b) + x)/(4*a**2*b**3 + 8*a*b**4*x**2 + 4*b**5*x**4), Eq(p, -3)), (-2*a**2*log(-I*sqrt(a)*sqrt(1/b) + x)/(2*a*b**3 + 2*b**4*x**2) - 2*a**2*log(I*sqrt(a)*sqrt(1/b) + x)/(2*a*b**3 + 2*b**4*x**2) - 2*a**2/(2*a*b**3 + 2*b**4*x**2) - 2*a*b*x**2*log(-I*sqrt(a)*sqrt(1/b) + x)/(2*a*b**3 + 2*b**4*x**2) - 2*a*b*x**2*log(I*sqrt(a)*sqrt(1/b) + x)/(2*a*b**3 + 2*b**4*x**2) + b**2*x**4/(2*a*b**3 + 2*b**4*x**2), Eq(p, -2)), (a**2*log(-I*sqrt(a)*sqrt(1/b) + x)/(2*b**3) + a**2*log(I*sqrt(a)*sqrt(1/b) + x)/(2*b**3) - a*x**2/(2*b**2) + x**4/(4*b), Eq(p, -1)), (2*a**3*(a + b*x**2)**p/(2*b**3*p**3 + 12*b**3*p**2 + 22*b**3*p + 12*b**3) - 2*a**2*b*p*x**2*(a + b*x**2)**p/(2*b**3*p**3 + 12*b**3*p**2 + 22*b**3*p + 12*b**3) + a*b**2*p**2*x**4*(a + b*x**2)**p/(2*b**3*p**3 + 12*b**3*p**2 + 22*b**3*p + 12*b**3) + a*b**2*p*x**4*(a + b*x**2)**p/(2*b**3*p**3 + 12*b**3*p**2 + 22*b**3*p + 12*b**3) + b**3*p**2*x**6*(a + b*x**2)**p/(2*b**3*p**3 + 12*b**3*p**2 + 22*b**3*p + 12*b**3) + 3*b**3*p*x**6*(a + b*x**2)**p/(2*b**3*p**3 + 12*b**3*p**2 + 22*b**3*p + 12*b**3) + 2*b**3*x**6*(a + b*x**2)**p/(2*b**3*p**3 + 12*b**3*p**2 + 22*b**3*p + 12*b**3), True))","C",0
392,1,1386,0,25.946085," ","integrate(x**3*(e*x+d)**2*(b*x**2+a)**p,x)","\frac{2 a^{p} d e x^{5} {{}_{2}F_{1}\left(\begin{matrix} \frac{5}{2}, - p \\ \frac{7}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{5} + d^{2} \left(\begin{cases} \frac{a^{p} x^{4}}{4} & \text{for}\: b = 0 \\\frac{a \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 a b^{2} + 2 b^{3} x^{2}} + \frac{a \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 a b^{2} + 2 b^{3} x^{2}} + \frac{a}{2 a b^{2} + 2 b^{3} x^{2}} + \frac{b x^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 a b^{2} + 2 b^{3} x^{2}} + \frac{b x^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 a b^{2} + 2 b^{3} x^{2}} & \text{for}\: p = -2 \\- \frac{a \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 b^{2}} - \frac{a \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 b^{2}} + \frac{x^{2}}{2 b} & \text{for}\: p = -1 \\- \frac{a^{2} \left(a + b x^{2}\right)^{p}}{2 b^{2} p^{2} + 6 b^{2} p + 4 b^{2}} + \frac{a b p x^{2} \left(a + b x^{2}\right)^{p}}{2 b^{2} p^{2} + 6 b^{2} p + 4 b^{2}} + \frac{b^{2} p x^{4} \left(a + b x^{2}\right)^{p}}{2 b^{2} p^{2} + 6 b^{2} p + 4 b^{2}} + \frac{b^{2} x^{4} \left(a + b x^{2}\right)^{p}}{2 b^{2} p^{2} + 6 b^{2} p + 4 b^{2}} & \text{otherwise} \end{cases}\right) + e^{2} \left(\begin{cases} \frac{a^{p} x^{6}}{6} & \text{for}\: b = 0 \\\frac{2 a^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{4 a^{2} b^{3} + 8 a b^{4} x^{2} + 4 b^{5} x^{4}} + \frac{2 a^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{4 a^{2} b^{3} + 8 a b^{4} x^{2} + 4 b^{5} x^{4}} + \frac{3 a^{2}}{4 a^{2} b^{3} + 8 a b^{4} x^{2} + 4 b^{5} x^{4}} + \frac{4 a b x^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{4 a^{2} b^{3} + 8 a b^{4} x^{2} + 4 b^{5} x^{4}} + \frac{4 a b x^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{4 a^{2} b^{3} + 8 a b^{4} x^{2} + 4 b^{5} x^{4}} + \frac{4 a b x^{2}}{4 a^{2} b^{3} + 8 a b^{4} x^{2} + 4 b^{5} x^{4}} + \frac{2 b^{2} x^{4} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{4 a^{2} b^{3} + 8 a b^{4} x^{2} + 4 b^{5} x^{4}} + \frac{2 b^{2} x^{4} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{4 a^{2} b^{3} + 8 a b^{4} x^{2} + 4 b^{5} x^{4}} & \text{for}\: p = -3 \\- \frac{2 a^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 a b^{3} + 2 b^{4} x^{2}} - \frac{2 a^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 a b^{3} + 2 b^{4} x^{2}} - \frac{2 a^{2}}{2 a b^{3} + 2 b^{4} x^{2}} - \frac{2 a b x^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 a b^{3} + 2 b^{4} x^{2}} - \frac{2 a b x^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 a b^{3} + 2 b^{4} x^{2}} + \frac{b^{2} x^{4}}{2 a b^{3} + 2 b^{4} x^{2}} & \text{for}\: p = -2 \\\frac{a^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 b^{3}} + \frac{a^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 b^{3}} - \frac{a x^{2}}{2 b^{2}} + \frac{x^{4}}{4 b} & \text{for}\: p = -1 \\\frac{2 a^{3} \left(a + b x^{2}\right)^{p}}{2 b^{3} p^{3} + 12 b^{3} p^{2} + 22 b^{3} p + 12 b^{3}} - \frac{2 a^{2} b p x^{2} \left(a + b x^{2}\right)^{p}}{2 b^{3} p^{3} + 12 b^{3} p^{2} + 22 b^{3} p + 12 b^{3}} + \frac{a b^{2} p^{2} x^{4} \left(a + b x^{2}\right)^{p}}{2 b^{3} p^{3} + 12 b^{3} p^{2} + 22 b^{3} p + 12 b^{3}} + \frac{a b^{2} p x^{4} \left(a + b x^{2}\right)^{p}}{2 b^{3} p^{3} + 12 b^{3} p^{2} + 22 b^{3} p + 12 b^{3}} + \frac{b^{3} p^{2} x^{6} \left(a + b x^{2}\right)^{p}}{2 b^{3} p^{3} + 12 b^{3} p^{2} + 22 b^{3} p + 12 b^{3}} + \frac{3 b^{3} p x^{6} \left(a + b x^{2}\right)^{p}}{2 b^{3} p^{3} + 12 b^{3} p^{2} + 22 b^{3} p + 12 b^{3}} + \frac{2 b^{3} x^{6} \left(a + b x^{2}\right)^{p}}{2 b^{3} p^{3} + 12 b^{3} p^{2} + 22 b^{3} p + 12 b^{3}} & \text{otherwise} \end{cases}\right)"," ",0,"2*a**p*d*e*x**5*hyper((5/2, -p), (7/2,), b*x**2*exp_polar(I*pi)/a)/5 + d**2*Piecewise((a**p*x**4/4, Eq(b, 0)), (a*log(-I*sqrt(a)*sqrt(1/b) + x)/(2*a*b**2 + 2*b**3*x**2) + a*log(I*sqrt(a)*sqrt(1/b) + x)/(2*a*b**2 + 2*b**3*x**2) + a/(2*a*b**2 + 2*b**3*x**2) + b*x**2*log(-I*sqrt(a)*sqrt(1/b) + x)/(2*a*b**2 + 2*b**3*x**2) + b*x**2*log(I*sqrt(a)*sqrt(1/b) + x)/(2*a*b**2 + 2*b**3*x**2), Eq(p, -2)), (-a*log(-I*sqrt(a)*sqrt(1/b) + x)/(2*b**2) - a*log(I*sqrt(a)*sqrt(1/b) + x)/(2*b**2) + x**2/(2*b), Eq(p, -1)), (-a**2*(a + b*x**2)**p/(2*b**2*p**2 + 6*b**2*p + 4*b**2) + a*b*p*x**2*(a + b*x**2)**p/(2*b**2*p**2 + 6*b**2*p + 4*b**2) + b**2*p*x**4*(a + b*x**2)**p/(2*b**2*p**2 + 6*b**2*p + 4*b**2) + b**2*x**4*(a + b*x**2)**p/(2*b**2*p**2 + 6*b**2*p + 4*b**2), True)) + e**2*Piecewise((a**p*x**6/6, Eq(b, 0)), (2*a**2*log(-I*sqrt(a)*sqrt(1/b) + x)/(4*a**2*b**3 + 8*a*b**4*x**2 + 4*b**5*x**4) + 2*a**2*log(I*sqrt(a)*sqrt(1/b) + x)/(4*a**2*b**3 + 8*a*b**4*x**2 + 4*b**5*x**4) + 3*a**2/(4*a**2*b**3 + 8*a*b**4*x**2 + 4*b**5*x**4) + 4*a*b*x**2*log(-I*sqrt(a)*sqrt(1/b) + x)/(4*a**2*b**3 + 8*a*b**4*x**2 + 4*b**5*x**4) + 4*a*b*x**2*log(I*sqrt(a)*sqrt(1/b) + x)/(4*a**2*b**3 + 8*a*b**4*x**2 + 4*b**5*x**4) + 4*a*b*x**2/(4*a**2*b**3 + 8*a*b**4*x**2 + 4*b**5*x**4) + 2*b**2*x**4*log(-I*sqrt(a)*sqrt(1/b) + x)/(4*a**2*b**3 + 8*a*b**4*x**2 + 4*b**5*x**4) + 2*b**2*x**4*log(I*sqrt(a)*sqrt(1/b) + x)/(4*a**2*b**3 + 8*a*b**4*x**2 + 4*b**5*x**4), Eq(p, -3)), (-2*a**2*log(-I*sqrt(a)*sqrt(1/b) + x)/(2*a*b**3 + 2*b**4*x**2) - 2*a**2*log(I*sqrt(a)*sqrt(1/b) + x)/(2*a*b**3 + 2*b**4*x**2) - 2*a**2/(2*a*b**3 + 2*b**4*x**2) - 2*a*b*x**2*log(-I*sqrt(a)*sqrt(1/b) + x)/(2*a*b**3 + 2*b**4*x**2) - 2*a*b*x**2*log(I*sqrt(a)*sqrt(1/b) + x)/(2*a*b**3 + 2*b**4*x**2) + b**2*x**4/(2*a*b**3 + 2*b**4*x**2), Eq(p, -2)), (a**2*log(-I*sqrt(a)*sqrt(1/b) + x)/(2*b**3) + a**2*log(I*sqrt(a)*sqrt(1/b) + x)/(2*b**3) - a*x**2/(2*b**2) + x**4/(4*b), Eq(p, -1)), (2*a**3*(a + b*x**2)**p/(2*b**3*p**3 + 12*b**3*p**2 + 22*b**3*p + 12*b**3) - 2*a**2*b*p*x**2*(a + b*x**2)**p/(2*b**3*p**3 + 12*b**3*p**2 + 22*b**3*p + 12*b**3) + a*b**2*p**2*x**4*(a + b*x**2)**p/(2*b**3*p**3 + 12*b**3*p**2 + 22*b**3*p + 12*b**3) + a*b**2*p*x**4*(a + b*x**2)**p/(2*b**3*p**3 + 12*b**3*p**2 + 22*b**3*p + 12*b**3) + b**3*p**2*x**6*(a + b*x**2)**p/(2*b**3*p**3 + 12*b**3*p**2 + 22*b**3*p + 12*b**3) + 3*b**3*p*x**6*(a + b*x**2)**p/(2*b**3*p**3 + 12*b**3*p**2 + 22*b**3*p + 12*b**3) + 2*b**3*x**6*(a + b*x**2)**p/(2*b**3*p**3 + 12*b**3*p**2 + 22*b**3*p + 12*b**3), True))","C",0
393,1,430,0,21.177800," ","integrate(x**2*(e*x+d)**2*(b*x**2+a)**p,x)","\frac{a^{p} d^{2} x^{3} {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{2}, - p \\ \frac{5}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{3} + \frac{a^{p} e^{2} x^{5} {{}_{2}F_{1}\left(\begin{matrix} \frac{5}{2}, - p \\ \frac{7}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{5} + 2 d e \left(\begin{cases} \frac{a^{p} x^{4}}{4} & \text{for}\: b = 0 \\\frac{a \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 a b^{2} + 2 b^{3} x^{2}} + \frac{a \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 a b^{2} + 2 b^{3} x^{2}} + \frac{a}{2 a b^{2} + 2 b^{3} x^{2}} + \frac{b x^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 a b^{2} + 2 b^{3} x^{2}} + \frac{b x^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 a b^{2} + 2 b^{3} x^{2}} & \text{for}\: p = -2 \\- \frac{a \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 b^{2}} - \frac{a \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 b^{2}} + \frac{x^{2}}{2 b} & \text{for}\: p = -1 \\- \frac{a^{2} \left(a + b x^{2}\right)^{p}}{2 b^{2} p^{2} + 6 b^{2} p + 4 b^{2}} + \frac{a b p x^{2} \left(a + b x^{2}\right)^{p}}{2 b^{2} p^{2} + 6 b^{2} p + 4 b^{2}} + \frac{b^{2} p x^{4} \left(a + b x^{2}\right)^{p}}{2 b^{2} p^{2} + 6 b^{2} p + 4 b^{2}} + \frac{b^{2} x^{4} \left(a + b x^{2}\right)^{p}}{2 b^{2} p^{2} + 6 b^{2} p + 4 b^{2}} & \text{otherwise} \end{cases}\right)"," ",0,"a**p*d**2*x**3*hyper((3/2, -p), (5/2,), b*x**2*exp_polar(I*pi)/a)/3 + a**p*e**2*x**5*hyper((5/2, -p), (7/2,), b*x**2*exp_polar(I*pi)/a)/5 + 2*d*e*Piecewise((a**p*x**4/4, Eq(b, 0)), (a*log(-I*sqrt(a)*sqrt(1/b) + x)/(2*a*b**2 + 2*b**3*x**2) + a*log(I*sqrt(a)*sqrt(1/b) + x)/(2*a*b**2 + 2*b**3*x**2) + a/(2*a*b**2 + 2*b**3*x**2) + b*x**2*log(-I*sqrt(a)*sqrt(1/b) + x)/(2*a*b**2 + 2*b**3*x**2) + b*x**2*log(I*sqrt(a)*sqrt(1/b) + x)/(2*a*b**2 + 2*b**3*x**2), Eq(p, -2)), (-a*log(-I*sqrt(a)*sqrt(1/b) + x)/(2*b**2) - a*log(I*sqrt(a)*sqrt(1/b) + x)/(2*b**2) + x**2/(2*b), Eq(p, -1)), (-a**2*(a + b*x**2)**p/(2*b**2*p**2 + 6*b**2*p + 4*b**2) + a*b*p*x**2*(a + b*x**2)**p/(2*b**2*p**2 + 6*b**2*p + 4*b**2) + b**2*p*x**4*(a + b*x**2)**p/(2*b**2*p**2 + 6*b**2*p + 4*b**2) + b**2*x**4*(a + b*x**2)**p/(2*b**2*p**2 + 6*b**2*p + 4*b**2), True))","C",0
394,1,439,0,12.909005," ","integrate(x*(e*x+d)**2*(b*x**2+a)**p,x)","\frac{2 a^{p} d e x^{3} {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{2}, - p \\ \frac{5}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{3} + d^{2} \left(\begin{cases} \frac{a^{p} x^{2}}{2} & \text{for}\: b = 0 \\\frac{\begin{cases} \frac{\left(a + b x^{2}\right)^{p + 1}}{p + 1} & \text{for}\: p \neq -1 \\\log{\left(a + b x^{2} \right)} & \text{otherwise} \end{cases}}{2 b} & \text{otherwise} \end{cases}\right) + e^{2} \left(\begin{cases} \frac{a^{p} x^{4}}{4} & \text{for}\: b = 0 \\\frac{a \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 a b^{2} + 2 b^{3} x^{2}} + \frac{a \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 a b^{2} + 2 b^{3} x^{2}} + \frac{a}{2 a b^{2} + 2 b^{3} x^{2}} + \frac{b x^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 a b^{2} + 2 b^{3} x^{2}} + \frac{b x^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 a b^{2} + 2 b^{3} x^{2}} & \text{for}\: p = -2 \\- \frac{a \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 b^{2}} - \frac{a \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 b^{2}} + \frac{x^{2}}{2 b} & \text{for}\: p = -1 \\- \frac{a^{2} \left(a + b x^{2}\right)^{p}}{2 b^{2} p^{2} + 6 b^{2} p + 4 b^{2}} + \frac{a b p x^{2} \left(a + b x^{2}\right)^{p}}{2 b^{2} p^{2} + 6 b^{2} p + 4 b^{2}} + \frac{b^{2} p x^{4} \left(a + b x^{2}\right)^{p}}{2 b^{2} p^{2} + 6 b^{2} p + 4 b^{2}} + \frac{b^{2} x^{4} \left(a + b x^{2}\right)^{p}}{2 b^{2} p^{2} + 6 b^{2} p + 4 b^{2}} & \text{otherwise} \end{cases}\right)"," ",0,"2*a**p*d*e*x**3*hyper((3/2, -p), (5/2,), b*x**2*exp_polar(I*pi)/a)/3 + d**2*Piecewise((a**p*x**2/2, Eq(b, 0)), (Piecewise(((a + b*x**2)**(p + 1)/(p + 1), Ne(p, -1)), (log(a + b*x**2), True))/(2*b), True)) + e**2*Piecewise((a**p*x**4/4, Eq(b, 0)), (a*log(-I*sqrt(a)*sqrt(1/b) + x)/(2*a*b**2 + 2*b**3*x**2) + a*log(I*sqrt(a)*sqrt(1/b) + x)/(2*a*b**2 + 2*b**3*x**2) + a/(2*a*b**2 + 2*b**3*x**2) + b*x**2*log(-I*sqrt(a)*sqrt(1/b) + x)/(2*a*b**2 + 2*b**3*x**2) + b*x**2*log(I*sqrt(a)*sqrt(1/b) + x)/(2*a*b**2 + 2*b**3*x**2), Eq(p, -2)), (-a*log(-I*sqrt(a)*sqrt(1/b) + x)/(2*b**2) - a*log(I*sqrt(a)*sqrt(1/b) + x)/(2*b**2) + x**2/(2*b), Eq(p, -1)), (-a**2*(a + b*x**2)**p/(2*b**2*p**2 + 6*b**2*p + 4*b**2) + a*b*p*x**2*(a + b*x**2)**p/(2*b**2*p**2 + 6*b**2*p + 4*b**2) + b**2*p*x**4*(a + b*x**2)**p/(2*b**2*p**2 + 6*b**2*p + 4*b**2) + b**2*x**4*(a + b*x**2)**p/(2*b**2*p**2 + 6*b**2*p + 4*b**2), True))","A",0
395,1,97,0,11.608959," ","integrate((e*x+d)**2*(b*x**2+a)**p,x)","a^{p} d^{2} x {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, - p \\ \frac{3}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)} + \frac{a^{p} e^{2} x^{3} {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{2}, - p \\ \frac{5}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{3} + 2 d e \left(\begin{cases} \frac{a^{p} x^{2}}{2} & \text{for}\: b = 0 \\\frac{\begin{cases} \frac{\left(a + b x^{2}\right)^{p + 1}}{p + 1} & \text{for}\: p \neq -1 \\\log{\left(a + b x^{2} \right)} & \text{otherwise} \end{cases}}{2 b} & \text{otherwise} \end{cases}\right)"," ",0,"a**p*d**2*x*hyper((1/2, -p), (3/2,), b*x**2*exp_polar(I*pi)/a) + a**p*e**2*x**3*hyper((3/2, -p), (5/2,), b*x**2*exp_polar(I*pi)/a)/3 + 2*d*e*Piecewise((a**p*x**2/2, Eq(b, 0)), (Piecewise(((a + b*x**2)**(p + 1)/(p + 1), Ne(p, -1)), (log(a + b*x**2), True))/(2*b), True))","A",0
396,1,109,0,12.064382," ","integrate((e*x+d)**2*(b*x**2+a)**p/x,x)","2 a^{p} d e x {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, - p \\ \frac{3}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)} - \frac{b^{p} d^{2} x^{2 p} \Gamma\left(- p\right) {{}_{2}F_{1}\left(\begin{matrix} - p, - p \\ 1 - p \end{matrix}\middle| {\frac{a e^{i \pi}}{b x^{2}}} \right)}}{2 \Gamma\left(1 - p\right)} + e^{2} \left(\begin{cases} \frac{a^{p} x^{2}}{2} & \text{for}\: b = 0 \\\frac{\begin{cases} \frac{\left(a + b x^{2}\right)^{p + 1}}{p + 1} & \text{for}\: p \neq -1 \\\log{\left(a + b x^{2} \right)} & \text{otherwise} \end{cases}}{2 b} & \text{otherwise} \end{cases}\right)"," ",0,"2*a**p*d*e*x*hyper((1/2, -p), (3/2,), b*x**2*exp_polar(I*pi)/a) - b**p*d**2*x**(2*p)*gamma(-p)*hyper((-p, -p), (1 - p,), a*exp_polar(I*pi)/(b*x**2))/(2*gamma(1 - p)) + e**2*Piecewise((a**p*x**2/2, Eq(b, 0)), (Piecewise(((a + b*x**2)**(p + 1)/(p + 1), Ne(p, -1)), (log(a + b*x**2), True))/(2*b), True))","A",0
397,1,95,0,13.566885," ","integrate((e*x+d)**2*(b*x**2+a)**p/x**2,x)","- \frac{a^{p} d^{2} {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, - p \\ \frac{1}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{x} + a^{p} e^{2} x {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, - p \\ \frac{3}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)} - \frac{b^{p} d e x^{2 p} \Gamma\left(- p\right) {{}_{2}F_{1}\left(\begin{matrix} - p, - p \\ 1 - p \end{matrix}\middle| {\frac{a e^{i \pi}}{b x^{2}}} \right)}}{\Gamma\left(1 - p\right)}"," ",0,"-a**p*d**2*hyper((-1/2, -p), (1/2,), b*x**2*exp_polar(I*pi)/a)/x + a**p*e**2*x*hyper((1/2, -p), (3/2,), b*x**2*exp_polar(I*pi)/a) - b**p*d*e*x**(2*p)*gamma(-p)*hyper((-p, -p), (1 - p,), a*exp_polar(I*pi)/(b*x**2))/gamma(1 - p)","C",0
398,1,119,0,18.620643," ","integrate((e*x+d)**2*(b*x**2+a)**p/x**3,x)","- \frac{2 a^{p} d e {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, - p \\ \frac{1}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{x} - \frac{b^{p} d^{2} x^{2 p} \Gamma\left(1 - p\right) {{}_{2}F_{1}\left(\begin{matrix} - p, 1 - p \\ 2 - p \end{matrix}\middle| {\frac{a e^{i \pi}}{b x^{2}}} \right)}}{2 x^{2} \Gamma\left(2 - p\right)} - \frac{b^{p} e^{2} x^{2 p} \Gamma\left(- p\right) {{}_{2}F_{1}\left(\begin{matrix} - p, - p \\ 1 - p \end{matrix}\middle| {\frac{a e^{i \pi}}{b x^{2}}} \right)}}{2 \Gamma\left(1 - p\right)}"," ",0,"-2*a**p*d*e*hyper((-1/2, -p), (1/2,), b*x**2*exp_polar(I*pi)/a)/x - b**p*d**2*x**(2*p)*gamma(1 - p)*hyper((-p, 1 - p), (2 - p,), a*exp_polar(I*pi)/(b*x**2))/(2*x**2*gamma(2 - p)) - b**p*e**2*x**(2*p)*gamma(-p)*hyper((-p, -p), (1 - p,), a*exp_polar(I*pi)/(b*x**2))/(2*gamma(1 - p))","C",0
399,1,3082,0,74.610690," ","integrate(x**5*(e*x+d)**3*(b*x**2+a)**p,x)","\frac{3 a^{p} d^{2} e x^{7} {{}_{2}F_{1}\left(\begin{matrix} \frac{7}{2}, - p \\ \frac{9}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{7} + \frac{a^{p} e^{3} x^{9} {{}_{2}F_{1}\left(\begin{matrix} \frac{9}{2}, - p \\ \frac{11}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{9} + d^{3} \left(\begin{cases} \frac{a^{p} x^{6}}{6} & \text{for}\: b = 0 \\\frac{2 a^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{4 a^{2} b^{3} + 8 a b^{4} x^{2} + 4 b^{5} x^{4}} + \frac{2 a^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{4 a^{2} b^{3} + 8 a b^{4} x^{2} + 4 b^{5} x^{4}} + \frac{3 a^{2}}{4 a^{2} b^{3} + 8 a b^{4} x^{2} + 4 b^{5} x^{4}} + \frac{4 a b x^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{4 a^{2} b^{3} + 8 a b^{4} x^{2} + 4 b^{5} x^{4}} + \frac{4 a b x^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{4 a^{2} b^{3} + 8 a b^{4} x^{2} + 4 b^{5} x^{4}} + \frac{4 a b x^{2}}{4 a^{2} b^{3} + 8 a b^{4} x^{2} + 4 b^{5} x^{4}} + \frac{2 b^{2} x^{4} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{4 a^{2} b^{3} + 8 a b^{4} x^{2} + 4 b^{5} x^{4}} + \frac{2 b^{2} x^{4} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{4 a^{2} b^{3} + 8 a b^{4} x^{2} + 4 b^{5} x^{4}} & \text{for}\: p = -3 \\- \frac{2 a^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 a b^{3} + 2 b^{4} x^{2}} - \frac{2 a^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 a b^{3} + 2 b^{4} x^{2}} - \frac{2 a^{2}}{2 a b^{3} + 2 b^{4} x^{2}} - \frac{2 a b x^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 a b^{3} + 2 b^{4} x^{2}} - \frac{2 a b x^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 a b^{3} + 2 b^{4} x^{2}} + \frac{b^{2} x^{4}}{2 a b^{3} + 2 b^{4} x^{2}} & \text{for}\: p = -2 \\\frac{a^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 b^{3}} + \frac{a^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 b^{3}} - \frac{a x^{2}}{2 b^{2}} + \frac{x^{4}}{4 b} & \text{for}\: p = -1 \\\frac{2 a^{3} \left(a + b x^{2}\right)^{p}}{2 b^{3} p^{3} + 12 b^{3} p^{2} + 22 b^{3} p + 12 b^{3}} - \frac{2 a^{2} b p x^{2} \left(a + b x^{2}\right)^{p}}{2 b^{3} p^{3} + 12 b^{3} p^{2} + 22 b^{3} p + 12 b^{3}} + \frac{a b^{2} p^{2} x^{4} \left(a + b x^{2}\right)^{p}}{2 b^{3} p^{3} + 12 b^{3} p^{2} + 22 b^{3} p + 12 b^{3}} + \frac{a b^{2} p x^{4} \left(a + b x^{2}\right)^{p}}{2 b^{3} p^{3} + 12 b^{3} p^{2} + 22 b^{3} p + 12 b^{3}} + \frac{b^{3} p^{2} x^{6} \left(a + b x^{2}\right)^{p}}{2 b^{3} p^{3} + 12 b^{3} p^{2} + 22 b^{3} p + 12 b^{3}} + \frac{3 b^{3} p x^{6} \left(a + b x^{2}\right)^{p}}{2 b^{3} p^{3} + 12 b^{3} p^{2} + 22 b^{3} p + 12 b^{3}} + \frac{2 b^{3} x^{6} \left(a + b x^{2}\right)^{p}}{2 b^{3} p^{3} + 12 b^{3} p^{2} + 22 b^{3} p + 12 b^{3}} & \text{otherwise} \end{cases}\right) + 3 d e^{2} \left(\begin{cases} \frac{a^{p} x^{8}}{8} & \text{for}\: b = 0 \\\frac{6 a^{3} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{12 a^{3} b^{4} + 36 a^{2} b^{5} x^{2} + 36 a b^{6} x^{4} + 12 b^{7} x^{6}} + \frac{6 a^{3} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{12 a^{3} b^{4} + 36 a^{2} b^{5} x^{2} + 36 a b^{6} x^{4} + 12 b^{7} x^{6}} + \frac{11 a^{3}}{12 a^{3} b^{4} + 36 a^{2} b^{5} x^{2} + 36 a b^{6} x^{4} + 12 b^{7} x^{6}} + \frac{18 a^{2} b x^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{12 a^{3} b^{4} + 36 a^{2} b^{5} x^{2} + 36 a b^{6} x^{4} + 12 b^{7} x^{6}} + \frac{18 a^{2} b x^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{12 a^{3} b^{4} + 36 a^{2} b^{5} x^{2} + 36 a b^{6} x^{4} + 12 b^{7} x^{6}} + \frac{27 a^{2} b x^{2}}{12 a^{3} b^{4} + 36 a^{2} b^{5} x^{2} + 36 a b^{6} x^{4} + 12 b^{7} x^{6}} + \frac{18 a b^{2} x^{4} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{12 a^{3} b^{4} + 36 a^{2} b^{5} x^{2} + 36 a b^{6} x^{4} + 12 b^{7} x^{6}} + \frac{18 a b^{2} x^{4} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{12 a^{3} b^{4} + 36 a^{2} b^{5} x^{2} + 36 a b^{6} x^{4} + 12 b^{7} x^{6}} + \frac{18 a b^{2} x^{4}}{12 a^{3} b^{4} + 36 a^{2} b^{5} x^{2} + 36 a b^{6} x^{4} + 12 b^{7} x^{6}} + \frac{6 b^{3} x^{6} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{12 a^{3} b^{4} + 36 a^{2} b^{5} x^{2} + 36 a b^{6} x^{4} + 12 b^{7} x^{6}} + \frac{6 b^{3} x^{6} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{12 a^{3} b^{4} + 36 a^{2} b^{5} x^{2} + 36 a b^{6} x^{4} + 12 b^{7} x^{6}} & \text{for}\: p = -4 \\- \frac{6 a^{3} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{4 a^{2} b^{4} + 8 a b^{5} x^{2} + 4 b^{6} x^{4}} - \frac{6 a^{3} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{4 a^{2} b^{4} + 8 a b^{5} x^{2} + 4 b^{6} x^{4}} - \frac{9 a^{3}}{4 a^{2} b^{4} + 8 a b^{5} x^{2} + 4 b^{6} x^{4}} - \frac{12 a^{2} b x^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{4 a^{2} b^{4} + 8 a b^{5} x^{2} + 4 b^{6} x^{4}} - \frac{12 a^{2} b x^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{4 a^{2} b^{4} + 8 a b^{5} x^{2} + 4 b^{6} x^{4}} - \frac{12 a^{2} b x^{2}}{4 a^{2} b^{4} + 8 a b^{5} x^{2} + 4 b^{6} x^{4}} - \frac{6 a b^{2} x^{4} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{4 a^{2} b^{4} + 8 a b^{5} x^{2} + 4 b^{6} x^{4}} - \frac{6 a b^{2} x^{4} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{4 a^{2} b^{4} + 8 a b^{5} x^{2} + 4 b^{6} x^{4}} + \frac{2 b^{3} x^{6}}{4 a^{2} b^{4} + 8 a b^{5} x^{2} + 4 b^{6} x^{4}} & \text{for}\: p = -3 \\\frac{6 a^{3} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{4 a b^{4} + 4 b^{5} x^{2}} + \frac{6 a^{3} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{4 a b^{4} + 4 b^{5} x^{2}} + \frac{6 a^{3}}{4 a b^{4} + 4 b^{5} x^{2}} + \frac{6 a^{2} b x^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{4 a b^{4} + 4 b^{5} x^{2}} + \frac{6 a^{2} b x^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{4 a b^{4} + 4 b^{5} x^{2}} - \frac{3 a b^{2} x^{4}}{4 a b^{4} + 4 b^{5} x^{2}} + \frac{b^{3} x^{6}}{4 a b^{4} + 4 b^{5} x^{2}} & \text{for}\: p = -2 \\- \frac{a^{3} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 b^{4}} - \frac{a^{3} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 b^{4}} + \frac{a^{2} x^{2}}{2 b^{3}} - \frac{a x^{4}}{4 b^{2}} + \frac{x^{6}}{6 b} & \text{for}\: p = -1 \\- \frac{6 a^{4} \left(a + b x^{2}\right)^{p}}{2 b^{4} p^{4} + 20 b^{4} p^{3} + 70 b^{4} p^{2} + 100 b^{4} p + 48 b^{4}} + \frac{6 a^{3} b p x^{2} \left(a + b x^{2}\right)^{p}}{2 b^{4} p^{4} + 20 b^{4} p^{3} + 70 b^{4} p^{2} + 100 b^{4} p + 48 b^{4}} - \frac{3 a^{2} b^{2} p^{2} x^{4} \left(a + b x^{2}\right)^{p}}{2 b^{4} p^{4} + 20 b^{4} p^{3} + 70 b^{4} p^{2} + 100 b^{4} p + 48 b^{4}} - \frac{3 a^{2} b^{2} p x^{4} \left(a + b x^{2}\right)^{p}}{2 b^{4} p^{4} + 20 b^{4} p^{3} + 70 b^{4} p^{2} + 100 b^{4} p + 48 b^{4}} + \frac{a b^{3} p^{3} x^{6} \left(a + b x^{2}\right)^{p}}{2 b^{4} p^{4} + 20 b^{4} p^{3} + 70 b^{4} p^{2} + 100 b^{4} p + 48 b^{4}} + \frac{3 a b^{3} p^{2} x^{6} \left(a + b x^{2}\right)^{p}}{2 b^{4} p^{4} + 20 b^{4} p^{3} + 70 b^{4} p^{2} + 100 b^{4} p + 48 b^{4}} + \frac{2 a b^{3} p x^{6} \left(a + b x^{2}\right)^{p}}{2 b^{4} p^{4} + 20 b^{4} p^{3} + 70 b^{4} p^{2} + 100 b^{4} p + 48 b^{4}} + \frac{b^{4} p^{3} x^{8} \left(a + b x^{2}\right)^{p}}{2 b^{4} p^{4} + 20 b^{4} p^{3} + 70 b^{4} p^{2} + 100 b^{4} p + 48 b^{4}} + \frac{6 b^{4} p^{2} x^{8} \left(a + b x^{2}\right)^{p}}{2 b^{4} p^{4} + 20 b^{4} p^{3} + 70 b^{4} p^{2} + 100 b^{4} p + 48 b^{4}} + \frac{11 b^{4} p x^{8} \left(a + b x^{2}\right)^{p}}{2 b^{4} p^{4} + 20 b^{4} p^{3} + 70 b^{4} p^{2} + 100 b^{4} p + 48 b^{4}} + \frac{6 b^{4} x^{8} \left(a + b x^{2}\right)^{p}}{2 b^{4} p^{4} + 20 b^{4} p^{3} + 70 b^{4} p^{2} + 100 b^{4} p + 48 b^{4}} & \text{otherwise} \end{cases}\right)"," ",0,"3*a**p*d**2*e*x**7*hyper((7/2, -p), (9/2,), b*x**2*exp_polar(I*pi)/a)/7 + a**p*e**3*x**9*hyper((9/2, -p), (11/2,), b*x**2*exp_polar(I*pi)/a)/9 + d**3*Piecewise((a**p*x**6/6, Eq(b, 0)), (2*a**2*log(-I*sqrt(a)*sqrt(1/b) + x)/(4*a**2*b**3 + 8*a*b**4*x**2 + 4*b**5*x**4) + 2*a**2*log(I*sqrt(a)*sqrt(1/b) + x)/(4*a**2*b**3 + 8*a*b**4*x**2 + 4*b**5*x**4) + 3*a**2/(4*a**2*b**3 + 8*a*b**4*x**2 + 4*b**5*x**4) + 4*a*b*x**2*log(-I*sqrt(a)*sqrt(1/b) + x)/(4*a**2*b**3 + 8*a*b**4*x**2 + 4*b**5*x**4) + 4*a*b*x**2*log(I*sqrt(a)*sqrt(1/b) + x)/(4*a**2*b**3 + 8*a*b**4*x**2 + 4*b**5*x**4) + 4*a*b*x**2/(4*a**2*b**3 + 8*a*b**4*x**2 + 4*b**5*x**4) + 2*b**2*x**4*log(-I*sqrt(a)*sqrt(1/b) + x)/(4*a**2*b**3 + 8*a*b**4*x**2 + 4*b**5*x**4) + 2*b**2*x**4*log(I*sqrt(a)*sqrt(1/b) + x)/(4*a**2*b**3 + 8*a*b**4*x**2 + 4*b**5*x**4), Eq(p, -3)), (-2*a**2*log(-I*sqrt(a)*sqrt(1/b) + x)/(2*a*b**3 + 2*b**4*x**2) - 2*a**2*log(I*sqrt(a)*sqrt(1/b) + x)/(2*a*b**3 + 2*b**4*x**2) - 2*a**2/(2*a*b**3 + 2*b**4*x**2) - 2*a*b*x**2*log(-I*sqrt(a)*sqrt(1/b) + x)/(2*a*b**3 + 2*b**4*x**2) - 2*a*b*x**2*log(I*sqrt(a)*sqrt(1/b) + x)/(2*a*b**3 + 2*b**4*x**2) + b**2*x**4/(2*a*b**3 + 2*b**4*x**2), Eq(p, -2)), (a**2*log(-I*sqrt(a)*sqrt(1/b) + x)/(2*b**3) + a**2*log(I*sqrt(a)*sqrt(1/b) + x)/(2*b**3) - a*x**2/(2*b**2) + x**4/(4*b), Eq(p, -1)), (2*a**3*(a + b*x**2)**p/(2*b**3*p**3 + 12*b**3*p**2 + 22*b**3*p + 12*b**3) - 2*a**2*b*p*x**2*(a + b*x**2)**p/(2*b**3*p**3 + 12*b**3*p**2 + 22*b**3*p + 12*b**3) + a*b**2*p**2*x**4*(a + b*x**2)**p/(2*b**3*p**3 + 12*b**3*p**2 + 22*b**3*p + 12*b**3) + a*b**2*p*x**4*(a + b*x**2)**p/(2*b**3*p**3 + 12*b**3*p**2 + 22*b**3*p + 12*b**3) + b**3*p**2*x**6*(a + b*x**2)**p/(2*b**3*p**3 + 12*b**3*p**2 + 22*b**3*p + 12*b**3) + 3*b**3*p*x**6*(a + b*x**2)**p/(2*b**3*p**3 + 12*b**3*p**2 + 22*b**3*p + 12*b**3) + 2*b**3*x**6*(a + b*x**2)**p/(2*b**3*p**3 + 12*b**3*p**2 + 22*b**3*p + 12*b**3), True)) + 3*d*e**2*Piecewise((a**p*x**8/8, Eq(b, 0)), (6*a**3*log(-I*sqrt(a)*sqrt(1/b) + x)/(12*a**3*b**4 + 36*a**2*b**5*x**2 + 36*a*b**6*x**4 + 12*b**7*x**6) + 6*a**3*log(I*sqrt(a)*sqrt(1/b) + x)/(12*a**3*b**4 + 36*a**2*b**5*x**2 + 36*a*b**6*x**4 + 12*b**7*x**6) + 11*a**3/(12*a**3*b**4 + 36*a**2*b**5*x**2 + 36*a*b**6*x**4 + 12*b**7*x**6) + 18*a**2*b*x**2*log(-I*sqrt(a)*sqrt(1/b) + x)/(12*a**3*b**4 + 36*a**2*b**5*x**2 + 36*a*b**6*x**4 + 12*b**7*x**6) + 18*a**2*b*x**2*log(I*sqrt(a)*sqrt(1/b) + x)/(12*a**3*b**4 + 36*a**2*b**5*x**2 + 36*a*b**6*x**4 + 12*b**7*x**6) + 27*a**2*b*x**2/(12*a**3*b**4 + 36*a**2*b**5*x**2 + 36*a*b**6*x**4 + 12*b**7*x**6) + 18*a*b**2*x**4*log(-I*sqrt(a)*sqrt(1/b) + x)/(12*a**3*b**4 + 36*a**2*b**5*x**2 + 36*a*b**6*x**4 + 12*b**7*x**6) + 18*a*b**2*x**4*log(I*sqrt(a)*sqrt(1/b) + x)/(12*a**3*b**4 + 36*a**2*b**5*x**2 + 36*a*b**6*x**4 + 12*b**7*x**6) + 18*a*b**2*x**4/(12*a**3*b**4 + 36*a**2*b**5*x**2 + 36*a*b**6*x**4 + 12*b**7*x**6) + 6*b**3*x**6*log(-I*sqrt(a)*sqrt(1/b) + x)/(12*a**3*b**4 + 36*a**2*b**5*x**2 + 36*a*b**6*x**4 + 12*b**7*x**6) + 6*b**3*x**6*log(I*sqrt(a)*sqrt(1/b) + x)/(12*a**3*b**4 + 36*a**2*b**5*x**2 + 36*a*b**6*x**4 + 12*b**7*x**6), Eq(p, -4)), (-6*a**3*log(-I*sqrt(a)*sqrt(1/b) + x)/(4*a**2*b**4 + 8*a*b**5*x**2 + 4*b**6*x**4) - 6*a**3*log(I*sqrt(a)*sqrt(1/b) + x)/(4*a**2*b**4 + 8*a*b**5*x**2 + 4*b**6*x**4) - 9*a**3/(4*a**2*b**4 + 8*a*b**5*x**2 + 4*b**6*x**4) - 12*a**2*b*x**2*log(-I*sqrt(a)*sqrt(1/b) + x)/(4*a**2*b**4 + 8*a*b**5*x**2 + 4*b**6*x**4) - 12*a**2*b*x**2*log(I*sqrt(a)*sqrt(1/b) + x)/(4*a**2*b**4 + 8*a*b**5*x**2 + 4*b**6*x**4) - 12*a**2*b*x**2/(4*a**2*b**4 + 8*a*b**5*x**2 + 4*b**6*x**4) - 6*a*b**2*x**4*log(-I*sqrt(a)*sqrt(1/b) + x)/(4*a**2*b**4 + 8*a*b**5*x**2 + 4*b**6*x**4) - 6*a*b**2*x**4*log(I*sqrt(a)*sqrt(1/b) + x)/(4*a**2*b**4 + 8*a*b**5*x**2 + 4*b**6*x**4) + 2*b**3*x**6/(4*a**2*b**4 + 8*a*b**5*x**2 + 4*b**6*x**4), Eq(p, -3)), (6*a**3*log(-I*sqrt(a)*sqrt(1/b) + x)/(4*a*b**4 + 4*b**5*x**2) + 6*a**3*log(I*sqrt(a)*sqrt(1/b) + x)/(4*a*b**4 + 4*b**5*x**2) + 6*a**3/(4*a*b**4 + 4*b**5*x**2) + 6*a**2*b*x**2*log(-I*sqrt(a)*sqrt(1/b) + x)/(4*a*b**4 + 4*b**5*x**2) + 6*a**2*b*x**2*log(I*sqrt(a)*sqrt(1/b) + x)/(4*a*b**4 + 4*b**5*x**2) - 3*a*b**2*x**4/(4*a*b**4 + 4*b**5*x**2) + b**3*x**6/(4*a*b**4 + 4*b**5*x**2), Eq(p, -2)), (-a**3*log(-I*sqrt(a)*sqrt(1/b) + x)/(2*b**4) - a**3*log(I*sqrt(a)*sqrt(1/b) + x)/(2*b**4) + a**2*x**2/(2*b**3) - a*x**4/(4*b**2) + x**6/(6*b), Eq(p, -1)), (-6*a**4*(a + b*x**2)**p/(2*b**4*p**4 + 20*b**4*p**3 + 70*b**4*p**2 + 100*b**4*p + 48*b**4) + 6*a**3*b*p*x**2*(a + b*x**2)**p/(2*b**4*p**4 + 20*b**4*p**3 + 70*b**4*p**2 + 100*b**4*p + 48*b**4) - 3*a**2*b**2*p**2*x**4*(a + b*x**2)**p/(2*b**4*p**4 + 20*b**4*p**3 + 70*b**4*p**2 + 100*b**4*p + 48*b**4) - 3*a**2*b**2*p*x**4*(a + b*x**2)**p/(2*b**4*p**4 + 20*b**4*p**3 + 70*b**4*p**2 + 100*b**4*p + 48*b**4) + a*b**3*p**3*x**6*(a + b*x**2)**p/(2*b**4*p**4 + 20*b**4*p**3 + 70*b**4*p**2 + 100*b**4*p + 48*b**4) + 3*a*b**3*p**2*x**6*(a + b*x**2)**p/(2*b**4*p**4 + 20*b**4*p**3 + 70*b**4*p**2 + 100*b**4*p + 48*b**4) + 2*a*b**3*p*x**6*(a + b*x**2)**p/(2*b**4*p**4 + 20*b**4*p**3 + 70*b**4*p**2 + 100*b**4*p + 48*b**4) + b**4*p**3*x**8*(a + b*x**2)**p/(2*b**4*p**4 + 20*b**4*p**3 + 70*b**4*p**2 + 100*b**4*p + 48*b**4) + 6*b**4*p**2*x**8*(a + b*x**2)**p/(2*b**4*p**4 + 20*b**4*p**3 + 70*b**4*p**2 + 100*b**4*p + 48*b**4) + 11*b**4*p*x**8*(a + b*x**2)**p/(2*b**4*p**4 + 20*b**4*p**3 + 70*b**4*p**2 + 100*b**4*p + 48*b**4) + 6*b**4*x**8*(a + b*x**2)**p/(2*b**4*p**4 + 20*b**4*p**3 + 70*b**4*p**2 + 100*b**4*p + 48*b**4), True))","C",0
400,1,3082,0,57.337415," ","integrate(x**4*(e*x+d)**3*(b*x**2+a)**p,x)","\frac{a^{p} d^{3} x^{5} {{}_{2}F_{1}\left(\begin{matrix} \frac{5}{2}, - p \\ \frac{7}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{5} + \frac{3 a^{p} d e^{2} x^{7} {{}_{2}F_{1}\left(\begin{matrix} \frac{7}{2}, - p \\ \frac{9}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{7} + 3 d^{2} e \left(\begin{cases} \frac{a^{p} x^{6}}{6} & \text{for}\: b = 0 \\\frac{2 a^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{4 a^{2} b^{3} + 8 a b^{4} x^{2} + 4 b^{5} x^{4}} + \frac{2 a^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{4 a^{2} b^{3} + 8 a b^{4} x^{2} + 4 b^{5} x^{4}} + \frac{3 a^{2}}{4 a^{2} b^{3} + 8 a b^{4} x^{2} + 4 b^{5} x^{4}} + \frac{4 a b x^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{4 a^{2} b^{3} + 8 a b^{4} x^{2} + 4 b^{5} x^{4}} + \frac{4 a b x^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{4 a^{2} b^{3} + 8 a b^{4} x^{2} + 4 b^{5} x^{4}} + \frac{4 a b x^{2}}{4 a^{2} b^{3} + 8 a b^{4} x^{2} + 4 b^{5} x^{4}} + \frac{2 b^{2} x^{4} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{4 a^{2} b^{3} + 8 a b^{4} x^{2} + 4 b^{5} x^{4}} + \frac{2 b^{2} x^{4} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{4 a^{2} b^{3} + 8 a b^{4} x^{2} + 4 b^{5} x^{4}} & \text{for}\: p = -3 \\- \frac{2 a^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 a b^{3} + 2 b^{4} x^{2}} - \frac{2 a^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 a b^{3} + 2 b^{4} x^{2}} - \frac{2 a^{2}}{2 a b^{3} + 2 b^{4} x^{2}} - \frac{2 a b x^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 a b^{3} + 2 b^{4} x^{2}} - \frac{2 a b x^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 a b^{3} + 2 b^{4} x^{2}} + \frac{b^{2} x^{4}}{2 a b^{3} + 2 b^{4} x^{2}} & \text{for}\: p = -2 \\\frac{a^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 b^{3}} + \frac{a^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 b^{3}} - \frac{a x^{2}}{2 b^{2}} + \frac{x^{4}}{4 b} & \text{for}\: p = -1 \\\frac{2 a^{3} \left(a + b x^{2}\right)^{p}}{2 b^{3} p^{3} + 12 b^{3} p^{2} + 22 b^{3} p + 12 b^{3}} - \frac{2 a^{2} b p x^{2} \left(a + b x^{2}\right)^{p}}{2 b^{3} p^{3} + 12 b^{3} p^{2} + 22 b^{3} p + 12 b^{3}} + \frac{a b^{2} p^{2} x^{4} \left(a + b x^{2}\right)^{p}}{2 b^{3} p^{3} + 12 b^{3} p^{2} + 22 b^{3} p + 12 b^{3}} + \frac{a b^{2} p x^{4} \left(a + b x^{2}\right)^{p}}{2 b^{3} p^{3} + 12 b^{3} p^{2} + 22 b^{3} p + 12 b^{3}} + \frac{b^{3} p^{2} x^{6} \left(a + b x^{2}\right)^{p}}{2 b^{3} p^{3} + 12 b^{3} p^{2} + 22 b^{3} p + 12 b^{3}} + \frac{3 b^{3} p x^{6} \left(a + b x^{2}\right)^{p}}{2 b^{3} p^{3} + 12 b^{3} p^{2} + 22 b^{3} p + 12 b^{3}} + \frac{2 b^{3} x^{6} \left(a + b x^{2}\right)^{p}}{2 b^{3} p^{3} + 12 b^{3} p^{2} + 22 b^{3} p + 12 b^{3}} & \text{otherwise} \end{cases}\right) + e^{3} \left(\begin{cases} \frac{a^{p} x^{8}}{8} & \text{for}\: b = 0 \\\frac{6 a^{3} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{12 a^{3} b^{4} + 36 a^{2} b^{5} x^{2} + 36 a b^{6} x^{4} + 12 b^{7} x^{6}} + \frac{6 a^{3} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{12 a^{3} b^{4} + 36 a^{2} b^{5} x^{2} + 36 a b^{6} x^{4} + 12 b^{7} x^{6}} + \frac{11 a^{3}}{12 a^{3} b^{4} + 36 a^{2} b^{5} x^{2} + 36 a b^{6} x^{4} + 12 b^{7} x^{6}} + \frac{18 a^{2} b x^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{12 a^{3} b^{4} + 36 a^{2} b^{5} x^{2} + 36 a b^{6} x^{4} + 12 b^{7} x^{6}} + \frac{18 a^{2} b x^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{12 a^{3} b^{4} + 36 a^{2} b^{5} x^{2} + 36 a b^{6} x^{4} + 12 b^{7} x^{6}} + \frac{27 a^{2} b x^{2}}{12 a^{3} b^{4} + 36 a^{2} b^{5} x^{2} + 36 a b^{6} x^{4} + 12 b^{7} x^{6}} + \frac{18 a b^{2} x^{4} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{12 a^{3} b^{4} + 36 a^{2} b^{5} x^{2} + 36 a b^{6} x^{4} + 12 b^{7} x^{6}} + \frac{18 a b^{2} x^{4} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{12 a^{3} b^{4} + 36 a^{2} b^{5} x^{2} + 36 a b^{6} x^{4} + 12 b^{7} x^{6}} + \frac{18 a b^{2} x^{4}}{12 a^{3} b^{4} + 36 a^{2} b^{5} x^{2} + 36 a b^{6} x^{4} + 12 b^{7} x^{6}} + \frac{6 b^{3} x^{6} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{12 a^{3} b^{4} + 36 a^{2} b^{5} x^{2} + 36 a b^{6} x^{4} + 12 b^{7} x^{6}} + \frac{6 b^{3} x^{6} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{12 a^{3} b^{4} + 36 a^{2} b^{5} x^{2} + 36 a b^{6} x^{4} + 12 b^{7} x^{6}} & \text{for}\: p = -4 \\- \frac{6 a^{3} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{4 a^{2} b^{4} + 8 a b^{5} x^{2} + 4 b^{6} x^{4}} - \frac{6 a^{3} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{4 a^{2} b^{4} + 8 a b^{5} x^{2} + 4 b^{6} x^{4}} - \frac{9 a^{3}}{4 a^{2} b^{4} + 8 a b^{5} x^{2} + 4 b^{6} x^{4}} - \frac{12 a^{2} b x^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{4 a^{2} b^{4} + 8 a b^{5} x^{2} + 4 b^{6} x^{4}} - \frac{12 a^{2} b x^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{4 a^{2} b^{4} + 8 a b^{5} x^{2} + 4 b^{6} x^{4}} - \frac{12 a^{2} b x^{2}}{4 a^{2} b^{4} + 8 a b^{5} x^{2} + 4 b^{6} x^{4}} - \frac{6 a b^{2} x^{4} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{4 a^{2} b^{4} + 8 a b^{5} x^{2} + 4 b^{6} x^{4}} - \frac{6 a b^{2} x^{4} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{4 a^{2} b^{4} + 8 a b^{5} x^{2} + 4 b^{6} x^{4}} + \frac{2 b^{3} x^{6}}{4 a^{2} b^{4} + 8 a b^{5} x^{2} + 4 b^{6} x^{4}} & \text{for}\: p = -3 \\\frac{6 a^{3} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{4 a b^{4} + 4 b^{5} x^{2}} + \frac{6 a^{3} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{4 a b^{4} + 4 b^{5} x^{2}} + \frac{6 a^{3}}{4 a b^{4} + 4 b^{5} x^{2}} + \frac{6 a^{2} b x^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{4 a b^{4} + 4 b^{5} x^{2}} + \frac{6 a^{2} b x^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{4 a b^{4} + 4 b^{5} x^{2}} - \frac{3 a b^{2} x^{4}}{4 a b^{4} + 4 b^{5} x^{2}} + \frac{b^{3} x^{6}}{4 a b^{4} + 4 b^{5} x^{2}} & \text{for}\: p = -2 \\- \frac{a^{3} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 b^{4}} - \frac{a^{3} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 b^{4}} + \frac{a^{2} x^{2}}{2 b^{3}} - \frac{a x^{4}}{4 b^{2}} + \frac{x^{6}}{6 b} & \text{for}\: p = -1 \\- \frac{6 a^{4} \left(a + b x^{2}\right)^{p}}{2 b^{4} p^{4} + 20 b^{4} p^{3} + 70 b^{4} p^{2} + 100 b^{4} p + 48 b^{4}} + \frac{6 a^{3} b p x^{2} \left(a + b x^{2}\right)^{p}}{2 b^{4} p^{4} + 20 b^{4} p^{3} + 70 b^{4} p^{2} + 100 b^{4} p + 48 b^{4}} - \frac{3 a^{2} b^{2} p^{2} x^{4} \left(a + b x^{2}\right)^{p}}{2 b^{4} p^{4} + 20 b^{4} p^{3} + 70 b^{4} p^{2} + 100 b^{4} p + 48 b^{4}} - \frac{3 a^{2} b^{2} p x^{4} \left(a + b x^{2}\right)^{p}}{2 b^{4} p^{4} + 20 b^{4} p^{3} + 70 b^{4} p^{2} + 100 b^{4} p + 48 b^{4}} + \frac{a b^{3} p^{3} x^{6} \left(a + b x^{2}\right)^{p}}{2 b^{4} p^{4} + 20 b^{4} p^{3} + 70 b^{4} p^{2} + 100 b^{4} p + 48 b^{4}} + \frac{3 a b^{3} p^{2} x^{6} \left(a + b x^{2}\right)^{p}}{2 b^{4} p^{4} + 20 b^{4} p^{3} + 70 b^{4} p^{2} + 100 b^{4} p + 48 b^{4}} + \frac{2 a b^{3} p x^{6} \left(a + b x^{2}\right)^{p}}{2 b^{4} p^{4} + 20 b^{4} p^{3} + 70 b^{4} p^{2} + 100 b^{4} p + 48 b^{4}} + \frac{b^{4} p^{3} x^{8} \left(a + b x^{2}\right)^{p}}{2 b^{4} p^{4} + 20 b^{4} p^{3} + 70 b^{4} p^{2} + 100 b^{4} p + 48 b^{4}} + \frac{6 b^{4} p^{2} x^{8} \left(a + b x^{2}\right)^{p}}{2 b^{4} p^{4} + 20 b^{4} p^{3} + 70 b^{4} p^{2} + 100 b^{4} p + 48 b^{4}} + \frac{11 b^{4} p x^{8} \left(a + b x^{2}\right)^{p}}{2 b^{4} p^{4} + 20 b^{4} p^{3} + 70 b^{4} p^{2} + 100 b^{4} p + 48 b^{4}} + \frac{6 b^{4} x^{8} \left(a + b x^{2}\right)^{p}}{2 b^{4} p^{4} + 20 b^{4} p^{3} + 70 b^{4} p^{2} + 100 b^{4} p + 48 b^{4}} & \text{otherwise} \end{cases}\right)"," ",0,"a**p*d**3*x**5*hyper((5/2, -p), (7/2,), b*x**2*exp_polar(I*pi)/a)/5 + 3*a**p*d*e**2*x**7*hyper((7/2, -p), (9/2,), b*x**2*exp_polar(I*pi)/a)/7 + 3*d**2*e*Piecewise((a**p*x**6/6, Eq(b, 0)), (2*a**2*log(-I*sqrt(a)*sqrt(1/b) + x)/(4*a**2*b**3 + 8*a*b**4*x**2 + 4*b**5*x**4) + 2*a**2*log(I*sqrt(a)*sqrt(1/b) + x)/(4*a**2*b**3 + 8*a*b**4*x**2 + 4*b**5*x**4) + 3*a**2/(4*a**2*b**3 + 8*a*b**4*x**2 + 4*b**5*x**4) + 4*a*b*x**2*log(-I*sqrt(a)*sqrt(1/b) + x)/(4*a**2*b**3 + 8*a*b**4*x**2 + 4*b**5*x**4) + 4*a*b*x**2*log(I*sqrt(a)*sqrt(1/b) + x)/(4*a**2*b**3 + 8*a*b**4*x**2 + 4*b**5*x**4) + 4*a*b*x**2/(4*a**2*b**3 + 8*a*b**4*x**2 + 4*b**5*x**4) + 2*b**2*x**4*log(-I*sqrt(a)*sqrt(1/b) + x)/(4*a**2*b**3 + 8*a*b**4*x**2 + 4*b**5*x**4) + 2*b**2*x**4*log(I*sqrt(a)*sqrt(1/b) + x)/(4*a**2*b**3 + 8*a*b**4*x**2 + 4*b**5*x**4), Eq(p, -3)), (-2*a**2*log(-I*sqrt(a)*sqrt(1/b) + x)/(2*a*b**3 + 2*b**4*x**2) - 2*a**2*log(I*sqrt(a)*sqrt(1/b) + x)/(2*a*b**3 + 2*b**4*x**2) - 2*a**2/(2*a*b**3 + 2*b**4*x**2) - 2*a*b*x**2*log(-I*sqrt(a)*sqrt(1/b) + x)/(2*a*b**3 + 2*b**4*x**2) - 2*a*b*x**2*log(I*sqrt(a)*sqrt(1/b) + x)/(2*a*b**3 + 2*b**4*x**2) + b**2*x**4/(2*a*b**3 + 2*b**4*x**2), Eq(p, -2)), (a**2*log(-I*sqrt(a)*sqrt(1/b) + x)/(2*b**3) + a**2*log(I*sqrt(a)*sqrt(1/b) + x)/(2*b**3) - a*x**2/(2*b**2) + x**4/(4*b), Eq(p, -1)), (2*a**3*(a + b*x**2)**p/(2*b**3*p**3 + 12*b**3*p**2 + 22*b**3*p + 12*b**3) - 2*a**2*b*p*x**2*(a + b*x**2)**p/(2*b**3*p**3 + 12*b**3*p**2 + 22*b**3*p + 12*b**3) + a*b**2*p**2*x**4*(a + b*x**2)**p/(2*b**3*p**3 + 12*b**3*p**2 + 22*b**3*p + 12*b**3) + a*b**2*p*x**4*(a + b*x**2)**p/(2*b**3*p**3 + 12*b**3*p**2 + 22*b**3*p + 12*b**3) + b**3*p**2*x**6*(a + b*x**2)**p/(2*b**3*p**3 + 12*b**3*p**2 + 22*b**3*p + 12*b**3) + 3*b**3*p*x**6*(a + b*x**2)**p/(2*b**3*p**3 + 12*b**3*p**2 + 22*b**3*p + 12*b**3) + 2*b**3*x**6*(a + b*x**2)**p/(2*b**3*p**3 + 12*b**3*p**2 + 22*b**3*p + 12*b**3), True)) + e**3*Piecewise((a**p*x**8/8, Eq(b, 0)), (6*a**3*log(-I*sqrt(a)*sqrt(1/b) + x)/(12*a**3*b**4 + 36*a**2*b**5*x**2 + 36*a*b**6*x**4 + 12*b**7*x**6) + 6*a**3*log(I*sqrt(a)*sqrt(1/b) + x)/(12*a**3*b**4 + 36*a**2*b**5*x**2 + 36*a*b**6*x**4 + 12*b**7*x**6) + 11*a**3/(12*a**3*b**4 + 36*a**2*b**5*x**2 + 36*a*b**6*x**4 + 12*b**7*x**6) + 18*a**2*b*x**2*log(-I*sqrt(a)*sqrt(1/b) + x)/(12*a**3*b**4 + 36*a**2*b**5*x**2 + 36*a*b**6*x**4 + 12*b**7*x**6) + 18*a**2*b*x**2*log(I*sqrt(a)*sqrt(1/b) + x)/(12*a**3*b**4 + 36*a**2*b**5*x**2 + 36*a*b**6*x**4 + 12*b**7*x**6) + 27*a**2*b*x**2/(12*a**3*b**4 + 36*a**2*b**5*x**2 + 36*a*b**6*x**4 + 12*b**7*x**6) + 18*a*b**2*x**4*log(-I*sqrt(a)*sqrt(1/b) + x)/(12*a**3*b**4 + 36*a**2*b**5*x**2 + 36*a*b**6*x**4 + 12*b**7*x**6) + 18*a*b**2*x**4*log(I*sqrt(a)*sqrt(1/b) + x)/(12*a**3*b**4 + 36*a**2*b**5*x**2 + 36*a*b**6*x**4 + 12*b**7*x**6) + 18*a*b**2*x**4/(12*a**3*b**4 + 36*a**2*b**5*x**2 + 36*a*b**6*x**4 + 12*b**7*x**6) + 6*b**3*x**6*log(-I*sqrt(a)*sqrt(1/b) + x)/(12*a**3*b**4 + 36*a**2*b**5*x**2 + 36*a*b**6*x**4 + 12*b**7*x**6) + 6*b**3*x**6*log(I*sqrt(a)*sqrt(1/b) + x)/(12*a**3*b**4 + 36*a**2*b**5*x**2 + 36*a*b**6*x**4 + 12*b**7*x**6), Eq(p, -4)), (-6*a**3*log(-I*sqrt(a)*sqrt(1/b) + x)/(4*a**2*b**4 + 8*a*b**5*x**2 + 4*b**6*x**4) - 6*a**3*log(I*sqrt(a)*sqrt(1/b) + x)/(4*a**2*b**4 + 8*a*b**5*x**2 + 4*b**6*x**4) - 9*a**3/(4*a**2*b**4 + 8*a*b**5*x**2 + 4*b**6*x**4) - 12*a**2*b*x**2*log(-I*sqrt(a)*sqrt(1/b) + x)/(4*a**2*b**4 + 8*a*b**5*x**2 + 4*b**6*x**4) - 12*a**2*b*x**2*log(I*sqrt(a)*sqrt(1/b) + x)/(4*a**2*b**4 + 8*a*b**5*x**2 + 4*b**6*x**4) - 12*a**2*b*x**2/(4*a**2*b**4 + 8*a*b**5*x**2 + 4*b**6*x**4) - 6*a*b**2*x**4*log(-I*sqrt(a)*sqrt(1/b) + x)/(4*a**2*b**4 + 8*a*b**5*x**2 + 4*b**6*x**4) - 6*a*b**2*x**4*log(I*sqrt(a)*sqrt(1/b) + x)/(4*a**2*b**4 + 8*a*b**5*x**2 + 4*b**6*x**4) + 2*b**3*x**6/(4*a**2*b**4 + 8*a*b**5*x**2 + 4*b**6*x**4), Eq(p, -3)), (6*a**3*log(-I*sqrt(a)*sqrt(1/b) + x)/(4*a*b**4 + 4*b**5*x**2) + 6*a**3*log(I*sqrt(a)*sqrt(1/b) + x)/(4*a*b**4 + 4*b**5*x**2) + 6*a**3/(4*a*b**4 + 4*b**5*x**2) + 6*a**2*b*x**2*log(-I*sqrt(a)*sqrt(1/b) + x)/(4*a*b**4 + 4*b**5*x**2) + 6*a**2*b*x**2*log(I*sqrt(a)*sqrt(1/b) + x)/(4*a*b**4 + 4*b**5*x**2) - 3*a*b**2*x**4/(4*a*b**4 + 4*b**5*x**2) + b**3*x**6/(4*a*b**4 + 4*b**5*x**2), Eq(p, -2)), (-a**3*log(-I*sqrt(a)*sqrt(1/b) + x)/(2*b**4) - a**3*log(I*sqrt(a)*sqrt(1/b) + x)/(2*b**4) + a**2*x**2/(2*b**3) - a*x**4/(4*b**2) + x**6/(6*b), Eq(p, -1)), (-6*a**4*(a + b*x**2)**p/(2*b**4*p**4 + 20*b**4*p**3 + 70*b**4*p**2 + 100*b**4*p + 48*b**4) + 6*a**3*b*p*x**2*(a + b*x**2)**p/(2*b**4*p**4 + 20*b**4*p**3 + 70*b**4*p**2 + 100*b**4*p + 48*b**4) - 3*a**2*b**2*p**2*x**4*(a + b*x**2)**p/(2*b**4*p**4 + 20*b**4*p**3 + 70*b**4*p**2 + 100*b**4*p + 48*b**4) - 3*a**2*b**2*p*x**4*(a + b*x**2)**p/(2*b**4*p**4 + 20*b**4*p**3 + 70*b**4*p**2 + 100*b**4*p + 48*b**4) + a*b**3*p**3*x**6*(a + b*x**2)**p/(2*b**4*p**4 + 20*b**4*p**3 + 70*b**4*p**2 + 100*b**4*p + 48*b**4) + 3*a*b**3*p**2*x**6*(a + b*x**2)**p/(2*b**4*p**4 + 20*b**4*p**3 + 70*b**4*p**2 + 100*b**4*p + 48*b**4) + 2*a*b**3*p*x**6*(a + b*x**2)**p/(2*b**4*p**4 + 20*b**4*p**3 + 70*b**4*p**2 + 100*b**4*p + 48*b**4) + b**4*p**3*x**8*(a + b*x**2)**p/(2*b**4*p**4 + 20*b**4*p**3 + 70*b**4*p**2 + 100*b**4*p + 48*b**4) + 6*b**4*p**2*x**8*(a + b*x**2)**p/(2*b**4*p**4 + 20*b**4*p**3 + 70*b**4*p**2 + 100*b**4*p + 48*b**4) + 11*b**4*p*x**8*(a + b*x**2)**p/(2*b**4*p**4 + 20*b**4*p**3 + 70*b**4*p**2 + 100*b**4*p + 48*b**4) + 6*b**4*x**8*(a + b*x**2)**p/(2*b**4*p**4 + 20*b**4*p**3 + 70*b**4*p**2 + 100*b**4*p + 48*b**4), True))","C",0
401,1,1421,0,42.195516," ","integrate(x**3*(e*x+d)**3*(b*x**2+a)**p,x)","\frac{3 a^{p} d^{2} e x^{5} {{}_{2}F_{1}\left(\begin{matrix} \frac{5}{2}, - p \\ \frac{7}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{5} + \frac{a^{p} e^{3} x^{7} {{}_{2}F_{1}\left(\begin{matrix} \frac{7}{2}, - p \\ \frac{9}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{7} + d^{3} \left(\begin{cases} \frac{a^{p} x^{4}}{4} & \text{for}\: b = 0 \\\frac{a \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 a b^{2} + 2 b^{3} x^{2}} + \frac{a \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 a b^{2} + 2 b^{3} x^{2}} + \frac{a}{2 a b^{2} + 2 b^{3} x^{2}} + \frac{b x^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 a b^{2} + 2 b^{3} x^{2}} + \frac{b x^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 a b^{2} + 2 b^{3} x^{2}} & \text{for}\: p = -2 \\- \frac{a \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 b^{2}} - \frac{a \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 b^{2}} + \frac{x^{2}}{2 b} & \text{for}\: p = -1 \\- \frac{a^{2} \left(a + b x^{2}\right)^{p}}{2 b^{2} p^{2} + 6 b^{2} p + 4 b^{2}} + \frac{a b p x^{2} \left(a + b x^{2}\right)^{p}}{2 b^{2} p^{2} + 6 b^{2} p + 4 b^{2}} + \frac{b^{2} p x^{4} \left(a + b x^{2}\right)^{p}}{2 b^{2} p^{2} + 6 b^{2} p + 4 b^{2}} + \frac{b^{2} x^{4} \left(a + b x^{2}\right)^{p}}{2 b^{2} p^{2} + 6 b^{2} p + 4 b^{2}} & \text{otherwise} \end{cases}\right) + 3 d e^{2} \left(\begin{cases} \frac{a^{p} x^{6}}{6} & \text{for}\: b = 0 \\\frac{2 a^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{4 a^{2} b^{3} + 8 a b^{4} x^{2} + 4 b^{5} x^{4}} + \frac{2 a^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{4 a^{2} b^{3} + 8 a b^{4} x^{2} + 4 b^{5} x^{4}} + \frac{3 a^{2}}{4 a^{2} b^{3} + 8 a b^{4} x^{2} + 4 b^{5} x^{4}} + \frac{4 a b x^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{4 a^{2} b^{3} + 8 a b^{4} x^{2} + 4 b^{5} x^{4}} + \frac{4 a b x^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{4 a^{2} b^{3} + 8 a b^{4} x^{2} + 4 b^{5} x^{4}} + \frac{4 a b x^{2}}{4 a^{2} b^{3} + 8 a b^{4} x^{2} + 4 b^{5} x^{4}} + \frac{2 b^{2} x^{4} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{4 a^{2} b^{3} + 8 a b^{4} x^{2} + 4 b^{5} x^{4}} + \frac{2 b^{2} x^{4} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{4 a^{2} b^{3} + 8 a b^{4} x^{2} + 4 b^{5} x^{4}} & \text{for}\: p = -3 \\- \frac{2 a^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 a b^{3} + 2 b^{4} x^{2}} - \frac{2 a^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 a b^{3} + 2 b^{4} x^{2}} - \frac{2 a^{2}}{2 a b^{3} + 2 b^{4} x^{2}} - \frac{2 a b x^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 a b^{3} + 2 b^{4} x^{2}} - \frac{2 a b x^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 a b^{3} + 2 b^{4} x^{2}} + \frac{b^{2} x^{4}}{2 a b^{3} + 2 b^{4} x^{2}} & \text{for}\: p = -2 \\\frac{a^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 b^{3}} + \frac{a^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 b^{3}} - \frac{a x^{2}}{2 b^{2}} + \frac{x^{4}}{4 b} & \text{for}\: p = -1 \\\frac{2 a^{3} \left(a + b x^{2}\right)^{p}}{2 b^{3} p^{3} + 12 b^{3} p^{2} + 22 b^{3} p + 12 b^{3}} - \frac{2 a^{2} b p x^{2} \left(a + b x^{2}\right)^{p}}{2 b^{3} p^{3} + 12 b^{3} p^{2} + 22 b^{3} p + 12 b^{3}} + \frac{a b^{2} p^{2} x^{4} \left(a + b x^{2}\right)^{p}}{2 b^{3} p^{3} + 12 b^{3} p^{2} + 22 b^{3} p + 12 b^{3}} + \frac{a b^{2} p x^{4} \left(a + b x^{2}\right)^{p}}{2 b^{3} p^{3} + 12 b^{3} p^{2} + 22 b^{3} p + 12 b^{3}} + \frac{b^{3} p^{2} x^{6} \left(a + b x^{2}\right)^{p}}{2 b^{3} p^{3} + 12 b^{3} p^{2} + 22 b^{3} p + 12 b^{3}} + \frac{3 b^{3} p x^{6} \left(a + b x^{2}\right)^{p}}{2 b^{3} p^{3} + 12 b^{3} p^{2} + 22 b^{3} p + 12 b^{3}} + \frac{2 b^{3} x^{6} \left(a + b x^{2}\right)^{p}}{2 b^{3} p^{3} + 12 b^{3} p^{2} + 22 b^{3} p + 12 b^{3}} & \text{otherwise} \end{cases}\right)"," ",0,"3*a**p*d**2*e*x**5*hyper((5/2, -p), (7/2,), b*x**2*exp_polar(I*pi)/a)/5 + a**p*e**3*x**7*hyper((7/2, -p), (9/2,), b*x**2*exp_polar(I*pi)/a)/7 + d**3*Piecewise((a**p*x**4/4, Eq(b, 0)), (a*log(-I*sqrt(a)*sqrt(1/b) + x)/(2*a*b**2 + 2*b**3*x**2) + a*log(I*sqrt(a)*sqrt(1/b) + x)/(2*a*b**2 + 2*b**3*x**2) + a/(2*a*b**2 + 2*b**3*x**2) + b*x**2*log(-I*sqrt(a)*sqrt(1/b) + x)/(2*a*b**2 + 2*b**3*x**2) + b*x**2*log(I*sqrt(a)*sqrt(1/b) + x)/(2*a*b**2 + 2*b**3*x**2), Eq(p, -2)), (-a*log(-I*sqrt(a)*sqrt(1/b) + x)/(2*b**2) - a*log(I*sqrt(a)*sqrt(1/b) + x)/(2*b**2) + x**2/(2*b), Eq(p, -1)), (-a**2*(a + b*x**2)**p/(2*b**2*p**2 + 6*b**2*p + 4*b**2) + a*b*p*x**2*(a + b*x**2)**p/(2*b**2*p**2 + 6*b**2*p + 4*b**2) + b**2*p*x**4*(a + b*x**2)**p/(2*b**2*p**2 + 6*b**2*p + 4*b**2) + b**2*x**4*(a + b*x**2)**p/(2*b**2*p**2 + 6*b**2*p + 4*b**2), True)) + 3*d*e**2*Piecewise((a**p*x**6/6, Eq(b, 0)), (2*a**2*log(-I*sqrt(a)*sqrt(1/b) + x)/(4*a**2*b**3 + 8*a*b**4*x**2 + 4*b**5*x**4) + 2*a**2*log(I*sqrt(a)*sqrt(1/b) + x)/(4*a**2*b**3 + 8*a*b**4*x**2 + 4*b**5*x**4) + 3*a**2/(4*a**2*b**3 + 8*a*b**4*x**2 + 4*b**5*x**4) + 4*a*b*x**2*log(-I*sqrt(a)*sqrt(1/b) + x)/(4*a**2*b**3 + 8*a*b**4*x**2 + 4*b**5*x**4) + 4*a*b*x**2*log(I*sqrt(a)*sqrt(1/b) + x)/(4*a**2*b**3 + 8*a*b**4*x**2 + 4*b**5*x**4) + 4*a*b*x**2/(4*a**2*b**3 + 8*a*b**4*x**2 + 4*b**5*x**4) + 2*b**2*x**4*log(-I*sqrt(a)*sqrt(1/b) + x)/(4*a**2*b**3 + 8*a*b**4*x**2 + 4*b**5*x**4) + 2*b**2*x**4*log(I*sqrt(a)*sqrt(1/b) + x)/(4*a**2*b**3 + 8*a*b**4*x**2 + 4*b**5*x**4), Eq(p, -3)), (-2*a**2*log(-I*sqrt(a)*sqrt(1/b) + x)/(2*a*b**3 + 2*b**4*x**2) - 2*a**2*log(I*sqrt(a)*sqrt(1/b) + x)/(2*a*b**3 + 2*b**4*x**2) - 2*a**2/(2*a*b**3 + 2*b**4*x**2) - 2*a*b*x**2*log(-I*sqrt(a)*sqrt(1/b) + x)/(2*a*b**3 + 2*b**4*x**2) - 2*a*b*x**2*log(I*sqrt(a)*sqrt(1/b) + x)/(2*a*b**3 + 2*b**4*x**2) + b**2*x**4/(2*a*b**3 + 2*b**4*x**2), Eq(p, -2)), (a**2*log(-I*sqrt(a)*sqrt(1/b) + x)/(2*b**3) + a**2*log(I*sqrt(a)*sqrt(1/b) + x)/(2*b**3) - a*x**2/(2*b**2) + x**4/(4*b), Eq(p, -1)), (2*a**3*(a + b*x**2)**p/(2*b**3*p**3 + 12*b**3*p**2 + 22*b**3*p + 12*b**3) - 2*a**2*b*p*x**2*(a + b*x**2)**p/(2*b**3*p**3 + 12*b**3*p**2 + 22*b**3*p + 12*b**3) + a*b**2*p**2*x**4*(a + b*x**2)**p/(2*b**3*p**3 + 12*b**3*p**2 + 22*b**3*p + 12*b**3) + a*b**2*p*x**4*(a + b*x**2)**p/(2*b**3*p**3 + 12*b**3*p**2 + 22*b**3*p + 12*b**3) + b**3*p**2*x**6*(a + b*x**2)**p/(2*b**3*p**3 + 12*b**3*p**2 + 22*b**3*p + 12*b**3) + 3*b**3*p*x**6*(a + b*x**2)**p/(2*b**3*p**3 + 12*b**3*p**2 + 22*b**3*p + 12*b**3) + 2*b**3*x**6*(a + b*x**2)**p/(2*b**3*p**3 + 12*b**3*p**2 + 22*b**3*p + 12*b**3), True))","C",0
402,1,1421,0,29.714054," ","integrate(x**2*(e*x+d)**3*(b*x**2+a)**p,x)","\frac{a^{p} d^{3} x^{3} {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{2}, - p \\ \frac{5}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{3} + \frac{3 a^{p} d e^{2} x^{5} {{}_{2}F_{1}\left(\begin{matrix} \frac{5}{2}, - p \\ \frac{7}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{5} + 3 d^{2} e \left(\begin{cases} \frac{a^{p} x^{4}}{4} & \text{for}\: b = 0 \\\frac{a \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 a b^{2} + 2 b^{3} x^{2}} + \frac{a \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 a b^{2} + 2 b^{3} x^{2}} + \frac{a}{2 a b^{2} + 2 b^{3} x^{2}} + \frac{b x^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 a b^{2} + 2 b^{3} x^{2}} + \frac{b x^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 a b^{2} + 2 b^{3} x^{2}} & \text{for}\: p = -2 \\- \frac{a \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 b^{2}} - \frac{a \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 b^{2}} + \frac{x^{2}}{2 b} & \text{for}\: p = -1 \\- \frac{a^{2} \left(a + b x^{2}\right)^{p}}{2 b^{2} p^{2} + 6 b^{2} p + 4 b^{2}} + \frac{a b p x^{2} \left(a + b x^{2}\right)^{p}}{2 b^{2} p^{2} + 6 b^{2} p + 4 b^{2}} + \frac{b^{2} p x^{4} \left(a + b x^{2}\right)^{p}}{2 b^{2} p^{2} + 6 b^{2} p + 4 b^{2}} + \frac{b^{2} x^{4} \left(a + b x^{2}\right)^{p}}{2 b^{2} p^{2} + 6 b^{2} p + 4 b^{2}} & \text{otherwise} \end{cases}\right) + e^{3} \left(\begin{cases} \frac{a^{p} x^{6}}{6} & \text{for}\: b = 0 \\\frac{2 a^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{4 a^{2} b^{3} + 8 a b^{4} x^{2} + 4 b^{5} x^{4}} + \frac{2 a^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{4 a^{2} b^{3} + 8 a b^{4} x^{2} + 4 b^{5} x^{4}} + \frac{3 a^{2}}{4 a^{2} b^{3} + 8 a b^{4} x^{2} + 4 b^{5} x^{4}} + \frac{4 a b x^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{4 a^{2} b^{3} + 8 a b^{4} x^{2} + 4 b^{5} x^{4}} + \frac{4 a b x^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{4 a^{2} b^{3} + 8 a b^{4} x^{2} + 4 b^{5} x^{4}} + \frac{4 a b x^{2}}{4 a^{2} b^{3} + 8 a b^{4} x^{2} + 4 b^{5} x^{4}} + \frac{2 b^{2} x^{4} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{4 a^{2} b^{3} + 8 a b^{4} x^{2} + 4 b^{5} x^{4}} + \frac{2 b^{2} x^{4} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{4 a^{2} b^{3} + 8 a b^{4} x^{2} + 4 b^{5} x^{4}} & \text{for}\: p = -3 \\- \frac{2 a^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 a b^{3} + 2 b^{4} x^{2}} - \frac{2 a^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 a b^{3} + 2 b^{4} x^{2}} - \frac{2 a^{2}}{2 a b^{3} + 2 b^{4} x^{2}} - \frac{2 a b x^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 a b^{3} + 2 b^{4} x^{2}} - \frac{2 a b x^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 a b^{3} + 2 b^{4} x^{2}} + \frac{b^{2} x^{4}}{2 a b^{3} + 2 b^{4} x^{2}} & \text{for}\: p = -2 \\\frac{a^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 b^{3}} + \frac{a^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 b^{3}} - \frac{a x^{2}}{2 b^{2}} + \frac{x^{4}}{4 b} & \text{for}\: p = -1 \\\frac{2 a^{3} \left(a + b x^{2}\right)^{p}}{2 b^{3} p^{3} + 12 b^{3} p^{2} + 22 b^{3} p + 12 b^{3}} - \frac{2 a^{2} b p x^{2} \left(a + b x^{2}\right)^{p}}{2 b^{3} p^{3} + 12 b^{3} p^{2} + 22 b^{3} p + 12 b^{3}} + \frac{a b^{2} p^{2} x^{4} \left(a + b x^{2}\right)^{p}}{2 b^{3} p^{3} + 12 b^{3} p^{2} + 22 b^{3} p + 12 b^{3}} + \frac{a b^{2} p x^{4} \left(a + b x^{2}\right)^{p}}{2 b^{3} p^{3} + 12 b^{3} p^{2} + 22 b^{3} p + 12 b^{3}} + \frac{b^{3} p^{2} x^{6} \left(a + b x^{2}\right)^{p}}{2 b^{3} p^{3} + 12 b^{3} p^{2} + 22 b^{3} p + 12 b^{3}} + \frac{3 b^{3} p x^{6} \left(a + b x^{2}\right)^{p}}{2 b^{3} p^{3} + 12 b^{3} p^{2} + 22 b^{3} p + 12 b^{3}} + \frac{2 b^{3} x^{6} \left(a + b x^{2}\right)^{p}}{2 b^{3} p^{3} + 12 b^{3} p^{2} + 22 b^{3} p + 12 b^{3}} & \text{otherwise} \end{cases}\right)"," ",0,"a**p*d**3*x**3*hyper((3/2, -p), (5/2,), b*x**2*exp_polar(I*pi)/a)/3 + 3*a**p*d*e**2*x**5*hyper((5/2, -p), (7/2,), b*x**2*exp_polar(I*pi)/a)/5 + 3*d**2*e*Piecewise((a**p*x**4/4, Eq(b, 0)), (a*log(-I*sqrt(a)*sqrt(1/b) + x)/(2*a*b**2 + 2*b**3*x**2) + a*log(I*sqrt(a)*sqrt(1/b) + x)/(2*a*b**2 + 2*b**3*x**2) + a/(2*a*b**2 + 2*b**3*x**2) + b*x**2*log(-I*sqrt(a)*sqrt(1/b) + x)/(2*a*b**2 + 2*b**3*x**2) + b*x**2*log(I*sqrt(a)*sqrt(1/b) + x)/(2*a*b**2 + 2*b**3*x**2), Eq(p, -2)), (-a*log(-I*sqrt(a)*sqrt(1/b) + x)/(2*b**2) - a*log(I*sqrt(a)*sqrt(1/b) + x)/(2*b**2) + x**2/(2*b), Eq(p, -1)), (-a**2*(a + b*x**2)**p/(2*b**2*p**2 + 6*b**2*p + 4*b**2) + a*b*p*x**2*(a + b*x**2)**p/(2*b**2*p**2 + 6*b**2*p + 4*b**2) + b**2*p*x**4*(a + b*x**2)**p/(2*b**2*p**2 + 6*b**2*p + 4*b**2) + b**2*x**4*(a + b*x**2)**p/(2*b**2*p**2 + 6*b**2*p + 4*b**2), True)) + e**3*Piecewise((a**p*x**6/6, Eq(b, 0)), (2*a**2*log(-I*sqrt(a)*sqrt(1/b) + x)/(4*a**2*b**3 + 8*a*b**4*x**2 + 4*b**5*x**4) + 2*a**2*log(I*sqrt(a)*sqrt(1/b) + x)/(4*a**2*b**3 + 8*a*b**4*x**2 + 4*b**5*x**4) + 3*a**2/(4*a**2*b**3 + 8*a*b**4*x**2 + 4*b**5*x**4) + 4*a*b*x**2*log(-I*sqrt(a)*sqrt(1/b) + x)/(4*a**2*b**3 + 8*a*b**4*x**2 + 4*b**5*x**4) + 4*a*b*x**2*log(I*sqrt(a)*sqrt(1/b) + x)/(4*a**2*b**3 + 8*a*b**4*x**2 + 4*b**5*x**4) + 4*a*b*x**2/(4*a**2*b**3 + 8*a*b**4*x**2 + 4*b**5*x**4) + 2*b**2*x**4*log(-I*sqrt(a)*sqrt(1/b) + x)/(4*a**2*b**3 + 8*a*b**4*x**2 + 4*b**5*x**4) + 2*b**2*x**4*log(I*sqrt(a)*sqrt(1/b) + x)/(4*a**2*b**3 + 8*a*b**4*x**2 + 4*b**5*x**4), Eq(p, -3)), (-2*a**2*log(-I*sqrt(a)*sqrt(1/b) + x)/(2*a*b**3 + 2*b**4*x**2) - 2*a**2*log(I*sqrt(a)*sqrt(1/b) + x)/(2*a*b**3 + 2*b**4*x**2) - 2*a**2/(2*a*b**3 + 2*b**4*x**2) - 2*a*b*x**2*log(-I*sqrt(a)*sqrt(1/b) + x)/(2*a*b**3 + 2*b**4*x**2) - 2*a*b*x**2*log(I*sqrt(a)*sqrt(1/b) + x)/(2*a*b**3 + 2*b**4*x**2) + b**2*x**4/(2*a*b**3 + 2*b**4*x**2), Eq(p, -2)), (a**2*log(-I*sqrt(a)*sqrt(1/b) + x)/(2*b**3) + a**2*log(I*sqrt(a)*sqrt(1/b) + x)/(2*b**3) - a*x**2/(2*b**2) + x**4/(4*b), Eq(p, -1)), (2*a**3*(a + b*x**2)**p/(2*b**3*p**3 + 12*b**3*p**2 + 22*b**3*p + 12*b**3) - 2*a**2*b*p*x**2*(a + b*x**2)**p/(2*b**3*p**3 + 12*b**3*p**2 + 22*b**3*p + 12*b**3) + a*b**2*p**2*x**4*(a + b*x**2)**p/(2*b**3*p**3 + 12*b**3*p**2 + 22*b**3*p + 12*b**3) + a*b**2*p*x**4*(a + b*x**2)**p/(2*b**3*p**3 + 12*b**3*p**2 + 22*b**3*p + 12*b**3) + b**3*p**2*x**6*(a + b*x**2)**p/(2*b**3*p**3 + 12*b**3*p**2 + 22*b**3*p + 12*b**3) + 3*b**3*p*x**6*(a + b*x**2)**p/(2*b**3*p**3 + 12*b**3*p**2 + 22*b**3*p + 12*b**3) + 2*b**3*x**6*(a + b*x**2)**p/(2*b**3*p**3 + 12*b**3*p**2 + 22*b**3*p + 12*b**3), True))","C",0
403,1,471,0,22.795802," ","integrate(x*(e*x+d)**3*(b*x**2+a)**p,x)","a^{p} d^{2} e x^{3} {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{2}, - p \\ \frac{5}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)} + \frac{a^{p} e^{3} x^{5} {{}_{2}F_{1}\left(\begin{matrix} \frac{5}{2}, - p \\ \frac{7}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{5} + d^{3} \left(\begin{cases} \frac{a^{p} x^{2}}{2} & \text{for}\: b = 0 \\\frac{\begin{cases} \frac{\left(a + b x^{2}\right)^{p + 1}}{p + 1} & \text{for}\: p \neq -1 \\\log{\left(a + b x^{2} \right)} & \text{otherwise} \end{cases}}{2 b} & \text{otherwise} \end{cases}\right) + 3 d e^{2} \left(\begin{cases} \frac{a^{p} x^{4}}{4} & \text{for}\: b = 0 \\\frac{a \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 a b^{2} + 2 b^{3} x^{2}} + \frac{a \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 a b^{2} + 2 b^{3} x^{2}} + \frac{a}{2 a b^{2} + 2 b^{3} x^{2}} + \frac{b x^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 a b^{2} + 2 b^{3} x^{2}} + \frac{b x^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 a b^{2} + 2 b^{3} x^{2}} & \text{for}\: p = -2 \\- \frac{a \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 b^{2}} - \frac{a \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 b^{2}} + \frac{x^{2}}{2 b} & \text{for}\: p = -1 \\- \frac{a^{2} \left(a + b x^{2}\right)^{p}}{2 b^{2} p^{2} + 6 b^{2} p + 4 b^{2}} + \frac{a b p x^{2} \left(a + b x^{2}\right)^{p}}{2 b^{2} p^{2} + 6 b^{2} p + 4 b^{2}} + \frac{b^{2} p x^{4} \left(a + b x^{2}\right)^{p}}{2 b^{2} p^{2} + 6 b^{2} p + 4 b^{2}} + \frac{b^{2} x^{4} \left(a + b x^{2}\right)^{p}}{2 b^{2} p^{2} + 6 b^{2} p + 4 b^{2}} & \text{otherwise} \end{cases}\right)"," ",0,"a**p*d**2*e*x**3*hyper((3/2, -p), (5/2,), b*x**2*exp_polar(I*pi)/a) + a**p*e**3*x**5*hyper((5/2, -p), (7/2,), b*x**2*exp_polar(I*pi)/a)/5 + d**3*Piecewise((a**p*x**2/2, Eq(b, 0)), (Piecewise(((a + b*x**2)**(p + 1)/(p + 1), Ne(p, -1)), (log(a + b*x**2), True))/(2*b), True)) + 3*d*e**2*Piecewise((a**p*x**4/4, Eq(b, 0)), (a*log(-I*sqrt(a)*sqrt(1/b) + x)/(2*a*b**2 + 2*b**3*x**2) + a*log(I*sqrt(a)*sqrt(1/b) + x)/(2*a*b**2 + 2*b**3*x**2) + a/(2*a*b**2 + 2*b**3*x**2) + b*x**2*log(-I*sqrt(a)*sqrt(1/b) + x)/(2*a*b**2 + 2*b**3*x**2) + b*x**2*log(I*sqrt(a)*sqrt(1/b) + x)/(2*a*b**2 + 2*b**3*x**2), Eq(p, -2)), (-a*log(-I*sqrt(a)*sqrt(1/b) + x)/(2*b**2) - a*log(I*sqrt(a)*sqrt(1/b) + x)/(2*b**2) + x**2/(2*b), Eq(p, -1)), (-a**2*(a + b*x**2)**p/(2*b**2*p**2 + 6*b**2*p + 4*b**2) + a*b*p*x**2*(a + b*x**2)**p/(2*b**2*p**2 + 6*b**2*p + 4*b**2) + b**2*p*x**4*(a + b*x**2)**p/(2*b**2*p**2 + 6*b**2*p + 4*b**2) + b**2*x**4*(a + b*x**2)**p/(2*b**2*p**2 + 6*b**2*p + 4*b**2), True))","A",0
404,1,468,0,16.256713," ","integrate((e*x+d)**3*(b*x**2+a)**p,x)","a^{p} d^{3} x {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, - p \\ \frac{3}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)} + a^{p} d e^{2} x^{3} {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{2}, - p \\ \frac{5}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)} + 3 d^{2} e \left(\begin{cases} \frac{a^{p} x^{2}}{2} & \text{for}\: b = 0 \\\frac{\begin{cases} \frac{\left(a + b x^{2}\right)^{p + 1}}{p + 1} & \text{for}\: p \neq -1 \\\log{\left(a + b x^{2} \right)} & \text{otherwise} \end{cases}}{2 b} & \text{otherwise} \end{cases}\right) + e^{3} \left(\begin{cases} \frac{a^{p} x^{4}}{4} & \text{for}\: b = 0 \\\frac{a \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 a b^{2} + 2 b^{3} x^{2}} + \frac{a \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 a b^{2} + 2 b^{3} x^{2}} + \frac{a}{2 a b^{2} + 2 b^{3} x^{2}} + \frac{b x^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 a b^{2} + 2 b^{3} x^{2}} + \frac{b x^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 a b^{2} + 2 b^{3} x^{2}} & \text{for}\: p = -2 \\- \frac{a \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 b^{2}} - \frac{a \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + x \right)}}{2 b^{2}} + \frac{x^{2}}{2 b} & \text{for}\: p = -1 \\- \frac{a^{2} \left(a + b x^{2}\right)^{p}}{2 b^{2} p^{2} + 6 b^{2} p + 4 b^{2}} + \frac{a b p x^{2} \left(a + b x^{2}\right)^{p}}{2 b^{2} p^{2} + 6 b^{2} p + 4 b^{2}} + \frac{b^{2} p x^{4} \left(a + b x^{2}\right)^{p}}{2 b^{2} p^{2} + 6 b^{2} p + 4 b^{2}} + \frac{b^{2} x^{4} \left(a + b x^{2}\right)^{p}}{2 b^{2} p^{2} + 6 b^{2} p + 4 b^{2}} & \text{otherwise} \end{cases}\right)"," ",0,"a**p*d**3*x*hyper((1/2, -p), (3/2,), b*x**2*exp_polar(I*pi)/a) + a**p*d*e**2*x**3*hyper((3/2, -p), (5/2,), b*x**2*exp_polar(I*pi)/a) + 3*d**2*e*Piecewise((a**p*x**2/2, Eq(b, 0)), (Piecewise(((a + b*x**2)**(p + 1)/(p + 1), Ne(p, -1)), (log(a + b*x**2), True))/(2*b), True)) + e**3*Piecewise((a**p*x**4/4, Eq(b, 0)), (a*log(-I*sqrt(a)*sqrt(1/b) + x)/(2*a*b**2 + 2*b**3*x**2) + a*log(I*sqrt(a)*sqrt(1/b) + x)/(2*a*b**2 + 2*b**3*x**2) + a/(2*a*b**2 + 2*b**3*x**2) + b*x**2*log(-I*sqrt(a)*sqrt(1/b) + x)/(2*a*b**2 + 2*b**3*x**2) + b*x**2*log(I*sqrt(a)*sqrt(1/b) + x)/(2*a*b**2 + 2*b**3*x**2), Eq(p, -2)), (-a*log(-I*sqrt(a)*sqrt(1/b) + x)/(2*b**2) - a*log(I*sqrt(a)*sqrt(1/b) + x)/(2*b**2) + x**2/(2*b), Eq(p, -1)), (-a**2*(a + b*x**2)**p/(2*b**2*p**2 + 6*b**2*p + 4*b**2) + a*b*p*x**2*(a + b*x**2)**p/(2*b**2*p**2 + 6*b**2*p + 4*b**2) + b**2*p*x**4*(a + b*x**2)**p/(2*b**2*p**2 + 6*b**2*p + 4*b**2) + b**2*x**4*(a + b*x**2)**p/(2*b**2*p**2 + 6*b**2*p + 4*b**2), True))","C",0
405,1,144,0,17.622633," ","integrate((e*x+d)**3*(b*x**2+a)**p/x,x)","3 a^{p} d^{2} e x {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, - p \\ \frac{3}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)} + \frac{a^{p} e^{3} x^{3} {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{2}, - p \\ \frac{5}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{3} - \frac{b^{p} d^{3} x^{2 p} \Gamma\left(- p\right) {{}_{2}F_{1}\left(\begin{matrix} - p, - p \\ 1 - p \end{matrix}\middle| {\frac{a e^{i \pi}}{b x^{2}}} \right)}}{2 \Gamma\left(1 - p\right)} + 3 d e^{2} \left(\begin{cases} \frac{a^{p} x^{2}}{2} & \text{for}\: b = 0 \\\frac{\begin{cases} \frac{\left(a + b x^{2}\right)^{p + 1}}{p + 1} & \text{for}\: p \neq -1 \\\log{\left(a + b x^{2} \right)} & \text{otherwise} \end{cases}}{2 b} & \text{otherwise} \end{cases}\right)"," ",0,"3*a**p*d**2*e*x*hyper((1/2, -p), (3/2,), b*x**2*exp_polar(I*pi)/a) + a**p*e**3*x**3*hyper((3/2, -p), (5/2,), b*x**2*exp_polar(I*pi)/a)/3 - b**p*d**3*x**(2*p)*gamma(-p)*hyper((-p, -p), (1 - p,), a*exp_polar(I*pi)/(b*x**2))/(2*gamma(1 - p)) + 3*d*e**2*Piecewise((a**p*x**2/2, Eq(b, 0)), (Piecewise(((a + b*x**2)**(p + 1)/(p + 1), Ne(p, -1)), (log(a + b*x**2), True))/(2*b), True))","A",0
406,1,143,0,14.908063," ","integrate((e*x+d)**3*(b*x**2+a)**p/x**2,x)","- \frac{a^{p} d^{3} {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, - p \\ \frac{1}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{x} + 3 a^{p} d e^{2} x {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, - p \\ \frac{3}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)} - \frac{3 b^{p} d^{2} e x^{2 p} \Gamma\left(- p\right) {{}_{2}F_{1}\left(\begin{matrix} - p, - p \\ 1 - p \end{matrix}\middle| {\frac{a e^{i \pi}}{b x^{2}}} \right)}}{2 \Gamma\left(1 - p\right)} + e^{3} \left(\begin{cases} \frac{a^{p} x^{2}}{2} & \text{for}\: b = 0 \\\frac{\begin{cases} \frac{\left(a + b x^{2}\right)^{p + 1}}{p + 1} & \text{for}\: p \neq -1 \\\log{\left(a + b x^{2} \right)} & \text{otherwise} \end{cases}}{2 b} & \text{otherwise} \end{cases}\right)"," ",0,"-a**p*d**3*hyper((-1/2, -p), (1/2,), b*x**2*exp_polar(I*pi)/a)/x + 3*a**p*d*e**2*x*hyper((1/2, -p), (3/2,), b*x**2*exp_polar(I*pi)/a) - 3*b**p*d**2*e*x**(2*p)*gamma(-p)*hyper((-p, -p), (1 - p,), a*exp_polar(I*pi)/(b*x**2))/(2*gamma(1 - p)) + e**3*Piecewise((a**p*x**2/2, Eq(b, 0)), (Piecewise(((a + b*x**2)**(p + 1)/(p + 1), Ne(p, -1)), (log(a + b*x**2), True))/(2*b), True))","A",0
407,1,150,0,21.011014," ","integrate((e*x+d)**3*(b*x**2+a)**p/x**3,x)","- \frac{3 a^{p} d^{2} e {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, - p \\ \frac{1}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{x} + a^{p} e^{3} x {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, - p \\ \frac{3}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)} - \frac{b^{p} d^{3} x^{2 p} \Gamma\left(1 - p\right) {{}_{2}F_{1}\left(\begin{matrix} - p, 1 - p \\ 2 - p \end{matrix}\middle| {\frac{a e^{i \pi}}{b x^{2}}} \right)}}{2 x^{2} \Gamma\left(2 - p\right)} - \frac{3 b^{p} d e^{2} x^{2 p} \Gamma\left(- p\right) {{}_{2}F_{1}\left(\begin{matrix} - p, - p \\ 1 - p \end{matrix}\middle| {\frac{a e^{i \pi}}{b x^{2}}} \right)}}{2 \Gamma\left(1 - p\right)}"," ",0,"-3*a**p*d**2*e*hyper((-1/2, -p), (1/2,), b*x**2*exp_polar(I*pi)/a)/x + a**p*e**3*x*hyper((1/2, -p), (3/2,), b*x**2*exp_polar(I*pi)/a) - b**p*d**3*x**(2*p)*gamma(1 - p)*hyper((-p, 1 - p), (2 - p,), a*exp_polar(I*pi)/(b*x**2))/(2*x**2*gamma(2 - p)) - 3*b**p*d*e**2*x**(2*p)*gamma(-p)*hyper((-p, -p), (1 - p,), a*exp_polar(I*pi)/(b*x**2))/(2*gamma(1 - p))","C",0
408,-1,0,0,0.000000," ","integrate(x**4*(b*x**2+a)**p/(e*x+d),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
409,-1,0,0,0.000000," ","integrate(x**3*(b*x**2+a)**p/(e*x+d),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
410,0,0,0,0.000000," ","integrate(x**2*(b*x**2+a)**p/(e*x+d),x)","\int \frac{x^{2} \left(a + b x^{2}\right)^{p}}{d + e x}\, dx"," ",0,"Integral(x**2*(a + b*x**2)**p/(d + e*x), x)","F",0
411,0,0,0,0.000000," ","integrate(x*(b*x**2+a)**p/(e*x+d),x)","\int \frac{x \left(a + b x^{2}\right)^{p}}{d + e x}\, dx"," ",0,"Integral(x*(a + b*x**2)**p/(d + e*x), x)","F",0
412,0,0,0,0.000000," ","integrate((b*x**2+a)**p/(e*x+d),x)","\int \frac{\left(a + b x^{2}\right)^{p}}{d + e x}\, dx"," ",0,"Integral((a + b*x**2)**p/(d + e*x), x)","F",0
413,0,0,0,0.000000," ","integrate((b*x**2+a)**p/x/(e*x+d),x)","\int \frac{\left(a + b x^{2}\right)^{p}}{x \left(d + e x\right)}\, dx"," ",0,"Integral((a + b*x**2)**p/(x*(d + e*x)), x)","F",0
414,0,0,0,0.000000," ","integrate((b*x**2+a)**p/x**2/(e*x+d),x)","\int \frac{\left(a + b x^{2}\right)^{p}}{x^{2} \left(d + e x\right)}\, dx"," ",0,"Integral((a + b*x**2)**p/(x**2*(d + e*x)), x)","F",0
415,-1,0,0,0.000000," ","integrate((b*x**2+a)**p/x**3/(e*x+d),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
416,-1,0,0,0.000000," ","integrate(x**4*(b*x**2+a)**p/(e*x+d)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
417,-1,0,0,0.000000," ","integrate(x**3*(b*x**2+a)**p/(e*x+d)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
418,-1,0,0,0.000000," ","integrate(x**2*(b*x**2+a)**p/(e*x+d)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
419,0,0,0,0.000000," ","integrate(x*(b*x**2+a)**p/(e*x+d)**2,x)","\int \frac{x \left(a + b x^{2}\right)^{p}}{\left(d + e x\right)^{2}}\, dx"," ",0,"Integral(x*(a + b*x**2)**p/(d + e*x)**2, x)","F",0
420,0,0,0,0.000000," ","integrate((b*x**2+a)**p/(e*x+d)**2,x)","\int \frac{\left(a + b x^{2}\right)^{p}}{\left(d + e x\right)^{2}}\, dx"," ",0,"Integral((a + b*x**2)**p/(d + e*x)**2, x)","F",0
421,0,0,0,0.000000," ","integrate((b*x**2+a)**p/x/(e*x+d)**2,x)","\int \frac{\left(a + b x^{2}\right)^{p}}{x \left(d + e x\right)^{2}}\, dx"," ",0,"Integral((a + b*x**2)**p/(x*(d + e*x)**2), x)","F",0
422,-1,0,0,0.000000," ","integrate((b*x**2+a)**p/x**2/(e*x+d)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
423,-1,0,0,0.000000," ","integrate(x**4*(b*x**2+a)**p/(e*x+d)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
424,-1,0,0,0.000000," ","integrate(x**3*(b*x**2+a)**p/(e*x+d)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
425,-1,0,0,0.000000," ","integrate(x**2*(b*x**2+a)**p/(e*x+d)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
426,-1,0,0,0.000000," ","integrate(x*(b*x**2+a)**p/(e*x+d)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
427,-1,0,0,0.000000," ","integrate((b*x**2+a)**p/(e*x+d)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
428,-1,0,0,0.000000," ","integrate((b*x**2+a)**p/x/(e*x+d)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
429,-1,0,0,0.000000," ","integrate((b*x**2+a)**p/x**2/(e*x+d)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
430,-1,0,0,0.000000," ","integrate((g*x)**m*(e*x+d)**3*(c*x**2+a)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
431,1,172,0,170.872146," ","integrate((g*x)**m*(e*x+d)**2*(c*x**2+a)**p,x)","\frac{a^{p} d^{2} g^{m} x x^{m} \Gamma\left(\frac{m}{2} + \frac{1}{2}\right) {{}_{2}F_{1}\left(\begin{matrix} - p, \frac{m}{2} + \frac{1}{2} \\ \frac{m}{2} + \frac{3}{2} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)} + \frac{a^{p} d e g^{m} x^{2} x^{m} \Gamma\left(\frac{m}{2} + 1\right) {{}_{2}F_{1}\left(\begin{matrix} - p, \frac{m}{2} + 1 \\ \frac{m}{2} + 2 \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{\Gamma\left(\frac{m}{2} + 2\right)} + \frac{a^{p} e^{2} g^{m} x^{3} x^{m} \Gamma\left(\frac{m}{2} + \frac{3}{2}\right) {{}_{2}F_{1}\left(\begin{matrix} - p, \frac{m}{2} + \frac{3}{2} \\ \frac{m}{2} + \frac{5}{2} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 \Gamma\left(\frac{m}{2} + \frac{5}{2}\right)}"," ",0,"a**p*d**2*g**m*x*x**m*gamma(m/2 + 1/2)*hyper((-p, m/2 + 1/2), (m/2 + 3/2,), c*x**2*exp_polar(I*pi)/a)/(2*gamma(m/2 + 3/2)) + a**p*d*e*g**m*x**2*x**m*gamma(m/2 + 1)*hyper((-p, m/2 + 1), (m/2 + 2,), c*x**2*exp_polar(I*pi)/a)/gamma(m/2 + 2) + a**p*e**2*g**m*x**3*x**m*gamma(m/2 + 3/2)*hyper((-p, m/2 + 3/2), (m/2 + 5/2,), c*x**2*exp_polar(I*pi)/a)/(2*gamma(m/2 + 5/2))","C",0
432,1,109,0,88.937474," ","integrate((g*x)**m*(e*x+d)*(c*x**2+a)**p,x)","\frac{a^{p} d g^{m} x x^{m} \Gamma\left(\frac{m}{2} + \frac{1}{2}\right) {{}_{2}F_{1}\left(\begin{matrix} - p, \frac{m}{2} + \frac{1}{2} \\ \frac{m}{2} + \frac{3}{2} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)} + \frac{a^{p} e g^{m} x^{2} x^{m} \Gamma\left(\frac{m}{2} + 1\right) {{}_{2}F_{1}\left(\begin{matrix} - p, \frac{m}{2} + 1 \\ \frac{m}{2} + 2 \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 \Gamma\left(\frac{m}{2} + 2\right)}"," ",0,"a**p*d*g**m*x*x**m*gamma(m/2 + 1/2)*hyper((-p, m/2 + 1/2), (m/2 + 3/2,), c*x**2*exp_polar(I*pi)/a)/(2*gamma(m/2 + 3/2)) + a**p*e*g**m*x**2*x**m*gamma(m/2 + 1)*hyper((-p, m/2 + 1), (m/2 + 2,), c*x**2*exp_polar(I*pi)/a)/(2*gamma(m/2 + 2))","C",0
433,1,54,0,22.602269," ","integrate((g*x)**m*(c*x**2+a)**p,x)","\frac{a^{p} g^{m} x x^{m} \Gamma\left(\frac{m}{2} + \frac{1}{2}\right) {{}_{2}F_{1}\left(\begin{matrix} - p, \frac{m}{2} + \frac{1}{2} \\ \frac{m}{2} + \frac{3}{2} \end{matrix}\middle| {\frac{c x^{2} e^{i \pi}}{a}} \right)}}{2 \Gamma\left(\frac{m}{2} + \frac{3}{2}\right)}"," ",0,"a**p*g**m*x*x**m*gamma(m/2 + 1/2)*hyper((-p, m/2 + 1/2), (m/2 + 3/2,), c*x**2*exp_polar(I*pi)/a)/(2*gamma(m/2 + 3/2))","C",0
434,-1,0,0,0.000000," ","integrate((g*x)**m*(c*x**2+a)**p/(e*x+d),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
435,-1,0,0,0.000000," ","integrate((g*x)**m*(c*x**2+a)**p/(e*x+d)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
436,-1,0,0,0.000000," ","integrate((g*x)**m*(c*x**2+a)**p/(e*x+d)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
437,0,0,0,0.000000," ","integrate(x**3*(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(1/2)/(e*x+d),x)","\int \frac{x^{3} \sqrt{\left(d + e x\right) \left(a e + c d x\right)}}{d + e x}\, dx"," ",0,"Integral(x**3*sqrt((d + e*x)*(a*e + c*d*x))/(d + e*x), x)","F",0
438,0,0,0,0.000000," ","integrate(x**2*(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(1/2)/(e*x+d),x)","\int \frac{x^{2} \sqrt{\left(d + e x\right) \left(a e + c d x\right)}}{d + e x}\, dx"," ",0,"Integral(x**2*sqrt((d + e*x)*(a*e + c*d*x))/(d + e*x), x)","F",0
439,0,0,0,0.000000," ","integrate(x*(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(1/2)/(e*x+d),x)","\int \frac{x \sqrt{\left(d + e x\right) \left(a e + c d x\right)}}{d + e x}\, dx"," ",0,"Integral(x*sqrt((d + e*x)*(a*e + c*d*x))/(d + e*x), x)","F",0
440,0,0,0,0.000000," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(1/2)/(e*x+d),x)","\int \frac{\sqrt{\left(d + e x\right) \left(a e + c d x\right)}}{d + e x}\, dx"," ",0,"Integral(sqrt((d + e*x)*(a*e + c*d*x))/(d + e*x), x)","F",0
441,0,0,0,0.000000," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(1/2)/x/(e*x+d),x)","\int \frac{\sqrt{\left(d + e x\right) \left(a e + c d x\right)}}{x \left(d + e x\right)}\, dx"," ",0,"Integral(sqrt((d + e*x)*(a*e + c*d*x))/(x*(d + e*x)), x)","F",0
442,0,0,0,0.000000," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(1/2)/x**2/(e*x+d),x)","\int \frac{\sqrt{\left(d + e x\right) \left(a e + c d x\right)}}{x^{2} \left(d + e x\right)}\, dx"," ",0,"Integral(sqrt((d + e*x)*(a*e + c*d*x))/(x**2*(d + e*x)), x)","F",0
443,0,0,0,0.000000," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(1/2)/x**3/(e*x+d),x)","\int \frac{\sqrt{\left(d + e x\right) \left(a e + c d x\right)}}{x^{3} \left(d + e x\right)}\, dx"," ",0,"Integral(sqrt((d + e*x)*(a*e + c*d*x))/(x**3*(d + e*x)), x)","F",0
444,0,0,0,0.000000," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(1/2)/x**4/(e*x+d),x)","\int \frac{\sqrt{\left(d + e x\right) \left(a e + c d x\right)}}{x^{4} \left(d + e x\right)}\, dx"," ",0,"Integral(sqrt((d + e*x)*(a*e + c*d*x))/(x**4*(d + e*x)), x)","F",0
445,0,0,0,0.000000," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(1/2)/x**5/(e*x+d),x)","\int \frac{\sqrt{\left(d + e x\right) \left(a e + c d x\right)}}{x^{5} \left(d + e x\right)}\, dx"," ",0,"Integral(sqrt((d + e*x)*(a*e + c*d*x))/(x**5*(d + e*x)), x)","F",0
446,0,0,0,0.000000," ","integrate(x**3*(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(3/2)/(e*x+d),x)","\int \frac{x^{3} \left(\left(d + e x\right) \left(a e + c d x\right)\right)^{\frac{3}{2}}}{d + e x}\, dx"," ",0,"Integral(x**3*((d + e*x)*(a*e + c*d*x))**(3/2)/(d + e*x), x)","F",0
447,0,0,0,0.000000," ","integrate(x**2*(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(3/2)/(e*x+d),x)","\int \frac{x^{2} \left(\left(d + e x\right) \left(a e + c d x\right)\right)^{\frac{3}{2}}}{d + e x}\, dx"," ",0,"Integral(x**2*((d + e*x)*(a*e + c*d*x))**(3/2)/(d + e*x), x)","F",0
448,0,0,0,0.000000," ","integrate(x*(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(3/2)/(e*x+d),x)","\int \frac{x \left(\left(d + e x\right) \left(a e + c d x\right)\right)^{\frac{3}{2}}}{d + e x}\, dx"," ",0,"Integral(x*((d + e*x)*(a*e + c*d*x))**(3/2)/(d + e*x), x)","F",0
449,0,0,0,0.000000," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(3/2)/(e*x+d),x)","\int \frac{\left(\left(d + e x\right) \left(a e + c d x\right)\right)^{\frac{3}{2}}}{d + e x}\, dx"," ",0,"Integral(((d + e*x)*(a*e + c*d*x))**(3/2)/(d + e*x), x)","F",0
450,0,0,0,0.000000," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(3/2)/x/(e*x+d),x)","\int \frac{\left(\left(d + e x\right) \left(a e + c d x\right)\right)^{\frac{3}{2}}}{x \left(d + e x\right)}\, dx"," ",0,"Integral(((d + e*x)*(a*e + c*d*x))**(3/2)/(x*(d + e*x)), x)","F",0
451,0,0,0,0.000000," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(3/2)/x**2/(e*x+d),x)","\int \frac{\left(\left(d + e x\right) \left(a e + c d x\right)\right)^{\frac{3}{2}}}{x^{2} \left(d + e x\right)}\, dx"," ",0,"Integral(((d + e*x)*(a*e + c*d*x))**(3/2)/(x**2*(d + e*x)), x)","F",0
452,0,0,0,0.000000," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(3/2)/x**3/(e*x+d),x)","\int \frac{\left(\left(d + e x\right) \left(a e + c d x\right)\right)^{\frac{3}{2}}}{x^{3} \left(d + e x\right)}\, dx"," ",0,"Integral(((d + e*x)*(a*e + c*d*x))**(3/2)/(x**3*(d + e*x)), x)","F",0
453,0,0,0,0.000000," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(3/2)/x**4/(e*x+d),x)","\int \frac{\left(\left(d + e x\right) \left(a e + c d x\right)\right)^{\frac{3}{2}}}{x^{4} \left(d + e x\right)}\, dx"," ",0,"Integral(((d + e*x)*(a*e + c*d*x))**(3/2)/(x**4*(d + e*x)), x)","F",0
454,0,0,0,0.000000," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(3/2)/x**5/(e*x+d),x)","\int \frac{\left(\left(d + e x\right) \left(a e + c d x\right)\right)^{\frac{3}{2}}}{x^{5} \left(d + e x\right)}\, dx"," ",0,"Integral(((d + e*x)*(a*e + c*d*x))**(3/2)/(x**5*(d + e*x)), x)","F",0
455,-1,0,0,0.000000," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(3/2)/x**6/(e*x+d),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
456,-1,0,0,0.000000," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(3/2)/x**7/(e*x+d),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
457,-1,0,0,0.000000," ","integrate(x**3*(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(5/2)/(e*x+d),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
458,-1,0,0,0.000000," ","integrate(x**2*(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(5/2)/(e*x+d),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
459,0,0,0,0.000000," ","integrate(x*(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(5/2)/(e*x+d),x)","\int \frac{x \left(\left(d + e x\right) \left(a e + c d x\right)\right)^{\frac{5}{2}}}{d + e x}\, dx"," ",0,"Integral(x*((d + e*x)*(a*e + c*d*x))**(5/2)/(d + e*x), x)","F",0
460,0,0,0,0.000000," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(5/2)/(e*x+d),x)","\int \frac{\left(\left(d + e x\right) \left(a e + c d x\right)\right)^{\frac{5}{2}}}{d + e x}\, dx"," ",0,"Integral(((d + e*x)*(a*e + c*d*x))**(5/2)/(d + e*x), x)","F",0
461,0,0,0,0.000000," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(5/2)/x/(e*x+d),x)","\int \frac{\left(\left(d + e x\right) \left(a e + c d x\right)\right)^{\frac{5}{2}}}{x \left(d + e x\right)}\, dx"," ",0,"Integral(((d + e*x)*(a*e + c*d*x))**(5/2)/(x*(d + e*x)), x)","F",0
462,0,0,0,0.000000," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(5/2)/x**2/(e*x+d),x)","\int \frac{\left(\left(d + e x\right) \left(a e + c d x\right)\right)^{\frac{5}{2}}}{x^{2} \left(d + e x\right)}\, dx"," ",0,"Integral(((d + e*x)*(a*e + c*d*x))**(5/2)/(x**2*(d + e*x)), x)","F",0
463,-1,0,0,0.000000," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(5/2)/x**3/(e*x+d),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
464,-1,0,0,0.000000," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(5/2)/x**4/(e*x+d),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
465,-1,0,0,0.000000," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(5/2)/x**5/(e*x+d),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
466,-1,0,0,0.000000," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(5/2)/x**6/(e*x+d),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
467,-1,0,0,0.000000," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(5/2)/x**7/(e*x+d),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
468,-1,0,0,0.000000," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(5/2)/x**8/(e*x+d),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
469,-1,0,0,0.000000," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(5/2)/x**9/(e*x+d),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
470,0,0,0,0.000000," ","integrate(x**3/(e*x+d)/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(1/2),x)","\int \frac{x^{3}}{\sqrt{\left(d + e x\right) \left(a e + c d x\right)} \left(d + e x\right)}\, dx"," ",0,"Integral(x**3/(sqrt((d + e*x)*(a*e + c*d*x))*(d + e*x)), x)","F",0
471,0,0,0,0.000000," ","integrate(x**2/(e*x+d)/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(1/2),x)","\int \frac{x^{2}}{\sqrt{\left(d + e x\right) \left(a e + c d x\right)} \left(d + e x\right)}\, dx"," ",0,"Integral(x**2/(sqrt((d + e*x)*(a*e + c*d*x))*(d + e*x)), x)","F",0
472,0,0,0,0.000000," ","integrate(x/(e*x+d)/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(1/2),x)","\int \frac{x}{\sqrt{\left(d + e x\right) \left(a e + c d x\right)} \left(d + e x\right)}\, dx"," ",0,"Integral(x/(sqrt((d + e*x)*(a*e + c*d*x))*(d + e*x)), x)","F",0
473,0,0,0,0.000000," ","integrate(1/(e*x+d)/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(1/2),x)","\int \frac{1}{\sqrt{\left(d + e x\right) \left(a e + c d x\right)} \left(d + e x\right)}\, dx"," ",0,"Integral(1/(sqrt((d + e*x)*(a*e + c*d*x))*(d + e*x)), x)","F",0
474,0,0,0,0.000000," ","integrate(1/x/(e*x+d)/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(1/2),x)","\int \frac{1}{x \sqrt{\left(d + e x\right) \left(a e + c d x\right)} \left(d + e x\right)}\, dx"," ",0,"Integral(1/(x*sqrt((d + e*x)*(a*e + c*d*x))*(d + e*x)), x)","F",0
475,0,0,0,0.000000," ","integrate(1/x**2/(e*x+d)/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(1/2),x)","\int \frac{1}{x^{2} \sqrt{\left(d + e x\right) \left(a e + c d x\right)} \left(d + e x\right)}\, dx"," ",0,"Integral(1/(x**2*sqrt((d + e*x)*(a*e + c*d*x))*(d + e*x)), x)","F",0
476,0,0,0,0.000000," ","integrate(1/x**3/(e*x+d)/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(1/2),x)","\int \frac{1}{x^{3} \sqrt{\left(d + e x\right) \left(a e + c d x\right)} \left(d + e x\right)}\, dx"," ",0,"Integral(1/(x**3*sqrt((d + e*x)*(a*e + c*d*x))*(d + e*x)), x)","F",0
477,0,0,0,0.000000," ","integrate(x**5/(e*x+d)/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(3/2),x)","\int \frac{x^{5}}{\left(\left(d + e x\right) \left(a e + c d x\right)\right)^{\frac{3}{2}} \left(d + e x\right)}\, dx"," ",0,"Integral(x**5/(((d + e*x)*(a*e + c*d*x))**(3/2)*(d + e*x)), x)","F",0
478,0,0,0,0.000000," ","integrate(x**4/(e*x+d)/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(3/2),x)","\int \frac{x^{4}}{\left(\left(d + e x\right) \left(a e + c d x\right)\right)^{\frac{3}{2}} \left(d + e x\right)}\, dx"," ",0,"Integral(x**4/(((d + e*x)*(a*e + c*d*x))**(3/2)*(d + e*x)), x)","F",0
479,0,0,0,0.000000," ","integrate(x**3/(e*x+d)/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(3/2),x)","\int \frac{x^{3}}{\left(\left(d + e x\right) \left(a e + c d x\right)\right)^{\frac{3}{2}} \left(d + e x\right)}\, dx"," ",0,"Integral(x**3/(((d + e*x)*(a*e + c*d*x))**(3/2)*(d + e*x)), x)","F",0
480,0,0,0,0.000000," ","integrate(x**2/(e*x+d)/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(3/2),x)","\int \frac{x^{2}}{\left(\left(d + e x\right) \left(a e + c d x\right)\right)^{\frac{3}{2}} \left(d + e x\right)}\, dx"," ",0,"Integral(x**2/(((d + e*x)*(a*e + c*d*x))**(3/2)*(d + e*x)), x)","F",0
481,0,0,0,0.000000," ","integrate(x/(e*x+d)/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(3/2),x)","\int \frac{x}{\left(\left(d + e x\right) \left(a e + c d x\right)\right)^{\frac{3}{2}} \left(d + e x\right)}\, dx"," ",0,"Integral(x/(((d + e*x)*(a*e + c*d*x))**(3/2)*(d + e*x)), x)","F",0
482,0,0,0,0.000000," ","integrate(1/(e*x+d)/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(3/2),x)","\int \frac{1}{\left(\left(d + e x\right) \left(a e + c d x\right)\right)^{\frac{3}{2}} \left(d + e x\right)}\, dx"," ",0,"Integral(1/(((d + e*x)*(a*e + c*d*x))**(3/2)*(d + e*x)), x)","F",0
483,0,0,0,0.000000," ","integrate(1/x/(e*x+d)/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(3/2),x)","\int \frac{1}{x \left(\left(d + e x\right) \left(a e + c d x\right)\right)^{\frac{3}{2}} \left(d + e x\right)}\, dx"," ",0,"Integral(1/(x*((d + e*x)*(a*e + c*d*x))**(3/2)*(d + e*x)), x)","F",0
484,0,0,0,0.000000," ","integrate(1/x**2/(e*x+d)/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(3/2),x)","\int \frac{1}{x^{2} \left(\left(d + e x\right) \left(a e + c d x\right)\right)^{\frac{3}{2}} \left(d + e x\right)}\, dx"," ",0,"Integral(1/(x**2*((d + e*x)*(a*e + c*d*x))**(3/2)*(d + e*x)), x)","F",0
485,0,0,0,0.000000," ","integrate(1/x**3/(e*x+d)/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(3/2),x)","\int \frac{1}{x^{3} \left(\left(d + e x\right) \left(a e + c d x\right)\right)^{\frac{3}{2}} \left(d + e x\right)}\, dx"," ",0,"Integral(1/(x**3*((d + e*x)*(a*e + c*d*x))**(3/2)*(d + e*x)), x)","F",0
486,0,0,0,0.000000," ","integrate(1/x**4/(e*x+d)/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(3/2),x)","\int \frac{1}{x^{4} \left(\left(d + e x\right) \left(a e + c d x\right)\right)^{\frac{3}{2}} \left(d + e x\right)}\, dx"," ",0,"Integral(1/(x**4*((d + e*x)*(a*e + c*d*x))**(3/2)*(d + e*x)), x)","F",0
487,-1,0,0,0.000000," ","integrate(x**2/(e*x+d)/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
488,-1,0,0,0.000000," ","integrate(x**2/(e*x+d)/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
489,0,0,0,0.000000," ","integrate(x**3*(1+x)**(1/2)*(x**2-x+1)**(1/2),x)","\int x^{3} \sqrt{x + 1} \sqrt{x^{2} - x + 1}\, dx"," ",0,"Integral(x**3*sqrt(x + 1)*sqrt(x**2 - x + 1), x)","F",0
490,0,0,0,0.000000," ","integrate(x**2*(1+x)**(1/2)*(x**2-x+1)**(1/2),x)","\int x^{2} \sqrt{x + 1} \sqrt{x^{2} - x + 1}\, dx"," ",0,"Integral(x**2*sqrt(x + 1)*sqrt(x**2 - x + 1), x)","F",0
491,0,0,0,0.000000," ","integrate(x*(1+x)**(1/2)*(x**2-x+1)**(1/2),x)","\int x \sqrt{x + 1} \sqrt{x^{2} - x + 1}\, dx"," ",0,"Integral(x*sqrt(x + 1)*sqrt(x**2 - x + 1), x)","F",0
492,0,0,0,0.000000," ","integrate((1+x)**(1/2)*(x**2-x+1)**(1/2),x)","\int \sqrt{x + 1} \sqrt{x^{2} - x + 1}\, dx"," ",0,"Integral(sqrt(x + 1)*sqrt(x**2 - x + 1), x)","F",0
493,0,0,0,0.000000," ","integrate((1+x)**(1/2)*(x**2-x+1)**(1/2)/x,x)","\int \frac{\sqrt{x + 1} \sqrt{x^{2} - x + 1}}{x}\, dx"," ",0,"Integral(sqrt(x + 1)*sqrt(x**2 - x + 1)/x, x)","F",0
494,0,0,0,0.000000," ","integrate((1+x)**(1/2)*(x**2-x+1)**(1/2)/x**2,x)","\int \frac{\sqrt{x + 1} \sqrt{x^{2} - x + 1}}{x^{2}}\, dx"," ",0,"Integral(sqrt(x + 1)*sqrt(x**2 - x + 1)/x**2, x)","F",0
495,0,0,0,0.000000," ","integrate((1+x)**(1/2)*(x**2-x+1)**(1/2)/x**3,x)","\int \frac{\sqrt{x + 1} \sqrt{x^{2} - x + 1}}{x^{3}}\, dx"," ",0,"Integral(sqrt(x + 1)*sqrt(x**2 - x + 1)/x**3, x)","F",0
496,0,0,0,0.000000," ","integrate(x**3*(1+x)**(3/2)*(x**2-x+1)**(3/2),x)","\int x^{3} \left(x + 1\right)^{\frac{3}{2}} \left(x^{2} - x + 1\right)^{\frac{3}{2}}\, dx"," ",0,"Integral(x**3*(x + 1)**(3/2)*(x**2 - x + 1)**(3/2), x)","F",0
497,0,0,0,0.000000," ","integrate(x**2*(1+x)**(3/2)*(x**2-x+1)**(3/2),x)","\int x^{2} \left(x + 1\right)^{\frac{3}{2}} \left(x^{2} - x + 1\right)^{\frac{3}{2}}\, dx"," ",0,"Integral(x**2*(x + 1)**(3/2)*(x**2 - x + 1)**(3/2), x)","F",0
498,0,0,0,0.000000," ","integrate(x*(1+x)**(3/2)*(x**2-x+1)**(3/2),x)","\int x \left(x + 1\right)^{\frac{3}{2}} \left(x^{2} - x + 1\right)^{\frac{3}{2}}\, dx"," ",0,"Integral(x*(x + 1)**(3/2)*(x**2 - x + 1)**(3/2), x)","F",0
499,0,0,0,0.000000," ","integrate((1+x)**(3/2)*(x**2-x+1)**(3/2),x)","\int \left(x + 1\right)^{\frac{3}{2}} \left(x^{2} - x + 1\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((x + 1)**(3/2)*(x**2 - x + 1)**(3/2), x)","F",0
500,0,0,0,0.000000," ","integrate((1+x)**(3/2)*(x**2-x+1)**(3/2)/x,x)","\int \frac{\left(x + 1\right)^{\frac{3}{2}} \left(x^{2} - x + 1\right)^{\frac{3}{2}}}{x}\, dx"," ",0,"Integral((x + 1)**(3/2)*(x**2 - x + 1)**(3/2)/x, x)","F",0
501,0,0,0,0.000000," ","integrate((1+x)**(3/2)*(x**2-x+1)**(3/2)/x**2,x)","\int \frac{\left(x + 1\right)^{\frac{3}{2}} \left(x^{2} - x + 1\right)^{\frac{3}{2}}}{x^{2}}\, dx"," ",0,"Integral((x + 1)**(3/2)*(x**2 - x + 1)**(3/2)/x**2, x)","F",0
502,0,0,0,0.000000," ","integrate((1+x)**(3/2)*(x**2-x+1)**(3/2)/x**3,x)","\int \frac{\left(x + 1\right)^{\frac{3}{2}} \left(x^{2} - x + 1\right)^{\frac{3}{2}}}{x^{3}}\, dx"," ",0,"Integral((x + 1)**(3/2)*(x**2 - x + 1)**(3/2)/x**3, x)","F",0
503,0,0,0,0.000000," ","integrate(x**3/(1+x)**(1/2)/(x**2-x+1)**(1/2),x)","\int \frac{x^{3}}{\sqrt{x + 1} \sqrt{x^{2} - x + 1}}\, dx"," ",0,"Integral(x**3/(sqrt(x + 1)*sqrt(x**2 - x + 1)), x)","F",0
504,0,0,0,0.000000," ","integrate(x**2/(1+x)**(1/2)/(x**2-x+1)**(1/2),x)","\int \frac{x^{2}}{\sqrt{x + 1} \sqrt{x^{2} - x + 1}}\, dx"," ",0,"Integral(x**2/(sqrt(x + 1)*sqrt(x**2 - x + 1)), x)","F",0
505,0,0,0,0.000000," ","integrate(x/(1+x)**(1/2)/(x**2-x+1)**(1/2),x)","\int \frac{x}{\sqrt{x + 1} \sqrt{x^{2} - x + 1}}\, dx"," ",0,"Integral(x/(sqrt(x + 1)*sqrt(x**2 - x + 1)), x)","F",0
506,0,0,0,0.000000," ","integrate(1/(1+x)**(1/2)/(x**2-x+1)**(1/2),x)","\int \frac{1}{\sqrt{x + 1} \sqrt{x^{2} - x + 1}}\, dx"," ",0,"Integral(1/(sqrt(x + 1)*sqrt(x**2 - x + 1)), x)","F",0
507,0,0,0,0.000000," ","integrate(1/x/(1+x)**(1/2)/(x**2-x+1)**(1/2),x)","\int \frac{1}{x \sqrt{x + 1} \sqrt{x^{2} - x + 1}}\, dx"," ",0,"Integral(1/(x*sqrt(x + 1)*sqrt(x**2 - x + 1)), x)","F",0
508,0,0,0,0.000000," ","integrate(1/x**2/(1+x)**(1/2)/(x**2-x+1)**(1/2),x)","\int \frac{1}{x^{2} \sqrt{x + 1} \sqrt{x^{2} - x + 1}}\, dx"," ",0,"Integral(1/(x**2*sqrt(x + 1)*sqrt(x**2 - x + 1)), x)","F",0
509,0,0,0,0.000000," ","integrate(1/x**3/(1+x)**(1/2)/(x**2-x+1)**(1/2),x)","\int \frac{1}{x^{3} \sqrt{x + 1} \sqrt{x^{2} - x + 1}}\, dx"," ",0,"Integral(1/(x**3*sqrt(x + 1)*sqrt(x**2 - x + 1)), x)","F",0
510,0,0,0,0.000000," ","integrate(x**3/(1+x)**(3/2)/(x**2-x+1)**(3/2),x)","\int \frac{x^{3}}{\left(x + 1\right)^{\frac{3}{2}} \left(x^{2} - x + 1\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**3/((x + 1)**(3/2)*(x**2 - x + 1)**(3/2)), x)","F",0
511,0,0,0,0.000000," ","integrate(x**2/(1+x)**(3/2)/(x**2-x+1)**(3/2),x)","\int \frac{x^{2}}{\left(x + 1\right)^{\frac{3}{2}} \left(x^{2} - x + 1\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x**2/((x + 1)**(3/2)*(x**2 - x + 1)**(3/2)), x)","F",0
512,0,0,0,0.000000," ","integrate(x/(1+x)**(3/2)/(x**2-x+1)**(3/2),x)","\int \frac{x}{\left(x + 1\right)^{\frac{3}{2}} \left(x^{2} - x + 1\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x/((x + 1)**(3/2)*(x**2 - x + 1)**(3/2)), x)","F",0
513,0,0,0,0.000000," ","integrate(1/(1+x)**(3/2)/(x**2-x+1)**(3/2),x)","\int \frac{1}{\left(x + 1\right)^{\frac{3}{2}} \left(x^{2} - x + 1\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/((x + 1)**(3/2)*(x**2 - x + 1)**(3/2)), x)","F",0
514,0,0,0,0.000000," ","integrate(1/x/(1+x)**(3/2)/(x**2-x+1)**(3/2),x)","\int \frac{1}{x \left(x + 1\right)^{\frac{3}{2}} \left(x^{2} - x + 1\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/(x*(x + 1)**(3/2)*(x**2 - x + 1)**(3/2)), x)","F",0
515,0,0,0,0.000000," ","integrate(1/x**2/(1+x)**(3/2)/(x**2-x+1)**(3/2),x)","\int \frac{1}{x^{2} \left(x + 1\right)^{\frac{3}{2}} \left(x^{2} - x + 1\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/(x**2*(x + 1)**(3/2)*(x**2 - x + 1)**(3/2)), x)","F",0
516,0,0,0,0.000000," ","integrate(1/x**3/(1+x)**(3/2)/(x**2-x+1)**(3/2),x)","\int \frac{1}{x^{3} \left(x + 1\right)^{\frac{3}{2}} \left(x^{2} - x + 1\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/(x**3*(x + 1)**(3/2)*(x**2 - x + 1)**(3/2)), x)","F",0
517,0,0,0,0.000000," ","integrate(x**3/(1+x)**(5/2)/(x**2-x+1)**(5/2),x)","\int \frac{x^{3}}{\left(x + 1\right)^{\frac{5}{2}} \left(x^{2} - x + 1\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(x**3/((x + 1)**(5/2)*(x**2 - x + 1)**(5/2)), x)","F",0
518,0,0,0,0.000000," ","integrate(x**2/(1+x)**(5/2)/(x**2-x+1)**(5/2),x)","\int \frac{x^{2}}{\left(x + 1\right)^{\frac{5}{2}} \left(x^{2} - x + 1\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(x**2/((x + 1)**(5/2)*(x**2 - x + 1)**(5/2)), x)","F",0
519,0,0,0,0.000000," ","integrate(x/(1+x)**(5/2)/(x**2-x+1)**(5/2),x)","\int \frac{x}{\left(x + 1\right)^{\frac{5}{2}} \left(x^{2} - x + 1\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(x/((x + 1)**(5/2)*(x**2 - x + 1)**(5/2)), x)","F",0
520,0,0,0,0.000000," ","integrate(1/(1+x)**(5/2)/(x**2-x+1)**(5/2),x)","\int \frac{1}{\left(x + 1\right)^{\frac{5}{2}} \left(x^{2} - x + 1\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(1/((x + 1)**(5/2)*(x**2 - x + 1)**(5/2)), x)","F",0
521,0,0,0,0.000000," ","integrate(1/x/(1+x)**(5/2)/(x**2-x+1)**(5/2),x)","\int \frac{1}{x \left(x + 1\right)^{\frac{5}{2}} \left(x^{2} - x + 1\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(1/(x*(x + 1)**(5/2)*(x**2 - x + 1)**(5/2)), x)","F",0
522,0,0,0,0.000000," ","integrate(1/x**2/(1+x)**(5/2)/(x**2-x+1)**(5/2),x)","\int \frac{1}{x^{2} \left(x + 1\right)^{\frac{5}{2}} \left(x^{2} - x + 1\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(1/(x**2*(x + 1)**(5/2)*(x**2 - x + 1)**(5/2)), x)","F",0
523,0,0,0,0.000000," ","integrate(1/x**3/(1+x)**(5/2)/(x**2-x+1)**(5/2),x)","\int \frac{1}{x^{3} \left(x + 1\right)^{\frac{5}{2}} \left(x^{2} - x + 1\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(1/(x**3*(x + 1)**(5/2)*(x**2 - x + 1)**(5/2)), x)","F",0
524,1,88,0,0.242931," ","integrate(x/(-1+x)**3/(4*x**2+5*x+3)**2,x)","\frac{388 x^{3} - 407 x^{2} - 120 x - 45}{17664 x^{4} - 13248 x^{3} - 13248 x^{2} - 4416 x + 13248} + \frac{11 \log{\left(x - 1 \right)}}{2304} - \frac{11 \log{\left(x^{2} + \frac{5 x}{4} + \frac{3}{4} \right)}}{4608} + \frac{6023 \sqrt{23} \operatorname{atan}{\left(\frac{8 \sqrt{23} x}{23} + \frac{5 \sqrt{23}}{23} \right)}}{1218816}"," ",0,"(388*x**3 - 407*x**2 - 120*x - 45)/(17664*x**4 - 13248*x**3 - 13248*x**2 - 4416*x + 13248) + 11*log(x - 1)/2304 - 11*log(x**2 + 5*x/4 + 3/4)/4608 + 6023*sqrt(23)*atan(8*sqrt(23)*x/23 + 5*sqrt(23)/23)/1218816","A",0
525,-1,0,0,0.000000," ","integrate(x**4*(e*x+d)**(1/2)/(c*x**2+b*x+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
526,-1,0,0,0.000000," ","integrate(x**3*(e*x+d)**(1/2)/(c*x**2+b*x+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
527,-1,0,0,0.000000," ","integrate(x**2*(e*x+d)**(1/2)/(c*x**2+b*x+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
528,-1,0,0,0.000000," ","integrate(x*(e*x+d)**(1/2)/(c*x**2+b*x+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
529,1,155,0,50.095837," ","integrate((e*x+d)**(1/2)/(c*x**2+b*x+a),x)","2 e \operatorname{RootSum} {\left(t^{4} \left(256 a^{2} c^{3} e^{4} - 128 a b^{2} c^{2} e^{4} + 16 b^{4} c e^{4}\right) + t^{2} \left(- 16 a b c e^{3} + 32 a c^{2} d e^{2} + 4 b^{3} e^{3} - 8 b^{2} c d e^{2}\right) + a e^{2} - b d e + c d^{2}, \left( t \mapsto t \log{\left(64 t^{3} a c^{2} e^{2} - 16 t^{3} b^{2} c e^{2} - 2 t b e + 4 t c d + \sqrt{d + e x} \right)} \right)\right)}"," ",0,"2*e*RootSum(_t**4*(256*a**2*c**3*e**4 - 128*a*b**2*c**2*e**4 + 16*b**4*c*e**4) + _t**2*(-16*a*b*c*e**3 + 32*a*c**2*d*e**2 + 4*b**3*e**3 - 8*b**2*c*d*e**2) + a*e**2 - b*d*e + c*d**2, Lambda(_t, _t*log(64*_t**3*a*c**2*e**2 - 16*_t**3*b**2*c*e**2 - 2*_t*b*e + 4*_t*c*d + sqrt(d + e*x))))","A",0
530,-1,0,0,0.000000," ","integrate((e*x+d)**(1/2)/x/(c*x**2+b*x+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
531,-1,0,0,0.000000," ","integrate((e*x+d)**(1/2)/x**2/(c*x**2+b*x+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
532,-1,0,0,0.000000," ","integrate((e*x+d)**(1/2)/x**3/(c*x**2+b*x+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
533,-1,0,0,0.000000," ","integrate(x**4*(e*x+d)**(3/2)/(c*x**2+b*x+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
534,-1,0,0,0.000000," ","integrate(x**3*(e*x+d)**(3/2)/(c*x**2+b*x+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
535,-1,0,0,0.000000," ","integrate(x**2*(e*x+d)**(3/2)/(c*x**2+b*x+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
536,-1,0,0,0.000000," ","integrate(x*(e*x+d)**(3/2)/(c*x**2+b*x+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
537,-1,0,0,0.000000," ","integrate((e*x+d)**(3/2)/(c*x**2+b*x+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
538,-1,0,0,0.000000," ","integrate((e*x+d)**(3/2)/x/(c*x**2+b*x+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
539,-1,0,0,0.000000," ","integrate((e*x+d)**(3/2)/x**2/(c*x**2+b*x+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
540,-1,0,0,0.000000," ","integrate((e*x+d)**(3/2)/x**3/(c*x**2+b*x+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
541,-1,0,0,0.000000," ","integrate(x**m*(f*x+e)**n/(c*x**2+b*x+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
542,-2,0,0,0.000000," ","integrate(x**3*(f*x+e)**n/(c*x**2+b*x+a),x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
543,0,0,0,0.000000," ","integrate(x**2*(f*x+e)**n/(c*x**2+b*x+a),x)","\int \frac{x^{2} \left(e + f x\right)^{n}}{a + b x + c x^{2}}\, dx"," ",0,"Integral(x**2*(e + f*x)**n/(a + b*x + c*x**2), x)","F",0
544,0,0,0,0.000000," ","integrate(x*(f*x+e)**n/(c*x**2+b*x+a),x)","\int \frac{x \left(e + f x\right)^{n}}{a + b x + c x^{2}}\, dx"," ",0,"Integral(x*(e + f*x)**n/(a + b*x + c*x**2), x)","F",0
545,0,0,0,0.000000," ","integrate((f*x+e)**n/(c*x**2+b*x+a),x)","\int \frac{\left(e + f x\right)^{n}}{a + b x + c x^{2}}\, dx"," ",0,"Integral((e + f*x)**n/(a + b*x + c*x**2), x)","F",0
546,0,0,0,0.000000," ","integrate((f*x+e)**n/x/(c*x**2+b*x+a),x)","\int \frac{\left(e + f x\right)^{n}}{x \left(a + b x + c x^{2}\right)}\, dx"," ",0,"Integral((e + f*x)**n/(x*(a + b*x + c*x**2)), x)","F",0
547,-1,0,0,0.000000," ","integrate((f*x+e)**n/x**2/(c*x**2+b*x+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
548,1,150,0,0.604479," ","integrate((e*x+d)**4*(g*x+f)**2/(-e**2*x**2+d**2),x)","- \frac{8 d^{3} \left(d g + e f\right)^{2} \log{\left(- d + e x \right)}}{e^{3}} - \frac{e^{2} g^{2} x^{5}}{5} - x^{4} \left(d e g^{2} + \frac{e^{2} f g}{2}\right) - x^{3} \left(\frac{7 d^{2} g^{2}}{3} + \frac{8 d e f g}{3} + \frac{e^{2} f^{2}}{3}\right) - x^{2} \left(\frac{4 d^{3} g^{2}}{e} + 7 d^{2} f g + 2 d e f^{2}\right) - x \left(\frac{8 d^{4} g^{2}}{e^{2}} + \frac{16 d^{3} f g}{e} + 7 d^{2} f^{2}\right)"," ",0,"-8*d**3*(d*g + e*f)**2*log(-d + e*x)/e**3 - e**2*g**2*x**5/5 - x**4*(d*e*g**2 + e**2*f*g/2) - x**3*(7*d**2*g**2/3 + 8*d*e*f*g/3 + e**2*f**2/3) - x**2*(4*d**3*g**2/e + 7*d**2*f*g + 2*d*e*f**2) - x*(8*d**4*g**2/e**2 + 16*d**3*f*g/e + 7*d**2*f**2)","A",0
549,1,109,0,0.479314," ","integrate((e*x+d)**3*(g*x+f)**2/(-e**2*x**2+d**2),x)","- \frac{4 d^{2} \left(d g + e f\right)^{2} \log{\left(- d + e x \right)}}{e^{3}} - \frac{e g^{2} x^{4}}{4} - x^{3} \left(d g^{2} + \frac{2 e f g}{3}\right) - x^{2} \left(\frac{2 d^{2} g^{2}}{e} + 3 d f g + \frac{e f^{2}}{2}\right) - x \left(\frac{4 d^{3} g^{2}}{e^{2}} + \frac{8 d^{2} f g}{e} + 3 d f^{2}\right)"," ",0,"-4*d**2*(d*g + e*f)**2*log(-d + e*x)/e**3 - e*g**2*x**4/4 - x**3*(d*g**2 + 2*e*f*g/3) - x**2*(2*d**2*g**2/e + 3*d*f*g + e*f**2/2) - x*(4*d**3*g**2/e**2 + 8*d**2*f*g/e + 3*d*f**2)","A",0
550,1,70,0,0.381010," ","integrate((e*x+d)**2*(g*x+f)**2/(-e**2*x**2+d**2),x)","- \frac{2 d \left(d g + e f\right)^{2} \log{\left(- d + e x \right)}}{e^{3}} - \frac{g^{2} x^{3}}{3} - x^{2} \left(\frac{d g^{2}}{e} + f g\right) - x \left(\frac{2 d^{2} g^{2}}{e^{2}} + \frac{4 d f g}{e} + f^{2}\right)"," ",0,"-2*d*(d*g + e*f)**2*log(-d + e*x)/e**3 - g**2*x**3/3 - x**2*(d*g**2/e + f*g) - x*(2*d**2*g**2/e**2 + 4*d*f*g/e + f**2)","A",0
551,1,46,0,0.291494," ","integrate((e*x+d)*(g*x+f)**2/(-e**2*x**2+d**2),x)","- x \left(\frac{d g^{2}}{e^{2}} + \frac{2 f g}{e}\right) - \frac{g^{2} x^{2}}{2 e} - \frac{\left(d g + e f\right)^{2} \log{\left(- d + e x \right)}}{e^{3}}"," ",0,"-x*(d*g**2/e**2 + 2*f*g/e) - g**2*x**2/(2*e) - (d*g + e*f)**2*log(-d + e*x)/e**3","A",0
552,1,112,0,0.644970," ","integrate((g*x+f)**2/(-e**2*x**2+d**2),x)","- \frac{g^{2} x}{e^{2}} + \frac{\left(d g - e f\right)^{2} \log{\left(x + \frac{2 d^{2} f g + \frac{d \left(d g - e f\right)^{2}}{e}}{d^{2} g^{2} + e^{2} f^{2}} \right)}}{2 d e^{3}} - \frac{\left(d g + e f\right)^{2} \log{\left(x + \frac{2 d^{2} f g - \frac{d \left(d g + e f\right)^{2}}{e}}{d^{2} g^{2} + e^{2} f^{2}} \right)}}{2 d e^{3}}"," ",0,"-g**2*x/e**2 + (d*g - e*f)**2*log(x + (2*d**2*f*g + d*(d*g - e*f)**2/e)/(d**2*g**2 + e**2*f**2))/(2*d*e**3) - (d*g + e*f)**2*log(x + (2*d**2*f*g - d*(d*g + e*f)**2/e)/(d**2*g**2 + e**2*f**2))/(2*d*e**3)","B",0
553,1,182,0,1.002063," ","integrate((g*x+f)**2/(e*x+d)/(-e**2*x**2+d**2),x)","- \frac{d^{2} g^{2} - 2 d e f g + e^{2} f^{2}}{2 d^{2} e^{3} + 2 d e^{4} x} - \frac{\left(d g - e f\right) \left(3 d g + e f\right) \log{\left(x + \frac{- 2 d^{3} g^{2} + d \left(d g - e f\right) \left(3 d g + e f\right)}{d^{2} e g^{2} - 2 d e^{2} f g - e^{3} f^{2}} \right)}}{4 d^{2} e^{3}} - \frac{\left(d g + e f\right)^{2} \log{\left(x + \frac{- 2 d^{3} g^{2} + d \left(d g + e f\right)^{2}}{d^{2} e g^{2} - 2 d e^{2} f g - e^{3} f^{2}} \right)}}{4 d^{2} e^{3}}"," ",0,"-(d**2*g**2 - 2*d*e*f*g + e**2*f**2)/(2*d**2*e**3 + 2*d*e**4*x) - (d*g - e*f)*(3*d*g + e*f)*log(x + (-2*d**3*g**2 + d*(d*g - e*f)*(3*d*g + e*f))/(d**2*e*g**2 - 2*d*e**2*f*g - e**3*f**2))/(4*d**2*e**3) - (d*g + e*f)**2*log(x + (-2*d**3*g**2 + d*(d*g + e*f)**2)/(d**2*e*g**2 - 2*d*e**2*f*g - e**3*f**2))/(4*d**2*e**3)","B",0
554,1,185,0,1.026891," ","integrate((g*x+f)**2/(e*x+d)**2/(-e**2*x**2+d**2),x)","- \frac{- 2 d^{3} g^{2} + 2 d e^{2} f^{2} + x \left(- 3 d^{2} e g^{2} + 2 d e^{2} f g + e^{3} f^{2}\right)}{4 d^{4} e^{3} + 8 d^{3} e^{4} x + 4 d^{2} e^{5} x^{2}} - \frac{\left(d g + e f\right)^{2} \log{\left(- \frac{d \left(d g + e f\right)^{2}}{e \left(d^{2} g^{2} + 2 d e f g + e^{2} f^{2}\right)} + x \right)}}{8 d^{3} e^{3}} + \frac{\left(d g + e f\right)^{2} \log{\left(\frac{d \left(d g + e f\right)^{2}}{e \left(d^{2} g^{2} + 2 d e f g + e^{2} f^{2}\right)} + x \right)}}{8 d^{3} e^{3}}"," ",0,"-(-2*d**3*g**2 + 2*d*e**2*f**2 + x*(-3*d**2*e*g**2 + 2*d*e**2*f*g + e**3*f**2))/(4*d**4*e**3 + 8*d**3*e**4*x + 4*d**2*e**5*x**2) - (d*g + e*f)**2*log(-d*(d*g + e*f)**2/(e*(d**2*g**2 + 2*d*e*f*g + e**2*f**2)) + x)/(8*d**3*e**3) + (d*g + e*f)**2*log(d*(d*g + e*f)**2/(e*(d**2*g**2 + 2*d*e*f*g + e**2*f**2)) + x)/(8*d**3*e**3)","B",0
555,1,248,0,1.416362," ","integrate((g*x+f)**2/(e*x+d)**3/(-e**2*x**2+d**2),x)","- \frac{- 2 d^{4} g^{2} + 4 d^{3} e f g + 10 d^{2} e^{2} f^{2} + x^{2} \left(3 d^{2} e^{2} g^{2} + 6 d e^{3} f g + 3 e^{4} f^{2}\right) + x \left(- 3 d^{3} e g^{2} + 18 d^{2} e^{2} f g + 9 d e^{3} f^{2}\right)}{24 d^{6} e^{3} + 72 d^{5} e^{4} x + 72 d^{4} e^{5} x^{2} + 24 d^{3} e^{6} x^{3}} - \frac{\left(d g + e f\right)^{2} \log{\left(- \frac{d \left(d g + e f\right)^{2}}{e \left(d^{2} g^{2} + 2 d e f g + e^{2} f^{2}\right)} + x \right)}}{16 d^{4} e^{3}} + \frac{\left(d g + e f\right)^{2} \log{\left(\frac{d \left(d g + e f\right)^{2}}{e \left(d^{2} g^{2} + 2 d e f g + e^{2} f^{2}\right)} + x \right)}}{16 d^{4} e^{3}}"," ",0,"-(-2*d**4*g**2 + 4*d**3*e*f*g + 10*d**2*e**2*f**2 + x**2*(3*d**2*e**2*g**2 + 6*d*e**3*f*g + 3*e**4*f**2) + x*(-3*d**3*e*g**2 + 18*d**2*e**2*f*g + 9*d*e**3*f**2))/(24*d**6*e**3 + 72*d**5*e**4*x + 72*d**4*e**5*x**2 + 24*d**3*e**6*x**3) - (d*g + e*f)**2*log(-d*(d*g + e*f)**2/(e*(d**2*g**2 + 2*d*e*f*g + e**2*f**2)) + x)/(16*d**4*e**3) + (d*g + e*f)**2*log(d*(d*g + e*f)**2/(e*(d**2*g**2 + 2*d*e*f*g + e**2*f**2)) + x)/(16*d**4*e**3)","B",0
556,1,282,0,1.925094," ","integrate((g*x+f)**2/(e*x+d)**4/(-e**2*x**2+d**2),x)","- \frac{8 d^{4} f g + 16 d^{3} e f^{2} + x^{3} \left(3 d^{2} e^{2} g^{2} + 6 d e^{3} f g + 3 e^{4} f^{2}\right) + x^{2} \left(12 d^{3} e g^{2} + 24 d^{2} e^{2} f g + 12 d e^{3} f^{2}\right) + x \left(3 d^{4} g^{2} + 38 d^{3} e f g + 19 d^{2} e^{2} f^{2}\right)}{48 d^{8} e^{2} + 192 d^{7} e^{3} x + 288 d^{6} e^{4} x^{2} + 192 d^{5} e^{5} x^{3} + 48 d^{4} e^{6} x^{4}} - \frac{\left(d g + e f\right)^{2} \log{\left(- \frac{d \left(d g + e f\right)^{2}}{e \left(d^{2} g^{2} + 2 d e f g + e^{2} f^{2}\right)} + x \right)}}{32 d^{5} e^{3}} + \frac{\left(d g + e f\right)^{2} \log{\left(\frac{d \left(d g + e f\right)^{2}}{e \left(d^{2} g^{2} + 2 d e f g + e^{2} f^{2}\right)} + x \right)}}{32 d^{5} e^{3}}"," ",0,"-(8*d**4*f*g + 16*d**3*e*f**2 + x**3*(3*d**2*e**2*g**2 + 6*d*e**3*f*g + 3*e**4*f**2) + x**2*(12*d**3*e*g**2 + 24*d**2*e**2*f*g + 12*d*e**3*f**2) + x*(3*d**4*g**2 + 38*d**3*e*f*g + 19*d**2*e**2*f**2))/(48*d**8*e**2 + 192*d**7*e**3*x + 288*d**6*e**4*x**2 + 192*d**5*e**5*x**3 + 48*d**4*e**6*x**4) - (d*g + e*f)**2*log(-d*(d*g + e*f)**2/(e*(d**2*g**2 + 2*d*e*f*g + e**2*f**2)) + x)/(32*d**5*e**3) + (d*g + e*f)**2*log(d*(d*g + e*f)**2/(e*(d**2*g**2 + 2*d*e*f*g + e**2*f**2)) + x)/(32*d**5*e**3)","B",0
557,1,250,0,1.202842," ","integrate((e*x+d)**7*(g*x+f)**2/(-e**2*x**2+d**2)**2,x)","\frac{16 d^{4} \left(d g + e f\right) \left(9 d g + 5 e f\right) \log{\left(- d + e x \right)}}{e^{3}} + \frac{e^{3} g^{2} x^{6}}{6} + x^{5} \left(\frac{7 d e^{2} g^{2}}{5} + \frac{2 e^{3} f g}{5}\right) + x^{4} \left(\frac{23 d^{2} e g^{2}}{4} + \frac{7 d e^{2} f g}{2} + \frac{e^{3} f^{2}}{4}\right) + x^{3} \left(\frac{49 d^{3} g^{2}}{3} + \frac{46 d^{2} e f g}{3} + \frac{7 d e^{2} f^{2}}{3}\right) + x^{2} \left(\frac{40 d^{4} g^{2}}{e} + 49 d^{3} f g + \frac{23 d^{2} e f^{2}}{2}\right) + x \left(\frac{112 d^{5} g^{2}}{e^{2}} + \frac{160 d^{4} f g}{e} + 49 d^{3} f^{2}\right) + \frac{- 32 d^{7} g^{2} - 64 d^{6} e f g - 32 d^{5} e^{2} f^{2}}{- d e^{3} + e^{4} x}"," ",0,"16*d**4*(d*g + e*f)*(9*d*g + 5*e*f)*log(-d + e*x)/e**3 + e**3*g**2*x**6/6 + x**5*(7*d*e**2*g**2/5 + 2*e**3*f*g/5) + x**4*(23*d**2*e*g**2/4 + 7*d*e**2*f*g/2 + e**3*f**2/4) + x**3*(49*d**3*g**2/3 + 46*d**2*e*f*g/3 + 7*d*e**2*f**2/3) + x**2*(40*d**4*g**2/e + 49*d**3*f*g + 23*d**2*e*f**2/2) + x*(112*d**5*g**2/e**2 + 160*d**4*f*g/e + 49*d**3*f**2) + (-32*d**7*g**2 - 64*d**6*e*f*g - 32*d**5*e**2*f**2)/(-d*e**3 + e**4*x)","A",0
558,1,199,0,1.013574," ","integrate((e*x+d)**6*(g*x+f)**2/(-e**2*x**2+d**2)**2,x)","\frac{32 d^{3} \left(d g + e f\right) \left(2 d g + e f\right) \log{\left(- d + e x \right)}}{e^{3}} + \frac{e^{2} g^{2} x^{5}}{5} + x^{4} \left(\frac{3 d e g^{2}}{2} + \frac{e^{2} f g}{2}\right) + x^{3} \left(\frac{17 d^{2} g^{2}}{3} + 4 d e f g + \frac{e^{2} f^{2}}{3}\right) + x^{2} \left(\frac{16 d^{3} g^{2}}{e} + 17 d^{2} f g + 3 d e f^{2}\right) + x \left(\frac{48 d^{4} g^{2}}{e^{2}} + \frac{64 d^{3} f g}{e} + 17 d^{2} f^{2}\right) + \frac{- 16 d^{6} g^{2} - 32 d^{5} e f g - 16 d^{4} e^{2} f^{2}}{- d e^{3} + e^{4} x}"," ",0,"32*d**3*(d*g + e*f)*(2*d*g + e*f)*log(-d + e*x)/e**3 + e**2*g**2*x**5/5 + x**4*(3*d*e*g**2/2 + e**2*f*g/2) + x**3*(17*d**2*g**2/3 + 4*d*e*f*g + e**2*f**2/3) + x**2*(16*d**3*g**2/e + 17*d**2*f*g + 3*d*e*f**2) + x*(48*d**4*g**2/e**2 + 64*d**3*f*g/e + 17*d**2*f**2) + (-16*d**6*g**2 - 32*d**5*e*f*g - 16*d**4*e**2*f**2)/(-d*e**3 + e**4*x)","A",0
559,1,162,0,0.854376," ","integrate((e*x+d)**5*(g*x+f)**2/(-e**2*x**2+d**2)**2,x)","\frac{4 d^{2} \left(d g + e f\right) \left(7 d g + 3 e f\right) \log{\left(- d + e x \right)}}{e^{3}} + \frac{e g^{2} x^{4}}{4} + x^{3} \left(\frac{5 d g^{2}}{3} + \frac{2 e f g}{3}\right) + x^{2} \left(\frac{6 d^{2} g^{2}}{e} + 5 d f g + \frac{e f^{2}}{2}\right) + x \left(\frac{20 d^{3} g^{2}}{e^{2}} + \frac{24 d^{2} f g}{e} + 5 d f^{2}\right) + \frac{- 8 d^{5} g^{2} - 16 d^{4} e f g - 8 d^{3} e^{2} f^{2}}{- d e^{3} + e^{4} x}"," ",0,"4*d**2*(d*g + e*f)*(7*d*g + 3*e*f)*log(-d + e*x)/e**3 + e*g**2*x**4/4 + x**3*(5*d*g**2/3 + 2*e*f*g/3) + x**2*(6*d**2*g**2/e + 5*d*f*g + e*f**2/2) + x*(20*d**3*g**2/e**2 + 24*d**2*f*g/e + 5*d*f**2) + (-8*d**5*g**2 - 16*d**4*e*f*g - 8*d**3*e**2*f**2)/(-d*e**3 + e**4*x)","A",0
560,1,119,0,0.742807," ","integrate((e*x+d)**4*(g*x+f)**2/(-e**2*x**2+d**2)**2,x)","\frac{4 d \left(d g + e f\right) \left(3 d g + e f\right) \log{\left(- d + e x \right)}}{e^{3}} + \frac{g^{2} x^{3}}{3} + x^{2} \left(\frac{2 d g^{2}}{e} + f g\right) + x \left(\frac{8 d^{2} g^{2}}{e^{2}} + \frac{8 d f g}{e} + f^{2}\right) + \frac{- 4 d^{4} g^{2} - 8 d^{3} e f g - 4 d^{2} e^{2} f^{2}}{- d e^{3} + e^{4} x}"," ",0,"4*d*(d*g + e*f)*(3*d*g + e*f)*log(-d + e*x)/e**3 + g**2*x**3/3 + x**2*(2*d*g**2/e + f*g) + x*(8*d**2*g**2/e**2 + 8*d*f*g/e + f**2) + (-4*d**4*g**2 - 8*d**3*e*f*g - 4*d**2*e**2*f**2)/(-d*e**3 + e**4*x)","A",0
561,1,94,0,0.585929," ","integrate((e*x+d)**3*(g*x+f)**2/(-e**2*x**2+d**2)**2,x)","x \left(\frac{3 d g^{2}}{e^{2}} + \frac{2 f g}{e}\right) + \frac{- 2 d^{3} g^{2} - 4 d^{2} e f g - 2 d e^{2} f^{2}}{- d e^{3} + e^{4} x} + \frac{g^{2} x^{2}}{2 e} + \frac{\left(d g + e f\right) \left(5 d g + e f\right) \log{\left(- d + e x \right)}}{e^{3}}"," ",0,"x*(3*d*g**2/e**2 + 2*f*g/e) + (-2*d**3*g**2 - 4*d**2*e*f*g - 2*d*e**2*f**2)/(-d*e**3 + e**4*x) + g**2*x**2/(2*e) + (d*g + e*f)*(5*d*g + e*f)*log(-d + e*x)/e**3","A",0
562,1,61,0,0.401622," ","integrate((e*x+d)**2*(g*x+f)**2/(-e**2*x**2+d**2)**2,x)","\frac{- d^{2} g^{2} - 2 d e f g - e^{2} f^{2}}{- d e^{3} + e^{4} x} + \frac{g^{2} x}{e^{2}} + \frac{2 g \left(d g + e f\right) \log{\left(- d + e x \right)}}{e^{3}}"," ",0,"(-d**2*g**2 - 2*d*e*f*g - e**2*f**2)/(-d*e**3 + e**4*x) + g**2*x/e**2 + 2*g*(d*g + e*f)*log(-d + e*x)/e**3","A",0
563,1,182,0,1.039784," ","integrate((e*x+d)*(g*x+f)**2/(-e**2*x**2+d**2)**2,x)","\frac{- d^{2} g^{2} - 2 d e f g - e^{2} f^{2}}{- 2 d^{2} e^{3} + 2 d e^{4} x} + \frac{\left(d g - e f\right)^{2} \log{\left(x + \frac{2 d^{3} g^{2} - d \left(d g - e f\right)^{2}}{d^{2} e g^{2} + 2 d e^{2} f g - e^{3} f^{2}} \right)}}{4 d^{2} e^{3}} + \frac{\left(d g + e f\right) \left(3 d g - e f\right) \log{\left(x + \frac{2 d^{3} g^{2} - d \left(d g + e f\right) \left(3 d g - e f\right)}{d^{2} e g^{2} + 2 d e^{2} f g - e^{3} f^{2}} \right)}}{4 d^{2} e^{3}}"," ",0,"(-d**2*g**2 - 2*d*e*f*g - e**2*f**2)/(-2*d**2*e**3 + 2*d*e**4*x) + (d*g - e*f)**2*log(x + (2*d**3*g**2 - d*(d*g - e*f)**2)/(d**2*e*g**2 + 2*d*e**2*f*g - e**3*f**2))/(4*d**2*e**3) + (d*g + e*f)*(3*d*g - e*f)*log(x + (2*d**3*g**2 - d*(d*g + e*f)*(3*d*g - e*f))/(d**2*e*g**2 + 2*d*e**2*f*g - e**3*f**2))/(4*d**2*e**3)","B",0
564,1,156,0,0.714157," ","integrate((g*x+f)**2/(-e**2*x**2+d**2)**2,x)","\frac{- 2 d^{2} f g + x \left(- d^{2} g^{2} - e^{2} f^{2}\right)}{- 2 d^{4} e^{2} + 2 d^{2} e^{4} x^{2}} + \frac{\left(d g - e f\right) \left(d g + e f\right) \log{\left(- \frac{d \left(d g - e f\right) \left(d g + e f\right)}{e \left(d^{2} g^{2} - e^{2} f^{2}\right)} + x \right)}}{4 d^{3} e^{3}} - \frac{\left(d g - e f\right) \left(d g + e f\right) \log{\left(\frac{d \left(d g - e f\right) \left(d g + e f\right)}{e \left(d^{2} g^{2} - e^{2} f^{2}\right)} + x \right)}}{4 d^{3} e^{3}}"," ",0,"(-2*d**2*f*g + x*(-d**2*g**2 - e**2*f**2))/(-2*d**4*e**2 + 2*d**2*e**4*x**2) + (d*g - e*f)*(d*g + e*f)*log(-d*(d*g - e*f)*(d*g + e*f)/(e*(d**2*g**2 - e**2*f**2)) + x)/(4*d**3*e**3) - (d*g - e*f)*(d*g + e*f)*log(d*(d*g - e*f)*(d*g + e*f)/(e*(d**2*g**2 - e**2*f**2)) + x)/(4*d**3*e**3)","B",0
565,1,279,0,1.263691," ","integrate((g*x+f)**2/(e*x+d)/(-e**2*x**2+d**2)**2,x)","\frac{- 2 d^{4} g^{2} - 4 d^{3} e f g + 2 d^{2} e^{2} f^{2} + x^{2} \left(d^{2} e^{2} g^{2} - 2 d e^{3} f g - 3 e^{4} f^{2}\right) + x \left(- 3 d^{3} e g^{2} - 2 d^{2} e^{2} f g - 3 d e^{3} f^{2}\right)}{- 8 d^{6} e^{3} - 8 d^{5} e^{4} x + 8 d^{4} e^{5} x^{2} + 8 d^{3} e^{6} x^{3}} + \frac{\left(d g - 3 e f\right) \left(d g + e f\right) \log{\left(- \frac{d \left(d g - 3 e f\right) \left(d g + e f\right)}{e \left(d^{2} g^{2} - 2 d e f g - 3 e^{2} f^{2}\right)} + x \right)}}{16 d^{4} e^{3}} - \frac{\left(d g - 3 e f\right) \left(d g + e f\right) \log{\left(\frac{d \left(d g - 3 e f\right) \left(d g + e f\right)}{e \left(d^{2} g^{2} - 2 d e f g - 3 e^{2} f^{2}\right)} + x \right)}}{16 d^{4} e^{3}}"," ",0,"(-2*d**4*g**2 - 4*d**3*e*f*g + 2*d**2*e**2*f**2 + x**2*(d**2*e**2*g**2 - 2*d*e**3*f*g - 3*e**4*f**2) + x*(-3*d**3*e*g**2 - 2*d**2*e**2*f*g - 3*d*e**3*f**2))/(-8*d**6*e**3 - 8*d**5*e**4*x + 8*d**4*e**5*x**2 + 8*d**3*e**6*x**3) + (d*g - 3*e*f)*(d*g + e*f)*log(-d*(d*g - 3*e*f)*(d*g + e*f)/(e*(d**2*g**2 - 2*d*e*f*g - 3*e**2*f**2)) + x)/(16*d**4*e**3) - (d*g - 3*e*f)*(d*g + e*f)*log(d*(d*g - 3*e*f)*(d*g + e*f)/(e*(d**2*g**2 - 2*d*e*f*g - 3*e**2*f**2)) + x)/(16*d**4*e**3)","B",0
566,1,241,0,1.359755," ","integrate((g*x+f)**2/(e*x+d)**2/(-e**2*x**2+d**2)**2,x)","\frac{- 2 d^{5} g^{2} - 2 d^{4} e f g + 4 d^{3} e^{2} f^{2} + x^{3} \left(- 3 d e^{4} f g - 3 e^{5} f^{2}\right) + x^{2} \left(- 6 d^{2} e^{3} f g - 6 d e^{4} f^{2}\right) + x \left(- 4 d^{4} e g^{2} - d^{3} e^{2} f g - d^{2} e^{3} f^{2}\right)}{- 12 d^{8} e^{3} - 24 d^{7} e^{4} x + 24 d^{5} e^{6} x^{3} + 12 d^{4} e^{7} x^{4}} - \frac{f \left(d g + e f\right) \log{\left(- \frac{d f \left(d g + e f\right)}{e \left(d f g + e f^{2}\right)} + x \right)}}{8 d^{5} e^{2}} + \frac{f \left(d g + e f\right) \log{\left(\frac{d f \left(d g + e f\right)}{e \left(d f g + e f^{2}\right)} + x \right)}}{8 d^{5} e^{2}}"," ",0,"(-2*d**5*g**2 - 2*d**4*e*f*g + 4*d**3*e**2*f**2 + x**3*(-3*d*e**4*f*g - 3*e**5*f**2) + x**2*(-6*d**2*e**3*f*g - 6*d*e**4*f**2) + x*(-4*d**4*e*g**2 - d**3*e**2*f*g - d**2*e**3*f**2))/(-12*d**8*e**3 - 24*d**7*e**4*x + 24*d**5*e**6*x**3 + 12*d**4*e**7*x**4) - f*(d*g + e*f)*log(-d*f*(d*g + e*f)/(e*(d*f*g + e*f**2)) + x)/(8*d**5*e**2) + f*(d*g + e*f)*log(d*f*(d*g + e*f)/(e*(d*f*g + e*f**2)) + x)/(8*d**5*e**2)","A",0
567,1,376,0,1.927660," ","integrate((g*x+f)**2/(e*x+d)**3/(-e**2*x**2+d**2)**2,x)","\frac{- 8 d^{6} g^{2} + 32 d^{4} e^{2} f^{2} + x^{4} \left(- 3 d^{2} e^{4} g^{2} - 18 d e^{5} f g - 15 e^{6} f^{2}\right) + x^{3} \left(- 9 d^{3} e^{3} g^{2} - 54 d^{2} e^{4} f g - 45 d e^{5} f^{2}\right) + x^{2} \left(- 7 d^{4} e^{2} g^{2} - 42 d^{3} e^{3} f g - 35 d^{2} e^{4} f^{2}\right) + x \left(- 21 d^{5} e g^{2} + 18 d^{4} e^{2} f g + 15 d^{3} e^{3} f^{2}\right)}{- 96 d^{10} e^{3} - 288 d^{9} e^{4} x - 192 d^{8} e^{5} x^{2} + 192 d^{7} e^{6} x^{3} + 288 d^{6} e^{7} x^{4} + 96 d^{5} e^{8} x^{5}} - \frac{\left(d g + e f\right) \left(d g + 5 e f\right) \log{\left(- \frac{d \left(d g + e f\right) \left(d g + 5 e f\right)}{e \left(d^{2} g^{2} + 6 d e f g + 5 e^{2} f^{2}\right)} + x \right)}}{64 d^{6} e^{3}} + \frac{\left(d g + e f\right) \left(d g + 5 e f\right) \log{\left(\frac{d \left(d g + e f\right) \left(d g + 5 e f\right)}{e \left(d^{2} g^{2} + 6 d e f g + 5 e^{2} f^{2}\right)} + x \right)}}{64 d^{6} e^{3}}"," ",0,"(-8*d**6*g**2 + 32*d**4*e**2*f**2 + x**4*(-3*d**2*e**4*g**2 - 18*d*e**5*f*g - 15*e**6*f**2) + x**3*(-9*d**3*e**3*g**2 - 54*d**2*e**4*f*g - 45*d*e**5*f**2) + x**2*(-7*d**4*e**2*g**2 - 42*d**3*e**3*f*g - 35*d**2*e**4*f**2) + x*(-21*d**5*e*g**2 + 18*d**4*e**2*f*g + 15*d**3*e**3*f**2))/(-96*d**10*e**3 - 288*d**9*e**4*x - 192*d**8*e**5*x**2 + 192*d**7*e**6*x**3 + 288*d**6*e**7*x**4 + 96*d**5*e**8*x**5) - (d*g + e*f)*(d*g + 5*e*f)*log(-d*(d*g + e*f)*(d*g + 5*e*f)/(e*(d**2*g**2 + 6*d*e*f*g + 5*e**2*f**2)) + x)/(64*d**6*e**3) + (d*g + e*f)*(d*g + 5*e*f)*log(d*(d*g + e*f)*(d*g + 5*e*f)/(e*(d**2*g**2 + 6*d*e*f*g + 5*e**2*f**2)) + x)/(64*d**6*e**3)","B",0
568,1,427,0,2.151839," ","integrate((g*x+f)**2/(e*x+d)**4/(-e**2*x**2+d**2)**2,x)","\frac{- 16 d^{7} g^{2} + 32 d^{6} e f g + 144 d^{5} e^{2} f^{2} + x^{5} \left(- 15 d^{2} e^{5} g^{2} - 60 d e^{6} f g - 45 e^{7} f^{2}\right) + x^{4} \left(- 60 d^{3} e^{4} g^{2} - 240 d^{2} e^{5} f g - 180 d e^{6} f^{2}\right) + x^{3} \left(- 80 d^{4} e^{3} g^{2} - 320 d^{3} e^{4} f g - 240 d^{2} e^{5} f^{2}\right) + x^{2} \left(- 20 d^{5} e^{2} g^{2} - 80 d^{4} e^{3} f g - 60 d^{3} e^{4} f^{2}\right) + x \left(- 49 d^{6} e g^{2} + 188 d^{5} e^{2} f g + 141 d^{4} e^{3} f^{2}\right)}{- 480 d^{12} e^{3} - 1920 d^{11} e^{4} x - 2400 d^{10} e^{5} x^{2} + 2400 d^{8} e^{7} x^{4} + 1920 d^{7} e^{8} x^{5} + 480 d^{6} e^{9} x^{6}} - \frac{\left(d g + e f\right) \left(d g + 3 e f\right) \log{\left(- \frac{d \left(d g + e f\right) \left(d g + 3 e f\right)}{e \left(d^{2} g^{2} + 4 d e f g + 3 e^{2} f^{2}\right)} + x \right)}}{64 d^{7} e^{3}} + \frac{\left(d g + e f\right) \left(d g + 3 e f\right) \log{\left(\frac{d \left(d g + e f\right) \left(d g + 3 e f\right)}{e \left(d^{2} g^{2} + 4 d e f g + 3 e^{2} f^{2}\right)} + x \right)}}{64 d^{7} e^{3}}"," ",0,"(-16*d**7*g**2 + 32*d**6*e*f*g + 144*d**5*e**2*f**2 + x**5*(-15*d**2*e**5*g**2 - 60*d*e**6*f*g - 45*e**7*f**2) + x**4*(-60*d**3*e**4*g**2 - 240*d**2*e**5*f*g - 180*d*e**6*f**2) + x**3*(-80*d**4*e**3*g**2 - 320*d**3*e**4*f*g - 240*d**2*e**5*f**2) + x**2*(-20*d**5*e**2*g**2 - 80*d**4*e**3*f*g - 60*d**3*e**4*f**2) + x*(-49*d**6*e*g**2 + 188*d**5*e**2*f*g + 141*d**4*e**3*f**2))/(-480*d**12*e**3 - 1920*d**11*e**4*x - 2400*d**10*e**5*x**2 + 2400*d**8*e**7*x**4 + 1920*d**7*e**8*x**5 + 480*d**6*e**9*x**6) - (d*g + e*f)*(d*g + 3*e*f)*log(-d*(d*g + e*f)*(d*g + 3*e*f)/(e*(d**2*g**2 + 4*d*e*f*g + 3*e**2*f**2)) + x)/(64*d**7*e**3) + (d*g + e*f)*(d*g + 3*e*f)*log(d*(d*g + e*f)*(d*g + 3*e*f)/(e*(d**2*g**2 + 4*d*e*f*g + 3*e**2*f**2)) + x)/(64*d**7*e**3)","B",0
569,1,219,0,1.550750," ","integrate((e*x+d)**7*(g*x+f)**2/(-e**2*x**2+d**2)**3,x)","- \frac{8 d^{2} \left(13 d^{2} g^{2} + 14 d e f g + 3 e^{2} f^{2}\right) \log{\left(- d + e x \right)}}{e^{3}} - \frac{e g^{2} x^{4}}{4} - x^{3} \left(\frac{7 d g^{2}}{3} + \frac{2 e f g}{3}\right) - x^{2} \left(\frac{12 d^{2} g^{2}}{e} + 7 d f g + \frac{e f^{2}}{2}\right) - x \left(\frac{56 d^{3} g^{2}}{e^{2}} + \frac{48 d^{2} f g}{e} + 7 d f^{2}\right) - \frac{56 d^{6} g^{2} + 80 d^{5} e f g + 24 d^{4} e^{2} f^{2} + x \left(- 64 d^{5} e g^{2} - 96 d^{4} e^{2} f g - 32 d^{3} e^{3} f^{2}\right)}{d^{2} e^{3} - 2 d e^{4} x + e^{5} x^{2}}"," ",0,"-8*d**2*(13*d**2*g**2 + 14*d*e*f*g + 3*e**2*f**2)*log(-d + e*x)/e**3 - e*g**2*x**4/4 - x**3*(7*d*g**2/3 + 2*e*f*g/3) - x**2*(12*d**2*g**2/e + 7*d*f*g + e*f**2/2) - x*(56*d**3*g**2/e**2 + 48*d**2*f*g/e + 7*d*f**2) - (56*d**6*g**2 + 80*d**5*e*f*g + 24*d**4*e**2*f**2 + x*(-64*d**5*e*g**2 - 96*d**4*e**2*f*g - 32*d**3*e**3*f**2))/(d**2*e**3 - 2*d*e**4*x + e**5*x**2)","A",0
570,1,178,0,1.372294," ","integrate((e*x+d)**6*(g*x+f)**2/(-e**2*x**2+d**2)**3,x)","- \frac{2 d \left(19 d^{2} g^{2} + 18 d e f g + 3 e^{2} f^{2}\right) \log{\left(- d + e x \right)}}{e^{3}} - \frac{g^{2} x^{3}}{3} - x^{2} \left(\frac{3 d g^{2}}{e} + f g\right) - x \left(\frac{18 d^{2} g^{2}}{e^{2}} + \frac{12 d f g}{e} + f^{2}\right) - \frac{24 d^{5} g^{2} + 32 d^{4} e f g + 8 d^{3} e^{2} f^{2} + x \left(- 28 d^{4} e g^{2} - 40 d^{3} e^{2} f g - 12 d^{2} e^{3} f^{2}\right)}{d^{2} e^{3} - 2 d e^{4} x + e^{5} x^{2}}"," ",0,"-2*d*(19*d**2*g**2 + 18*d*e*f*g + 3*e**2*f**2)*log(-d + e*x)/e**3 - g**2*x**3/3 - x**2*(3*d*g**2/e + f*g) - x*(18*d**2*g**2/e**2 + 12*d*f*g/e + f**2) - (24*d**5*g**2 + 32*d**4*e*f*g + 8*d**3*e**2*f**2 + x*(-28*d**4*e*g**2 - 40*d**3*e**2*f*g - 12*d**2*e**3*f**2))/(d**2*e**3 - 2*d*e**4*x + e**5*x**2)","A",0
571,1,151,0,1.212388," ","integrate((e*x+d)**5*(g*x+f)**2/(-e**2*x**2+d**2)**3,x)","- x \left(\frac{5 d g^{2}}{e^{2}} + \frac{2 f g}{e}\right) - \frac{10 d^{4} g^{2} + 12 d^{3} e f g + 2 d^{2} e^{2} f^{2} + x \left(- 12 d^{3} e g^{2} - 16 d^{2} e^{2} f g - 4 d e^{3} f^{2}\right)}{d^{2} e^{3} - 2 d e^{4} x + e^{5} x^{2}} - \frac{g^{2} x^{2}}{2 e} - \frac{\left(13 d^{2} g^{2} + 10 d e f g + e^{2} f^{2}\right) \log{\left(- d + e x \right)}}{e^{3}}"," ",0,"-x*(5*d*g**2/e**2 + 2*f*g/e) - (10*d**4*g**2 + 12*d**3*e*f*g + 2*d**2*e**2*f**2 + x*(-12*d**3*e*g**2 - 16*d**2*e**2*f*g - 4*d*e**3*f**2))/(d**2*e**3 - 2*d*e**4*x + e**5*x**2) - g**2*x**2/(2*e) - (13*d**2*g**2 + 10*d*e*f*g + e**2*f**2)*log(-d + e*x)/e**3","A",0
572,1,102,0,0.871762," ","integrate((e*x+d)**4*(g*x+f)**2/(-e**2*x**2+d**2)**3,x)","- \frac{4 d^{3} g^{2} + 4 d^{2} e f g + x \left(- 5 d^{2} e g^{2} - 6 d e^{2} f g - e^{3} f^{2}\right)}{d^{2} e^{3} - 2 d e^{4} x + e^{5} x^{2}} - \frac{g^{2} x}{e^{2}} - \frac{2 g \left(2 d g + e f\right) \log{\left(- d + e x \right)}}{e^{3}}"," ",0,"-(4*d**3*g**2 + 4*d**2*e*f*g + x*(-5*d**2*e*g**2 - 6*d*e**2*f*g - e**3*f**2))/(d**2*e**3 - 2*d*e**4*x + e**5*x**2) - g**2*x/e**2 - 2*g*(2*d*g + e*f)*log(-d + e*x)/e**3","A",0
573,1,83,0,0.539837," ","integrate((e*x+d)**3*(g*x+f)**2/(-e**2*x**2+d**2)**3,x)","- \frac{3 d^{2} g^{2} + 2 d e f g - e^{2} f^{2} + x \left(- 4 d e g^{2} - 4 e^{2} f g\right)}{2 d^{2} e^{3} - 4 d e^{4} x + 2 e^{5} x^{2}} - \frac{g^{2} \log{\left(- d + e x \right)}}{e^{3}}"," ",0,"-(3*d**2*g**2 + 2*d*e*f*g - e**2*f**2 + x*(-4*d*e*g**2 - 4*e**2*f*g))/(2*d**2*e**3 - 4*d*e**4*x + 2*e**5*x**2) - g**2*log(-d + e*x)/e**3","A",0
574,1,185,0,1.010869," ","integrate((e*x+d)**2*(g*x+f)**2/(-e**2*x**2+d**2)**3,x)","- \frac{2 d^{3} g^{2} - 2 d e^{2} f^{2} + x \left(- 3 d^{2} e g^{2} - 2 d e^{2} f g + e^{3} f^{2}\right)}{4 d^{4} e^{3} - 8 d^{3} e^{4} x + 4 d^{2} e^{5} x^{2}} - \frac{\left(d g - e f\right)^{2} \log{\left(- \frac{d \left(d g - e f\right)^{2}}{e \left(d^{2} g^{2} - 2 d e f g + e^{2} f^{2}\right)} + x \right)}}{8 d^{3} e^{3}} + \frac{\left(d g - e f\right)^{2} \log{\left(\frac{d \left(d g - e f\right)^{2}}{e \left(d^{2} g^{2} - 2 d e f g + e^{2} f^{2}\right)} + x \right)}}{8 d^{3} e^{3}}"," ",0,"-(2*d**3*g**2 - 2*d*e**2*f**2 + x*(-3*d**2*e*g**2 - 2*d*e**2*f*g + e**3*f**2))/(4*d**4*e**3 - 8*d**3*e**4*x + 4*d**2*e**5*x**2) - (d*g - e*f)**2*log(-d*(d*g - e*f)**2/(e*(d**2*g**2 - 2*d*e*f*g + e**2*f**2)) + x)/(8*d**3*e**3) + (d*g - e*f)**2*log(d*(d*g - e*f)**2/(e*(d**2*g**2 - 2*d*e*f*g + e**2*f**2)) + x)/(8*d**3*e**3)","B",0
575,1,277,0,1.324811," ","integrate((e*x+d)*(g*x+f)**2/(-e**2*x**2+d**2)**3,x)","- \frac{2 d^{4} g^{2} - 4 d^{3} e f g - 2 d^{2} e^{2} f^{2} + x^{2} \left(- d^{2} e^{2} g^{2} - 2 d e^{3} f g + 3 e^{4} f^{2}\right) + x \left(- 3 d^{3} e g^{2} + 2 d^{2} e^{2} f g - 3 d e^{3} f^{2}\right)}{8 d^{6} e^{3} - 8 d^{5} e^{4} x - 8 d^{4} e^{5} x^{2} + 8 d^{3} e^{6} x^{3}} + \frac{\left(d g - e f\right) \left(d g + 3 e f\right) \log{\left(- \frac{d \left(d g - e f\right) \left(d g + 3 e f\right)}{e \left(d^{2} g^{2} + 2 d e f g - 3 e^{2} f^{2}\right)} + x \right)}}{16 d^{4} e^{3}} - \frac{\left(d g - e f\right) \left(d g + 3 e f\right) \log{\left(\frac{d \left(d g - e f\right) \left(d g + 3 e f\right)}{e \left(d^{2} g^{2} + 2 d e f g - 3 e^{2} f^{2}\right)} + x \right)}}{16 d^{4} e^{3}}"," ",0,"-(2*d**4*g**2 - 4*d**3*e*f*g - 2*d**2*e**2*f**2 + x**2*(-d**2*e**2*g**2 - 2*d*e**3*f*g + 3*e**4*f**2) + x*(-3*d**3*e*g**2 + 2*d**2*e**2*f*g - 3*d*e**3*f**2))/(8*d**6*e**3 - 8*d**5*e**4*x - 8*d**4*e**5*x**2 + 8*d**3*e**6*x**3) + (d*g - e*f)*(d*g + 3*e*f)*log(-d*(d*g - e*f)*(d*g + 3*e*f)/(e*(d**2*g**2 + 2*d*e*f*g - 3*e**2*f**2)) + x)/(16*d**4*e**3) - (d*g - e*f)*(d*g + 3*e*f)*log(d*(d*g - e*f)*(d*g + 3*e*f)/(e*(d**2*g**2 + 2*d*e*f*g - 3*e**2*f**2)) + x)/(16*d**4*e**3)","B",0
576,1,144,0,0.997739," ","integrate((g*x+f)**2/(-e**2*x**2+d**2)**3,x)","- \frac{- 4 d^{4} f g + x^{3} \left(- d^{2} e^{2} g^{2} + 3 e^{4} f^{2}\right) + x \left(- d^{4} g^{2} - 5 d^{2} e^{2} f^{2}\right)}{8 d^{8} e^{2} - 16 d^{6} e^{4} x^{2} + 8 d^{4} e^{6} x^{4}} + \frac{\left(d^{2} g^{2} - 3 e^{2} f^{2}\right) \log{\left(- \frac{d}{e} + x \right)}}{16 d^{5} e^{3}} - \frac{\left(d^{2} g^{2} - 3 e^{2} f^{2}\right) \log{\left(\frac{d}{e} + x \right)}}{16 d^{5} e^{3}}"," ",0,"-(-4*d**4*f*g + x**3*(-d**2*e**2*g**2 + 3*e**4*f**2) + x*(-d**4*g**2 - 5*d**2*e**2*f**2))/(8*d**8*e**2 - 16*d**6*e**4*x**2 + 8*d**4*e**6*x**4) + (d**2*g**2 - 3*e**2*f**2)*log(-d/e + x)/(16*d**5*e**3) - (d**2*g**2 - 3*e**2*f**2)*log(d/e + x)/(16*d**5*e**3)","A",0
577,1,321,0,1.830555," ","integrate((g*x+f)**2/(e*x+d)/(-e**2*x**2+d**2)**3,x)","- \frac{- 4 d^{6} g^{2} - 16 d^{5} e f g + 8 d^{4} e^{2} f^{2} + x^{4} \left(- 3 d^{2} e^{4} g^{2} + 6 d e^{5} f g + 15 e^{6} f^{2}\right) + x^{3} \left(- 3 d^{3} e^{3} g^{2} + 6 d^{2} e^{4} f g + 15 d e^{5} f^{2}\right) + x^{2} \left(5 d^{4} e^{2} g^{2} - 10 d^{3} e^{3} f g - 25 d^{2} e^{4} f^{2}\right) + x \left(- 7 d^{5} e g^{2} - 10 d^{4} e^{2} f g - 25 d^{3} e^{3} f^{2}\right)}{48 d^{10} e^{3} + 48 d^{9} e^{4} x - 96 d^{8} e^{5} x^{2} - 96 d^{7} e^{6} x^{3} + 48 d^{6} e^{7} x^{4} + 48 d^{5} e^{8} x^{5}} + \frac{\left(d^{2} g^{2} - 2 d e f g - 5 e^{2} f^{2}\right) \log{\left(- \frac{d}{e} + x \right)}}{32 d^{6} e^{3}} - \frac{\left(d^{2} g^{2} - 2 d e f g - 5 e^{2} f^{2}\right) \log{\left(\frac{d}{e} + x \right)}}{32 d^{6} e^{3}}"," ",0,"-(-4*d**6*g**2 - 16*d**5*e*f*g + 8*d**4*e**2*f**2 + x**4*(-3*d**2*e**4*g**2 + 6*d*e**5*f*g + 15*e**6*f**2) + x**3*(-3*d**3*e**3*g**2 + 6*d**2*e**4*f*g + 15*d*e**5*f**2) + x**2*(5*d**4*e**2*g**2 - 10*d**3*e**3*f*g - 25*d**2*e**4*f**2) + x*(-7*d**5*e*g**2 - 10*d**4*e**2*f*g - 25*d**3*e**3*f**2))/(48*d**10*e**3 + 48*d**9*e**4*x - 96*d**8*e**5*x**2 - 96*d**7*e**6*x**3 + 48*d**6*e**7*x**4 + 48*d**5*e**8*x**5) + (d**2*g**2 - 2*d*e*f*g - 5*e**2*f**2)*log(-d/e + x)/(32*d**6*e**3) - (d**2*g**2 - 2*d*e*f*g - 5*e**2*f**2)*log(d/e + x)/(32*d**6*e**3)","A",0
578,1,372,0,2.145753," ","integrate((g*x+f)**2/(e*x+d)**2/(-e**2*x**2+d**2)**3,x)","- \frac{- 16 d^{7} g^{2} - 32 d^{6} e f g + 48 d^{5} e^{2} f^{2} + x^{5} \left(- 3 d^{2} e^{5} g^{2} + 30 d e^{6} f g + 45 e^{7} f^{2}\right) + x^{4} \left(- 6 d^{3} e^{4} g^{2} + 60 d^{2} e^{5} f g + 90 d e^{6} f^{2}\right) + x^{3} \left(2 d^{4} e^{3} g^{2} - 20 d^{3} e^{4} f g - 30 d^{2} e^{5} f^{2}\right) + x^{2} \left(10 d^{5} e^{2} g^{2} - 100 d^{4} e^{3} f g - 150 d^{3} e^{4} f^{2}\right) + x \left(- 35 d^{6} e g^{2} - 34 d^{5} e^{2} f g - 51 d^{4} e^{3} f^{2}\right)}{192 d^{12} e^{3} + 384 d^{11} e^{4} x - 192 d^{10} e^{5} x^{2} - 768 d^{9} e^{6} x^{3} - 192 d^{8} e^{7} x^{4} + 384 d^{7} e^{8} x^{5} + 192 d^{6} e^{9} x^{6}} + \frac{\left(d^{2} g^{2} - 10 d e f g - 15 e^{2} f^{2}\right) \log{\left(- \frac{d}{e} + x \right)}}{128 d^{7} e^{3}} - \frac{\left(d^{2} g^{2} - 10 d e f g - 15 e^{2} f^{2}\right) \log{\left(\frac{d}{e} + x \right)}}{128 d^{7} e^{3}}"," ",0,"-(-16*d**7*g**2 - 32*d**6*e*f*g + 48*d**5*e**2*f**2 + x**5*(-3*d**2*e**5*g**2 + 30*d*e**6*f*g + 45*e**7*f**2) + x**4*(-6*d**3*e**4*g**2 + 60*d**2*e**5*f*g + 90*d*e**6*f**2) + x**3*(2*d**4*e**3*g**2 - 20*d**3*e**4*f*g - 30*d**2*e**5*f**2) + x**2*(10*d**5*e**2*g**2 - 100*d**4*e**3*f*g - 150*d**3*e**4*f**2) + x*(-35*d**6*e*g**2 - 34*d**5*e**2*f*g - 51*d**4*e**3*f**2))/(192*d**12*e**3 + 384*d**11*e**4*x - 192*d**10*e**5*x**2 - 768*d**9*e**6*x**3 - 192*d**8*e**7*x**4 + 384*d**7*e**8*x**5 + 192*d**6*e**9*x**6) + (d**2*g**2 - 10*d*e*f*g - 15*e**2*f**2)*log(-d/e + x)/(128*d**7*e**3) - (d**2*g**2 - 10*d*e*f*g - 15*e**2*f**2)*log(d/e + x)/(128*d**7*e**3)","A",0
579,-1,0,0,0.000000," ","integrate((e*x+d)**3*(g*x+f)**5/(-e**2*x**2+d**2)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
580,-1,0,0,0.000000," ","integrate((e*x+d)**3*(g*x+f)**4/(-e**2*x**2+d**2)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
581,0,0,0,0.000000," ","integrate((e*x+d)**3*(g*x+f)**3/(-e**2*x**2+d**2)**(7/2),x)","\int \frac{\left(d + e x\right)^{3} \left(f + g x\right)^{3}}{\left(- \left(- d + e x\right) \left(d + e x\right)\right)^{\frac{7}{2}}}\, dx"," ",0,"Integral((d + e*x)**3*(f + g*x)**3/(-(-d + e*x)*(d + e*x))**(7/2), x)","F",0
582,0,0,0,0.000000," ","integrate((e*x+d)**3*(g*x+f)**2/(-e**2*x**2+d**2)**(7/2),x)","\int \frac{\left(d + e x\right)^{3} \left(f + g x\right)^{2}}{\left(- \left(- d + e x\right) \left(d + e x\right)\right)^{\frac{7}{2}}}\, dx"," ",0,"Integral((d + e*x)**3*(f + g*x)**2/(-(-d + e*x)*(d + e*x))**(7/2), x)","F",0
583,0,0,0,0.000000," ","integrate((e*x+d)**3*(g*x+f)/(-e**2*x**2+d**2)**(7/2),x)","\int \frac{\left(d + e x\right)^{3} \left(f + g x\right)}{\left(- \left(- d + e x\right) \left(d + e x\right)\right)^{\frac{7}{2}}}\, dx"," ",0,"Integral((d + e*x)**3*(f + g*x)/(-(-d + e*x)*(d + e*x))**(7/2), x)","F",0
584,0,0,0,0.000000," ","integrate((e*x+d)**3/(-e**2*x**2+d**2)**(7/2),x)","\int \frac{\left(d + e x\right)^{3}}{\left(- \left(- d + e x\right) \left(d + e x\right)\right)^{\frac{7}{2}}}\, dx"," ",0,"Integral((d + e*x)**3/(-(-d + e*x)*(d + e*x))**(7/2), x)","F",0
585,0,0,0,0.000000," ","integrate((e*x+d)**3/(g*x+f)/(-e**2*x**2+d**2)**(7/2),x)","\int \frac{\left(d + e x\right)^{3}}{\left(- \left(- d + e x\right) \left(d + e x\right)\right)^{\frac{7}{2}} \left(f + g x\right)}\, dx"," ",0,"Integral((d + e*x)**3/((-(-d + e*x)*(d + e*x))**(7/2)*(f + g*x)), x)","F",0
586,0,0,0,0.000000," ","integrate((e*x+d)**3/(g*x+f)**2/(-e**2*x**2+d**2)**(7/2),x)","\int \frac{\left(d + e x\right)^{3}}{\left(- \left(- d + e x\right) \left(d + e x\right)\right)^{\frac{7}{2}} \left(f + g x\right)^{2}}\, dx"," ",0,"Integral((d + e*x)**3/((-(-d + e*x)*(d + e*x))**(7/2)*(f + g*x)**2), x)","F",0
587,0,0,0,0.000000," ","integrate((e*x+d)**3/(g*x+f)**3/(-e**2*x**2+d**2)**(7/2),x)","\int \frac{\left(d + e x\right)^{3}}{\left(- \left(- d + e x\right) \left(d + e x\right)\right)^{\frac{7}{2}} \left(f + g x\right)^{3}}\, dx"," ",0,"Integral((d + e*x)**3/((-(-d + e*x)*(d + e*x))**(7/2)*(f + g*x)**3), x)","F",0
588,1,107,0,87.878632," ","integrate((c*x**2+a)/(e*x+d)**(3/2)/(g*x+f),x)","\frac{2 c \sqrt{d + e x}}{e^{2} g} + \frac{2 \left(a g^{2} + c f^{2}\right) \operatorname{atan}{\left(\frac{\sqrt{d + e x}}{\sqrt{- \frac{d g - e f}{g}}} \right)}}{g^{2} \sqrt{- \frac{d g - e f}{g}} \left(d g - e f\right)} + \frac{2 \left(a e^{2} + c d^{2}\right)}{e^{2} \sqrt{d + e x} \left(d g - e f\right)}"," ",0,"2*c*sqrt(d + e*x)/(e**2*g) + 2*(a*g**2 + c*f**2)*atan(sqrt(d + e*x)/sqrt(-(d*g - e*f)/g))/(g**2*sqrt(-(d*g - e*f)/g)*(d*g - e*f)) + 2*(a*e**2 + c*d**2)/(e**2*sqrt(d + e*x)*(d*g - e*f))","A",0
589,-1,0,0,0.000000," ","integrate((e*x+d)**3*(c*x**2+a)/(g*x+f)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
590,1,673,0,108.501275," ","integrate((e*x+d)**2*(c*x**2+a)/(g*x+f)**(1/2),x)","\begin{cases} \frac{- \frac{2 a d^{2} f}{\sqrt{f + g x}} - 2 a d^{2} \left(- \frac{f}{\sqrt{f + g x}} - \sqrt{f + g x}\right) - \frac{4 a d e f \left(- \frac{f}{\sqrt{f + g x}} - \sqrt{f + g x}\right)}{g} - \frac{4 a d e \left(\frac{f^{2}}{\sqrt{f + g x}} + 2 f \sqrt{f + g x} - \frac{\left(f + g x\right)^{\frac{3}{2}}}{3}\right)}{g} - \frac{2 a e^{2} f \left(\frac{f^{2}}{\sqrt{f + g x}} + 2 f \sqrt{f + g x} - \frac{\left(f + g x\right)^{\frac{3}{2}}}{3}\right)}{g^{2}} - \frac{2 a e^{2} \left(- \frac{f^{3}}{\sqrt{f + g x}} - 3 f^{2} \sqrt{f + g x} + f \left(f + g x\right)^{\frac{3}{2}} - \frac{\left(f + g x\right)^{\frac{5}{2}}}{5}\right)}{g^{2}} - \frac{2 c d^{2} f \left(\frac{f^{2}}{\sqrt{f + g x}} + 2 f \sqrt{f + g x} - \frac{\left(f + g x\right)^{\frac{3}{2}}}{3}\right)}{g^{2}} - \frac{2 c d^{2} \left(- \frac{f^{3}}{\sqrt{f + g x}} - 3 f^{2} \sqrt{f + g x} + f \left(f + g x\right)^{\frac{3}{2}} - \frac{\left(f + g x\right)^{\frac{5}{2}}}{5}\right)}{g^{2}} - \frac{4 c d e f \left(- \frac{f^{3}}{\sqrt{f + g x}} - 3 f^{2} \sqrt{f + g x} + f \left(f + g x\right)^{\frac{3}{2}} - \frac{\left(f + g x\right)^{\frac{5}{2}}}{5}\right)}{g^{3}} - \frac{4 c d e \left(\frac{f^{4}}{\sqrt{f + g x}} + 4 f^{3} \sqrt{f + g x} - 2 f^{2} \left(f + g x\right)^{\frac{3}{2}} + \frac{4 f \left(f + g x\right)^{\frac{5}{2}}}{5} - \frac{\left(f + g x\right)^{\frac{7}{2}}}{7}\right)}{g^{3}} - \frac{2 c e^{2} f \left(\frac{f^{4}}{\sqrt{f + g x}} + 4 f^{3} \sqrt{f + g x} - 2 f^{2} \left(f + g x\right)^{\frac{3}{2}} + \frac{4 f \left(f + g x\right)^{\frac{5}{2}}}{5} - \frac{\left(f + g x\right)^{\frac{7}{2}}}{7}\right)}{g^{4}} - \frac{2 c e^{2} \left(- \frac{f^{5}}{\sqrt{f + g x}} - 5 f^{4} \sqrt{f + g x} + \frac{10 f^{3} \left(f + g x\right)^{\frac{3}{2}}}{3} - 2 f^{2} \left(f + g x\right)^{\frac{5}{2}} + \frac{5 f \left(f + g x\right)^{\frac{7}{2}}}{7} - \frac{\left(f + g x\right)^{\frac{9}{2}}}{9}\right)}{g^{4}}}{g} & \text{for}\: g \neq 0 \\\frac{a d^{2} x + a d e x^{2} + \frac{c d e x^{4}}{2} + \frac{c e^{2} x^{5}}{5} + \frac{x^{3} \left(a e^{2} + c d^{2}\right)}{3}}{\sqrt{f}} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((-2*a*d**2*f/sqrt(f + g*x) - 2*a*d**2*(-f/sqrt(f + g*x) - sqrt(f + g*x)) - 4*a*d*e*f*(-f/sqrt(f + g*x) - sqrt(f + g*x))/g - 4*a*d*e*(f**2/sqrt(f + g*x) + 2*f*sqrt(f + g*x) - (f + g*x)**(3/2)/3)/g - 2*a*e**2*f*(f**2/sqrt(f + g*x) + 2*f*sqrt(f + g*x) - (f + g*x)**(3/2)/3)/g**2 - 2*a*e**2*(-f**3/sqrt(f + g*x) - 3*f**2*sqrt(f + g*x) + f*(f + g*x)**(3/2) - (f + g*x)**(5/2)/5)/g**2 - 2*c*d**2*f*(f**2/sqrt(f + g*x) + 2*f*sqrt(f + g*x) - (f + g*x)**(3/2)/3)/g**2 - 2*c*d**2*(-f**3/sqrt(f + g*x) - 3*f**2*sqrt(f + g*x) + f*(f + g*x)**(3/2) - (f + g*x)**(5/2)/5)/g**2 - 4*c*d*e*f*(-f**3/sqrt(f + g*x) - 3*f**2*sqrt(f + g*x) + f*(f + g*x)**(3/2) - (f + g*x)**(5/2)/5)/g**3 - 4*c*d*e*(f**4/sqrt(f + g*x) + 4*f**3*sqrt(f + g*x) - 2*f**2*(f + g*x)**(3/2) + 4*f*(f + g*x)**(5/2)/5 - (f + g*x)**(7/2)/7)/g**3 - 2*c*e**2*f*(f**4/sqrt(f + g*x) + 4*f**3*sqrt(f + g*x) - 2*f**2*(f + g*x)**(3/2) + 4*f*(f + g*x)**(5/2)/5 - (f + g*x)**(7/2)/7)/g**4 - 2*c*e**2*(-f**5/sqrt(f + g*x) - 5*f**4*sqrt(f + g*x) + 10*f**3*(f + g*x)**(3/2)/3 - 2*f**2*(f + g*x)**(5/2) + 5*f*(f + g*x)**(7/2)/7 - (f + g*x)**(9/2)/9)/g**4)/g, Ne(g, 0)), ((a*d**2*x + a*d*e*x**2 + c*d*e*x**4/2 + c*e**2*x**5/5 + x**3*(a*e**2 + c*d**2)/3)/sqrt(f), True))","A",0
591,1,374,0,61.128579," ","integrate((e*x+d)*(c*x**2+a)/(g*x+f)**(1/2),x)","\begin{cases} \frac{- \frac{2 a d f}{\sqrt{f + g x}} - 2 a d \left(- \frac{f}{\sqrt{f + g x}} - \sqrt{f + g x}\right) - \frac{2 a e f \left(- \frac{f}{\sqrt{f + g x}} - \sqrt{f + g x}\right)}{g} - \frac{2 a e \left(\frac{f^{2}}{\sqrt{f + g x}} + 2 f \sqrt{f + g x} - \frac{\left(f + g x\right)^{\frac{3}{2}}}{3}\right)}{g} - \frac{2 c d f \left(\frac{f^{2}}{\sqrt{f + g x}} + 2 f \sqrt{f + g x} - \frac{\left(f + g x\right)^{\frac{3}{2}}}{3}\right)}{g^{2}} - \frac{2 c d \left(- \frac{f^{3}}{\sqrt{f + g x}} - 3 f^{2} \sqrt{f + g x} + f \left(f + g x\right)^{\frac{3}{2}} - \frac{\left(f + g x\right)^{\frac{5}{2}}}{5}\right)}{g^{2}} - \frac{2 c e f \left(- \frac{f^{3}}{\sqrt{f + g x}} - 3 f^{2} \sqrt{f + g x} + f \left(f + g x\right)^{\frac{3}{2}} - \frac{\left(f + g x\right)^{\frac{5}{2}}}{5}\right)}{g^{3}} - \frac{2 c e \left(\frac{f^{4}}{\sqrt{f + g x}} + 4 f^{3} \sqrt{f + g x} - 2 f^{2} \left(f + g x\right)^{\frac{3}{2}} + \frac{4 f \left(f + g x\right)^{\frac{5}{2}}}{5} - \frac{\left(f + g x\right)^{\frac{7}{2}}}{7}\right)}{g^{3}}}{g} & \text{for}\: g \neq 0 \\\frac{a d x + \frac{a e x^{2}}{2} + \frac{c d x^{3}}{3} + \frac{c e x^{4}}{4}}{\sqrt{f}} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((-2*a*d*f/sqrt(f + g*x) - 2*a*d*(-f/sqrt(f + g*x) - sqrt(f + g*x)) - 2*a*e*f*(-f/sqrt(f + g*x) - sqrt(f + g*x))/g - 2*a*e*(f**2/sqrt(f + g*x) + 2*f*sqrt(f + g*x) - (f + g*x)**(3/2)/3)/g - 2*c*d*f*(f**2/sqrt(f + g*x) + 2*f*sqrt(f + g*x) - (f + g*x)**(3/2)/3)/g**2 - 2*c*d*(-f**3/sqrt(f + g*x) - 3*f**2*sqrt(f + g*x) + f*(f + g*x)**(3/2) - (f + g*x)**(5/2)/5)/g**2 - 2*c*e*f*(-f**3/sqrt(f + g*x) - 3*f**2*sqrt(f + g*x) + f*(f + g*x)**(3/2) - (f + g*x)**(5/2)/5)/g**3 - 2*c*e*(f**4/sqrt(f + g*x) + 4*f**3*sqrt(f + g*x) - 2*f**2*(f + g*x)**(3/2) + 4*f*(f + g*x)**(5/2)/5 - (f + g*x)**(7/2)/7)/g**3)/g, Ne(g, 0)), ((a*d*x + a*e*x**2/2 + c*d*x**3/3 + c*e*x**4/4)/sqrt(f), True))","A",0
592,1,150,0,13.097517," ","integrate((c*x**2+a)/(g*x+f)**(1/2),x)","\begin{cases} \frac{- \frac{2 a f}{\sqrt{f + g x}} - 2 a \left(- \frac{f}{\sqrt{f + g x}} - \sqrt{f + g x}\right) - \frac{2 c f \left(\frac{f^{2}}{\sqrt{f + g x}} + 2 f \sqrt{f + g x} - \frac{\left(f + g x\right)^{\frac{3}{2}}}{3}\right)}{g^{2}} - \frac{2 c \left(- \frac{f^{3}}{\sqrt{f + g x}} - 3 f^{2} \sqrt{f + g x} + f \left(f + g x\right)^{\frac{3}{2}} - \frac{\left(f + g x\right)^{\frac{5}{2}}}{5}\right)}{g^{2}}}{g} & \text{for}\: g \neq 0 \\\frac{a x + \frac{c x^{3}}{3}}{\sqrt{f}} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((-2*a*f/sqrt(f + g*x) - 2*a*(-f/sqrt(f + g*x) - sqrt(f + g*x)) - 2*c*f*(f**2/sqrt(f + g*x) + 2*f*sqrt(f + g*x) - (f + g*x)**(3/2)/3)/g**2 - 2*c*(-f**3/sqrt(f + g*x) - 3*f**2*sqrt(f + g*x) + f*(f + g*x)**(3/2) - (f + g*x)**(5/2)/5)/g**2)/g, Ne(g, 0)), ((a*x + c*x**3/3)/sqrt(f), True))","A",0
593,1,100,0,48.655345," ","integrate((c*x**2+a)/(e*x+d)/(g*x+f)**(1/2),x)","\frac{2 c \left(f + g x\right)^{\frac{3}{2}}}{3 e g^{2}} - \frac{2 c \sqrt{f + g x} \left(d g + e f\right)}{e^{2} g^{2}} - \frac{2 \left(a e^{2} + c d^{2}\right) \operatorname{atan}{\left(\frac{1}{\sqrt{\frac{e}{d g - e f}} \sqrt{f + g x}} \right)}}{e^{2} \sqrt{\frac{e}{d g - e f}} \left(d g - e f\right)}"," ",0,"2*c*(f + g*x)**(3/2)/(3*e*g**2) - 2*c*sqrt(f + g*x)*(d*g + e*f)/(e**2*g**2) - 2*(a*e**2 + c*d**2)*atan(1/(sqrt(e/(d*g - e*f))*sqrt(f + g*x)))/(e**2*sqrt(e/(d*g - e*f))*(d*g - e*f))","A",0
594,-1,0,0,0.000000," ","integrate((c*x**2+a)/(e*x+d)**2/(g*x+f)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
595,-1,0,0,0.000000," ","integrate((c*x**2+a)/(e*x+d)**3/(g*x+f)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
596,1,328,0,110.872850," ","integrate((e*x+d)**3*(c*x**2+a)/(g*x+f)**(3/2),x)","\frac{2 c e^{3} \left(f + g x\right)^{\frac{9}{2}}}{9 g^{6}} + \frac{\left(f + g x\right)^{\frac{7}{2}} \left(6 c d e^{2} g - 10 c e^{3} f\right)}{7 g^{6}} + \frac{\left(f + g x\right)^{\frac{5}{2}} \left(2 a e^{3} g^{2} + 6 c d^{2} e g^{2} - 24 c d e^{2} f g + 20 c e^{3} f^{2}\right)}{5 g^{6}} + \frac{\left(f + g x\right)^{\frac{3}{2}} \left(6 a d e^{2} g^{3} - 6 a e^{3} f g^{2} + 2 c d^{3} g^{3} - 18 c d^{2} e f g^{2} + 36 c d e^{2} f^{2} g - 20 c e^{3} f^{3}\right)}{3 g^{6}} + \frac{\sqrt{f + g x} \left(6 a d^{2} e g^{4} - 12 a d e^{2} f g^{3} + 6 a e^{3} f^{2} g^{2} - 4 c d^{3} f g^{3} + 18 c d^{2} e f^{2} g^{2} - 24 c d e^{2} f^{3} g + 10 c e^{3} f^{4}\right)}{g^{6}} - \frac{2 \left(a g^{2} + c f^{2}\right) \left(d g - e f\right)^{3}}{g^{6} \sqrt{f + g x}}"," ",0,"2*c*e**3*(f + g*x)**(9/2)/(9*g**6) + (f + g*x)**(7/2)*(6*c*d*e**2*g - 10*c*e**3*f)/(7*g**6) + (f + g*x)**(5/2)*(2*a*e**3*g**2 + 6*c*d**2*e*g**2 - 24*c*d*e**2*f*g + 20*c*e**3*f**2)/(5*g**6) + (f + g*x)**(3/2)*(6*a*d*e**2*g**3 - 6*a*e**3*f*g**2 + 2*c*d**3*g**3 - 18*c*d**2*e*f*g**2 + 36*c*d*e**2*f**2*g - 20*c*e**3*f**3)/(3*g**6) + sqrt(f + g*x)*(6*a*d**2*e*g**4 - 12*a*d*e**2*f*g**3 + 6*a*e**3*f**2*g**2 - 4*c*d**3*f*g**3 + 18*c*d**2*e*f**2*g**2 - 24*c*d*e**2*f**3*g + 10*c*e**3*f**4)/g**6 - 2*(a*g**2 + c*f**2)*(d*g - e*f)**3/(g**6*sqrt(f + g*x))","A",0
597,1,204,0,50.850904," ","integrate((e*x+d)**2*(c*x**2+a)/(g*x+f)**(3/2),x)","\frac{2 c e^{2} \left(f + g x\right)^{\frac{7}{2}}}{7 g^{5}} + \frac{\left(f + g x\right)^{\frac{5}{2}} \left(4 c d e g - 8 c e^{2} f\right)}{5 g^{5}} + \frac{\left(f + g x\right)^{\frac{3}{2}} \left(2 a e^{2} g^{2} + 2 c d^{2} g^{2} - 12 c d e f g + 12 c e^{2} f^{2}\right)}{3 g^{5}} + \frac{\sqrt{f + g x} \left(4 a d e g^{3} - 4 a e^{2} f g^{2} - 4 c d^{2} f g^{2} + 12 c d e f^{2} g - 8 c e^{2} f^{3}\right)}{g^{5}} - \frac{2 \left(a g^{2} + c f^{2}\right) \left(d g - e f\right)^{2}}{g^{5} \sqrt{f + g x}}"," ",0,"2*c*e**2*(f + g*x)**(7/2)/(7*g**5) + (f + g*x)**(5/2)*(4*c*d*e*g - 8*c*e**2*f)/(5*g**5) + (f + g*x)**(3/2)*(2*a*e**2*g**2 + 2*c*d**2*g**2 - 12*c*d*e*f*g + 12*c*e**2*f**2)/(3*g**5) + sqrt(f + g*x)*(4*a*d*e*g**3 - 4*a*e**2*f*g**2 - 4*c*d**2*f*g**2 + 12*c*d*e*f**2*g - 8*c*e**2*f**3)/g**5 - 2*(a*g**2 + c*f**2)*(d*g - e*f)**2/(g**5*sqrt(f + g*x))","A",0
598,1,112,0,25.284909," ","integrate((e*x+d)*(c*x**2+a)/(g*x+f)**(3/2),x)","\frac{2 c e \left(f + g x\right)^{\frac{5}{2}}}{5 g^{4}} + \frac{\left(f + g x\right)^{\frac{3}{2}} \left(2 c d g - 6 c e f\right)}{3 g^{4}} + \frac{\sqrt{f + g x} \left(2 a e g^{2} - 4 c d f g + 6 c e f^{2}\right)}{g^{4}} - \frac{2 \left(a g^{2} + c f^{2}\right) \left(d g - e f\right)}{g^{4} \sqrt{f + g x}}"," ",0,"2*c*e*(f + g*x)**(5/2)/(5*g**4) + (f + g*x)**(3/2)*(2*c*d*g - 6*c*e*f)/(3*g**4) + sqrt(f + g*x)*(2*a*e*g**2 - 4*c*d*f*g + 6*c*e*f**2)/g**4 - 2*(a*g**2 + c*f**2)*(d*g - e*f)/(g**4*sqrt(f + g*x))","A",0
599,1,58,0,10.144348," ","integrate((c*x**2+a)/(g*x+f)**(3/2),x)","- \frac{4 c f \sqrt{f + g x}}{g^{3}} + \frac{2 c \left(f + g x\right)^{\frac{3}{2}}}{3 g^{3}} - \frac{2 \left(a g^{2} + c f^{2}\right)}{g^{3} \sqrt{f + g x}}"," ",0,"-4*c*f*sqrt(f + g*x)/g**3 + 2*c*(f + g*x)**(3/2)/(3*g**3) - 2*(a*g**2 + c*f**2)/(g**3*sqrt(f + g*x))","A",0
600,1,104,0,41.279207," ","integrate((c*x**2+a)/(e*x+d)/(g*x+f)**(3/2),x)","\frac{2 c \sqrt{f + g x}}{e g^{2}} - \frac{2 \left(a g^{2} + c f^{2}\right)}{g^{2} \sqrt{f + g x} \left(d g - e f\right)} - \frac{2 \left(a e^{2} + c d^{2}\right) \operatorname{atan}{\left(\frac{\sqrt{f + g x}}{\sqrt{\frac{d g - e f}{e}}} \right)}}{e^{2} \sqrt{\frac{d g - e f}{e}} \left(d g - e f\right)}"," ",0,"2*c*sqrt(f + g*x)/(e*g**2) - 2*(a*g**2 + c*f**2)/(g**2*sqrt(f + g*x)*(d*g - e*f)) - 2*(a*e**2 + c*d**2)*atan(sqrt(f + g*x)/sqrt((d*g - e*f)/e))/(e**2*sqrt((d*g - e*f)/e)*(d*g - e*f))","A",0
601,-1,0,0,0.000000," ","integrate((c*x**2+a)/(e*x+d)**2/(g*x+f)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
602,-1,0,0,0.000000," ","integrate((c*x**2+a)/(e*x+d)**3/(g*x+f)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
603,0,0,0,0.000000," ","integrate((c*x**2+a)/(e*x+d)**(1/2)/(g*x+f)**(1/2),x)","\int \frac{a + c x^{2}}{\sqrt{d + e x} \sqrt{f + g x}}\, dx"," ",0,"Integral((a + c*x**2)/(sqrt(d + e*x)*sqrt(f + g*x)), x)","F",0
604,1,129,0,43.481788," ","integrate((2*x**2-1)/(-1+x)**(1/2)/(1+x)**(1/2),x)","- \begin{cases} 2 \operatorname{acosh}{\left(\frac{\sqrt{2} \sqrt{x + 1}}{2} \right)} & \text{for}\: \frac{\left|{x + 1}\right|}{2} > 1 \\- 2 i \operatorname{asin}{\left(\frac{\sqrt{2} \sqrt{x + 1}}{2} \right)} & \text{otherwise} \end{cases} + \frac{{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}{x^{2}}} \right)}}{2 \pi^{\frac{3}{2}}} - \frac{i {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}}{x^{2}}} \right)}}{2 \pi^{\frac{3}{2}}}"," ",0,"-Piecewise((2*acosh(sqrt(2)*sqrt(x + 1)/2), Abs(x + 1)/2 > 1), (-2*I*asin(sqrt(2)*sqrt(x + 1)/2), True)) + meijerg(((-3/4, -1/4), (-1/2, -1/2, 0, 1)), ((-1, -3/4, -1/2, -1/4, 0, 0), ()), x**(-2))/(2*pi**(3/2)) - I*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)/x**2)/(2*pi**(3/2))","C",0
605,0,0,0,0.000000," ","integrate((e*x+d)**(3/2)*(g*x+f)**(1/2)/(c*x**2+a),x)","\int \frac{\left(d + e x\right)^{\frac{3}{2}} \sqrt{f + g x}}{a + c x^{2}}\, dx"," ",0,"Integral((d + e*x)**(3/2)*sqrt(f + g*x)/(a + c*x**2), x)","F",0
606,0,0,0,0.000000," ","integrate((e*x+d)**(1/2)*(g*x+f)**(1/2)/(c*x**2+a),x)","\int \frac{\sqrt{d + e x} \sqrt{f + g x}}{a + c x^{2}}\, dx"," ",0,"Integral(sqrt(d + e*x)*sqrt(f + g*x)/(a + c*x**2), x)","F",0
607,0,0,0,0.000000," ","integrate((g*x+f)**(1/2)/(e*x+d)**(1/2)/(c*x**2+a),x)","\int \frac{\sqrt{f + g x}}{\left(a + c x^{2}\right) \sqrt{d + e x}}\, dx"," ",0,"Integral(sqrt(f + g*x)/((a + c*x**2)*sqrt(d + e*x)), x)","F",0
608,-1,0,0,0.000000," ","integrate((g*x+f)**(1/2)/(e*x+d)**(3/2)/(c*x**2+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
609,-1,0,0,0.000000," ","integrate((g*x+f)**(1/2)/(e*x+d)**(5/2)/(c*x**2+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
610,0,0,0,0.000000," ","integrate((e*x+d)**(3/2)/(c*x**2+a)/(g*x+f)**(1/2),x)","\int \frac{\left(d + e x\right)^{\frac{3}{2}}}{\left(a + c x^{2}\right) \sqrt{f + g x}}\, dx"," ",0,"Integral((d + e*x)**(3/2)/((a + c*x**2)*sqrt(f + g*x)), x)","F",0
611,0,0,0,0.000000," ","integrate((e*x+d)**(1/2)/(c*x**2+a)/(g*x+f)**(1/2),x)","\int \frac{\sqrt{d + e x}}{\left(a + c x^{2}\right) \sqrt{f + g x}}\, dx"," ",0,"Integral(sqrt(d + e*x)/((a + c*x**2)*sqrt(f + g*x)), x)","F",0
612,0,0,0,0.000000," ","integrate(1/(e*x+d)**(1/2)/(c*x**2+a)/(g*x+f)**(1/2),x)","\int \frac{1}{\left(a + c x^{2}\right) \sqrt{d + e x} \sqrt{f + g x}}\, dx"," ",0,"Integral(1/((a + c*x**2)*sqrt(d + e*x)*sqrt(f + g*x)), x)","F",0
613,0,0,0,0.000000," ","integrate(1/(e*x+d)**(3/2)/(c*x**2+a)/(g*x+f)**(1/2),x)","\int \frac{1}{\left(a + c x^{2}\right) \left(d + e x\right)^{\frac{3}{2}} \sqrt{f + g x}}\, dx"," ",0,"Integral(1/((a + c*x**2)*(d + e*x)**(3/2)*sqrt(f + g*x)), x)","F",0
614,-1,0,0,0.000000," ","integrate((e*x+d)**(3/2)/(g*x+f)**(3/2)/(c*x**2+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
615,-1,0,0,0.000000," ","integrate((e*x+d)**(1/2)/(g*x+f)**(3/2)/(c*x**2+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
616,0,0,0,0.000000," ","integrate(1/(e*x+d)**(1/2)/(g*x+f)**(3/2)/(c*x**2+a),x)","\int \frac{1}{\left(a + c x^{2}\right) \sqrt{d + e x} \left(f + g x\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/((a + c*x**2)*sqrt(d + e*x)*(f + g*x)**(3/2)), x)","F",0
617,0,0,0,0.000000," ","integrate(1/(e*x+d)**(3/2)/(g*x+f)**(3/2)/(c*x**2+a),x)","\int \frac{1}{\left(a + c x^{2}\right) \left(d + e x\right)^{\frac{3}{2}} \left(f + g x\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/((a + c*x**2)*(d + e*x)**(3/2)*(f + g*x)**(3/2)), x)","F",0
618,0,0,0,0.000000," ","integrate(x**(1/2)/(x**2+1)/(1+x)**(1/2),x)","\int \frac{\sqrt{x}}{\sqrt{x + 1} \left(x^{2} + 1\right)}\, dx"," ",0,"Integral(sqrt(x)/(sqrt(x + 1)*(x**2 + 1)), x)","F",0
619,0,0,0,0.000000," ","integrate((g*x+f)**2*(-x**2+1)**(1/2)/(1-x)**4,x)","\int \frac{\sqrt{- \left(x - 1\right) \left(x + 1\right)} \left(f + g x\right)^{2}}{\left(x - 1\right)^{4}}\, dx"," ",0,"Integral(sqrt(-(x - 1)*(x + 1))*(f + g*x)**2/(x - 1)**4, x)","F",0
620,0,0,0,0.000000," ","integrate((-a**2*x**2+1)**(3/2)/(-a*x+1)**2/(d*x+c),x)","\int \frac{\left(- \left(a x - 1\right) \left(a x + 1\right)\right)^{\frac{3}{2}}}{\left(c + d x\right) \left(a x - 1\right)^{2}}\, dx"," ",0,"Integral((-(a*x - 1)*(a*x + 1))**(3/2)/((c + d*x)*(a*x - 1)**2), x)","F",0
621,0,0,0,0.000000," ","integrate((a*x+1)**2/(d*x+c)/(-a**2*x**2+1)**(1/2),x)","\int \frac{\left(a x + 1\right)^{2}}{\sqrt{- \left(a x - 1\right) \left(a x + 1\right)} \left(c + d x\right)}\, dx"," ",0,"Integral((a*x + 1)**2/(sqrt(-(a*x - 1)*(a*x + 1))*(c + d*x)), x)","F",0
622,0,0,0,0.000000," ","integrate((e*x+d)**3*(g*x+f)**(1/2)*(c*x**2+a)**(1/2),x)","\int \sqrt{a + c x^{2}} \left(d + e x\right)^{3} \sqrt{f + g x}\, dx"," ",0,"Integral(sqrt(a + c*x**2)*(d + e*x)**3*sqrt(f + g*x), x)","F",0
623,0,0,0,0.000000," ","integrate((e*x+d)**2*(g*x+f)**(1/2)*(c*x**2+a)**(1/2),x)","\int \sqrt{a + c x^{2}} \left(d + e x\right)^{2} \sqrt{f + g x}\, dx"," ",0,"Integral(sqrt(a + c*x**2)*(d + e*x)**2*sqrt(f + g*x), x)","F",0
624,0,0,0,0.000000," ","integrate((e*x+d)*(g*x+f)**(1/2)*(c*x**2+a)**(1/2),x)","\int \sqrt{a + c x^{2}} \left(d + e x\right) \sqrt{f + g x}\, dx"," ",0,"Integral(sqrt(a + c*x**2)*(d + e*x)*sqrt(f + g*x), x)","F",0
625,0,0,0,0.000000," ","integrate((g*x+f)**(1/2)*(c*x**2+a)**(1/2),x)","\int \sqrt{a + c x^{2}} \sqrt{f + g x}\, dx"," ",0,"Integral(sqrt(a + c*x**2)*sqrt(f + g*x), x)","F",0
626,0,0,0,0.000000," ","integrate((g*x+f)**(1/2)*(c*x**2+a)**(1/2)/(e*x+d),x)","\int \frac{\sqrt{a + c x^{2}} \sqrt{f + g x}}{d + e x}\, dx"," ",0,"Integral(sqrt(a + c*x**2)*sqrt(f + g*x)/(d + e*x), x)","F",0
627,0,0,0,0.000000," ","integrate((g*x+f)**(1/2)*(c*x**2+a)**(1/2)/(e*x+d)**2,x)","\int \frac{\sqrt{a + c x^{2}} \sqrt{f + g x}}{\left(d + e x\right)^{2}}\, dx"," ",0,"Integral(sqrt(a + c*x**2)*sqrt(f + g*x)/(d + e*x)**2, x)","F",0
628,-1,0,0,0.000000," ","integrate((g*x+f)**(1/2)*(c*x**2+a)**(1/2)/(e*x+d)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
629,0,0,0,0.000000," ","integrate((e*x+d)**3*(c*x**2+a)**(1/2)/(g*x+f)**(1/2),x)","\int \frac{\sqrt{a + c x^{2}} \left(d + e x\right)^{3}}{\sqrt{f + g x}}\, dx"," ",0,"Integral(sqrt(a + c*x**2)*(d + e*x)**3/sqrt(f + g*x), x)","F",0
630,0,0,0,0.000000," ","integrate((e*x+d)**2*(c*x**2+a)**(1/2)/(g*x+f)**(1/2),x)","\int \frac{\sqrt{a + c x^{2}} \left(d + e x\right)^{2}}{\sqrt{f + g x}}\, dx"," ",0,"Integral(sqrt(a + c*x**2)*(d + e*x)**2/sqrt(f + g*x), x)","F",0
631,0,0,0,0.000000," ","integrate((e*x+d)*(c*x**2+a)**(1/2)/(g*x+f)**(1/2),x)","\int \frac{\sqrt{a + c x^{2}} \left(d + e x\right)}{\sqrt{f + g x}}\, dx"," ",0,"Integral(sqrt(a + c*x**2)*(d + e*x)/sqrt(f + g*x), x)","F",0
632,0,0,0,0.000000," ","integrate((c*x**2+a)**(1/2)/(g*x+f)**(1/2),x)","\int \frac{\sqrt{a + c x^{2}}}{\sqrt{f + g x}}\, dx"," ",0,"Integral(sqrt(a + c*x**2)/sqrt(f + g*x), x)","F",0
633,0,0,0,0.000000," ","integrate((c*x**2+a)**(1/2)/(e*x+d)/(g*x+f)**(1/2),x)","\int \frac{\sqrt{a + c x^{2}}}{\left(d + e x\right) \sqrt{f + g x}}\, dx"," ",0,"Integral(sqrt(a + c*x**2)/((d + e*x)*sqrt(f + g*x)), x)","F",0
634,0,0,0,0.000000," ","integrate((c*x**2+a)**(1/2)/(e*x+d)**2/(g*x+f)**(1/2),x)","\int \frac{\sqrt{a + c x^{2}}}{\left(d + e x\right)^{2} \sqrt{f + g x}}\, dx"," ",0,"Integral(sqrt(a + c*x**2)/((d + e*x)**2*sqrt(f + g*x)), x)","F",0
635,-1,0,0,0.000000," ","integrate((c*x**2+a)**(1/2)/(e*x+d)**3/(g*x+f)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
636,0,0,0,0.000000," ","integrate((e*x+d)**3*(g*x+f)**(1/2)/(c*x**2+a)**(1/2),x)","\int \frac{\left(d + e x\right)^{3} \sqrt{f + g x}}{\sqrt{a + c x^{2}}}\, dx"," ",0,"Integral((d + e*x)**3*sqrt(f + g*x)/sqrt(a + c*x**2), x)","F",0
637,0,0,0,0.000000," ","integrate((e*x+d)**2*(g*x+f)**(1/2)/(c*x**2+a)**(1/2),x)","\int \frac{\left(d + e x\right)^{2} \sqrt{f + g x}}{\sqrt{a + c x^{2}}}\, dx"," ",0,"Integral((d + e*x)**2*sqrt(f + g*x)/sqrt(a + c*x**2), x)","F",0
638,0,0,0,0.000000," ","integrate((e*x+d)*(g*x+f)**(1/2)/(c*x**2+a)**(1/2),x)","\int \frac{\left(d + e x\right) \sqrt{f + g x}}{\sqrt{a + c x^{2}}}\, dx"," ",0,"Integral((d + e*x)*sqrt(f + g*x)/sqrt(a + c*x**2), x)","F",0
639,0,0,0,0.000000," ","integrate((g*x+f)**(1/2)/(c*x**2+a)**(1/2),x)","\int \frac{\sqrt{f + g x}}{\sqrt{a + c x^{2}}}\, dx"," ",0,"Integral(sqrt(f + g*x)/sqrt(a + c*x**2), x)","F",0
640,0,0,0,0.000000," ","integrate((g*x+f)**(1/2)/(e*x+d)/(c*x**2+a)**(1/2),x)","\int \frac{\sqrt{f + g x}}{\sqrt{a + c x^{2}} \left(d + e x\right)}\, dx"," ",0,"Integral(sqrt(f + g*x)/(sqrt(a + c*x**2)*(d + e*x)), x)","F",0
641,0,0,0,0.000000," ","integrate((g*x+f)**(1/2)/(e*x+d)**2/(c*x**2+a)**(1/2),x)","\int \frac{\sqrt{f + g x}}{\sqrt{a + c x^{2}} \left(d + e x\right)^{2}}\, dx"," ",0,"Integral(sqrt(f + g*x)/(sqrt(a + c*x**2)*(d + e*x)**2), x)","F",0
642,-1,0,0,0.000000," ","integrate((g*x+f)**(1/2)/(e*x+d)**3/(c*x**2+a)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
643,0,0,0,0.000000," ","integrate((g*x+f)**(5/2)/(e*x+d)/(c*x**2+a)**(1/2),x)","\int \frac{\left(f + g x\right)^{\frac{5}{2}}}{\sqrt{a + c x^{2}} \left(d + e x\right)}\, dx"," ",0,"Integral((f + g*x)**(5/2)/(sqrt(a + c*x**2)*(d + e*x)), x)","F",0
644,0,0,0,0.000000," ","integrate((g*x+f)**(3/2)/(e*x+d)/(c*x**2+a)**(1/2),x)","\int \frac{\left(f + g x\right)^{\frac{3}{2}}}{\sqrt{a + c x^{2}} \left(d + e x\right)}\, dx"," ",0,"Integral((f + g*x)**(3/2)/(sqrt(a + c*x**2)*(d + e*x)), x)","F",0
645,0,0,0,0.000000," ","integrate((e*x+d)**3/(g*x+f)**(1/2)/(c*x**2+a)**(1/2),x)","\int \frac{\left(d + e x\right)^{3}}{\sqrt{a + c x^{2}} \sqrt{f + g x}}\, dx"," ",0,"Integral((d + e*x)**3/(sqrt(a + c*x**2)*sqrt(f + g*x)), x)","F",0
646,0,0,0,0.000000," ","integrate((e*x+d)**2/(g*x+f)**(1/2)/(c*x**2+a)**(1/2),x)","\int \frac{\left(d + e x\right)^{2}}{\sqrt{a + c x^{2}} \sqrt{f + g x}}\, dx"," ",0,"Integral((d + e*x)**2/(sqrt(a + c*x**2)*sqrt(f + g*x)), x)","F",0
647,0,0,0,0.000000," ","integrate((e*x+d)/(g*x+f)**(1/2)/(c*x**2+a)**(1/2),x)","\int \frac{d + e x}{\sqrt{a + c x^{2}} \sqrt{f + g x}}\, dx"," ",0,"Integral((d + e*x)/(sqrt(a + c*x**2)*sqrt(f + g*x)), x)","F",0
648,0,0,0,0.000000," ","integrate(1/(g*x+f)**(1/2)/(c*x**2+a)**(1/2),x)","\int \frac{1}{\sqrt{a + c x^{2}} \sqrt{f + g x}}\, dx"," ",0,"Integral(1/(sqrt(a + c*x**2)*sqrt(f + g*x)), x)","F",0
649,0,0,0,0.000000," ","integrate(1/(e*x+d)/(g*x+f)**(1/2)/(c*x**2+a)**(1/2),x)","\int \frac{1}{\sqrt{a + c x^{2}} \left(d + e x\right) \sqrt{f + g x}}\, dx"," ",0,"Integral(1/(sqrt(a + c*x**2)*(d + e*x)*sqrt(f + g*x)), x)","F",0
650,0,0,0,0.000000," ","integrate(1/(e*x+d)**2/(g*x+f)**(1/2)/(c*x**2+a)**(1/2),x)","\int \frac{1}{\sqrt{a + c x^{2}} \left(d + e x\right)^{2} \sqrt{f + g x}}\, dx"," ",0,"Integral(1/(sqrt(a + c*x**2)*(d + e*x)**2*sqrt(f + g*x)), x)","F",0
651,-1,0,0,0.000000," ","integrate(1/(e*x+d)**3/(g*x+f)**(1/2)/(c*x**2+a)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
652,0,0,0,0.000000," ","integrate(1/(e*x+d)/(g*x+f)**(3/2)/(c*x**2+a)**(1/2),x)","\int \frac{1}{\sqrt{a + c x^{2}} \left(d + e x\right) \left(f + g x\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/(sqrt(a + c*x**2)*(d + e*x)*(f + g*x)**(3/2)), x)","F",0
653,0,0,0,0.000000," ","integrate(1/(e*x+d)/(g*x+f)**(5/2)/(c*x**2+a)**(1/2),x)","\int \frac{1}{\sqrt{a + c x^{2}} \left(d + e x\right) \left(f + g x\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(1/(sqrt(a + c*x**2)*(d + e*x)*(f + g*x)**(5/2)), x)","F",0
654,0,0,0,0.000000," ","integrate(1/(e*x+d)/(g*x+f)**(1/2)/(c*x**2+1)**(1/2),x)","\int \frac{1}{\left(d + e x\right) \sqrt{f + g x} \sqrt{c x^{2} + 1}}\, dx"," ",0,"Integral(1/((d + e*x)*sqrt(f + g*x)*sqrt(c*x**2 + 1)), x)","F",0
655,0,0,0,0.000000," ","integrate(1/(e*x+d)**(1/2)/(g*x+f)**(1/2)/(c*x**2+a)**(1/2),x)","\int \frac{1}{\sqrt{a + c x^{2}} \sqrt{d + e x} \sqrt{f + g x}}\, dx"," ",0,"Integral(1/(sqrt(a + c*x**2)*sqrt(d + e*x)*sqrt(f + g*x)), x)","F",0
656,0,0,0,0.000000," ","integrate(1/(-1+x)**(1/2)/(1+x)**(1/2)/(2*x**2-1)**(1/2),x)","\int \frac{1}{\sqrt{x - 1} \sqrt{x + 1} \sqrt{2 x^{2} - 1}}\, dx"," ",0,"Integral(1/(sqrt(x - 1)*sqrt(x + 1)*sqrt(2*x**2 - 1)), x)","F",0
657,0,0,0,0.000000," ","integrate((g*x+f)**3*(e*x+d)**(1/2)/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(1/2),x)","\int \frac{\sqrt{d + e x} \left(f + g x\right)^{3}}{\sqrt{\left(d + e x\right) \left(a e + c d x\right)}}\, dx"," ",0,"Integral(sqrt(d + e*x)*(f + g*x)**3/sqrt((d + e*x)*(a*e + c*d*x)), x)","F",0
658,0,0,0,0.000000," ","integrate((g*x+f)**2*(e*x+d)**(1/2)/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(1/2),x)","\int \frac{\sqrt{d + e x} \left(f + g x\right)^{2}}{\sqrt{\left(d + e x\right) \left(a e + c d x\right)}}\, dx"," ",0,"Integral(sqrt(d + e*x)*(f + g*x)**2/sqrt((d + e*x)*(a*e + c*d*x)), x)","F",0
659,0,0,0,0.000000," ","integrate((g*x+f)*(e*x+d)**(1/2)/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(1/2),x)","\int \frac{\sqrt{d + e x} \left(f + g x\right)}{\sqrt{\left(d + e x\right) \left(a e + c d x\right)}}\, dx"," ",0,"Integral(sqrt(d + e*x)*(f + g*x)/sqrt((d + e*x)*(a*e + c*d*x)), x)","F",0
660,0,0,0,0.000000," ","integrate((e*x+d)**(1/2)/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(1/2),x)","\int \frac{\sqrt{d + e x}}{\sqrt{\left(d + e x\right) \left(a e + c d x\right)}}\, dx"," ",0,"Integral(sqrt(d + e*x)/sqrt((d + e*x)*(a*e + c*d*x)), x)","F",0
661,0,0,0,0.000000," ","integrate((e*x+d)**(1/2)/(g*x+f)/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(1/2),x)","\int \frac{\sqrt{d + e x}}{\sqrt{\left(d + e x\right) \left(a e + c d x\right)} \left(f + g x\right)}\, dx"," ",0,"Integral(sqrt(d + e*x)/(sqrt((d + e*x)*(a*e + c*d*x))*(f + g*x)), x)","F",0
662,0,0,0,0.000000," ","integrate((e*x+d)**(1/2)/(g*x+f)**2/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(1/2),x)","\int \frac{\sqrt{d + e x}}{\sqrt{\left(d + e x\right) \left(a e + c d x\right)} \left(f + g x\right)^{2}}\, dx"," ",0,"Integral(sqrt(d + e*x)/(sqrt((d + e*x)*(a*e + c*d*x))*(f + g*x)**2), x)","F",0
663,-1,0,0,0.000000," ","integrate((e*x+d)**(1/2)/(g*x+f)**3/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
664,-1,0,0,0.000000," ","integrate((e*x+d)**(1/2)/(g*x+f)**4/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
665,-1,0,0,0.000000," ","integrate((e*x+d)**(3/2)*(g*x+f)**3/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
666,-1,0,0,0.000000," ","integrate((e*x+d)**(3/2)*(g*x+f)**2/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
667,0,0,0,0.000000," ","integrate((e*x+d)**(3/2)*(g*x+f)/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(3/2),x)","\int \frac{\left(d + e x\right)^{\frac{3}{2}} \left(f + g x\right)}{\left(\left(d + e x\right) \left(a e + c d x\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((d + e*x)**(3/2)*(f + g*x)/((d + e*x)*(a*e + c*d*x))**(3/2), x)","F",0
668,0,0,0,0.000000," ","integrate((e*x+d)**(3/2)/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(3/2),x)","\int \frac{\left(d + e x\right)^{\frac{3}{2}}}{\left(\left(d + e x\right) \left(a e + c d x\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((d + e*x)**(3/2)/((d + e*x)*(a*e + c*d*x))**(3/2), x)","F",0
669,-1,0,0,0.000000," ","integrate((e*x+d)**(3/2)/(g*x+f)/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
670,-1,0,0,0.000000," ","integrate((e*x+d)**(3/2)/(g*x+f)**2/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
671,-1,0,0,0.000000," ","integrate((e*x+d)**(3/2)/(g*x+f)**3/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
672,-1,0,0,0.000000," ","integrate((e*x+d)**(5/2)*(g*x+f)**3/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
673,-1,0,0,0.000000," ","integrate((e*x+d)**(5/2)*(g*x+f)**2/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
674,-1,0,0,0.000000," ","integrate((e*x+d)**(5/2)*(g*x+f)/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
675,-1,0,0,0.000000," ","integrate((e*x+d)**(5/2)/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
676,-1,0,0,0.000000," ","integrate((e*x+d)**(5/2)/(g*x+f)/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
677,-1,0,0,0.000000," ","integrate((e*x+d)**(5/2)/(g*x+f)**2/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
678,-1,0,0,0.000000," ","integrate((e*x+d)**(5/2)/(g*x+f)**3/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
679,-1,0,0,0.000000," ","integrate((g*x+f)**4*(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(1/2)/(e*x+d)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
680,0,0,0,0.000000," ","integrate((g*x+f)**3*(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(1/2)/(e*x+d)**(1/2),x)","\int \frac{\sqrt{\left(d + e x\right) \left(a e + c d x\right)} \left(f + g x\right)^{3}}{\sqrt{d + e x}}\, dx"," ",0,"Integral(sqrt((d + e*x)*(a*e + c*d*x))*(f + g*x)**3/sqrt(d + e*x), x)","F",0
681,0,0,0,0.000000," ","integrate((g*x+f)**2*(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(1/2)/(e*x+d)**(1/2),x)","\int \frac{\sqrt{\left(d + e x\right) \left(a e + c d x\right)} \left(f + g x\right)^{2}}{\sqrt{d + e x}}\, dx"," ",0,"Integral(sqrt((d + e*x)*(a*e + c*d*x))*(f + g*x)**2/sqrt(d + e*x), x)","F",0
682,0,0,0,0.000000," ","integrate((g*x+f)*(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(1/2)/(e*x+d)**(1/2),x)","\int \frac{\sqrt{\left(d + e x\right) \left(a e + c d x\right)} \left(f + g x\right)}{\sqrt{d + e x}}\, dx"," ",0,"Integral(sqrt((d + e*x)*(a*e + c*d*x))*(f + g*x)/sqrt(d + e*x), x)","F",0
683,0,0,0,0.000000," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(1/2)/(e*x+d)**(1/2),x)","\int \frac{\sqrt{\left(d + e x\right) \left(a e + c d x\right)}}{\sqrt{d + e x}}\, dx"," ",0,"Integral(sqrt((d + e*x)*(a*e + c*d*x))/sqrt(d + e*x), x)","F",0
684,0,0,0,0.000000," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(1/2)/(g*x+f)/(e*x+d)**(1/2),x)","\int \frac{\sqrt{\left(d + e x\right) \left(a e + c d x\right)}}{\sqrt{d + e x} \left(f + g x\right)}\, dx"," ",0,"Integral(sqrt((d + e*x)*(a*e + c*d*x))/(sqrt(d + e*x)*(f + g*x)), x)","F",0
685,0,0,0,0.000000," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(1/2)/(g*x+f)**2/(e*x+d)**(1/2),x)","\int \frac{\sqrt{\left(d + e x\right) \left(a e + c d x\right)}}{\sqrt{d + e x} \left(f + g x\right)^{2}}\, dx"," ",0,"Integral(sqrt((d + e*x)*(a*e + c*d*x))/(sqrt(d + e*x)*(f + g*x)**2), x)","F",0
686,0,0,0,0.000000," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(1/2)/(g*x+f)**3/(e*x+d)**(1/2),x)","\int \frac{\sqrt{\left(d + e x\right) \left(a e + c d x\right)}}{\sqrt{d + e x} \left(f + g x\right)^{3}}\, dx"," ",0,"Integral(sqrt((d + e*x)*(a*e + c*d*x))/(sqrt(d + e*x)*(f + g*x)**3), x)","F",0
687,0,0,0,0.000000," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(1/2)/(g*x+f)**4/(e*x+d)**(1/2),x)","\int \frac{\sqrt{\left(d + e x\right) \left(a e + c d x\right)}}{\sqrt{d + e x} \left(f + g x\right)^{4}}\, dx"," ",0,"Integral(sqrt((d + e*x)*(a*e + c*d*x))/(sqrt(d + e*x)*(f + g*x)**4), x)","F",0
688,-1,0,0,0.000000," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(1/2)/(g*x+f)**5/(e*x+d)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
689,-1,0,0,0.000000," ","integrate((g*x+f)**4*(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(3/2)/(e*x+d)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
690,-1,0,0,0.000000," ","integrate((g*x+f)**3*(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(3/2)/(e*x+d)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
691,-1,0,0,0.000000," ","integrate((g*x+f)**2*(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(3/2)/(e*x+d)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
692,0,0,0,0.000000," ","integrate((g*x+f)*(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(3/2)/(e*x+d)**(3/2),x)","\int \frac{\left(\left(d + e x\right) \left(a e + c d x\right)\right)^{\frac{3}{2}} \left(f + g x\right)}{\left(d + e x\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(((d + e*x)*(a*e + c*d*x))**(3/2)*(f + g*x)/(d + e*x)**(3/2), x)","F",0
693,0,0,0,0.000000," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(3/2)/(e*x+d)**(3/2),x)","\int \frac{\left(\left(d + e x\right) \left(a e + c d x\right)\right)^{\frac{3}{2}}}{\left(d + e x\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(((d + e*x)*(a*e + c*d*x))**(3/2)/(d + e*x)**(3/2), x)","F",0
694,0,0,0,0.000000," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(3/2)/(e*x+d)**(3/2)/(g*x+f),x)","\int \frac{\left(\left(d + e x\right) \left(a e + c d x\right)\right)^{\frac{3}{2}}}{\left(d + e x\right)^{\frac{3}{2}} \left(f + g x\right)}\, dx"," ",0,"Integral(((d + e*x)*(a*e + c*d*x))**(3/2)/((d + e*x)**(3/2)*(f + g*x)), x)","F",0
695,-1,0,0,0.000000," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(3/2)/(e*x+d)**(3/2)/(g*x+f)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
696,-1,0,0,0.000000," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(3/2)/(e*x+d)**(3/2)/(g*x+f)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
697,-1,0,0,0.000000," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(3/2)/(e*x+d)**(3/2)/(g*x+f)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
698,-1,0,0,0.000000," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(3/2)/(e*x+d)**(3/2)/(g*x+f)**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
699,-1,0,0,0.000000," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(3/2)/(e*x+d)**(3/2)/(g*x+f)**6,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
700,-1,0,0,0.000000," ","integrate((g*x+f)**4*(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(5/2)/(e*x+d)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
701,-1,0,0,0.000000," ","integrate((g*x+f)**3*(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(5/2)/(e*x+d)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
702,-1,0,0,0.000000," ","integrate((g*x+f)**2*(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(5/2)/(e*x+d)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
703,-1,0,0,0.000000," ","integrate((g*x+f)*(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(5/2)/(e*x+d)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
704,-1,0,0,0.000000," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(5/2)/(e*x+d)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
705,-1,0,0,0.000000," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(5/2)/(e*x+d)**(5/2)/(g*x+f),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
706,-1,0,0,0.000000," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(5/2)/(e*x+d)**(5/2)/(g*x+f)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
707,-1,0,0,0.000000," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(5/2)/(e*x+d)**(5/2)/(g*x+f)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
708,-1,0,0,0.000000," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(5/2)/(e*x+d)**(5/2)/(g*x+f)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
709,-1,0,0,0.000000," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(5/2)/(e*x+d)**(5/2)/(g*x+f)**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
710,-1,0,0,0.000000," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(5/2)/(e*x+d)**(5/2)/(g*x+f)**6,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
711,-1,0,0,0.000000," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(5/2)/(e*x+d)**(5/2)/(g*x+f)**7,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
712,-1,0,0,0.000000," ","integrate((g*x+f)**(5/2)*(e*x+d)**(1/2)/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
713,0,0,0,0.000000," ","integrate((g*x+f)**(3/2)*(e*x+d)**(1/2)/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(1/2),x)","\int \frac{\sqrt{d + e x} \left(f + g x\right)^{\frac{3}{2}}}{\sqrt{\left(d + e x\right) \left(a e + c d x\right)}}\, dx"," ",0,"Integral(sqrt(d + e*x)*(f + g*x)**(3/2)/sqrt((d + e*x)*(a*e + c*d*x)), x)","F",0
714,0,0,0,0.000000," ","integrate((g*x+f)**(1/2)*(e*x+d)**(1/2)/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(1/2),x)","\int \frac{\sqrt{d + e x} \sqrt{f + g x}}{\sqrt{\left(d + e x\right) \left(a e + c d x\right)}}\, dx"," ",0,"Integral(sqrt(d + e*x)*sqrt(f + g*x)/sqrt((d + e*x)*(a*e + c*d*x)), x)","F",0
715,0,0,0,0.000000," ","integrate((e*x+d)**(1/2)/(g*x+f)**(1/2)/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(1/2),x)","\int \frac{\sqrt{d + e x}}{\sqrt{\left(d + e x\right) \left(a e + c d x\right)} \sqrt{f + g x}}\, dx"," ",0,"Integral(sqrt(d + e*x)/(sqrt((d + e*x)*(a*e + c*d*x))*sqrt(f + g*x)), x)","F",0
716,0,0,0,0.000000," ","integrate((e*x+d)**(1/2)/(g*x+f)**(3/2)/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(1/2),x)","\int \frac{\sqrt{d + e x}}{\sqrt{\left(d + e x\right) \left(a e + c d x\right)} \left(f + g x\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(sqrt(d + e*x)/(sqrt((d + e*x)*(a*e + c*d*x))*(f + g*x)**(3/2)), x)","F",0
717,-1,0,0,0.000000," ","integrate((e*x+d)**(1/2)/(g*x+f)**(5/2)/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
718,-1,0,0,0.000000," ","integrate((e*x+d)**(1/2)/(g*x+f)**(7/2)/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
719,-1,0,0,0.000000," ","integrate((e*x+d)**(1/2)/(g*x+f)**(9/2)/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
720,-1,0,0,0.000000," ","integrate((e*x+d)**(3/2)*(g*x+f)**(5/2)/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
721,-1,0,0,0.000000," ","integrate((e*x+d)**(3/2)*(g*x+f)**(3/2)/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
722,0,0,0,0.000000," ","integrate((e*x+d)**(3/2)*(g*x+f)**(1/2)/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(3/2),x)","\int \frac{\left(d + e x\right)^{\frac{3}{2}} \sqrt{f + g x}}{\left(\left(d + e x\right) \left(a e + c d x\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((d + e*x)**(3/2)*sqrt(f + g*x)/((d + e*x)*(a*e + c*d*x))**(3/2), x)","F",0
723,0,0,0,0.000000," ","integrate((e*x+d)**(3/2)/(g*x+f)**(1/2)/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(3/2),x)","\int \frac{\left(d + e x\right)^{\frac{3}{2}}}{\left(\left(d + e x\right) \left(a e + c d x\right)\right)^{\frac{3}{2}} \sqrt{f + g x}}\, dx"," ",0,"Integral((d + e*x)**(3/2)/(((d + e*x)*(a*e + c*d*x))**(3/2)*sqrt(f + g*x)), x)","F",0
724,-1,0,0,0.000000," ","integrate((e*x+d)**(3/2)/(g*x+f)**(3/2)/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
725,-1,0,0,0.000000," ","integrate((e*x+d)**(3/2)/(g*x+f)**(5/2)/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
726,-1,0,0,0.000000," ","integrate((e*x+d)**(3/2)/(g*x+f)**(7/2)/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
727,-1,0,0,0.000000," ","integrate((e*x+d)**(5/2)*(g*x+f)**(5/2)/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
728,-1,0,0,0.000000," ","integrate((e*x+d)**(5/2)*(g*x+f)**(3/2)/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
729,-1,0,0,0.000000," ","integrate((e*x+d)**(5/2)*(g*x+f)**(1/2)/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
730,-1,0,0,0.000000," ","integrate((e*x+d)**(5/2)/(g*x+f)**(1/2)/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
731,-1,0,0,0.000000," ","integrate((e*x+d)**(5/2)/(g*x+f)**(3/2)/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
732,-1,0,0,0.000000," ","integrate((e*x+d)**(5/2)/(g*x+f)**(5/2)/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
733,-1,0,0,0.000000," ","integrate((g*x+f)**(5/2)*(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(1/2)/(e*x+d)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
734,-1,0,0,0.000000," ","integrate((g*x+f)**(3/2)*(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(1/2)/(e*x+d)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
735,0,0,0,0.000000," ","integrate((g*x+f)**(1/2)*(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(1/2)/(e*x+d)**(1/2),x)","\int \frac{\sqrt{\left(d + e x\right) \left(a e + c d x\right)} \sqrt{f + g x}}{\sqrt{d + e x}}\, dx"," ",0,"Integral(sqrt((d + e*x)*(a*e + c*d*x))*sqrt(f + g*x)/sqrt(d + e*x), x)","F",0
736,0,0,0,0.000000," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(1/2)/(g*x+f)**(1/2)/(e*x+d)**(1/2),x)","\int \frac{\sqrt{\left(d + e x\right) \left(a e + c d x\right)}}{\sqrt{d + e x} \sqrt{f + g x}}\, dx"," ",0,"Integral(sqrt((d + e*x)*(a*e + c*d*x))/(sqrt(d + e*x)*sqrt(f + g*x)), x)","F",0
737,0,0,0,0.000000," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(1/2)/(g*x+f)**(3/2)/(e*x+d)**(1/2),x)","\int \frac{\sqrt{\left(d + e x\right) \left(a e + c d x\right)}}{\sqrt{d + e x} \left(f + g x\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(sqrt((d + e*x)*(a*e + c*d*x))/(sqrt(d + e*x)*(f + g*x)**(3/2)), x)","F",0
738,0,0,0,0.000000," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(1/2)/(g*x+f)**(5/2)/(e*x+d)**(1/2),x)","\int \frac{\sqrt{\left(d + e x\right) \left(a e + c d x\right)}}{\sqrt{d + e x} \left(f + g x\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(sqrt((d + e*x)*(a*e + c*d*x))/(sqrt(d + e*x)*(f + g*x)**(5/2)), x)","F",0
739,-1,0,0,0.000000," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(1/2)/(g*x+f)**(7/2)/(e*x+d)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
740,-1,0,0,0.000000," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(1/2)/(g*x+f)**(9/2)/(e*x+d)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
741,-1,0,0,0.000000," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(1/2)/(g*x+f)**(11/2)/(e*x+d)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
742,-1,0,0,0.000000," ","integrate((g*x+f)**(3/2)*(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(3/2)/(e*x+d)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
743,0,0,0,0.000000," ","integrate((g*x+f)**(1/2)*(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(3/2)/(e*x+d)**(3/2),x)","\int \frac{\left(\left(d + e x\right) \left(a e + c d x\right)\right)^{\frac{3}{2}} \sqrt{f + g x}}{\left(d + e x\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(((d + e*x)*(a*e + c*d*x))**(3/2)*sqrt(f + g*x)/(d + e*x)**(3/2), x)","F",0
744,-1,0,0,0.000000," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(3/2)/(e*x+d)**(3/2)/(g*x+f)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
745,-1,0,0,0.000000," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(3/2)/(e*x+d)**(3/2)/(g*x+f)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
746,-1,0,0,0.000000," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(3/2)/(e*x+d)**(3/2)/(g*x+f)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
747,-1,0,0,0.000000," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(3/2)/(e*x+d)**(3/2)/(g*x+f)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
748,-1,0,0,0.000000," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(3/2)/(e*x+d)**(3/2)/(g*x+f)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
749,-1,0,0,0.000000," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(3/2)/(e*x+d)**(3/2)/(g*x+f)**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
750,-1,0,0,0.000000," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(3/2)/(e*x+d)**(3/2)/(g*x+f)**(13/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
751,-1,0,0,0.000000," ","integrate((g*x+f)**(3/2)*(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(5/2)/(e*x+d)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
752,-1,0,0,0.000000," ","integrate((g*x+f)**(1/2)*(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(5/2)/(e*x+d)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
753,-1,0,0,0.000000," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(5/2)/(e*x+d)**(5/2)/(g*x+f)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
754,-1,0,0,0.000000," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(5/2)/(e*x+d)**(5/2)/(g*x+f)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
755,-1,0,0,0.000000," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(5/2)/(e*x+d)**(5/2)/(g*x+f)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
756,-1,0,0,0.000000," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(5/2)/(e*x+d)**(5/2)/(g*x+f)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
757,-1,0,0,0.000000," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(5/2)/(e*x+d)**(5/2)/(g*x+f)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
758,-1,0,0,0.000000," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(5/2)/(e*x+d)**(5/2)/(g*x+f)**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
759,-1,0,0,0.000000," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(5/2)/(e*x+d)**(5/2)/(g*x+f)**(13/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
760,-1,0,0,0.000000," ","integrate((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(5/2)/(e*x+d)**(5/2)/(g*x+f)**(15/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
761,-1,0,0,0.000000," ","integrate((e*x+d)**(5/2)*(g*x+f)**n/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
762,-2,0,0,0.000000," ","integrate((e*x+d)**(3/2)*(g*x+f)**n/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(3/2),x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
763,-1,0,0,0.000000," ","integrate((e*x+d)**(1/2)*(g*x+f)**n/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
764,0,0,0,0.000000," ","integrate((g*x+f)**n*(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(1/2)/(e*x+d)**(1/2),x)","\int \frac{\sqrt{\left(d + e x\right) \left(a e + c d x\right)} \left(f + g x\right)^{n}}{\sqrt{d + e x}}\, dx"," ",0,"Integral(sqrt((d + e*x)*(a*e + c*d*x))*(f + g*x)**n/sqrt(d + e*x), x)","F",0
765,-1,0,0,0.000000," ","integrate((g*x+f)**n*(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(3/2)/(e*x+d)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
766,-1,0,0,0.000000," ","integrate((g*x+f)**n*(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(5/2)/(e*x+d)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
767,-2,0,0,0.000000," ","integrate((e*x+d)**m*(g*x+f)**n/((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**m),x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
768,-1,0,0,0.000000," ","integrate((e*x+d)**m*(g*x+f)**3/((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**m),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
769,-1,0,0,0.000000," ","integrate((e*x+d)**m*(g*x+f)**2/((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**m),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
770,-2,0,0,0.000000," ","integrate((e*x+d)**m*(g*x+f)/((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**m),x)","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError","F(-2)",0
771,-2,0,0,0.000000," ","integrate((e*x+d)**m/((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**m),x)","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError","F(-2)",0
772,-1,0,0,0.000000," ","integrate((e*x+d)**m/(g*x+f)/((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**m),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
773,-1,0,0,0.000000," ","integrate((e*x+d)**m/(g*x+f)**2/((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**m),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
774,-2,0,0,0.000000," ","integrate((e*x+d)**m/(g*x+f)**3/((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**m),x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
775,-1,0,0,0.000000," ","integrate((e*x+d)**m*(g*x+f)**(3/2)/((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**m),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
776,-1,0,0,0.000000," ","integrate((e*x+d)**m*(g*x+f)**(1/2)/((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**m),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
777,-1,0,0,0.000000," ","integrate((e*x+d)**m/(g*x+f)**(1/2)/((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**m),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
778,-1,0,0,0.000000," ","integrate((e*x+d)**m/(g*x+f)**(3/2)/((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**m),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
779,-1,0,0,0.000000," ","integrate((e*x+d)**m/(g*x+f)**(5/2)/((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**m),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
780,-1,0,0,0.000000," ","integrate((c*d*x+a*e)**n*(e*x+d)**m/((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**m),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
781,-1,0,0,0.000000," ","integrate((e*x+d)**m*(c*d**2*e*g-e*(a*e**2+c*d**2)*g-c*d*e**2*g*x)**(-1+m)/((a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**m),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
782,-1,0,0,0.000000," ","integrate((e*x+d)**(3/2)*(g*x+f)**n/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
783,-1,0,0,0.000000," ","integrate((e*x+d)**(3/2)*(g*x+f)**4/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
784,0,0,0,0.000000," ","integrate((e*x+d)**(3/2)*(g*x+f)**3/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(1/2),x)","\int \frac{\left(d + e x\right)^{\frac{3}{2}} \left(f + g x\right)^{3}}{\sqrt{\left(d + e x\right) \left(a e + c d x\right)}}\, dx"," ",0,"Integral((d + e*x)**(3/2)*(f + g*x)**3/sqrt((d + e*x)*(a*e + c*d*x)), x)","F",0
785,0,0,0,0.000000," ","integrate((e*x+d)**(3/2)*(g*x+f)**2/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(1/2),x)","\int \frac{\left(d + e x\right)^{\frac{3}{2}} \left(f + g x\right)^{2}}{\sqrt{\left(d + e x\right) \left(a e + c d x\right)}}\, dx"," ",0,"Integral((d + e*x)**(3/2)*(f + g*x)**2/sqrt((d + e*x)*(a*e + c*d*x)), x)","F",0
786,0,0,0,0.000000," ","integrate((e*x+d)**(3/2)*(g*x+f)/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(1/2),x)","\int \frac{\left(d + e x\right)^{\frac{3}{2}} \left(f + g x\right)}{\sqrt{\left(d + e x\right) \left(a e + c d x\right)}}\, dx"," ",0,"Integral((d + e*x)**(3/2)*(f + g*x)/sqrt((d + e*x)*(a*e + c*d*x)), x)","F",0
787,0,0,0,0.000000," ","integrate((e*x+d)**(3/2)/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(1/2),x)","\int \frac{\left(d + e x\right)^{\frac{3}{2}}}{\sqrt{\left(d + e x\right) \left(a e + c d x\right)}}\, dx"," ",0,"Integral((d + e*x)**(3/2)/sqrt((d + e*x)*(a*e + c*d*x)), x)","F",0
788,0,0,0,0.000000," ","integrate((e*x+d)**(3/2)/(g*x+f)/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(1/2),x)","\int \frac{\left(d + e x\right)^{\frac{3}{2}}}{\sqrt{\left(d + e x\right) \left(a e + c d x\right)} \left(f + g x\right)}\, dx"," ",0,"Integral((d + e*x)**(3/2)/(sqrt((d + e*x)*(a*e + c*d*x))*(f + g*x)), x)","F",0
789,-1,0,0,0.000000," ","integrate((e*x+d)**(3/2)/(g*x+f)**2/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
790,-1,0,0,0.000000," ","integrate((e*x+d)**(3/2)/(g*x+f)**3/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
791,-1,0,0,0.000000," ","integrate((e*x+d)**(3/2)/(g*x+f)**4/(a*d*e+(a*e**2+c*d**2)*x+c*d*e*x**2)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
792,-1,0,0,0.000000," ","integrate((c*x**2+b*x+a)**3/(-d*x+1)**(1/2)/(d*x+1)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
793,-1,0,0,0.000000," ","integrate((c*x**2+b*x+a)**2/(-d*x+1)**(1/2)/(d*x+1)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
794,1,282,0,49.710768," ","integrate((c*x**2+b*x+a)/(-d*x+1)**(1/2)/(d*x+1)**(1/2),x)","- \frac{i 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}{d^{2} x^{2}}} \right)}}{4 \pi^{\frac{3}{2}} d} + \frac{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}}{d^{2} x^{2}}} \right)}}{4 \pi^{\frac{3}{2}} d} - \frac{i 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}{d^{2} x^{2}}} \right)}}{4 \pi^{\frac{3}{2}} d^{2}} - \frac{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}}{d^{2} x^{2}}} \right)}}{4 \pi^{\frac{3}{2}} d^{2}} - \frac{i c {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}{d^{2} x^{2}}} \right)}}{4 \pi^{\frac{3}{2}} d^{3}} + \frac{c {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}}{d^{2} x^{2}}} \right)}}{4 \pi^{\frac{3}{2}} d^{3}}"," ",0,"-I*a*meijerg(((1/4, 3/4), (1/2, 1/2, 1, 1)), ((0, 1/4, 1/2, 3/4, 1, 0), ()), 1/(d**2*x**2))/(4*pi**(3/2)*d) + 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)/(d**2*x**2))/(4*pi**(3/2)*d) - I*b*meijerg(((-1/4, 1/4), (0, 0, 1/2, 1)), ((-1/2, -1/4, 0, 1/4, 1/2, 0), ()), 1/(d**2*x**2))/(4*pi**(3/2)*d**2) - 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)/(d**2*x**2))/(4*pi**(3/2)*d**2) - I*c*meijerg(((-3/4, -1/4), (-1/2, -1/2, 0, 1)), ((-1, -3/4, -1/2, -1/4, 0, 0), ()), 1/(d**2*x**2))/(4*pi**(3/2)*d**3) + c*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)/(d**2*x**2))/(4*pi**(3/2)*d**3)","C",0
795,0,0,0,0.000000," ","integrate(1/(c*x**2+b*x+a)/(-d*x+1)**(1/2)/(d*x+1)**(1/2),x)","\int \frac{1}{\sqrt{- d x + 1} \sqrt{d x + 1} \left(a + b x + c x^{2}\right)}\, dx"," ",0,"Integral(1/(sqrt(-d*x + 1)*sqrt(d*x + 1)*(a + b*x + c*x**2)), x)","F",0
796,-1,0,0,0.000000," ","integrate(1/(c*x**2+b*x+a)**2/(-d*x+1)**(1/2)/(d*x+1)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
797,-1,0,0,0.000000," ","integrate((c*x**2+b*x+a)**3/(-d*x+1)**(3/2)/(d*x+1)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
798,-1,0,0,0.000000," ","integrate((c*x**2+b*x+a)**2/(-d*x+1)**(3/2)/(d*x+1)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
799,-1,0,0,0.000000," ","integrate((c*x**2+b*x+a)/(-d*x+1)**(3/2)/(d*x+1)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
800,-1,0,0,0.000000," ","integrate(1/(-d*x+1)**(3/2)/(d*x+1)**(3/2)/(c*x**2+b*x+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
801,-1,0,0,0.000000," ","integrate(1/(-d*x+1)**(3/2)/(d*x+1)**(3/2)/(c*x**2+b*x+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
802,-1,0,0,0.000000," ","integrate((-e*x+1)**m*(e*x+1)**m*(c*x**2+a)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
803,-1,0,0,0.000000," ","integrate((-e*x+d)**m*(e*x+d)**m*(c*x**2+a)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
804,-1,0,0,0.000000," ","integrate((e*x+d)**m*(-e*f*x+d*f)**m*(c*x**2+a)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
805,-1,0,0,0.000000," ","integrate((e*x+d)**3*(g*x+f)**n*(c*e*x**2+2*c*d*x+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
806,1,11946,0,11.821082," ","integrate((e*x+d)**2*(g*x+f)**n*(c*e*x**2+2*c*d*x+a),x)","\begin{cases} f^{n} \left(a d^{2} x + a d e x^{2} + \frac{a e^{2} x^{3}}{3} + c d^{3} x^{2} + \frac{5 c d^{2} e x^{3}}{3} + c d e^{2} x^{4} + \frac{c e^{3} x^{5}}{5}\right) & \text{for}\: g = 0 \\- \frac{3 a d^{2} g^{4}}{12 f^{4} g^{5} + 48 f^{3} g^{6} x + 72 f^{2} g^{7} x^{2} + 48 f g^{8} x^{3} + 12 g^{9} x^{4}} - \frac{2 a d e f g^{3}}{12 f^{4} g^{5} + 48 f^{3} g^{6} x + 72 f^{2} g^{7} x^{2} + 48 f g^{8} x^{3} + 12 g^{9} x^{4}} - \frac{8 a d e g^{4} x}{12 f^{4} g^{5} + 48 f^{3} g^{6} x + 72 f^{2} g^{7} x^{2} + 48 f g^{8} x^{3} + 12 g^{9} x^{4}} - \frac{a e^{2} f^{2} g^{2}}{12 f^{4} g^{5} + 48 f^{3} g^{6} x + 72 f^{2} g^{7} x^{2} + 48 f g^{8} x^{3} + 12 g^{9} x^{4}} - \frac{4 a e^{2} f g^{3} x}{12 f^{4} g^{5} + 48 f^{3} g^{6} x + 72 f^{2} g^{7} x^{2} + 48 f g^{8} x^{3} + 12 g^{9} x^{4}} - \frac{6 a e^{2} g^{4} x^{2}}{12 f^{4} g^{5} + 48 f^{3} g^{6} x + 72 f^{2} g^{7} x^{2} + 48 f g^{8} x^{3} + 12 g^{9} x^{4}} - \frac{2 c d^{3} f g^{3}}{12 f^{4} g^{5} + 48 f^{3} g^{6} x + 72 f^{2} g^{7} x^{2} + 48 f g^{8} x^{3} + 12 g^{9} x^{4}} - \frac{8 c d^{3} g^{4} x}{12 f^{4} g^{5} + 48 f^{3} g^{6} x + 72 f^{2} g^{7} x^{2} + 48 f g^{8} x^{3} + 12 g^{9} x^{4}} - \frac{5 c d^{2} e f^{2} g^{2}}{12 f^{4} g^{5} + 48 f^{3} g^{6} x + 72 f^{2} g^{7} x^{2} + 48 f g^{8} x^{3} + 12 g^{9} x^{4}} - \frac{20 c d^{2} e f g^{3} x}{12 f^{4} g^{5} + 48 f^{3} g^{6} x + 72 f^{2} g^{7} x^{2} + 48 f g^{8} x^{3} + 12 g^{9} x^{4}} - \frac{30 c d^{2} e g^{4} x^{2}}{12 f^{4} g^{5} + 48 f^{3} g^{6} x + 72 f^{2} g^{7} x^{2} + 48 f g^{8} x^{3} + 12 g^{9} x^{4}} - \frac{12 c d e^{2} f^{3} g}{12 f^{4} g^{5} + 48 f^{3} g^{6} x + 72 f^{2} g^{7} x^{2} + 48 f g^{8} x^{3} + 12 g^{9} x^{4}} - \frac{48 c d e^{2} f^{2} g^{2} x}{12 f^{4} g^{5} + 48 f^{3} g^{6} x + 72 f^{2} g^{7} x^{2} + 48 f g^{8} x^{3} + 12 g^{9} x^{4}} - \frac{72 c d e^{2} f g^{3} x^{2}}{12 f^{4} g^{5} + 48 f^{3} g^{6} x + 72 f^{2} g^{7} x^{2} + 48 f g^{8} x^{3} + 12 g^{9} x^{4}} - \frac{48 c d e^{2} g^{4} x^{3}}{12 f^{4} g^{5} + 48 f^{3} g^{6} x + 72 f^{2} g^{7} x^{2} + 48 f g^{8} x^{3} + 12 g^{9} x^{4}} + \frac{12 c e^{3} f^{4} \log{\left(\frac{f}{g} + x \right)}}{12 f^{4} g^{5} + 48 f^{3} g^{6} x + 72 f^{2} g^{7} x^{2} + 48 f g^{8} x^{3} + 12 g^{9} x^{4}} + \frac{25 c e^{3} f^{4}}{12 f^{4} g^{5} + 48 f^{3} g^{6} x + 72 f^{2} g^{7} x^{2} + 48 f g^{8} x^{3} + 12 g^{9} x^{4}} + \frac{48 c e^{3} f^{3} g x \log{\left(\frac{f}{g} + x \right)}}{12 f^{4} g^{5} + 48 f^{3} g^{6} x + 72 f^{2} g^{7} x^{2} + 48 f g^{8} x^{3} + 12 g^{9} x^{4}} + \frac{88 c e^{3} f^{3} g x}{12 f^{4} g^{5} + 48 f^{3} g^{6} x + 72 f^{2} g^{7} x^{2} + 48 f g^{8} x^{3} + 12 g^{9} x^{4}} + \frac{72 c e^{3} f^{2} g^{2} x^{2} \log{\left(\frac{f}{g} + x \right)}}{12 f^{4} g^{5} + 48 f^{3} g^{6} x + 72 f^{2} g^{7} x^{2} + 48 f g^{8} x^{3} + 12 g^{9} x^{4}} + \frac{108 c e^{3} f^{2} g^{2} x^{2}}{12 f^{4} g^{5} + 48 f^{3} g^{6} x + 72 f^{2} g^{7} x^{2} + 48 f g^{8} x^{3} + 12 g^{9} x^{4}} + \frac{48 c e^{3} f g^{3} x^{3} \log{\left(\frac{f}{g} + x \right)}}{12 f^{4} g^{5} + 48 f^{3} g^{6} x + 72 f^{2} g^{7} x^{2} + 48 f g^{8} x^{3} + 12 g^{9} x^{4}} + \frac{48 c e^{3} f g^{3} x^{3}}{12 f^{4} g^{5} + 48 f^{3} g^{6} x + 72 f^{2} g^{7} x^{2} + 48 f g^{8} x^{3} + 12 g^{9} x^{4}} + \frac{12 c e^{3} g^{4} x^{4} \log{\left(\frac{f}{g} + x \right)}}{12 f^{4} g^{5} + 48 f^{3} g^{6} x + 72 f^{2} g^{7} x^{2} + 48 f g^{8} x^{3} + 12 g^{9} x^{4}} & \text{for}\: n = -5 \\- \frac{a d^{2} g^{4}}{3 f^{3} g^{5} + 9 f^{2} g^{6} x + 9 f g^{7} x^{2} + 3 g^{8} x^{3}} - \frac{a d e f g^{3}}{3 f^{3} g^{5} + 9 f^{2} g^{6} x + 9 f g^{7} x^{2} + 3 g^{8} x^{3}} - \frac{3 a d e g^{4} x}{3 f^{3} g^{5} + 9 f^{2} g^{6} x + 9 f g^{7} x^{2} + 3 g^{8} x^{3}} - \frac{a e^{2} f^{2} g^{2}}{3 f^{3} g^{5} + 9 f^{2} g^{6} x + 9 f g^{7} x^{2} + 3 g^{8} x^{3}} - \frac{3 a e^{2} f g^{3} x}{3 f^{3} g^{5} + 9 f^{2} g^{6} x + 9 f g^{7} x^{2} + 3 g^{8} x^{3}} - \frac{3 a e^{2} g^{4} x^{2}}{3 f^{3} g^{5} + 9 f^{2} g^{6} x + 9 f g^{7} x^{2} + 3 g^{8} x^{3}} - \frac{c d^{3} f g^{3}}{3 f^{3} g^{5} + 9 f^{2} g^{6} x + 9 f g^{7} x^{2} + 3 g^{8} x^{3}} - \frac{3 c d^{3} g^{4} x}{3 f^{3} g^{5} + 9 f^{2} g^{6} x + 9 f g^{7} x^{2} + 3 g^{8} x^{3}} - \frac{5 c d^{2} e f^{2} g^{2}}{3 f^{3} g^{5} + 9 f^{2} g^{6} x + 9 f g^{7} x^{2} + 3 g^{8} x^{3}} - \frac{15 c d^{2} e f g^{3} x}{3 f^{3} g^{5} + 9 f^{2} g^{6} x + 9 f g^{7} x^{2} + 3 g^{8} x^{3}} - \frac{15 c d^{2} e g^{4} x^{2}}{3 f^{3} g^{5} + 9 f^{2} g^{6} x + 9 f g^{7} x^{2} + 3 g^{8} x^{3}} + \frac{12 c d e^{2} f^{3} g \log{\left(\frac{f}{g} + x \right)}}{3 f^{3} g^{5} + 9 f^{2} g^{6} x + 9 f g^{7} x^{2} + 3 g^{8} x^{3}} + \frac{22 c d e^{2} f^{3} g}{3 f^{3} g^{5} + 9 f^{2} g^{6} x + 9 f g^{7} x^{2} + 3 g^{8} x^{3}} + \frac{36 c d e^{2} f^{2} g^{2} x \log{\left(\frac{f}{g} + x \right)}}{3 f^{3} g^{5} + 9 f^{2} g^{6} x + 9 f g^{7} x^{2} + 3 g^{8} x^{3}} + \frac{54 c d e^{2} f^{2} g^{2} x}{3 f^{3} g^{5} + 9 f^{2} g^{6} x + 9 f g^{7} x^{2} + 3 g^{8} x^{3}} + \frac{36 c d e^{2} f g^{3} x^{2} \log{\left(\frac{f}{g} + x \right)}}{3 f^{3} g^{5} + 9 f^{2} g^{6} x + 9 f g^{7} x^{2} + 3 g^{8} x^{3}} + \frac{36 c d e^{2} f g^{3} x^{2}}{3 f^{3} g^{5} + 9 f^{2} g^{6} x + 9 f g^{7} x^{2} + 3 g^{8} x^{3}} + \frac{12 c d e^{2} g^{4} x^{3} \log{\left(\frac{f}{g} + x \right)}}{3 f^{3} g^{5} + 9 f^{2} g^{6} x + 9 f g^{7} x^{2} + 3 g^{8} x^{3}} - \frac{12 c e^{3} f^{4} \log{\left(\frac{f}{g} + x \right)}}{3 f^{3} g^{5} + 9 f^{2} g^{6} x + 9 f g^{7} x^{2} + 3 g^{8} x^{3}} - \frac{22 c e^{3} f^{4}}{3 f^{3} g^{5} + 9 f^{2} g^{6} x + 9 f g^{7} x^{2} + 3 g^{8} x^{3}} - \frac{36 c e^{3} f^{3} g x \log{\left(\frac{f}{g} + x \right)}}{3 f^{3} g^{5} + 9 f^{2} g^{6} x + 9 f g^{7} x^{2} + 3 g^{8} x^{3}} - \frac{54 c e^{3} f^{3} g x}{3 f^{3} g^{5} + 9 f^{2} g^{6} x + 9 f g^{7} x^{2} + 3 g^{8} x^{3}} - \frac{36 c e^{3} f^{2} g^{2} x^{2} \log{\left(\frac{f}{g} + x \right)}}{3 f^{3} g^{5} + 9 f^{2} g^{6} x + 9 f g^{7} x^{2} + 3 g^{8} x^{3}} - \frac{36 c e^{3} f^{2} g^{2} x^{2}}{3 f^{3} g^{5} + 9 f^{2} g^{6} x + 9 f g^{7} x^{2} + 3 g^{8} x^{3}} - \frac{12 c e^{3} f g^{3} x^{3} \log{\left(\frac{f}{g} + x \right)}}{3 f^{3} g^{5} + 9 f^{2} g^{6} x + 9 f g^{7} x^{2} + 3 g^{8} x^{3}} + \frac{3 c e^{3} g^{4} x^{4}}{3 f^{3} g^{5} + 9 f^{2} g^{6} x + 9 f g^{7} x^{2} + 3 g^{8} x^{3}} & \text{for}\: n = -4 \\- \frac{a d^{2} g^{4}}{2 f^{2} g^{5} + 4 f g^{6} x + 2 g^{7} x^{2}} - \frac{2 a d e f g^{3}}{2 f^{2} g^{5} + 4 f g^{6} x + 2 g^{7} x^{2}} - \frac{4 a d e g^{4} x}{2 f^{2} g^{5} + 4 f g^{6} x + 2 g^{7} x^{2}} + \frac{2 a e^{2} f^{2} g^{2} \log{\left(\frac{f}{g} + x \right)}}{2 f^{2} g^{5} + 4 f g^{6} x + 2 g^{7} x^{2}} + \frac{3 a e^{2} f^{2} g^{2}}{2 f^{2} g^{5} + 4 f g^{6} x + 2 g^{7} x^{2}} + \frac{4 a e^{2} f g^{3} x \log{\left(\frac{f}{g} + x \right)}}{2 f^{2} g^{5} + 4 f g^{6} x + 2 g^{7} x^{2}} + \frac{4 a e^{2} f g^{3} x}{2 f^{2} g^{5} + 4 f g^{6} x + 2 g^{7} x^{2}} + \frac{2 a e^{2} g^{4} x^{2} \log{\left(\frac{f}{g} + x \right)}}{2 f^{2} g^{5} + 4 f g^{6} x + 2 g^{7} x^{2}} - \frac{2 c d^{3} f g^{3}}{2 f^{2} g^{5} + 4 f g^{6} x + 2 g^{7} x^{2}} - \frac{4 c d^{3} g^{4} x}{2 f^{2} g^{5} + 4 f g^{6} x + 2 g^{7} x^{2}} + \frac{10 c d^{2} e f^{2} g^{2} \log{\left(\frac{f}{g} + x \right)}}{2 f^{2} g^{5} + 4 f g^{6} x + 2 g^{7} x^{2}} + \frac{15 c d^{2} e f^{2} g^{2}}{2 f^{2} g^{5} + 4 f g^{6} x + 2 g^{7} x^{2}} + \frac{20 c d^{2} e f g^{3} x \log{\left(\frac{f}{g} + x \right)}}{2 f^{2} g^{5} + 4 f g^{6} x + 2 g^{7} x^{2}} + \frac{20 c d^{2} e f g^{3} x}{2 f^{2} g^{5} + 4 f g^{6} x + 2 g^{7} x^{2}} + \frac{10 c d^{2} e g^{4} x^{2} \log{\left(\frac{f}{g} + x \right)}}{2 f^{2} g^{5} + 4 f g^{6} x + 2 g^{7} x^{2}} - \frac{24 c d e^{2} f^{3} g \log{\left(\frac{f}{g} + x \right)}}{2 f^{2} g^{5} + 4 f g^{6} x + 2 g^{7} x^{2}} - \frac{36 c d e^{2} f^{3} g}{2 f^{2} g^{5} + 4 f g^{6} x + 2 g^{7} x^{2}} - \frac{48 c d e^{2} f^{2} g^{2} x \log{\left(\frac{f}{g} + x \right)}}{2 f^{2} g^{5} + 4 f g^{6} x + 2 g^{7} x^{2}} - \frac{48 c d e^{2} f^{2} g^{2} x}{2 f^{2} g^{5} + 4 f g^{6} x + 2 g^{7} x^{2}} - \frac{24 c d e^{2} f g^{3} x^{2} \log{\left(\frac{f}{g} + x \right)}}{2 f^{2} g^{5} + 4 f g^{6} x + 2 g^{7} x^{2}} + \frac{8 c d e^{2} g^{4} x^{3}}{2 f^{2} g^{5} + 4 f g^{6} x + 2 g^{7} x^{2}} + \frac{12 c e^{3} f^{4} \log{\left(\frac{f}{g} + x \right)}}{2 f^{2} g^{5} + 4 f g^{6} x + 2 g^{7} x^{2}} + \frac{18 c e^{3} f^{4}}{2 f^{2} g^{5} + 4 f g^{6} x + 2 g^{7} x^{2}} + \frac{24 c e^{3} f^{3} g x \log{\left(\frac{f}{g} + x \right)}}{2 f^{2} g^{5} + 4 f g^{6} x + 2 g^{7} x^{2}} + \frac{24 c e^{3} f^{3} g x}{2 f^{2} g^{5} + 4 f g^{6} x + 2 g^{7} x^{2}} + \frac{12 c e^{3} f^{2} g^{2} x^{2} \log{\left(\frac{f}{g} + x \right)}}{2 f^{2} g^{5} + 4 f g^{6} x + 2 g^{7} x^{2}} - \frac{4 c e^{3} f g^{3} x^{3}}{2 f^{2} g^{5} + 4 f g^{6} x + 2 g^{7} x^{2}} + \frac{c e^{3} g^{4} x^{4}}{2 f^{2} g^{5} + 4 f g^{6} x + 2 g^{7} x^{2}} & \text{for}\: n = -3 \\- \frac{3 a d^{2} g^{4}}{3 f g^{5} + 3 g^{6} x} + \frac{6 a d e f g^{3} \log{\left(\frac{f}{g} + x \right)}}{3 f g^{5} + 3 g^{6} x} + \frac{6 a d e f g^{3}}{3 f g^{5} + 3 g^{6} x} + \frac{6 a d e g^{4} x \log{\left(\frac{f}{g} + x \right)}}{3 f g^{5} + 3 g^{6} x} - \frac{6 a e^{2} f^{2} g^{2} \log{\left(\frac{f}{g} + x \right)}}{3 f g^{5} + 3 g^{6} x} - \frac{6 a e^{2} f^{2} g^{2}}{3 f g^{5} + 3 g^{6} x} - \frac{6 a e^{2} f g^{3} x \log{\left(\frac{f}{g} + x \right)}}{3 f g^{5} + 3 g^{6} x} + \frac{3 a e^{2} g^{4} x^{2}}{3 f g^{5} + 3 g^{6} x} + \frac{6 c d^{3} f g^{3} \log{\left(\frac{f}{g} + x \right)}}{3 f g^{5} + 3 g^{6} x} + \frac{6 c d^{3} f g^{3}}{3 f g^{5} + 3 g^{6} x} + \frac{6 c d^{3} g^{4} x \log{\left(\frac{f}{g} + x \right)}}{3 f g^{5} + 3 g^{6} x} - \frac{30 c d^{2} e f^{2} g^{2} \log{\left(\frac{f}{g} + x \right)}}{3 f g^{5} + 3 g^{6} x} - \frac{30 c d^{2} e f^{2} g^{2}}{3 f g^{5} + 3 g^{6} x} - \frac{30 c d^{2} e f g^{3} x \log{\left(\frac{f}{g} + x \right)}}{3 f g^{5} + 3 g^{6} x} + \frac{15 c d^{2} e g^{4} x^{2}}{3 f g^{5} + 3 g^{6} x} + \frac{36 c d e^{2} f^{3} g \log{\left(\frac{f}{g} + x \right)}}{3 f g^{5} + 3 g^{6} x} + \frac{36 c d e^{2} f^{3} g}{3 f g^{5} + 3 g^{6} x} + \frac{36 c d e^{2} f^{2} g^{2} x \log{\left(\frac{f}{g} + x \right)}}{3 f g^{5} + 3 g^{6} x} - \frac{18 c d e^{2} f g^{3} x^{2}}{3 f g^{5} + 3 g^{6} x} + \frac{6 c d e^{2} g^{4} x^{3}}{3 f g^{5} + 3 g^{6} x} - \frac{12 c e^{3} f^{4} \log{\left(\frac{f}{g} + x \right)}}{3 f g^{5} + 3 g^{6} x} - \frac{12 c e^{3} f^{4}}{3 f g^{5} + 3 g^{6} x} - \frac{12 c e^{3} f^{3} g x \log{\left(\frac{f}{g} + x \right)}}{3 f g^{5} + 3 g^{6} x} + \frac{6 c e^{3} f^{2} g^{2} x^{2}}{3 f g^{5} + 3 g^{6} x} - \frac{2 c e^{3} f g^{3} x^{3}}{3 f g^{5} + 3 g^{6} x} + \frac{c e^{3} g^{4} x^{4}}{3 f g^{5} + 3 g^{6} x} & \text{for}\: n = -2 \\\frac{a d^{2} \log{\left(\frac{f}{g} + x \right)}}{g} - \frac{2 a d e f \log{\left(\frac{f}{g} + x \right)}}{g^{2}} + \frac{2 a d e x}{g} + \frac{a e^{2} f^{2} \log{\left(\frac{f}{g} + x \right)}}{g^{3}} - \frac{a e^{2} f x}{g^{2}} + \frac{a e^{2} x^{2}}{2 g} - \frac{2 c d^{3} f \log{\left(\frac{f}{g} + x \right)}}{g^{2}} + \frac{2 c d^{3} x}{g} + \frac{5 c d^{2} e f^{2} \log{\left(\frac{f}{g} + x \right)}}{g^{3}} - \frac{5 c d^{2} e f x}{g^{2}} + \frac{5 c d^{2} e x^{2}}{2 g} - \frac{4 c d e^{2} f^{3} \log{\left(\frac{f}{g} + x \right)}}{g^{4}} + \frac{4 c d e^{2} f^{2} x}{g^{3}} - \frac{2 c d e^{2} f x^{2}}{g^{2}} + \frac{4 c d e^{2} x^{3}}{3 g} + \frac{c e^{3} f^{4} \log{\left(\frac{f}{g} + x \right)}}{g^{5}} - \frac{c e^{3} f^{3} x}{g^{4}} + \frac{c e^{3} f^{2} x^{2}}{2 g^{3}} - \frac{c e^{3} f x^{3}}{3 g^{2}} + \frac{c e^{3} x^{4}}{4 g} & \text{for}\: n = -1 \\\frac{a d^{2} f g^{4} n^{4} \left(f + g x\right)^{n}}{g^{5} n^{5} + 15 g^{5} n^{4} + 85 g^{5} n^{3} + 225 g^{5} n^{2} + 274 g^{5} n + 120 g^{5}} + \frac{14 a d^{2} f g^{4} n^{3} \left(f + g x\right)^{n}}{g^{5} n^{5} + 15 g^{5} n^{4} + 85 g^{5} n^{3} + 225 g^{5} n^{2} + 274 g^{5} n + 120 g^{5}} + \frac{71 a d^{2} f g^{4} n^{2} \left(f + g x\right)^{n}}{g^{5} n^{5} + 15 g^{5} n^{4} + 85 g^{5} n^{3} + 225 g^{5} n^{2} + 274 g^{5} n + 120 g^{5}} + \frac{154 a d^{2} f g^{4} n \left(f + g x\right)^{n}}{g^{5} n^{5} + 15 g^{5} n^{4} + 85 g^{5} n^{3} + 225 g^{5} n^{2} + 274 g^{5} n + 120 g^{5}} + \frac{120 a d^{2} f g^{4} \left(f + g x\right)^{n}}{g^{5} n^{5} + 15 g^{5} n^{4} + 85 g^{5} n^{3} + 225 g^{5} n^{2} + 274 g^{5} n + 120 g^{5}} + \frac{a d^{2} g^{5} n^{4} x \left(f + g x\right)^{n}}{g^{5} n^{5} + 15 g^{5} n^{4} + 85 g^{5} n^{3} + 225 g^{5} n^{2} + 274 g^{5} n + 120 g^{5}} + \frac{14 a d^{2} g^{5} n^{3} x \left(f + g x\right)^{n}}{g^{5} n^{5} + 15 g^{5} n^{4} + 85 g^{5} n^{3} + 225 g^{5} n^{2} + 274 g^{5} n + 120 g^{5}} + \frac{71 a d^{2} g^{5} n^{2} x \left(f + g x\right)^{n}}{g^{5} n^{5} + 15 g^{5} n^{4} + 85 g^{5} n^{3} + 225 g^{5} n^{2} + 274 g^{5} n + 120 g^{5}} + \frac{154 a d^{2} g^{5} n x \left(f + g x\right)^{n}}{g^{5} n^{5} + 15 g^{5} n^{4} + 85 g^{5} n^{3} + 225 g^{5} n^{2} + 274 g^{5} n + 120 g^{5}} + \frac{120 a d^{2} g^{5} x \left(f + g x\right)^{n}}{g^{5} n^{5} + 15 g^{5} n^{4} + 85 g^{5} n^{3} + 225 g^{5} n^{2} + 274 g^{5} n + 120 g^{5}} - \frac{2 a d e f^{2} g^{3} n^{3} \left(f + g x\right)^{n}}{g^{5} n^{5} + 15 g^{5} n^{4} + 85 g^{5} n^{3} + 225 g^{5} n^{2} + 274 g^{5} n + 120 g^{5}} - \frac{24 a d e f^{2} g^{3} n^{2} \left(f + g x\right)^{n}}{g^{5} n^{5} + 15 g^{5} n^{4} + 85 g^{5} n^{3} + 225 g^{5} n^{2} + 274 g^{5} n + 120 g^{5}} - \frac{94 a d e f^{2} g^{3} n \left(f + g x\right)^{n}}{g^{5} n^{5} + 15 g^{5} n^{4} + 85 g^{5} n^{3} + 225 g^{5} n^{2} + 274 g^{5} n + 120 g^{5}} - \frac{120 a d e f^{2} g^{3} \left(f + g x\right)^{n}}{g^{5} n^{5} + 15 g^{5} n^{4} + 85 g^{5} n^{3} + 225 g^{5} n^{2} + 274 g^{5} n + 120 g^{5}} + \frac{2 a d e f g^{4} n^{4} x \left(f + g x\right)^{n}}{g^{5} n^{5} + 15 g^{5} n^{4} + 85 g^{5} n^{3} + 225 g^{5} n^{2} + 274 g^{5} n + 120 g^{5}} + \frac{24 a d e f g^{4} n^{3} x \left(f + g x\right)^{n}}{g^{5} n^{5} + 15 g^{5} n^{4} + 85 g^{5} n^{3} + 225 g^{5} n^{2} + 274 g^{5} n + 120 g^{5}} + \frac{94 a d e f g^{4} n^{2} x \left(f + g x\right)^{n}}{g^{5} n^{5} + 15 g^{5} n^{4} + 85 g^{5} n^{3} + 225 g^{5} n^{2} + 274 g^{5} n + 120 g^{5}} + \frac{120 a d e f g^{4} n x \left(f + g x\right)^{n}}{g^{5} n^{5} + 15 g^{5} n^{4} + 85 g^{5} n^{3} + 225 g^{5} n^{2} + 274 g^{5} n + 120 g^{5}} + \frac{2 a d e g^{5} n^{4} x^{2} \left(f + g x\right)^{n}}{g^{5} n^{5} + 15 g^{5} n^{4} + 85 g^{5} n^{3} + 225 g^{5} n^{2} + 274 g^{5} n + 120 g^{5}} + \frac{26 a d e g^{5} n^{3} x^{2} \left(f + g x\right)^{n}}{g^{5} n^{5} + 15 g^{5} n^{4} + 85 g^{5} n^{3} + 225 g^{5} n^{2} + 274 g^{5} n + 120 g^{5}} + \frac{118 a d e g^{5} n^{2} x^{2} \left(f + g x\right)^{n}}{g^{5} n^{5} + 15 g^{5} n^{4} + 85 g^{5} n^{3} + 225 g^{5} n^{2} + 274 g^{5} n + 120 g^{5}} + \frac{214 a d e g^{5} n x^{2} \left(f + g x\right)^{n}}{g^{5} n^{5} + 15 g^{5} n^{4} + 85 g^{5} n^{3} + 225 g^{5} n^{2} + 274 g^{5} n + 120 g^{5}} + \frac{120 a d e g^{5} x^{2} \left(f + g x\right)^{n}}{g^{5} n^{5} + 15 g^{5} n^{4} + 85 g^{5} n^{3} + 225 g^{5} n^{2} + 274 g^{5} n + 120 g^{5}} + \frac{2 a e^{2} f^{3} g^{2} n^{2} \left(f + g x\right)^{n}}{g^{5} n^{5} + 15 g^{5} n^{4} + 85 g^{5} n^{3} + 225 g^{5} n^{2} + 274 g^{5} n + 120 g^{5}} + \frac{18 a e^{2} f^{3} g^{2} n \left(f + g x\right)^{n}}{g^{5} n^{5} + 15 g^{5} n^{4} + 85 g^{5} n^{3} + 225 g^{5} n^{2} + 274 g^{5} n + 120 g^{5}} + \frac{40 a e^{2} f^{3} g^{2} \left(f + g x\right)^{n}}{g^{5} n^{5} + 15 g^{5} n^{4} + 85 g^{5} n^{3} + 225 g^{5} n^{2} + 274 g^{5} n + 120 g^{5}} - \frac{2 a e^{2} f^{2} g^{3} n^{3} x \left(f + g x\right)^{n}}{g^{5} n^{5} + 15 g^{5} n^{4} + 85 g^{5} n^{3} + 225 g^{5} n^{2} + 274 g^{5} n + 120 g^{5}} - \frac{18 a e^{2} f^{2} g^{3} n^{2} x \left(f + g x\right)^{n}}{g^{5} n^{5} + 15 g^{5} n^{4} + 85 g^{5} n^{3} + 225 g^{5} n^{2} + 274 g^{5} n + 120 g^{5}} - \frac{40 a e^{2} f^{2} g^{3} n x \left(f + g x\right)^{n}}{g^{5} n^{5} + 15 g^{5} n^{4} + 85 g^{5} n^{3} + 225 g^{5} n^{2} + 274 g^{5} n + 120 g^{5}} + \frac{a e^{2} f g^{4} n^{4} x^{2} \left(f + g x\right)^{n}}{g^{5} n^{5} + 15 g^{5} n^{4} + 85 g^{5} n^{3} + 225 g^{5} n^{2} + 274 g^{5} n + 120 g^{5}} + \frac{10 a e^{2} f g^{4} n^{3} x^{2} \left(f + g x\right)^{n}}{g^{5} n^{5} + 15 g^{5} n^{4} + 85 g^{5} n^{3} + 225 g^{5} n^{2} + 274 g^{5} n + 120 g^{5}} + \frac{29 a e^{2} f g^{4} n^{2} x^{2} \left(f + g x\right)^{n}}{g^{5} n^{5} + 15 g^{5} n^{4} + 85 g^{5} n^{3} + 225 g^{5} n^{2} + 274 g^{5} n + 120 g^{5}} + \frac{20 a e^{2} f g^{4} n x^{2} \left(f + g x\right)^{n}}{g^{5} n^{5} + 15 g^{5} n^{4} + 85 g^{5} n^{3} + 225 g^{5} n^{2} + 274 g^{5} n + 120 g^{5}} + \frac{a e^{2} g^{5} n^{4} x^{3} \left(f + g x\right)^{n}}{g^{5} n^{5} + 15 g^{5} n^{4} + 85 g^{5} n^{3} + 225 g^{5} n^{2} + 274 g^{5} n + 120 g^{5}} + \frac{12 a e^{2} g^{5} n^{3} x^{3} \left(f + g x\right)^{n}}{g^{5} n^{5} + 15 g^{5} n^{4} + 85 g^{5} n^{3} + 225 g^{5} n^{2} + 274 g^{5} n + 120 g^{5}} + \frac{49 a e^{2} g^{5} n^{2} x^{3} \left(f + g x\right)^{n}}{g^{5} n^{5} + 15 g^{5} n^{4} + 85 g^{5} n^{3} + 225 g^{5} n^{2} + 274 g^{5} n + 120 g^{5}} + \frac{78 a e^{2} g^{5} n x^{3} \left(f + g x\right)^{n}}{g^{5} n^{5} + 15 g^{5} n^{4} + 85 g^{5} n^{3} + 225 g^{5} n^{2} + 274 g^{5} n + 120 g^{5}} + \frac{40 a e^{2} g^{5} x^{3} \left(f + g x\right)^{n}}{g^{5} n^{5} + 15 g^{5} n^{4} + 85 g^{5} n^{3} + 225 g^{5} n^{2} + 274 g^{5} n + 120 g^{5}} - \frac{2 c d^{3} f^{2} g^{3} n^{3} \left(f + g x\right)^{n}}{g^{5} n^{5} + 15 g^{5} n^{4} + 85 g^{5} n^{3} + 225 g^{5} n^{2} + 274 g^{5} n + 120 g^{5}} - \frac{24 c d^{3} f^{2} g^{3} n^{2} \left(f + g x\right)^{n}}{g^{5} n^{5} + 15 g^{5} n^{4} + 85 g^{5} n^{3} + 225 g^{5} n^{2} + 274 g^{5} n + 120 g^{5}} - \frac{94 c d^{3} f^{2} g^{3} n \left(f + g x\right)^{n}}{g^{5} n^{5} + 15 g^{5} n^{4} + 85 g^{5} n^{3} + 225 g^{5} n^{2} + 274 g^{5} n + 120 g^{5}} - \frac{120 c d^{3} f^{2} g^{3} \left(f + g x\right)^{n}}{g^{5} n^{5} + 15 g^{5} n^{4} + 85 g^{5} n^{3} + 225 g^{5} n^{2} + 274 g^{5} n + 120 g^{5}} + \frac{2 c d^{3} f g^{4} n^{4} x \left(f + g x\right)^{n}}{g^{5} n^{5} + 15 g^{5} n^{4} + 85 g^{5} n^{3} + 225 g^{5} n^{2} + 274 g^{5} n + 120 g^{5}} + \frac{24 c d^{3} f g^{4} n^{3} x \left(f + g x\right)^{n}}{g^{5} n^{5} + 15 g^{5} n^{4} + 85 g^{5} n^{3} + 225 g^{5} n^{2} + 274 g^{5} n + 120 g^{5}} + \frac{94 c d^{3} f g^{4} n^{2} x \left(f + g x\right)^{n}}{g^{5} n^{5} + 15 g^{5} n^{4} + 85 g^{5} n^{3} + 225 g^{5} n^{2} + 274 g^{5} n + 120 g^{5}} + \frac{120 c d^{3} f g^{4} n x \left(f + g x\right)^{n}}{g^{5} n^{5} + 15 g^{5} n^{4} + 85 g^{5} n^{3} + 225 g^{5} n^{2} + 274 g^{5} n + 120 g^{5}} + \frac{2 c d^{3} g^{5} n^{4} x^{2} \left(f + g x\right)^{n}}{g^{5} n^{5} + 15 g^{5} n^{4} + 85 g^{5} n^{3} + 225 g^{5} n^{2} + 274 g^{5} n + 120 g^{5}} + \frac{26 c d^{3} g^{5} n^{3} x^{2} \left(f + g x\right)^{n}}{g^{5} n^{5} + 15 g^{5} n^{4} + 85 g^{5} n^{3} + 225 g^{5} n^{2} + 274 g^{5} n + 120 g^{5}} + \frac{118 c d^{3} g^{5} n^{2} x^{2} \left(f + g x\right)^{n}}{g^{5} n^{5} + 15 g^{5} n^{4} + 85 g^{5} n^{3} + 225 g^{5} n^{2} + 274 g^{5} n + 120 g^{5}} + \frac{214 c d^{3} g^{5} n x^{2} \left(f + g x\right)^{n}}{g^{5} n^{5} + 15 g^{5} n^{4} + 85 g^{5} n^{3} + 225 g^{5} n^{2} + 274 g^{5} n + 120 g^{5}} + \frac{120 c d^{3} g^{5} x^{2} \left(f + g x\right)^{n}}{g^{5} n^{5} + 15 g^{5} n^{4} + 85 g^{5} n^{3} + 225 g^{5} n^{2} + 274 g^{5} n + 120 g^{5}} + \frac{10 c d^{2} e f^{3} g^{2} n^{2} \left(f + g x\right)^{n}}{g^{5} n^{5} + 15 g^{5} n^{4} + 85 g^{5} n^{3} + 225 g^{5} n^{2} + 274 g^{5} n + 120 g^{5}} + \frac{90 c d^{2} e f^{3} g^{2} n \left(f + g x\right)^{n}}{g^{5} n^{5} + 15 g^{5} n^{4} + 85 g^{5} n^{3} + 225 g^{5} n^{2} + 274 g^{5} n + 120 g^{5}} + \frac{200 c d^{2} e f^{3} g^{2} \left(f + g x\right)^{n}}{g^{5} n^{5} + 15 g^{5} n^{4} + 85 g^{5} n^{3} + 225 g^{5} n^{2} + 274 g^{5} n + 120 g^{5}} - \frac{10 c d^{2} e f^{2} g^{3} n^{3} x \left(f + g x\right)^{n}}{g^{5} n^{5} + 15 g^{5} n^{4} + 85 g^{5} n^{3} + 225 g^{5} n^{2} + 274 g^{5} n + 120 g^{5}} - \frac{90 c d^{2} e f^{2} g^{3} n^{2} x \left(f + g x\right)^{n}}{g^{5} n^{5} + 15 g^{5} n^{4} + 85 g^{5} n^{3} + 225 g^{5} n^{2} + 274 g^{5} n + 120 g^{5}} - \frac{200 c d^{2} e f^{2} g^{3} n x \left(f + g x\right)^{n}}{g^{5} n^{5} + 15 g^{5} n^{4} + 85 g^{5} n^{3} + 225 g^{5} n^{2} + 274 g^{5} n + 120 g^{5}} + \frac{5 c d^{2} e f g^{4} n^{4} x^{2} \left(f + g x\right)^{n}}{g^{5} n^{5} + 15 g^{5} n^{4} + 85 g^{5} n^{3} + 225 g^{5} n^{2} + 274 g^{5} n + 120 g^{5}} + \frac{50 c d^{2} e f g^{4} n^{3} x^{2} \left(f + g x\right)^{n}}{g^{5} n^{5} + 15 g^{5} n^{4} + 85 g^{5} n^{3} + 225 g^{5} n^{2} + 274 g^{5} n + 120 g^{5}} + \frac{145 c d^{2} e f g^{4} n^{2} x^{2} \left(f + g x\right)^{n}}{g^{5} n^{5} + 15 g^{5} n^{4} + 85 g^{5} n^{3} + 225 g^{5} n^{2} + 274 g^{5} n + 120 g^{5}} + \frac{100 c d^{2} e f g^{4} n x^{2} \left(f + g x\right)^{n}}{g^{5} n^{5} + 15 g^{5} n^{4} + 85 g^{5} n^{3} + 225 g^{5} n^{2} + 274 g^{5} n + 120 g^{5}} + \frac{5 c d^{2} e g^{5} n^{4} x^{3} \left(f + g x\right)^{n}}{g^{5} n^{5} + 15 g^{5} n^{4} + 85 g^{5} n^{3} + 225 g^{5} n^{2} + 274 g^{5} n + 120 g^{5}} + \frac{60 c d^{2} e g^{5} n^{3} x^{3} \left(f + g x\right)^{n}}{g^{5} n^{5} + 15 g^{5} n^{4} + 85 g^{5} n^{3} + 225 g^{5} n^{2} + 274 g^{5} n + 120 g^{5}} + \frac{245 c d^{2} e g^{5} n^{2} x^{3} \left(f + g x\right)^{n}}{g^{5} n^{5} + 15 g^{5} n^{4} + 85 g^{5} n^{3} + 225 g^{5} n^{2} + 274 g^{5} n + 120 g^{5}} + \frac{390 c d^{2} e g^{5} n x^{3} \left(f + g x\right)^{n}}{g^{5} n^{5} + 15 g^{5} n^{4} + 85 g^{5} n^{3} + 225 g^{5} n^{2} + 274 g^{5} n + 120 g^{5}} + \frac{200 c d^{2} e g^{5} x^{3} \left(f + g x\right)^{n}}{g^{5} n^{5} + 15 g^{5} n^{4} + 85 g^{5} n^{3} + 225 g^{5} n^{2} + 274 g^{5} n + 120 g^{5}} - \frac{24 c d e^{2} f^{4} g n \left(f + g x\right)^{n}}{g^{5} n^{5} + 15 g^{5} n^{4} + 85 g^{5} n^{3} + 225 g^{5} n^{2} + 274 g^{5} n + 120 g^{5}} - \frac{120 c d e^{2} f^{4} g \left(f + g x\right)^{n}}{g^{5} n^{5} + 15 g^{5} n^{4} + 85 g^{5} n^{3} + 225 g^{5} n^{2} + 274 g^{5} n + 120 g^{5}} + \frac{24 c d e^{2} f^{3} g^{2} n^{2} x \left(f + g x\right)^{n}}{g^{5} n^{5} + 15 g^{5} n^{4} + 85 g^{5} n^{3} + 225 g^{5} n^{2} + 274 g^{5} n + 120 g^{5}} + \frac{120 c d e^{2} f^{3} g^{2} n x \left(f + g x\right)^{n}}{g^{5} n^{5} + 15 g^{5} n^{4} + 85 g^{5} n^{3} + 225 g^{5} n^{2} + 274 g^{5} n + 120 g^{5}} - \frac{12 c d e^{2} f^{2} g^{3} n^{3} x^{2} \left(f + g x\right)^{n}}{g^{5} n^{5} + 15 g^{5} n^{4} + 85 g^{5} n^{3} + 225 g^{5} n^{2} + 274 g^{5} n + 120 g^{5}} - \frac{72 c d e^{2} f^{2} g^{3} n^{2} x^{2} \left(f + g x\right)^{n}}{g^{5} n^{5} + 15 g^{5} n^{4} + 85 g^{5} n^{3} + 225 g^{5} n^{2} + 274 g^{5} n + 120 g^{5}} - \frac{60 c d e^{2} f^{2} g^{3} n x^{2} \left(f + g x\right)^{n}}{g^{5} n^{5} + 15 g^{5} n^{4} + 85 g^{5} n^{3} + 225 g^{5} n^{2} + 274 g^{5} n + 120 g^{5}} + \frac{4 c d e^{2} f g^{4} n^{4} x^{3} \left(f + g x\right)^{n}}{g^{5} n^{5} + 15 g^{5} n^{4} + 85 g^{5} n^{3} + 225 g^{5} n^{2} + 274 g^{5} n + 120 g^{5}} + \frac{32 c d e^{2} f g^{4} n^{3} x^{3} \left(f + g x\right)^{n}}{g^{5} n^{5} + 15 g^{5} n^{4} + 85 g^{5} n^{3} + 225 g^{5} n^{2} + 274 g^{5} n + 120 g^{5}} + \frac{68 c d e^{2} f g^{4} n^{2} x^{3} \left(f + g x\right)^{n}}{g^{5} n^{5} + 15 g^{5} n^{4} + 85 g^{5} n^{3} + 225 g^{5} n^{2} + 274 g^{5} n + 120 g^{5}} + \frac{40 c d e^{2} f g^{4} n x^{3} \left(f + g x\right)^{n}}{g^{5} n^{5} + 15 g^{5} n^{4} + 85 g^{5} n^{3} + 225 g^{5} n^{2} + 274 g^{5} n + 120 g^{5}} + \frac{4 c d e^{2} g^{5} n^{4} x^{4} \left(f + g x\right)^{n}}{g^{5} n^{5} + 15 g^{5} n^{4} + 85 g^{5} n^{3} + 225 g^{5} n^{2} + 274 g^{5} n + 120 g^{5}} + \frac{44 c d e^{2} g^{5} n^{3} x^{4} \left(f + g x\right)^{n}}{g^{5} n^{5} + 15 g^{5} n^{4} + 85 g^{5} n^{3} + 225 g^{5} n^{2} + 274 g^{5} n + 120 g^{5}} + \frac{164 c d e^{2} g^{5} n^{2} x^{4} \left(f + g x\right)^{n}}{g^{5} n^{5} + 15 g^{5} n^{4} + 85 g^{5} n^{3} + 225 g^{5} n^{2} + 274 g^{5} n + 120 g^{5}} + \frac{244 c d e^{2} g^{5} n x^{4} \left(f + g x\right)^{n}}{g^{5} n^{5} + 15 g^{5} n^{4} + 85 g^{5} n^{3} + 225 g^{5} n^{2} + 274 g^{5} n + 120 g^{5}} + \frac{120 c d e^{2} g^{5} x^{4} \left(f + g x\right)^{n}}{g^{5} n^{5} + 15 g^{5} n^{4} + 85 g^{5} n^{3} + 225 g^{5} n^{2} + 274 g^{5} n + 120 g^{5}} + \frac{24 c e^{3} f^{5} \left(f + g x\right)^{n}}{g^{5} n^{5} + 15 g^{5} n^{4} + 85 g^{5} n^{3} + 225 g^{5} n^{2} + 274 g^{5} n + 120 g^{5}} - \frac{24 c e^{3} f^{4} g n x \left(f + g x\right)^{n}}{g^{5} n^{5} + 15 g^{5} n^{4} + 85 g^{5} n^{3} + 225 g^{5} n^{2} + 274 g^{5} n + 120 g^{5}} + \frac{12 c e^{3} f^{3} g^{2} n^{2} x^{2} \left(f + g x\right)^{n}}{g^{5} n^{5} + 15 g^{5} n^{4} + 85 g^{5} n^{3} + 225 g^{5} n^{2} + 274 g^{5} n + 120 g^{5}} + \frac{12 c e^{3} f^{3} g^{2} n x^{2} \left(f + g x\right)^{n}}{g^{5} n^{5} + 15 g^{5} n^{4} + 85 g^{5} n^{3} + 225 g^{5} n^{2} + 274 g^{5} n + 120 g^{5}} - \frac{4 c e^{3} f^{2} g^{3} n^{3} x^{3} \left(f + g x\right)^{n}}{g^{5} n^{5} + 15 g^{5} n^{4} + 85 g^{5} n^{3} + 225 g^{5} n^{2} + 274 g^{5} n + 120 g^{5}} - \frac{12 c e^{3} f^{2} g^{3} n^{2} x^{3} \left(f + g x\right)^{n}}{g^{5} n^{5} + 15 g^{5} n^{4} + 85 g^{5} n^{3} + 225 g^{5} n^{2} + 274 g^{5} n + 120 g^{5}} - \frac{8 c e^{3} f^{2} g^{3} n x^{3} \left(f + g x\right)^{n}}{g^{5} n^{5} + 15 g^{5} n^{4} + 85 g^{5} n^{3} + 225 g^{5} n^{2} + 274 g^{5} n + 120 g^{5}} + \frac{c e^{3} f g^{4} n^{4} x^{4} \left(f + g x\right)^{n}}{g^{5} n^{5} + 15 g^{5} n^{4} + 85 g^{5} n^{3} + 225 g^{5} n^{2} + 274 g^{5} n + 120 g^{5}} + \frac{6 c e^{3} f g^{4} n^{3} x^{4} \left(f + g x\right)^{n}}{g^{5} n^{5} + 15 g^{5} n^{4} + 85 g^{5} n^{3} + 225 g^{5} n^{2} + 274 g^{5} n + 120 g^{5}} + \frac{11 c e^{3} f g^{4} n^{2} x^{4} \left(f + g x\right)^{n}}{g^{5} n^{5} + 15 g^{5} n^{4} + 85 g^{5} n^{3} + 225 g^{5} n^{2} + 274 g^{5} n + 120 g^{5}} + \frac{6 c e^{3} f g^{4} n x^{4} \left(f + g x\right)^{n}}{g^{5} n^{5} + 15 g^{5} n^{4} + 85 g^{5} n^{3} + 225 g^{5} n^{2} + 274 g^{5} n + 120 g^{5}} + \frac{c e^{3} g^{5} n^{4} x^{5} \left(f + g x\right)^{n}}{g^{5} n^{5} + 15 g^{5} n^{4} + 85 g^{5} n^{3} + 225 g^{5} n^{2} + 274 g^{5} n + 120 g^{5}} + \frac{10 c e^{3} g^{5} n^{3} x^{5} \left(f + g x\right)^{n}}{g^{5} n^{5} + 15 g^{5} n^{4} + 85 g^{5} n^{3} + 225 g^{5} n^{2} + 274 g^{5} n + 120 g^{5}} + \frac{35 c e^{3} g^{5} n^{2} x^{5} \left(f + g x\right)^{n}}{g^{5} n^{5} + 15 g^{5} n^{4} + 85 g^{5} n^{3} + 225 g^{5} n^{2} + 274 g^{5} n + 120 g^{5}} + \frac{50 c e^{3} g^{5} n x^{5} \left(f + g x\right)^{n}}{g^{5} n^{5} + 15 g^{5} n^{4} + 85 g^{5} n^{3} + 225 g^{5} n^{2} + 274 g^{5} n + 120 g^{5}} + \frac{24 c e^{3} g^{5} x^{5} \left(f + g x\right)^{n}}{g^{5} n^{5} + 15 g^{5} n^{4} + 85 g^{5} n^{3} + 225 g^{5} n^{2} + 274 g^{5} n + 120 g^{5}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((f**n*(a*d**2*x + a*d*e*x**2 + a*e**2*x**3/3 + c*d**3*x**2 + 5*c*d**2*e*x**3/3 + c*d*e**2*x**4 + c*e**3*x**5/5), Eq(g, 0)), (-3*a*d**2*g**4/(12*f**4*g**5 + 48*f**3*g**6*x + 72*f**2*g**7*x**2 + 48*f*g**8*x**3 + 12*g**9*x**4) - 2*a*d*e*f*g**3/(12*f**4*g**5 + 48*f**3*g**6*x + 72*f**2*g**7*x**2 + 48*f*g**8*x**3 + 12*g**9*x**4) - 8*a*d*e*g**4*x/(12*f**4*g**5 + 48*f**3*g**6*x + 72*f**2*g**7*x**2 + 48*f*g**8*x**3 + 12*g**9*x**4) - a*e**2*f**2*g**2/(12*f**4*g**5 + 48*f**3*g**6*x + 72*f**2*g**7*x**2 + 48*f*g**8*x**3 + 12*g**9*x**4) - 4*a*e**2*f*g**3*x/(12*f**4*g**5 + 48*f**3*g**6*x + 72*f**2*g**7*x**2 + 48*f*g**8*x**3 + 12*g**9*x**4) - 6*a*e**2*g**4*x**2/(12*f**4*g**5 + 48*f**3*g**6*x + 72*f**2*g**7*x**2 + 48*f*g**8*x**3 + 12*g**9*x**4) - 2*c*d**3*f*g**3/(12*f**4*g**5 + 48*f**3*g**6*x + 72*f**2*g**7*x**2 + 48*f*g**8*x**3 + 12*g**9*x**4) - 8*c*d**3*g**4*x/(12*f**4*g**5 + 48*f**3*g**6*x + 72*f**2*g**7*x**2 + 48*f*g**8*x**3 + 12*g**9*x**4) - 5*c*d**2*e*f**2*g**2/(12*f**4*g**5 + 48*f**3*g**6*x + 72*f**2*g**7*x**2 + 48*f*g**8*x**3 + 12*g**9*x**4) - 20*c*d**2*e*f*g**3*x/(12*f**4*g**5 + 48*f**3*g**6*x + 72*f**2*g**7*x**2 + 48*f*g**8*x**3 + 12*g**9*x**4) - 30*c*d**2*e*g**4*x**2/(12*f**4*g**5 + 48*f**3*g**6*x + 72*f**2*g**7*x**2 + 48*f*g**8*x**3 + 12*g**9*x**4) - 12*c*d*e**2*f**3*g/(12*f**4*g**5 + 48*f**3*g**6*x + 72*f**2*g**7*x**2 + 48*f*g**8*x**3 + 12*g**9*x**4) - 48*c*d*e**2*f**2*g**2*x/(12*f**4*g**5 + 48*f**3*g**6*x + 72*f**2*g**7*x**2 + 48*f*g**8*x**3 + 12*g**9*x**4) - 72*c*d*e**2*f*g**3*x**2/(12*f**4*g**5 + 48*f**3*g**6*x + 72*f**2*g**7*x**2 + 48*f*g**8*x**3 + 12*g**9*x**4) - 48*c*d*e**2*g**4*x**3/(12*f**4*g**5 + 48*f**3*g**6*x + 72*f**2*g**7*x**2 + 48*f*g**8*x**3 + 12*g**9*x**4) + 12*c*e**3*f**4*log(f/g + x)/(12*f**4*g**5 + 48*f**3*g**6*x + 72*f**2*g**7*x**2 + 48*f*g**8*x**3 + 12*g**9*x**4) + 25*c*e**3*f**4/(12*f**4*g**5 + 48*f**3*g**6*x + 72*f**2*g**7*x**2 + 48*f*g**8*x**3 + 12*g**9*x**4) + 48*c*e**3*f**3*g*x*log(f/g + x)/(12*f**4*g**5 + 48*f**3*g**6*x + 72*f**2*g**7*x**2 + 48*f*g**8*x**3 + 12*g**9*x**4) + 88*c*e**3*f**3*g*x/(12*f**4*g**5 + 48*f**3*g**6*x + 72*f**2*g**7*x**2 + 48*f*g**8*x**3 + 12*g**9*x**4) + 72*c*e**3*f**2*g**2*x**2*log(f/g + x)/(12*f**4*g**5 + 48*f**3*g**6*x + 72*f**2*g**7*x**2 + 48*f*g**8*x**3 + 12*g**9*x**4) + 108*c*e**3*f**2*g**2*x**2/(12*f**4*g**5 + 48*f**3*g**6*x + 72*f**2*g**7*x**2 + 48*f*g**8*x**3 + 12*g**9*x**4) + 48*c*e**3*f*g**3*x**3*log(f/g + x)/(12*f**4*g**5 + 48*f**3*g**6*x + 72*f**2*g**7*x**2 + 48*f*g**8*x**3 + 12*g**9*x**4) + 48*c*e**3*f*g**3*x**3/(12*f**4*g**5 + 48*f**3*g**6*x + 72*f**2*g**7*x**2 + 48*f*g**8*x**3 + 12*g**9*x**4) + 12*c*e**3*g**4*x**4*log(f/g + x)/(12*f**4*g**5 + 48*f**3*g**6*x + 72*f**2*g**7*x**2 + 48*f*g**8*x**3 + 12*g**9*x**4), Eq(n, -5)), (-a*d**2*g**4/(3*f**3*g**5 + 9*f**2*g**6*x + 9*f*g**7*x**2 + 3*g**8*x**3) - a*d*e*f*g**3/(3*f**3*g**5 + 9*f**2*g**6*x + 9*f*g**7*x**2 + 3*g**8*x**3) - 3*a*d*e*g**4*x/(3*f**3*g**5 + 9*f**2*g**6*x + 9*f*g**7*x**2 + 3*g**8*x**3) - a*e**2*f**2*g**2/(3*f**3*g**5 + 9*f**2*g**6*x + 9*f*g**7*x**2 + 3*g**8*x**3) - 3*a*e**2*f*g**3*x/(3*f**3*g**5 + 9*f**2*g**6*x + 9*f*g**7*x**2 + 3*g**8*x**3) - 3*a*e**2*g**4*x**2/(3*f**3*g**5 + 9*f**2*g**6*x + 9*f*g**7*x**2 + 3*g**8*x**3) - c*d**3*f*g**3/(3*f**3*g**5 + 9*f**2*g**6*x + 9*f*g**7*x**2 + 3*g**8*x**3) - 3*c*d**3*g**4*x/(3*f**3*g**5 + 9*f**2*g**6*x + 9*f*g**7*x**2 + 3*g**8*x**3) - 5*c*d**2*e*f**2*g**2/(3*f**3*g**5 + 9*f**2*g**6*x + 9*f*g**7*x**2 + 3*g**8*x**3) - 15*c*d**2*e*f*g**3*x/(3*f**3*g**5 + 9*f**2*g**6*x + 9*f*g**7*x**2 + 3*g**8*x**3) - 15*c*d**2*e*g**4*x**2/(3*f**3*g**5 + 9*f**2*g**6*x + 9*f*g**7*x**2 + 3*g**8*x**3) + 12*c*d*e**2*f**3*g*log(f/g + x)/(3*f**3*g**5 + 9*f**2*g**6*x + 9*f*g**7*x**2 + 3*g**8*x**3) + 22*c*d*e**2*f**3*g/(3*f**3*g**5 + 9*f**2*g**6*x + 9*f*g**7*x**2 + 3*g**8*x**3) + 36*c*d*e**2*f**2*g**2*x*log(f/g + x)/(3*f**3*g**5 + 9*f**2*g**6*x + 9*f*g**7*x**2 + 3*g**8*x**3) + 54*c*d*e**2*f**2*g**2*x/(3*f**3*g**5 + 9*f**2*g**6*x + 9*f*g**7*x**2 + 3*g**8*x**3) + 36*c*d*e**2*f*g**3*x**2*log(f/g + x)/(3*f**3*g**5 + 9*f**2*g**6*x + 9*f*g**7*x**2 + 3*g**8*x**3) + 36*c*d*e**2*f*g**3*x**2/(3*f**3*g**5 + 9*f**2*g**6*x + 9*f*g**7*x**2 + 3*g**8*x**3) + 12*c*d*e**2*g**4*x**3*log(f/g + x)/(3*f**3*g**5 + 9*f**2*g**6*x + 9*f*g**7*x**2 + 3*g**8*x**3) - 12*c*e**3*f**4*log(f/g + x)/(3*f**3*g**5 + 9*f**2*g**6*x + 9*f*g**7*x**2 + 3*g**8*x**3) - 22*c*e**3*f**4/(3*f**3*g**5 + 9*f**2*g**6*x + 9*f*g**7*x**2 + 3*g**8*x**3) - 36*c*e**3*f**3*g*x*log(f/g + x)/(3*f**3*g**5 + 9*f**2*g**6*x + 9*f*g**7*x**2 + 3*g**8*x**3) - 54*c*e**3*f**3*g*x/(3*f**3*g**5 + 9*f**2*g**6*x + 9*f*g**7*x**2 + 3*g**8*x**3) - 36*c*e**3*f**2*g**2*x**2*log(f/g + x)/(3*f**3*g**5 + 9*f**2*g**6*x + 9*f*g**7*x**2 + 3*g**8*x**3) - 36*c*e**3*f**2*g**2*x**2/(3*f**3*g**5 + 9*f**2*g**6*x + 9*f*g**7*x**2 + 3*g**8*x**3) - 12*c*e**3*f*g**3*x**3*log(f/g + x)/(3*f**3*g**5 + 9*f**2*g**6*x + 9*f*g**7*x**2 + 3*g**8*x**3) + 3*c*e**3*g**4*x**4/(3*f**3*g**5 + 9*f**2*g**6*x + 9*f*g**7*x**2 + 3*g**8*x**3), Eq(n, -4)), (-a*d**2*g**4/(2*f**2*g**5 + 4*f*g**6*x + 2*g**7*x**2) - 2*a*d*e*f*g**3/(2*f**2*g**5 + 4*f*g**6*x + 2*g**7*x**2) - 4*a*d*e*g**4*x/(2*f**2*g**5 + 4*f*g**6*x + 2*g**7*x**2) + 2*a*e**2*f**2*g**2*log(f/g + x)/(2*f**2*g**5 + 4*f*g**6*x + 2*g**7*x**2) + 3*a*e**2*f**2*g**2/(2*f**2*g**5 + 4*f*g**6*x + 2*g**7*x**2) + 4*a*e**2*f*g**3*x*log(f/g + x)/(2*f**2*g**5 + 4*f*g**6*x + 2*g**7*x**2) + 4*a*e**2*f*g**3*x/(2*f**2*g**5 + 4*f*g**6*x + 2*g**7*x**2) + 2*a*e**2*g**4*x**2*log(f/g + x)/(2*f**2*g**5 + 4*f*g**6*x + 2*g**7*x**2) - 2*c*d**3*f*g**3/(2*f**2*g**5 + 4*f*g**6*x + 2*g**7*x**2) - 4*c*d**3*g**4*x/(2*f**2*g**5 + 4*f*g**6*x + 2*g**7*x**2) + 10*c*d**2*e*f**2*g**2*log(f/g + x)/(2*f**2*g**5 + 4*f*g**6*x + 2*g**7*x**2) + 15*c*d**2*e*f**2*g**2/(2*f**2*g**5 + 4*f*g**6*x + 2*g**7*x**2) + 20*c*d**2*e*f*g**3*x*log(f/g + x)/(2*f**2*g**5 + 4*f*g**6*x + 2*g**7*x**2) + 20*c*d**2*e*f*g**3*x/(2*f**2*g**5 + 4*f*g**6*x + 2*g**7*x**2) + 10*c*d**2*e*g**4*x**2*log(f/g + x)/(2*f**2*g**5 + 4*f*g**6*x + 2*g**7*x**2) - 24*c*d*e**2*f**3*g*log(f/g + x)/(2*f**2*g**5 + 4*f*g**6*x + 2*g**7*x**2) - 36*c*d*e**2*f**3*g/(2*f**2*g**5 + 4*f*g**6*x + 2*g**7*x**2) - 48*c*d*e**2*f**2*g**2*x*log(f/g + x)/(2*f**2*g**5 + 4*f*g**6*x + 2*g**7*x**2) - 48*c*d*e**2*f**2*g**2*x/(2*f**2*g**5 + 4*f*g**6*x + 2*g**7*x**2) - 24*c*d*e**2*f*g**3*x**2*log(f/g + x)/(2*f**2*g**5 + 4*f*g**6*x + 2*g**7*x**2) + 8*c*d*e**2*g**4*x**3/(2*f**2*g**5 + 4*f*g**6*x + 2*g**7*x**2) + 12*c*e**3*f**4*log(f/g + x)/(2*f**2*g**5 + 4*f*g**6*x + 2*g**7*x**2) + 18*c*e**3*f**4/(2*f**2*g**5 + 4*f*g**6*x + 2*g**7*x**2) + 24*c*e**3*f**3*g*x*log(f/g + x)/(2*f**2*g**5 + 4*f*g**6*x + 2*g**7*x**2) + 24*c*e**3*f**3*g*x/(2*f**2*g**5 + 4*f*g**6*x + 2*g**7*x**2) + 12*c*e**3*f**2*g**2*x**2*log(f/g + x)/(2*f**2*g**5 + 4*f*g**6*x + 2*g**7*x**2) - 4*c*e**3*f*g**3*x**3/(2*f**2*g**5 + 4*f*g**6*x + 2*g**7*x**2) + c*e**3*g**4*x**4/(2*f**2*g**5 + 4*f*g**6*x + 2*g**7*x**2), Eq(n, -3)), (-3*a*d**2*g**4/(3*f*g**5 + 3*g**6*x) + 6*a*d*e*f*g**3*log(f/g + x)/(3*f*g**5 + 3*g**6*x) + 6*a*d*e*f*g**3/(3*f*g**5 + 3*g**6*x) + 6*a*d*e*g**4*x*log(f/g + x)/(3*f*g**5 + 3*g**6*x) - 6*a*e**2*f**2*g**2*log(f/g + x)/(3*f*g**5 + 3*g**6*x) - 6*a*e**2*f**2*g**2/(3*f*g**5 + 3*g**6*x) - 6*a*e**2*f*g**3*x*log(f/g + x)/(3*f*g**5 + 3*g**6*x) + 3*a*e**2*g**4*x**2/(3*f*g**5 + 3*g**6*x) + 6*c*d**3*f*g**3*log(f/g + x)/(3*f*g**5 + 3*g**6*x) + 6*c*d**3*f*g**3/(3*f*g**5 + 3*g**6*x) + 6*c*d**3*g**4*x*log(f/g + x)/(3*f*g**5 + 3*g**6*x) - 30*c*d**2*e*f**2*g**2*log(f/g + x)/(3*f*g**5 + 3*g**6*x) - 30*c*d**2*e*f**2*g**2/(3*f*g**5 + 3*g**6*x) - 30*c*d**2*e*f*g**3*x*log(f/g + x)/(3*f*g**5 + 3*g**6*x) + 15*c*d**2*e*g**4*x**2/(3*f*g**5 + 3*g**6*x) + 36*c*d*e**2*f**3*g*log(f/g + x)/(3*f*g**5 + 3*g**6*x) + 36*c*d*e**2*f**3*g/(3*f*g**5 + 3*g**6*x) + 36*c*d*e**2*f**2*g**2*x*log(f/g + x)/(3*f*g**5 + 3*g**6*x) - 18*c*d*e**2*f*g**3*x**2/(3*f*g**5 + 3*g**6*x) + 6*c*d*e**2*g**4*x**3/(3*f*g**5 + 3*g**6*x) - 12*c*e**3*f**4*log(f/g + x)/(3*f*g**5 + 3*g**6*x) - 12*c*e**3*f**4/(3*f*g**5 + 3*g**6*x) - 12*c*e**3*f**3*g*x*log(f/g + x)/(3*f*g**5 + 3*g**6*x) + 6*c*e**3*f**2*g**2*x**2/(3*f*g**5 + 3*g**6*x) - 2*c*e**3*f*g**3*x**3/(3*f*g**5 + 3*g**6*x) + c*e**3*g**4*x**4/(3*f*g**5 + 3*g**6*x), Eq(n, -2)), (a*d**2*log(f/g + x)/g - 2*a*d*e*f*log(f/g + x)/g**2 + 2*a*d*e*x/g + a*e**2*f**2*log(f/g + x)/g**3 - a*e**2*f*x/g**2 + a*e**2*x**2/(2*g) - 2*c*d**3*f*log(f/g + x)/g**2 + 2*c*d**3*x/g + 5*c*d**2*e*f**2*log(f/g + x)/g**3 - 5*c*d**2*e*f*x/g**2 + 5*c*d**2*e*x**2/(2*g) - 4*c*d*e**2*f**3*log(f/g + x)/g**4 + 4*c*d*e**2*f**2*x/g**3 - 2*c*d*e**2*f*x**2/g**2 + 4*c*d*e**2*x**3/(3*g) + c*e**3*f**4*log(f/g + x)/g**5 - c*e**3*f**3*x/g**4 + c*e**3*f**2*x**2/(2*g**3) - c*e**3*f*x**3/(3*g**2) + c*e**3*x**4/(4*g), Eq(n, -1)), (a*d**2*f*g**4*n**4*(f + g*x)**n/(g**5*n**5 + 15*g**5*n**4 + 85*g**5*n**3 + 225*g**5*n**2 + 274*g**5*n + 120*g**5) + 14*a*d**2*f*g**4*n**3*(f + g*x)**n/(g**5*n**5 + 15*g**5*n**4 + 85*g**5*n**3 + 225*g**5*n**2 + 274*g**5*n + 120*g**5) + 71*a*d**2*f*g**4*n**2*(f + g*x)**n/(g**5*n**5 + 15*g**5*n**4 + 85*g**5*n**3 + 225*g**5*n**2 + 274*g**5*n + 120*g**5) + 154*a*d**2*f*g**4*n*(f + g*x)**n/(g**5*n**5 + 15*g**5*n**4 + 85*g**5*n**3 + 225*g**5*n**2 + 274*g**5*n + 120*g**5) + 120*a*d**2*f*g**4*(f + g*x)**n/(g**5*n**5 + 15*g**5*n**4 + 85*g**5*n**3 + 225*g**5*n**2 + 274*g**5*n + 120*g**5) + a*d**2*g**5*n**4*x*(f + g*x)**n/(g**5*n**5 + 15*g**5*n**4 + 85*g**5*n**3 + 225*g**5*n**2 + 274*g**5*n + 120*g**5) + 14*a*d**2*g**5*n**3*x*(f + g*x)**n/(g**5*n**5 + 15*g**5*n**4 + 85*g**5*n**3 + 225*g**5*n**2 + 274*g**5*n + 120*g**5) + 71*a*d**2*g**5*n**2*x*(f + g*x)**n/(g**5*n**5 + 15*g**5*n**4 + 85*g**5*n**3 + 225*g**5*n**2 + 274*g**5*n + 120*g**5) + 154*a*d**2*g**5*n*x*(f + g*x)**n/(g**5*n**5 + 15*g**5*n**4 + 85*g**5*n**3 + 225*g**5*n**2 + 274*g**5*n + 120*g**5) + 120*a*d**2*g**5*x*(f + g*x)**n/(g**5*n**5 + 15*g**5*n**4 + 85*g**5*n**3 + 225*g**5*n**2 + 274*g**5*n + 120*g**5) - 2*a*d*e*f**2*g**3*n**3*(f + g*x)**n/(g**5*n**5 + 15*g**5*n**4 + 85*g**5*n**3 + 225*g**5*n**2 + 274*g**5*n + 120*g**5) - 24*a*d*e*f**2*g**3*n**2*(f + g*x)**n/(g**5*n**5 + 15*g**5*n**4 + 85*g**5*n**3 + 225*g**5*n**2 + 274*g**5*n + 120*g**5) - 94*a*d*e*f**2*g**3*n*(f + g*x)**n/(g**5*n**5 + 15*g**5*n**4 + 85*g**5*n**3 + 225*g**5*n**2 + 274*g**5*n + 120*g**5) - 120*a*d*e*f**2*g**3*(f + g*x)**n/(g**5*n**5 + 15*g**5*n**4 + 85*g**5*n**3 + 225*g**5*n**2 + 274*g**5*n + 120*g**5) + 2*a*d*e*f*g**4*n**4*x*(f + g*x)**n/(g**5*n**5 + 15*g**5*n**4 + 85*g**5*n**3 + 225*g**5*n**2 + 274*g**5*n + 120*g**5) + 24*a*d*e*f*g**4*n**3*x*(f + g*x)**n/(g**5*n**5 + 15*g**5*n**4 + 85*g**5*n**3 + 225*g**5*n**2 + 274*g**5*n + 120*g**5) + 94*a*d*e*f*g**4*n**2*x*(f + g*x)**n/(g**5*n**5 + 15*g**5*n**4 + 85*g**5*n**3 + 225*g**5*n**2 + 274*g**5*n + 120*g**5) + 120*a*d*e*f*g**4*n*x*(f + g*x)**n/(g**5*n**5 + 15*g**5*n**4 + 85*g**5*n**3 + 225*g**5*n**2 + 274*g**5*n + 120*g**5) + 2*a*d*e*g**5*n**4*x**2*(f + g*x)**n/(g**5*n**5 + 15*g**5*n**4 + 85*g**5*n**3 + 225*g**5*n**2 + 274*g**5*n + 120*g**5) + 26*a*d*e*g**5*n**3*x**2*(f + g*x)**n/(g**5*n**5 + 15*g**5*n**4 + 85*g**5*n**3 + 225*g**5*n**2 + 274*g**5*n + 120*g**5) + 118*a*d*e*g**5*n**2*x**2*(f + g*x)**n/(g**5*n**5 + 15*g**5*n**4 + 85*g**5*n**3 + 225*g**5*n**2 + 274*g**5*n + 120*g**5) + 214*a*d*e*g**5*n*x**2*(f + g*x)**n/(g**5*n**5 + 15*g**5*n**4 + 85*g**5*n**3 + 225*g**5*n**2 + 274*g**5*n + 120*g**5) + 120*a*d*e*g**5*x**2*(f + g*x)**n/(g**5*n**5 + 15*g**5*n**4 + 85*g**5*n**3 + 225*g**5*n**2 + 274*g**5*n + 120*g**5) + 2*a*e**2*f**3*g**2*n**2*(f + g*x)**n/(g**5*n**5 + 15*g**5*n**4 + 85*g**5*n**3 + 225*g**5*n**2 + 274*g**5*n + 120*g**5) + 18*a*e**2*f**3*g**2*n*(f + g*x)**n/(g**5*n**5 + 15*g**5*n**4 + 85*g**5*n**3 + 225*g**5*n**2 + 274*g**5*n + 120*g**5) + 40*a*e**2*f**3*g**2*(f + g*x)**n/(g**5*n**5 + 15*g**5*n**4 + 85*g**5*n**3 + 225*g**5*n**2 + 274*g**5*n + 120*g**5) - 2*a*e**2*f**2*g**3*n**3*x*(f + g*x)**n/(g**5*n**5 + 15*g**5*n**4 + 85*g**5*n**3 + 225*g**5*n**2 + 274*g**5*n + 120*g**5) - 18*a*e**2*f**2*g**3*n**2*x*(f + g*x)**n/(g**5*n**5 + 15*g**5*n**4 + 85*g**5*n**3 + 225*g**5*n**2 + 274*g**5*n + 120*g**5) - 40*a*e**2*f**2*g**3*n*x*(f + g*x)**n/(g**5*n**5 + 15*g**5*n**4 + 85*g**5*n**3 + 225*g**5*n**2 + 274*g**5*n + 120*g**5) + a*e**2*f*g**4*n**4*x**2*(f + g*x)**n/(g**5*n**5 + 15*g**5*n**4 + 85*g**5*n**3 + 225*g**5*n**2 + 274*g**5*n + 120*g**5) + 10*a*e**2*f*g**4*n**3*x**2*(f + g*x)**n/(g**5*n**5 + 15*g**5*n**4 + 85*g**5*n**3 + 225*g**5*n**2 + 274*g**5*n + 120*g**5) + 29*a*e**2*f*g**4*n**2*x**2*(f + g*x)**n/(g**5*n**5 + 15*g**5*n**4 + 85*g**5*n**3 + 225*g**5*n**2 + 274*g**5*n + 120*g**5) + 20*a*e**2*f*g**4*n*x**2*(f + g*x)**n/(g**5*n**5 + 15*g**5*n**4 + 85*g**5*n**3 + 225*g**5*n**2 + 274*g**5*n + 120*g**5) + a*e**2*g**5*n**4*x**3*(f + g*x)**n/(g**5*n**5 + 15*g**5*n**4 + 85*g**5*n**3 + 225*g**5*n**2 + 274*g**5*n + 120*g**5) + 12*a*e**2*g**5*n**3*x**3*(f + g*x)**n/(g**5*n**5 + 15*g**5*n**4 + 85*g**5*n**3 + 225*g**5*n**2 + 274*g**5*n + 120*g**5) + 49*a*e**2*g**5*n**2*x**3*(f + g*x)**n/(g**5*n**5 + 15*g**5*n**4 + 85*g**5*n**3 + 225*g**5*n**2 + 274*g**5*n + 120*g**5) + 78*a*e**2*g**5*n*x**3*(f + g*x)**n/(g**5*n**5 + 15*g**5*n**4 + 85*g**5*n**3 + 225*g**5*n**2 + 274*g**5*n + 120*g**5) + 40*a*e**2*g**5*x**3*(f + g*x)**n/(g**5*n**5 + 15*g**5*n**4 + 85*g**5*n**3 + 225*g**5*n**2 + 274*g**5*n + 120*g**5) - 2*c*d**3*f**2*g**3*n**3*(f + g*x)**n/(g**5*n**5 + 15*g**5*n**4 + 85*g**5*n**3 + 225*g**5*n**2 + 274*g**5*n + 120*g**5) - 24*c*d**3*f**2*g**3*n**2*(f + g*x)**n/(g**5*n**5 + 15*g**5*n**4 + 85*g**5*n**3 + 225*g**5*n**2 + 274*g**5*n + 120*g**5) - 94*c*d**3*f**2*g**3*n*(f + g*x)**n/(g**5*n**5 + 15*g**5*n**4 + 85*g**5*n**3 + 225*g**5*n**2 + 274*g**5*n + 120*g**5) - 120*c*d**3*f**2*g**3*(f + g*x)**n/(g**5*n**5 + 15*g**5*n**4 + 85*g**5*n**3 + 225*g**5*n**2 + 274*g**5*n + 120*g**5) + 2*c*d**3*f*g**4*n**4*x*(f + g*x)**n/(g**5*n**5 + 15*g**5*n**4 + 85*g**5*n**3 + 225*g**5*n**2 + 274*g**5*n + 120*g**5) + 24*c*d**3*f*g**4*n**3*x*(f + g*x)**n/(g**5*n**5 + 15*g**5*n**4 + 85*g**5*n**3 + 225*g**5*n**2 + 274*g**5*n + 120*g**5) + 94*c*d**3*f*g**4*n**2*x*(f + g*x)**n/(g**5*n**5 + 15*g**5*n**4 + 85*g**5*n**3 + 225*g**5*n**2 + 274*g**5*n + 120*g**5) + 120*c*d**3*f*g**4*n*x*(f + g*x)**n/(g**5*n**5 + 15*g**5*n**4 + 85*g**5*n**3 + 225*g**5*n**2 + 274*g**5*n + 120*g**5) + 2*c*d**3*g**5*n**4*x**2*(f + g*x)**n/(g**5*n**5 + 15*g**5*n**4 + 85*g**5*n**3 + 225*g**5*n**2 + 274*g**5*n + 120*g**5) + 26*c*d**3*g**5*n**3*x**2*(f + g*x)**n/(g**5*n**5 + 15*g**5*n**4 + 85*g**5*n**3 + 225*g**5*n**2 + 274*g**5*n + 120*g**5) + 118*c*d**3*g**5*n**2*x**2*(f + g*x)**n/(g**5*n**5 + 15*g**5*n**4 + 85*g**5*n**3 + 225*g**5*n**2 + 274*g**5*n + 120*g**5) + 214*c*d**3*g**5*n*x**2*(f + g*x)**n/(g**5*n**5 + 15*g**5*n**4 + 85*g**5*n**3 + 225*g**5*n**2 + 274*g**5*n + 120*g**5) + 120*c*d**3*g**5*x**2*(f + g*x)**n/(g**5*n**5 + 15*g**5*n**4 + 85*g**5*n**3 + 225*g**5*n**2 + 274*g**5*n + 120*g**5) + 10*c*d**2*e*f**3*g**2*n**2*(f + g*x)**n/(g**5*n**5 + 15*g**5*n**4 + 85*g**5*n**3 + 225*g**5*n**2 + 274*g**5*n + 120*g**5) + 90*c*d**2*e*f**3*g**2*n*(f + g*x)**n/(g**5*n**5 + 15*g**5*n**4 + 85*g**5*n**3 + 225*g**5*n**2 + 274*g**5*n + 120*g**5) + 200*c*d**2*e*f**3*g**2*(f + g*x)**n/(g**5*n**5 + 15*g**5*n**4 + 85*g**5*n**3 + 225*g**5*n**2 + 274*g**5*n + 120*g**5) - 10*c*d**2*e*f**2*g**3*n**3*x*(f + g*x)**n/(g**5*n**5 + 15*g**5*n**4 + 85*g**5*n**3 + 225*g**5*n**2 + 274*g**5*n + 120*g**5) - 90*c*d**2*e*f**2*g**3*n**2*x*(f + g*x)**n/(g**5*n**5 + 15*g**5*n**4 + 85*g**5*n**3 + 225*g**5*n**2 + 274*g**5*n + 120*g**5) - 200*c*d**2*e*f**2*g**3*n*x*(f + g*x)**n/(g**5*n**5 + 15*g**5*n**4 + 85*g**5*n**3 + 225*g**5*n**2 + 274*g**5*n + 120*g**5) + 5*c*d**2*e*f*g**4*n**4*x**2*(f + g*x)**n/(g**5*n**5 + 15*g**5*n**4 + 85*g**5*n**3 + 225*g**5*n**2 + 274*g**5*n + 120*g**5) + 50*c*d**2*e*f*g**4*n**3*x**2*(f + g*x)**n/(g**5*n**5 + 15*g**5*n**4 + 85*g**5*n**3 + 225*g**5*n**2 + 274*g**5*n + 120*g**5) + 145*c*d**2*e*f*g**4*n**2*x**2*(f + g*x)**n/(g**5*n**5 + 15*g**5*n**4 + 85*g**5*n**3 + 225*g**5*n**2 + 274*g**5*n + 120*g**5) + 100*c*d**2*e*f*g**4*n*x**2*(f + g*x)**n/(g**5*n**5 + 15*g**5*n**4 + 85*g**5*n**3 + 225*g**5*n**2 + 274*g**5*n + 120*g**5) + 5*c*d**2*e*g**5*n**4*x**3*(f + g*x)**n/(g**5*n**5 + 15*g**5*n**4 + 85*g**5*n**3 + 225*g**5*n**2 + 274*g**5*n + 120*g**5) + 60*c*d**2*e*g**5*n**3*x**3*(f + g*x)**n/(g**5*n**5 + 15*g**5*n**4 + 85*g**5*n**3 + 225*g**5*n**2 + 274*g**5*n + 120*g**5) + 245*c*d**2*e*g**5*n**2*x**3*(f + g*x)**n/(g**5*n**5 + 15*g**5*n**4 + 85*g**5*n**3 + 225*g**5*n**2 + 274*g**5*n + 120*g**5) + 390*c*d**2*e*g**5*n*x**3*(f + g*x)**n/(g**5*n**5 + 15*g**5*n**4 + 85*g**5*n**3 + 225*g**5*n**2 + 274*g**5*n + 120*g**5) + 200*c*d**2*e*g**5*x**3*(f + g*x)**n/(g**5*n**5 + 15*g**5*n**4 + 85*g**5*n**3 + 225*g**5*n**2 + 274*g**5*n + 120*g**5) - 24*c*d*e**2*f**4*g*n*(f + g*x)**n/(g**5*n**5 + 15*g**5*n**4 + 85*g**5*n**3 + 225*g**5*n**2 + 274*g**5*n + 120*g**5) - 120*c*d*e**2*f**4*g*(f + g*x)**n/(g**5*n**5 + 15*g**5*n**4 + 85*g**5*n**3 + 225*g**5*n**2 + 274*g**5*n + 120*g**5) + 24*c*d*e**2*f**3*g**2*n**2*x*(f + g*x)**n/(g**5*n**5 + 15*g**5*n**4 + 85*g**5*n**3 + 225*g**5*n**2 + 274*g**5*n + 120*g**5) + 120*c*d*e**2*f**3*g**2*n*x*(f + g*x)**n/(g**5*n**5 + 15*g**5*n**4 + 85*g**5*n**3 + 225*g**5*n**2 + 274*g**5*n + 120*g**5) - 12*c*d*e**2*f**2*g**3*n**3*x**2*(f + g*x)**n/(g**5*n**5 + 15*g**5*n**4 + 85*g**5*n**3 + 225*g**5*n**2 + 274*g**5*n + 120*g**5) - 72*c*d*e**2*f**2*g**3*n**2*x**2*(f + g*x)**n/(g**5*n**5 + 15*g**5*n**4 + 85*g**5*n**3 + 225*g**5*n**2 + 274*g**5*n + 120*g**5) - 60*c*d*e**2*f**2*g**3*n*x**2*(f + g*x)**n/(g**5*n**5 + 15*g**5*n**4 + 85*g**5*n**3 + 225*g**5*n**2 + 274*g**5*n + 120*g**5) + 4*c*d*e**2*f*g**4*n**4*x**3*(f + g*x)**n/(g**5*n**5 + 15*g**5*n**4 + 85*g**5*n**3 + 225*g**5*n**2 + 274*g**5*n + 120*g**5) + 32*c*d*e**2*f*g**4*n**3*x**3*(f + g*x)**n/(g**5*n**5 + 15*g**5*n**4 + 85*g**5*n**3 + 225*g**5*n**2 + 274*g**5*n + 120*g**5) + 68*c*d*e**2*f*g**4*n**2*x**3*(f + g*x)**n/(g**5*n**5 + 15*g**5*n**4 + 85*g**5*n**3 + 225*g**5*n**2 + 274*g**5*n + 120*g**5) + 40*c*d*e**2*f*g**4*n*x**3*(f + g*x)**n/(g**5*n**5 + 15*g**5*n**4 + 85*g**5*n**3 + 225*g**5*n**2 + 274*g**5*n + 120*g**5) + 4*c*d*e**2*g**5*n**4*x**4*(f + g*x)**n/(g**5*n**5 + 15*g**5*n**4 + 85*g**5*n**3 + 225*g**5*n**2 + 274*g**5*n + 120*g**5) + 44*c*d*e**2*g**5*n**3*x**4*(f + g*x)**n/(g**5*n**5 + 15*g**5*n**4 + 85*g**5*n**3 + 225*g**5*n**2 + 274*g**5*n + 120*g**5) + 164*c*d*e**2*g**5*n**2*x**4*(f + g*x)**n/(g**5*n**5 + 15*g**5*n**4 + 85*g**5*n**3 + 225*g**5*n**2 + 274*g**5*n + 120*g**5) + 244*c*d*e**2*g**5*n*x**4*(f + g*x)**n/(g**5*n**5 + 15*g**5*n**4 + 85*g**5*n**3 + 225*g**5*n**2 + 274*g**5*n + 120*g**5) + 120*c*d*e**2*g**5*x**4*(f + g*x)**n/(g**5*n**5 + 15*g**5*n**4 + 85*g**5*n**3 + 225*g**5*n**2 + 274*g**5*n + 120*g**5) + 24*c*e**3*f**5*(f + g*x)**n/(g**5*n**5 + 15*g**5*n**4 + 85*g**5*n**3 + 225*g**5*n**2 + 274*g**5*n + 120*g**5) - 24*c*e**3*f**4*g*n*x*(f + g*x)**n/(g**5*n**5 + 15*g**5*n**4 + 85*g**5*n**3 + 225*g**5*n**2 + 274*g**5*n + 120*g**5) + 12*c*e**3*f**3*g**2*n**2*x**2*(f + g*x)**n/(g**5*n**5 + 15*g**5*n**4 + 85*g**5*n**3 + 225*g**5*n**2 + 274*g**5*n + 120*g**5) + 12*c*e**3*f**3*g**2*n*x**2*(f + g*x)**n/(g**5*n**5 + 15*g**5*n**4 + 85*g**5*n**3 + 225*g**5*n**2 + 274*g**5*n + 120*g**5) - 4*c*e**3*f**2*g**3*n**3*x**3*(f + g*x)**n/(g**5*n**5 + 15*g**5*n**4 + 85*g**5*n**3 + 225*g**5*n**2 + 274*g**5*n + 120*g**5) - 12*c*e**3*f**2*g**3*n**2*x**3*(f + g*x)**n/(g**5*n**5 + 15*g**5*n**4 + 85*g**5*n**3 + 225*g**5*n**2 + 274*g**5*n + 120*g**5) - 8*c*e**3*f**2*g**3*n*x**3*(f + g*x)**n/(g**5*n**5 + 15*g**5*n**4 + 85*g**5*n**3 + 225*g**5*n**2 + 274*g**5*n + 120*g**5) + c*e**3*f*g**4*n**4*x**4*(f + g*x)**n/(g**5*n**5 + 15*g**5*n**4 + 85*g**5*n**3 + 225*g**5*n**2 + 274*g**5*n + 120*g**5) + 6*c*e**3*f*g**4*n**3*x**4*(f + g*x)**n/(g**5*n**5 + 15*g**5*n**4 + 85*g**5*n**3 + 225*g**5*n**2 + 274*g**5*n + 120*g**5) + 11*c*e**3*f*g**4*n**2*x**4*(f + g*x)**n/(g**5*n**5 + 15*g**5*n**4 + 85*g**5*n**3 + 225*g**5*n**2 + 274*g**5*n + 120*g**5) + 6*c*e**3*f*g**4*n*x**4*(f + g*x)**n/(g**5*n**5 + 15*g**5*n**4 + 85*g**5*n**3 + 225*g**5*n**2 + 274*g**5*n + 120*g**5) + c*e**3*g**5*n**4*x**5*(f + g*x)**n/(g**5*n**5 + 15*g**5*n**4 + 85*g**5*n**3 + 225*g**5*n**2 + 274*g**5*n + 120*g**5) + 10*c*e**3*g**5*n**3*x**5*(f + g*x)**n/(g**5*n**5 + 15*g**5*n**4 + 85*g**5*n**3 + 225*g**5*n**2 + 274*g**5*n + 120*g**5) + 35*c*e**3*g**5*n**2*x**5*(f + g*x)**n/(g**5*n**5 + 15*g**5*n**4 + 85*g**5*n**3 + 225*g**5*n**2 + 274*g**5*n + 120*g**5) + 50*c*e**3*g**5*n*x**5*(f + g*x)**n/(g**5*n**5 + 15*g**5*n**4 + 85*g**5*n**3 + 225*g**5*n**2 + 274*g**5*n + 120*g**5) + 24*c*e**3*g**5*x**5*(f + g*x)**n/(g**5*n**5 + 15*g**5*n**4 + 85*g**5*n**3 + 225*g**5*n**2 + 274*g**5*n + 120*g**5), True))","A",0
807,1,4952,0,5.269437," ","integrate((e*x+d)*(g*x+f)**n*(c*e*x**2+2*c*d*x+a),x)","\begin{cases} f^{n} \left(a d x + \frac{a e x^{2}}{2} + c d^{2} x^{2} + c d e x^{3} + \frac{c e^{2} x^{4}}{4}\right) & \text{for}\: g = 0 \\- \frac{2 a d g^{3}}{6 f^{3} g^{4} + 18 f^{2} g^{5} x + 18 f g^{6} x^{2} + 6 g^{7} x^{3}} - \frac{a e f g^{2}}{6 f^{3} g^{4} + 18 f^{2} g^{5} x + 18 f g^{6} x^{2} + 6 g^{7} x^{3}} - \frac{3 a e g^{3} x}{6 f^{3} g^{4} + 18 f^{2} g^{5} x + 18 f g^{6} x^{2} + 6 g^{7} x^{3}} - \frac{2 c d^{2} f g^{2}}{6 f^{3} g^{4} + 18 f^{2} g^{5} x + 18 f g^{6} x^{2} + 6 g^{7} x^{3}} - \frac{6 c d^{2} g^{3} x}{6 f^{3} g^{4} + 18 f^{2} g^{5} x + 18 f g^{6} x^{2} + 6 g^{7} x^{3}} - \frac{6 c d e f^{2} g}{6 f^{3} g^{4} + 18 f^{2} g^{5} x + 18 f g^{6} x^{2} + 6 g^{7} x^{3}} - \frac{18 c d e f g^{2} x}{6 f^{3} g^{4} + 18 f^{2} g^{5} x + 18 f g^{6} x^{2} + 6 g^{7} x^{3}} - \frac{18 c d e g^{3} x^{2}}{6 f^{3} g^{4} + 18 f^{2} g^{5} x + 18 f g^{6} x^{2} + 6 g^{7} x^{3}} + \frac{6 c e^{2} f^{3} \log{\left(\frac{f}{g} + x \right)}}{6 f^{3} g^{4} + 18 f^{2} g^{5} x + 18 f g^{6} x^{2} + 6 g^{7} x^{3}} + \frac{11 c e^{2} f^{3}}{6 f^{3} g^{4} + 18 f^{2} g^{5} x + 18 f g^{6} x^{2} + 6 g^{7} x^{3}} + \frac{18 c e^{2} f^{2} g x \log{\left(\frac{f}{g} + x \right)}}{6 f^{3} g^{4} + 18 f^{2} g^{5} x + 18 f g^{6} x^{2} + 6 g^{7} x^{3}} + \frac{27 c e^{2} f^{2} g x}{6 f^{3} g^{4} + 18 f^{2} g^{5} x + 18 f g^{6} x^{2} + 6 g^{7} x^{3}} + \frac{18 c e^{2} f g^{2} x^{2} \log{\left(\frac{f}{g} + x \right)}}{6 f^{3} g^{4} + 18 f^{2} g^{5} x + 18 f g^{6} x^{2} + 6 g^{7} x^{3}} + \frac{18 c e^{2} f g^{2} x^{2}}{6 f^{3} g^{4} + 18 f^{2} g^{5} x + 18 f g^{6} x^{2} + 6 g^{7} x^{3}} + \frac{6 c e^{2} g^{3} x^{3} \log{\left(\frac{f}{g} + x \right)}}{6 f^{3} g^{4} + 18 f^{2} g^{5} x + 18 f g^{6} x^{2} + 6 g^{7} x^{3}} & \text{for}\: n = -4 \\- \frac{a d g^{3}}{2 f^{2} g^{4} + 4 f g^{5} x + 2 g^{6} x^{2}} - \frac{a e f g^{2}}{2 f^{2} g^{4} + 4 f g^{5} x + 2 g^{6} x^{2}} - \frac{2 a e g^{3} x}{2 f^{2} g^{4} + 4 f g^{5} x + 2 g^{6} x^{2}} - \frac{2 c d^{2} f g^{2}}{2 f^{2} g^{4} + 4 f g^{5} x + 2 g^{6} x^{2}} - \frac{4 c d^{2} g^{3} x}{2 f^{2} g^{4} + 4 f g^{5} x + 2 g^{6} x^{2}} + \frac{6 c d e f^{2} g \log{\left(\frac{f}{g} + x \right)}}{2 f^{2} g^{4} + 4 f g^{5} x + 2 g^{6} x^{2}} + \frac{9 c d e f^{2} g}{2 f^{2} g^{4} + 4 f g^{5} x + 2 g^{6} x^{2}} + \frac{12 c d e f g^{2} x \log{\left(\frac{f}{g} + x \right)}}{2 f^{2} g^{4} + 4 f g^{5} x + 2 g^{6} x^{2}} + \frac{12 c d e f g^{2} x}{2 f^{2} g^{4} + 4 f g^{5} x + 2 g^{6} x^{2}} + \frac{6 c d e g^{3} x^{2} \log{\left(\frac{f}{g} + x \right)}}{2 f^{2} g^{4} + 4 f g^{5} x + 2 g^{6} x^{2}} - \frac{6 c e^{2} f^{3} \log{\left(\frac{f}{g} + x \right)}}{2 f^{2} g^{4} + 4 f g^{5} x + 2 g^{6} x^{2}} - \frac{9 c e^{2} f^{3}}{2 f^{2} g^{4} + 4 f g^{5} x + 2 g^{6} x^{2}} - \frac{12 c e^{2} f^{2} g x \log{\left(\frac{f}{g} + x \right)}}{2 f^{2} g^{4} + 4 f g^{5} x + 2 g^{6} x^{2}} - \frac{12 c e^{2} f^{2} g x}{2 f^{2} g^{4} + 4 f g^{5} x + 2 g^{6} x^{2}} - \frac{6 c e^{2} f g^{2} x^{2} \log{\left(\frac{f}{g} + x \right)}}{2 f^{2} g^{4} + 4 f g^{5} x + 2 g^{6} x^{2}} + \frac{2 c e^{2} g^{3} x^{3}}{2 f^{2} g^{4} + 4 f g^{5} x + 2 g^{6} x^{2}} & \text{for}\: n = -3 \\- \frac{2 a d g^{3}}{2 f g^{4} + 2 g^{5} x} + \frac{2 a e f g^{2} \log{\left(\frac{f}{g} + x \right)}}{2 f g^{4} + 2 g^{5} x} + \frac{2 a e f g^{2}}{2 f g^{4} + 2 g^{5} x} + \frac{2 a e g^{3} x \log{\left(\frac{f}{g} + x \right)}}{2 f g^{4} + 2 g^{5} x} + \frac{4 c d^{2} f g^{2} \log{\left(\frac{f}{g} + x \right)}}{2 f g^{4} + 2 g^{5} x} + \frac{4 c d^{2} f g^{2}}{2 f g^{4} + 2 g^{5} x} + \frac{4 c d^{2} g^{3} x \log{\left(\frac{f}{g} + x \right)}}{2 f g^{4} + 2 g^{5} x} - \frac{12 c d e f^{2} g \log{\left(\frac{f}{g} + x \right)}}{2 f g^{4} + 2 g^{5} x} - \frac{12 c d e f^{2} g}{2 f g^{4} + 2 g^{5} x} - \frac{12 c d e f g^{2} x \log{\left(\frac{f}{g} + x \right)}}{2 f g^{4} + 2 g^{5} x} + \frac{6 c d e g^{3} x^{2}}{2 f g^{4} + 2 g^{5} x} + \frac{6 c e^{2} f^{3} \log{\left(\frac{f}{g} + x \right)}}{2 f g^{4} + 2 g^{5} x} + \frac{6 c e^{2} f^{3}}{2 f g^{4} + 2 g^{5} x} + \frac{6 c e^{2} f^{2} g x \log{\left(\frac{f}{g} + x \right)}}{2 f g^{4} + 2 g^{5} x} - \frac{3 c e^{2} f g^{2} x^{2}}{2 f g^{4} + 2 g^{5} x} + \frac{c e^{2} g^{3} x^{3}}{2 f g^{4} + 2 g^{5} x} & \text{for}\: n = -2 \\\frac{a d \log{\left(\frac{f}{g} + x \right)}}{g} - \frac{a e f \log{\left(\frac{f}{g} + x \right)}}{g^{2}} + \frac{a e x}{g} - \frac{2 c d^{2} f \log{\left(\frac{f}{g} + x \right)}}{g^{2}} + \frac{2 c d^{2} x}{g} + \frac{3 c d e f^{2} \log{\left(\frac{f}{g} + x \right)}}{g^{3}} - \frac{3 c d e f x}{g^{2}} + \frac{3 c d e x^{2}}{2 g} - \frac{c e^{2} f^{3} \log{\left(\frac{f}{g} + x \right)}}{g^{4}} + \frac{c e^{2} f^{2} x}{g^{3}} - \frac{c e^{2} f x^{2}}{2 g^{2}} + \frac{c e^{2} x^{3}}{3 g} & \text{for}\: n = -1 \\\frac{a d f g^{3} n^{3} \left(f + g x\right)^{n}}{g^{4} n^{4} + 10 g^{4} n^{3} + 35 g^{4} n^{2} + 50 g^{4} n + 24 g^{4}} + \frac{9 a d f g^{3} n^{2} \left(f + g x\right)^{n}}{g^{4} n^{4} + 10 g^{4} n^{3} + 35 g^{4} n^{2} + 50 g^{4} n + 24 g^{4}} + \frac{26 a d f g^{3} n \left(f + g x\right)^{n}}{g^{4} n^{4} + 10 g^{4} n^{3} + 35 g^{4} n^{2} + 50 g^{4} n + 24 g^{4}} + \frac{24 a d f g^{3} \left(f + g x\right)^{n}}{g^{4} n^{4} + 10 g^{4} n^{3} + 35 g^{4} n^{2} + 50 g^{4} n + 24 g^{4}} + \frac{a d g^{4} n^{3} x \left(f + g x\right)^{n}}{g^{4} n^{4} + 10 g^{4} n^{3} + 35 g^{4} n^{2} + 50 g^{4} n + 24 g^{4}} + \frac{9 a d g^{4} n^{2} x \left(f + g x\right)^{n}}{g^{4} n^{4} + 10 g^{4} n^{3} + 35 g^{4} n^{2} + 50 g^{4} n + 24 g^{4}} + \frac{26 a d g^{4} n x \left(f + g x\right)^{n}}{g^{4} n^{4} + 10 g^{4} n^{3} + 35 g^{4} n^{2} + 50 g^{4} n + 24 g^{4}} + \frac{24 a d g^{4} x \left(f + g x\right)^{n}}{g^{4} n^{4} + 10 g^{4} n^{3} + 35 g^{4} n^{2} + 50 g^{4} n + 24 g^{4}} - \frac{a e f^{2} g^{2} n^{2} \left(f + g x\right)^{n}}{g^{4} n^{4} + 10 g^{4} n^{3} + 35 g^{4} n^{2} + 50 g^{4} n + 24 g^{4}} - \frac{7 a e f^{2} g^{2} n \left(f + g x\right)^{n}}{g^{4} n^{4} + 10 g^{4} n^{3} + 35 g^{4} n^{2} + 50 g^{4} n + 24 g^{4}} - \frac{12 a e f^{2} g^{2} \left(f + g x\right)^{n}}{g^{4} n^{4} + 10 g^{4} n^{3} + 35 g^{4} n^{2} + 50 g^{4} n + 24 g^{4}} + \frac{a e f g^{3} n^{3} x \left(f + g x\right)^{n}}{g^{4} n^{4} + 10 g^{4} n^{3} + 35 g^{4} n^{2} + 50 g^{4} n + 24 g^{4}} + \frac{7 a e f g^{3} n^{2} x \left(f + g x\right)^{n}}{g^{4} n^{4} + 10 g^{4} n^{3} + 35 g^{4} n^{2} + 50 g^{4} n + 24 g^{4}} + \frac{12 a e f g^{3} n x \left(f + g x\right)^{n}}{g^{4} n^{4} + 10 g^{4} n^{3} + 35 g^{4} n^{2} + 50 g^{4} n + 24 g^{4}} + \frac{a e g^{4} n^{3} x^{2} \left(f + g x\right)^{n}}{g^{4} n^{4} + 10 g^{4} n^{3} + 35 g^{4} n^{2} + 50 g^{4} n + 24 g^{4}} + \frac{8 a e g^{4} n^{2} x^{2} \left(f + g x\right)^{n}}{g^{4} n^{4} + 10 g^{4} n^{3} + 35 g^{4} n^{2} + 50 g^{4} n + 24 g^{4}} + \frac{19 a e g^{4} n x^{2} \left(f + g x\right)^{n}}{g^{4} n^{4} + 10 g^{4} n^{3} + 35 g^{4} n^{2} + 50 g^{4} n + 24 g^{4}} + \frac{12 a e g^{4} x^{2} \left(f + g x\right)^{n}}{g^{4} n^{4} + 10 g^{4} n^{3} + 35 g^{4} n^{2} + 50 g^{4} n + 24 g^{4}} - \frac{2 c d^{2} f^{2} g^{2} n^{2} \left(f + g x\right)^{n}}{g^{4} n^{4} + 10 g^{4} n^{3} + 35 g^{4} n^{2} + 50 g^{4} n + 24 g^{4}} - \frac{14 c d^{2} f^{2} g^{2} n \left(f + g x\right)^{n}}{g^{4} n^{4} + 10 g^{4} n^{3} + 35 g^{4} n^{2} + 50 g^{4} n + 24 g^{4}} - \frac{24 c d^{2} f^{2} g^{2} \left(f + g x\right)^{n}}{g^{4} n^{4} + 10 g^{4} n^{3} + 35 g^{4} n^{2} + 50 g^{4} n + 24 g^{4}} + \frac{2 c d^{2} f g^{3} n^{3} x \left(f + g x\right)^{n}}{g^{4} n^{4} + 10 g^{4} n^{3} + 35 g^{4} n^{2} + 50 g^{4} n + 24 g^{4}} + \frac{14 c d^{2} f g^{3} n^{2} x \left(f + g x\right)^{n}}{g^{4} n^{4} + 10 g^{4} n^{3} + 35 g^{4} n^{2} + 50 g^{4} n + 24 g^{4}} + \frac{24 c d^{2} f g^{3} n x \left(f + g x\right)^{n}}{g^{4} n^{4} + 10 g^{4} n^{3} + 35 g^{4} n^{2} + 50 g^{4} n + 24 g^{4}} + \frac{2 c d^{2} g^{4} n^{3} x^{2} \left(f + g x\right)^{n}}{g^{4} n^{4} + 10 g^{4} n^{3} + 35 g^{4} n^{2} + 50 g^{4} n + 24 g^{4}} + \frac{16 c d^{2} g^{4} n^{2} x^{2} \left(f + g x\right)^{n}}{g^{4} n^{4} + 10 g^{4} n^{3} + 35 g^{4} n^{2} + 50 g^{4} n + 24 g^{4}} + \frac{38 c d^{2} g^{4} n x^{2} \left(f + g x\right)^{n}}{g^{4} n^{4} + 10 g^{4} n^{3} + 35 g^{4} n^{2} + 50 g^{4} n + 24 g^{4}} + \frac{24 c d^{2} g^{4} x^{2} \left(f + g x\right)^{n}}{g^{4} n^{4} + 10 g^{4} n^{3} + 35 g^{4} n^{2} + 50 g^{4} n + 24 g^{4}} + \frac{6 c d e f^{3} g n \left(f + g x\right)^{n}}{g^{4} n^{4} + 10 g^{4} n^{3} + 35 g^{4} n^{2} + 50 g^{4} n + 24 g^{4}} + \frac{24 c d e f^{3} g \left(f + g x\right)^{n}}{g^{4} n^{4} + 10 g^{4} n^{3} + 35 g^{4} n^{2} + 50 g^{4} n + 24 g^{4}} - \frac{6 c d e f^{2} g^{2} n^{2} x \left(f + g x\right)^{n}}{g^{4} n^{4} + 10 g^{4} n^{3} + 35 g^{4} n^{2} + 50 g^{4} n + 24 g^{4}} - \frac{24 c d e f^{2} g^{2} n x \left(f + g x\right)^{n}}{g^{4} n^{4} + 10 g^{4} n^{3} + 35 g^{4} n^{2} + 50 g^{4} n + 24 g^{4}} + \frac{3 c d e f g^{3} n^{3} x^{2} \left(f + g x\right)^{n}}{g^{4} n^{4} + 10 g^{4} n^{3} + 35 g^{4} n^{2} + 50 g^{4} n + 24 g^{4}} + \frac{15 c d e f g^{3} n^{2} x^{2} \left(f + g x\right)^{n}}{g^{4} n^{4} + 10 g^{4} n^{3} + 35 g^{4} n^{2} + 50 g^{4} n + 24 g^{4}} + \frac{12 c d e f g^{3} n x^{2} \left(f + g x\right)^{n}}{g^{4} n^{4} + 10 g^{4} n^{3} + 35 g^{4} n^{2} + 50 g^{4} n + 24 g^{4}} + \frac{3 c d e g^{4} n^{3} x^{3} \left(f + g x\right)^{n}}{g^{4} n^{4} + 10 g^{4} n^{3} + 35 g^{4} n^{2} + 50 g^{4} n + 24 g^{4}} + \frac{21 c d e g^{4} n^{2} x^{3} \left(f + g x\right)^{n}}{g^{4} n^{4} + 10 g^{4} n^{3} + 35 g^{4} n^{2} + 50 g^{4} n + 24 g^{4}} + \frac{42 c d e g^{4} n x^{3} \left(f + g x\right)^{n}}{g^{4} n^{4} + 10 g^{4} n^{3} + 35 g^{4} n^{2} + 50 g^{4} n + 24 g^{4}} + \frac{24 c d e g^{4} x^{3} \left(f + g x\right)^{n}}{g^{4} n^{4} + 10 g^{4} n^{3} + 35 g^{4} n^{2} + 50 g^{4} n + 24 g^{4}} - \frac{6 c e^{2} f^{4} \left(f + g x\right)^{n}}{g^{4} n^{4} + 10 g^{4} n^{3} + 35 g^{4} n^{2} + 50 g^{4} n + 24 g^{4}} + \frac{6 c e^{2} f^{3} g n x \left(f + g x\right)^{n}}{g^{4} n^{4} + 10 g^{4} n^{3} + 35 g^{4} n^{2} + 50 g^{4} n + 24 g^{4}} - \frac{3 c e^{2} f^{2} g^{2} n^{2} x^{2} \left(f + g x\right)^{n}}{g^{4} n^{4} + 10 g^{4} n^{3} + 35 g^{4} n^{2} + 50 g^{4} n + 24 g^{4}} - \frac{3 c e^{2} f^{2} g^{2} n x^{2} \left(f + g x\right)^{n}}{g^{4} n^{4} + 10 g^{4} n^{3} + 35 g^{4} n^{2} + 50 g^{4} n + 24 g^{4}} + \frac{c e^{2} f g^{3} n^{3} x^{3} \left(f + g x\right)^{n}}{g^{4} n^{4} + 10 g^{4} n^{3} + 35 g^{4} n^{2} + 50 g^{4} n + 24 g^{4}} + \frac{3 c e^{2} f g^{3} n^{2} x^{3} \left(f + g x\right)^{n}}{g^{4} n^{4} + 10 g^{4} n^{3} + 35 g^{4} n^{2} + 50 g^{4} n + 24 g^{4}} + \frac{2 c e^{2} f g^{3} n x^{3} \left(f + g x\right)^{n}}{g^{4} n^{4} + 10 g^{4} n^{3} + 35 g^{4} n^{2} + 50 g^{4} n + 24 g^{4}} + \frac{c e^{2} g^{4} n^{3} x^{4} \left(f + g x\right)^{n}}{g^{4} n^{4} + 10 g^{4} n^{3} + 35 g^{4} n^{2} + 50 g^{4} n + 24 g^{4}} + \frac{6 c e^{2} g^{4} n^{2} x^{4} \left(f + g x\right)^{n}}{g^{4} n^{4} + 10 g^{4} n^{3} + 35 g^{4} n^{2} + 50 g^{4} n + 24 g^{4}} + \frac{11 c e^{2} g^{4} n x^{4} \left(f + g x\right)^{n}}{g^{4} n^{4} + 10 g^{4} n^{3} + 35 g^{4} n^{2} + 50 g^{4} n + 24 g^{4}} + \frac{6 c e^{2} g^{4} x^{4} \left(f + g x\right)^{n}}{g^{4} n^{4} + 10 g^{4} n^{3} + 35 g^{4} n^{2} + 50 g^{4} n + 24 g^{4}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((f**n*(a*d*x + a*e*x**2/2 + c*d**2*x**2 + c*d*e*x**3 + c*e**2*x**4/4), Eq(g, 0)), (-2*a*d*g**3/(6*f**3*g**4 + 18*f**2*g**5*x + 18*f*g**6*x**2 + 6*g**7*x**3) - a*e*f*g**2/(6*f**3*g**4 + 18*f**2*g**5*x + 18*f*g**6*x**2 + 6*g**7*x**3) - 3*a*e*g**3*x/(6*f**3*g**4 + 18*f**2*g**5*x + 18*f*g**6*x**2 + 6*g**7*x**3) - 2*c*d**2*f*g**2/(6*f**3*g**4 + 18*f**2*g**5*x + 18*f*g**6*x**2 + 6*g**7*x**3) - 6*c*d**2*g**3*x/(6*f**3*g**4 + 18*f**2*g**5*x + 18*f*g**6*x**2 + 6*g**7*x**3) - 6*c*d*e*f**2*g/(6*f**3*g**4 + 18*f**2*g**5*x + 18*f*g**6*x**2 + 6*g**7*x**3) - 18*c*d*e*f*g**2*x/(6*f**3*g**4 + 18*f**2*g**5*x + 18*f*g**6*x**2 + 6*g**7*x**3) - 18*c*d*e*g**3*x**2/(6*f**3*g**4 + 18*f**2*g**5*x + 18*f*g**6*x**2 + 6*g**7*x**3) + 6*c*e**2*f**3*log(f/g + x)/(6*f**3*g**4 + 18*f**2*g**5*x + 18*f*g**6*x**2 + 6*g**7*x**3) + 11*c*e**2*f**3/(6*f**3*g**4 + 18*f**2*g**5*x + 18*f*g**6*x**2 + 6*g**7*x**3) + 18*c*e**2*f**2*g*x*log(f/g + x)/(6*f**3*g**4 + 18*f**2*g**5*x + 18*f*g**6*x**2 + 6*g**7*x**3) + 27*c*e**2*f**2*g*x/(6*f**3*g**4 + 18*f**2*g**5*x + 18*f*g**6*x**2 + 6*g**7*x**3) + 18*c*e**2*f*g**2*x**2*log(f/g + x)/(6*f**3*g**4 + 18*f**2*g**5*x + 18*f*g**6*x**2 + 6*g**7*x**3) + 18*c*e**2*f*g**2*x**2/(6*f**3*g**4 + 18*f**2*g**5*x + 18*f*g**6*x**2 + 6*g**7*x**3) + 6*c*e**2*g**3*x**3*log(f/g + x)/(6*f**3*g**4 + 18*f**2*g**5*x + 18*f*g**6*x**2 + 6*g**7*x**3), Eq(n, -4)), (-a*d*g**3/(2*f**2*g**4 + 4*f*g**5*x + 2*g**6*x**2) - a*e*f*g**2/(2*f**2*g**4 + 4*f*g**5*x + 2*g**6*x**2) - 2*a*e*g**3*x/(2*f**2*g**4 + 4*f*g**5*x + 2*g**6*x**2) - 2*c*d**2*f*g**2/(2*f**2*g**4 + 4*f*g**5*x + 2*g**6*x**2) - 4*c*d**2*g**3*x/(2*f**2*g**4 + 4*f*g**5*x + 2*g**6*x**2) + 6*c*d*e*f**2*g*log(f/g + x)/(2*f**2*g**4 + 4*f*g**5*x + 2*g**6*x**2) + 9*c*d*e*f**2*g/(2*f**2*g**4 + 4*f*g**5*x + 2*g**6*x**2) + 12*c*d*e*f*g**2*x*log(f/g + x)/(2*f**2*g**4 + 4*f*g**5*x + 2*g**6*x**2) + 12*c*d*e*f*g**2*x/(2*f**2*g**4 + 4*f*g**5*x + 2*g**6*x**2) + 6*c*d*e*g**3*x**2*log(f/g + x)/(2*f**2*g**4 + 4*f*g**5*x + 2*g**6*x**2) - 6*c*e**2*f**3*log(f/g + x)/(2*f**2*g**4 + 4*f*g**5*x + 2*g**6*x**2) - 9*c*e**2*f**3/(2*f**2*g**4 + 4*f*g**5*x + 2*g**6*x**2) - 12*c*e**2*f**2*g*x*log(f/g + x)/(2*f**2*g**4 + 4*f*g**5*x + 2*g**6*x**2) - 12*c*e**2*f**2*g*x/(2*f**2*g**4 + 4*f*g**5*x + 2*g**6*x**2) - 6*c*e**2*f*g**2*x**2*log(f/g + x)/(2*f**2*g**4 + 4*f*g**5*x + 2*g**6*x**2) + 2*c*e**2*g**3*x**3/(2*f**2*g**4 + 4*f*g**5*x + 2*g**6*x**2), Eq(n, -3)), (-2*a*d*g**3/(2*f*g**4 + 2*g**5*x) + 2*a*e*f*g**2*log(f/g + x)/(2*f*g**4 + 2*g**5*x) + 2*a*e*f*g**2/(2*f*g**4 + 2*g**5*x) + 2*a*e*g**3*x*log(f/g + x)/(2*f*g**4 + 2*g**5*x) + 4*c*d**2*f*g**2*log(f/g + x)/(2*f*g**4 + 2*g**5*x) + 4*c*d**2*f*g**2/(2*f*g**4 + 2*g**5*x) + 4*c*d**2*g**3*x*log(f/g + x)/(2*f*g**4 + 2*g**5*x) - 12*c*d*e*f**2*g*log(f/g + x)/(2*f*g**4 + 2*g**5*x) - 12*c*d*e*f**2*g/(2*f*g**4 + 2*g**5*x) - 12*c*d*e*f*g**2*x*log(f/g + x)/(2*f*g**4 + 2*g**5*x) + 6*c*d*e*g**3*x**2/(2*f*g**4 + 2*g**5*x) + 6*c*e**2*f**3*log(f/g + x)/(2*f*g**4 + 2*g**5*x) + 6*c*e**2*f**3/(2*f*g**4 + 2*g**5*x) + 6*c*e**2*f**2*g*x*log(f/g + x)/(2*f*g**4 + 2*g**5*x) - 3*c*e**2*f*g**2*x**2/(2*f*g**4 + 2*g**5*x) + c*e**2*g**3*x**3/(2*f*g**4 + 2*g**5*x), Eq(n, -2)), (a*d*log(f/g + x)/g - a*e*f*log(f/g + x)/g**2 + a*e*x/g - 2*c*d**2*f*log(f/g + x)/g**2 + 2*c*d**2*x/g + 3*c*d*e*f**2*log(f/g + x)/g**3 - 3*c*d*e*f*x/g**2 + 3*c*d*e*x**2/(2*g) - c*e**2*f**3*log(f/g + x)/g**4 + c*e**2*f**2*x/g**3 - c*e**2*f*x**2/(2*g**2) + c*e**2*x**3/(3*g), Eq(n, -1)), (a*d*f*g**3*n**3*(f + g*x)**n/(g**4*n**4 + 10*g**4*n**3 + 35*g**4*n**2 + 50*g**4*n + 24*g**4) + 9*a*d*f*g**3*n**2*(f + g*x)**n/(g**4*n**4 + 10*g**4*n**3 + 35*g**4*n**2 + 50*g**4*n + 24*g**4) + 26*a*d*f*g**3*n*(f + g*x)**n/(g**4*n**4 + 10*g**4*n**3 + 35*g**4*n**2 + 50*g**4*n + 24*g**4) + 24*a*d*f*g**3*(f + g*x)**n/(g**4*n**4 + 10*g**4*n**3 + 35*g**4*n**2 + 50*g**4*n + 24*g**4) + a*d*g**4*n**3*x*(f + g*x)**n/(g**4*n**4 + 10*g**4*n**3 + 35*g**4*n**2 + 50*g**4*n + 24*g**4) + 9*a*d*g**4*n**2*x*(f + g*x)**n/(g**4*n**4 + 10*g**4*n**3 + 35*g**4*n**2 + 50*g**4*n + 24*g**4) + 26*a*d*g**4*n*x*(f + g*x)**n/(g**4*n**4 + 10*g**4*n**3 + 35*g**4*n**2 + 50*g**4*n + 24*g**4) + 24*a*d*g**4*x*(f + g*x)**n/(g**4*n**4 + 10*g**4*n**3 + 35*g**4*n**2 + 50*g**4*n + 24*g**4) - a*e*f**2*g**2*n**2*(f + g*x)**n/(g**4*n**4 + 10*g**4*n**3 + 35*g**4*n**2 + 50*g**4*n + 24*g**4) - 7*a*e*f**2*g**2*n*(f + g*x)**n/(g**4*n**4 + 10*g**4*n**3 + 35*g**4*n**2 + 50*g**4*n + 24*g**4) - 12*a*e*f**2*g**2*(f + g*x)**n/(g**4*n**4 + 10*g**4*n**3 + 35*g**4*n**2 + 50*g**4*n + 24*g**4) + a*e*f*g**3*n**3*x*(f + g*x)**n/(g**4*n**4 + 10*g**4*n**3 + 35*g**4*n**2 + 50*g**4*n + 24*g**4) + 7*a*e*f*g**3*n**2*x*(f + g*x)**n/(g**4*n**4 + 10*g**4*n**3 + 35*g**4*n**2 + 50*g**4*n + 24*g**4) + 12*a*e*f*g**3*n*x*(f + g*x)**n/(g**4*n**4 + 10*g**4*n**3 + 35*g**4*n**2 + 50*g**4*n + 24*g**4) + a*e*g**4*n**3*x**2*(f + g*x)**n/(g**4*n**4 + 10*g**4*n**3 + 35*g**4*n**2 + 50*g**4*n + 24*g**4) + 8*a*e*g**4*n**2*x**2*(f + g*x)**n/(g**4*n**4 + 10*g**4*n**3 + 35*g**4*n**2 + 50*g**4*n + 24*g**4) + 19*a*e*g**4*n*x**2*(f + g*x)**n/(g**4*n**4 + 10*g**4*n**3 + 35*g**4*n**2 + 50*g**4*n + 24*g**4) + 12*a*e*g**4*x**2*(f + g*x)**n/(g**4*n**4 + 10*g**4*n**3 + 35*g**4*n**2 + 50*g**4*n + 24*g**4) - 2*c*d**2*f**2*g**2*n**2*(f + g*x)**n/(g**4*n**4 + 10*g**4*n**3 + 35*g**4*n**2 + 50*g**4*n + 24*g**4) - 14*c*d**2*f**2*g**2*n*(f + g*x)**n/(g**4*n**4 + 10*g**4*n**3 + 35*g**4*n**2 + 50*g**4*n + 24*g**4) - 24*c*d**2*f**2*g**2*(f + g*x)**n/(g**4*n**4 + 10*g**4*n**3 + 35*g**4*n**2 + 50*g**4*n + 24*g**4) + 2*c*d**2*f*g**3*n**3*x*(f + g*x)**n/(g**4*n**4 + 10*g**4*n**3 + 35*g**4*n**2 + 50*g**4*n + 24*g**4) + 14*c*d**2*f*g**3*n**2*x*(f + g*x)**n/(g**4*n**4 + 10*g**4*n**3 + 35*g**4*n**2 + 50*g**4*n + 24*g**4) + 24*c*d**2*f*g**3*n*x*(f + g*x)**n/(g**4*n**4 + 10*g**4*n**3 + 35*g**4*n**2 + 50*g**4*n + 24*g**4) + 2*c*d**2*g**4*n**3*x**2*(f + g*x)**n/(g**4*n**4 + 10*g**4*n**3 + 35*g**4*n**2 + 50*g**4*n + 24*g**4) + 16*c*d**2*g**4*n**2*x**2*(f + g*x)**n/(g**4*n**4 + 10*g**4*n**3 + 35*g**4*n**2 + 50*g**4*n + 24*g**4) + 38*c*d**2*g**4*n*x**2*(f + g*x)**n/(g**4*n**4 + 10*g**4*n**3 + 35*g**4*n**2 + 50*g**4*n + 24*g**4) + 24*c*d**2*g**4*x**2*(f + g*x)**n/(g**4*n**4 + 10*g**4*n**3 + 35*g**4*n**2 + 50*g**4*n + 24*g**4) + 6*c*d*e*f**3*g*n*(f + g*x)**n/(g**4*n**4 + 10*g**4*n**3 + 35*g**4*n**2 + 50*g**4*n + 24*g**4) + 24*c*d*e*f**3*g*(f + g*x)**n/(g**4*n**4 + 10*g**4*n**3 + 35*g**4*n**2 + 50*g**4*n + 24*g**4) - 6*c*d*e*f**2*g**2*n**2*x*(f + g*x)**n/(g**4*n**4 + 10*g**4*n**3 + 35*g**4*n**2 + 50*g**4*n + 24*g**4) - 24*c*d*e*f**2*g**2*n*x*(f + g*x)**n/(g**4*n**4 + 10*g**4*n**3 + 35*g**4*n**2 + 50*g**4*n + 24*g**4) + 3*c*d*e*f*g**3*n**3*x**2*(f + g*x)**n/(g**4*n**4 + 10*g**4*n**3 + 35*g**4*n**2 + 50*g**4*n + 24*g**4) + 15*c*d*e*f*g**3*n**2*x**2*(f + g*x)**n/(g**4*n**4 + 10*g**4*n**3 + 35*g**4*n**2 + 50*g**4*n + 24*g**4) + 12*c*d*e*f*g**3*n*x**2*(f + g*x)**n/(g**4*n**4 + 10*g**4*n**3 + 35*g**4*n**2 + 50*g**4*n + 24*g**4) + 3*c*d*e*g**4*n**3*x**3*(f + g*x)**n/(g**4*n**4 + 10*g**4*n**3 + 35*g**4*n**2 + 50*g**4*n + 24*g**4) + 21*c*d*e*g**4*n**2*x**3*(f + g*x)**n/(g**4*n**4 + 10*g**4*n**3 + 35*g**4*n**2 + 50*g**4*n + 24*g**4) + 42*c*d*e*g**4*n*x**3*(f + g*x)**n/(g**4*n**4 + 10*g**4*n**3 + 35*g**4*n**2 + 50*g**4*n + 24*g**4) + 24*c*d*e*g**4*x**3*(f + g*x)**n/(g**4*n**4 + 10*g**4*n**3 + 35*g**4*n**2 + 50*g**4*n + 24*g**4) - 6*c*e**2*f**4*(f + g*x)**n/(g**4*n**4 + 10*g**4*n**3 + 35*g**4*n**2 + 50*g**4*n + 24*g**4) + 6*c*e**2*f**3*g*n*x*(f + g*x)**n/(g**4*n**4 + 10*g**4*n**3 + 35*g**4*n**2 + 50*g**4*n + 24*g**4) - 3*c*e**2*f**2*g**2*n**2*x**2*(f + g*x)**n/(g**4*n**4 + 10*g**4*n**3 + 35*g**4*n**2 + 50*g**4*n + 24*g**4) - 3*c*e**2*f**2*g**2*n*x**2*(f + g*x)**n/(g**4*n**4 + 10*g**4*n**3 + 35*g**4*n**2 + 50*g**4*n + 24*g**4) + c*e**2*f*g**3*n**3*x**3*(f + g*x)**n/(g**4*n**4 + 10*g**4*n**3 + 35*g**4*n**2 + 50*g**4*n + 24*g**4) + 3*c*e**2*f*g**3*n**2*x**3*(f + g*x)**n/(g**4*n**4 + 10*g**4*n**3 + 35*g**4*n**2 + 50*g**4*n + 24*g**4) + 2*c*e**2*f*g**3*n*x**3*(f + g*x)**n/(g**4*n**4 + 10*g**4*n**3 + 35*g**4*n**2 + 50*g**4*n + 24*g**4) + c*e**2*g**4*n**3*x**4*(f + g*x)**n/(g**4*n**4 + 10*g**4*n**3 + 35*g**4*n**2 + 50*g**4*n + 24*g**4) + 6*c*e**2*g**4*n**2*x**4*(f + g*x)**n/(g**4*n**4 + 10*g**4*n**3 + 35*g**4*n**2 + 50*g**4*n + 24*g**4) + 11*c*e**2*g**4*n*x**4*(f + g*x)**n/(g**4*n**4 + 10*g**4*n**3 + 35*g**4*n**2 + 50*g**4*n + 24*g**4) + 6*c*e**2*g**4*x**4*(f + g*x)**n/(g**4*n**4 + 10*g**4*n**3 + 35*g**4*n**2 + 50*g**4*n + 24*g**4), True))","A",0
808,1,1489,0,2.212257," ","integrate((g*x+f)**n*(c*e*x**2+2*c*d*x+a),x)","\begin{cases} f^{n} \left(a x + c d x^{2} + \frac{c e x^{3}}{3}\right) & \text{for}\: g = 0 \\- \frac{a g^{2}}{2 f^{2} g^{3} + 4 f g^{4} x + 2 g^{5} x^{2}} - \frac{2 c d f g}{2 f^{2} g^{3} + 4 f g^{4} x + 2 g^{5} x^{2}} - \frac{4 c d g^{2} x}{2 f^{2} g^{3} + 4 f g^{4} x + 2 g^{5} x^{2}} + \frac{2 c e f^{2} \log{\left(\frac{f}{g} + x \right)}}{2 f^{2} g^{3} + 4 f g^{4} x + 2 g^{5} x^{2}} + \frac{3 c e f^{2}}{2 f^{2} g^{3} + 4 f g^{4} x + 2 g^{5} x^{2}} + \frac{4 c e f g x \log{\left(\frac{f}{g} + x \right)}}{2 f^{2} g^{3} + 4 f g^{4} x + 2 g^{5} x^{2}} + \frac{4 c e f g x}{2 f^{2} g^{3} + 4 f g^{4} x + 2 g^{5} x^{2}} + \frac{2 c e g^{2} x^{2} \log{\left(\frac{f}{g} + x \right)}}{2 f^{2} g^{3} + 4 f g^{4} x + 2 g^{5} x^{2}} & \text{for}\: n = -3 \\- \frac{a g^{2}}{f g^{3} + g^{4} x} + \frac{2 c d f g \log{\left(\frac{f}{g} + x \right)}}{f g^{3} + g^{4} x} + \frac{2 c d f g}{f g^{3} + g^{4} x} + \frac{2 c d g^{2} x \log{\left(\frac{f}{g} + x \right)}}{f g^{3} + g^{4} x} - \frac{2 c e f^{2} \log{\left(\frac{f}{g} + x \right)}}{f g^{3} + g^{4} x} - \frac{2 c e f^{2}}{f g^{3} + g^{4} x} - \frac{2 c e f g x \log{\left(\frac{f}{g} + x \right)}}{f g^{3} + g^{4} x} + \frac{c e g^{2} x^{2}}{f g^{3} + g^{4} x} & \text{for}\: n = -2 \\\frac{a \log{\left(\frac{f}{g} + x \right)}}{g} - \frac{2 c d f \log{\left(\frac{f}{g} + x \right)}}{g^{2}} + \frac{2 c d x}{g} + \frac{c e f^{2} \log{\left(\frac{f}{g} + x \right)}}{g^{3}} - \frac{c e f x}{g^{2}} + \frac{c e x^{2}}{2 g} & \text{for}\: n = -1 \\\frac{a f g^{2} n^{2} \left(f + g x\right)^{n}}{g^{3} n^{3} + 6 g^{3} n^{2} + 11 g^{3} n + 6 g^{3}} + \frac{5 a f g^{2} n \left(f + g x\right)^{n}}{g^{3} n^{3} + 6 g^{3} n^{2} + 11 g^{3} n + 6 g^{3}} + \frac{6 a f g^{2} \left(f + g x\right)^{n}}{g^{3} n^{3} + 6 g^{3} n^{2} + 11 g^{3} n + 6 g^{3}} + \frac{a g^{3} n^{2} x \left(f + g x\right)^{n}}{g^{3} n^{3} + 6 g^{3} n^{2} + 11 g^{3} n + 6 g^{3}} + \frac{5 a g^{3} n x \left(f + g x\right)^{n}}{g^{3} n^{3} + 6 g^{3} n^{2} + 11 g^{3} n + 6 g^{3}} + \frac{6 a g^{3} x \left(f + g x\right)^{n}}{g^{3} n^{3} + 6 g^{3} n^{2} + 11 g^{3} n + 6 g^{3}} - \frac{2 c d f^{2} g n \left(f + g x\right)^{n}}{g^{3} n^{3} + 6 g^{3} n^{2} + 11 g^{3} n + 6 g^{3}} - \frac{6 c d f^{2} g \left(f + g x\right)^{n}}{g^{3} n^{3} + 6 g^{3} n^{2} + 11 g^{3} n + 6 g^{3}} + \frac{2 c d f g^{2} n^{2} x \left(f + g x\right)^{n}}{g^{3} n^{3} + 6 g^{3} n^{2} + 11 g^{3} n + 6 g^{3}} + \frac{6 c d f g^{2} n x \left(f + g x\right)^{n}}{g^{3} n^{3} + 6 g^{3} n^{2} + 11 g^{3} n + 6 g^{3}} + \frac{2 c d g^{3} n^{2} x^{2} \left(f + g x\right)^{n}}{g^{3} n^{3} + 6 g^{3} n^{2} + 11 g^{3} n + 6 g^{3}} + \frac{8 c d g^{3} n x^{2} \left(f + g x\right)^{n}}{g^{3} n^{3} + 6 g^{3} n^{2} + 11 g^{3} n + 6 g^{3}} + \frac{6 c d g^{3} x^{2} \left(f + g x\right)^{n}}{g^{3} n^{3} + 6 g^{3} n^{2} + 11 g^{3} n + 6 g^{3}} + \frac{2 c e f^{3} \left(f + g x\right)^{n}}{g^{3} n^{3} + 6 g^{3} n^{2} + 11 g^{3} n + 6 g^{3}} - \frac{2 c e f^{2} g n x \left(f + g x\right)^{n}}{g^{3} n^{3} + 6 g^{3} n^{2} + 11 g^{3} n + 6 g^{3}} + \frac{c e f g^{2} n^{2} x^{2} \left(f + g x\right)^{n}}{g^{3} n^{3} + 6 g^{3} n^{2} + 11 g^{3} n + 6 g^{3}} + \frac{c e f g^{2} n x^{2} \left(f + g x\right)^{n}}{g^{3} n^{3} + 6 g^{3} n^{2} + 11 g^{3} n + 6 g^{3}} + \frac{c e g^{3} n^{2} x^{3} \left(f + g x\right)^{n}}{g^{3} n^{3} + 6 g^{3} n^{2} + 11 g^{3} n + 6 g^{3}} + \frac{3 c e g^{3} n x^{3} \left(f + g x\right)^{n}}{g^{3} n^{3} + 6 g^{3} n^{2} + 11 g^{3} n + 6 g^{3}} + \frac{2 c e g^{3} x^{3} \left(f + g x\right)^{n}}{g^{3} n^{3} + 6 g^{3} n^{2} + 11 g^{3} n + 6 g^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((f**n*(a*x + c*d*x**2 + c*e*x**3/3), Eq(g, 0)), (-a*g**2/(2*f**2*g**3 + 4*f*g**4*x + 2*g**5*x**2) - 2*c*d*f*g/(2*f**2*g**3 + 4*f*g**4*x + 2*g**5*x**2) - 4*c*d*g**2*x/(2*f**2*g**3 + 4*f*g**4*x + 2*g**5*x**2) + 2*c*e*f**2*log(f/g + x)/(2*f**2*g**3 + 4*f*g**4*x + 2*g**5*x**2) + 3*c*e*f**2/(2*f**2*g**3 + 4*f*g**4*x + 2*g**5*x**2) + 4*c*e*f*g*x*log(f/g + x)/(2*f**2*g**3 + 4*f*g**4*x + 2*g**5*x**2) + 4*c*e*f*g*x/(2*f**2*g**3 + 4*f*g**4*x + 2*g**5*x**2) + 2*c*e*g**2*x**2*log(f/g + x)/(2*f**2*g**3 + 4*f*g**4*x + 2*g**5*x**2), Eq(n, -3)), (-a*g**2/(f*g**3 + g**4*x) + 2*c*d*f*g*log(f/g + x)/(f*g**3 + g**4*x) + 2*c*d*f*g/(f*g**3 + g**4*x) + 2*c*d*g**2*x*log(f/g + x)/(f*g**3 + g**4*x) - 2*c*e*f**2*log(f/g + x)/(f*g**3 + g**4*x) - 2*c*e*f**2/(f*g**3 + g**4*x) - 2*c*e*f*g*x*log(f/g + x)/(f*g**3 + g**4*x) + c*e*g**2*x**2/(f*g**3 + g**4*x), Eq(n, -2)), (a*log(f/g + x)/g - 2*c*d*f*log(f/g + x)/g**2 + 2*c*d*x/g + c*e*f**2*log(f/g + x)/g**3 - c*e*f*x/g**2 + c*e*x**2/(2*g), Eq(n, -1)), (a*f*g**2*n**2*(f + g*x)**n/(g**3*n**3 + 6*g**3*n**2 + 11*g**3*n + 6*g**3) + 5*a*f*g**2*n*(f + g*x)**n/(g**3*n**3 + 6*g**3*n**2 + 11*g**3*n + 6*g**3) + 6*a*f*g**2*(f + g*x)**n/(g**3*n**3 + 6*g**3*n**2 + 11*g**3*n + 6*g**3) + a*g**3*n**2*x*(f + g*x)**n/(g**3*n**3 + 6*g**3*n**2 + 11*g**3*n + 6*g**3) + 5*a*g**3*n*x*(f + g*x)**n/(g**3*n**3 + 6*g**3*n**2 + 11*g**3*n + 6*g**3) + 6*a*g**3*x*(f + g*x)**n/(g**3*n**3 + 6*g**3*n**2 + 11*g**3*n + 6*g**3) - 2*c*d*f**2*g*n*(f + g*x)**n/(g**3*n**3 + 6*g**3*n**2 + 11*g**3*n + 6*g**3) - 6*c*d*f**2*g*(f + g*x)**n/(g**3*n**3 + 6*g**3*n**2 + 11*g**3*n + 6*g**3) + 2*c*d*f*g**2*n**2*x*(f + g*x)**n/(g**3*n**3 + 6*g**3*n**2 + 11*g**3*n + 6*g**3) + 6*c*d*f*g**2*n*x*(f + g*x)**n/(g**3*n**3 + 6*g**3*n**2 + 11*g**3*n + 6*g**3) + 2*c*d*g**3*n**2*x**2*(f + g*x)**n/(g**3*n**3 + 6*g**3*n**2 + 11*g**3*n + 6*g**3) + 8*c*d*g**3*n*x**2*(f + g*x)**n/(g**3*n**3 + 6*g**3*n**2 + 11*g**3*n + 6*g**3) + 6*c*d*g**3*x**2*(f + g*x)**n/(g**3*n**3 + 6*g**3*n**2 + 11*g**3*n + 6*g**3) + 2*c*e*f**3*(f + g*x)**n/(g**3*n**3 + 6*g**3*n**2 + 11*g**3*n + 6*g**3) - 2*c*e*f**2*g*n*x*(f + g*x)**n/(g**3*n**3 + 6*g**3*n**2 + 11*g**3*n + 6*g**3) + c*e*f*g**2*n**2*x**2*(f + g*x)**n/(g**3*n**3 + 6*g**3*n**2 + 11*g**3*n + 6*g**3) + c*e*f*g**2*n*x**2*(f + g*x)**n/(g**3*n**3 + 6*g**3*n**2 + 11*g**3*n + 6*g**3) + c*e*g**3*n**2*x**3*(f + g*x)**n/(g**3*n**3 + 6*g**3*n**2 + 11*g**3*n + 6*g**3) + 3*c*e*g**3*n*x**3*(f + g*x)**n/(g**3*n**3 + 6*g**3*n**2 + 11*g**3*n + 6*g**3) + 2*c*e*g**3*x**3*(f + g*x)**n/(g**3*n**3 + 6*g**3*n**2 + 11*g**3*n + 6*g**3), True))","A",0
809,0,0,0,0.000000," ","integrate((g*x+f)**n*(c*e*x**2+2*c*d*x+a)/(e*x+d),x)","\int \frac{\left(f + g x\right)^{n} \left(a + 2 c d x + c e x^{2}\right)}{d + e x}\, dx"," ",0,"Integral((f + g*x)**n*(a + 2*c*d*x + c*e*x**2)/(d + e*x), x)","F",0
810,-2,0,0,0.000000," ","integrate((g*x+f)**n*(c*e*x**2+2*c*d*x+a)/(e*x+d)**2,x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
811,0,0,0,0.000000," ","integrate((g*x+f)**n*(c*e*x**2+2*c*d*x+a)/(e*x+d)**3,x)","\int \frac{\left(f + g x\right)^{n} \left(a + 2 c d x + c e x^{2}\right)}{\left(d + e x\right)^{3}}\, dx"," ",0,"Integral((f + g*x)**n*(a + 2*c*d*x + c*e*x**2)/(d + e*x)**3, x)","F",0
812,0,0,0,0.000000," ","integrate((g*x+f)**n*(c*e*x**2+2*c*d*x+a)/(e*x+d)**4,x)","\int \frac{\left(f + g x\right)^{n} \left(a + 2 c d x + c e x^{2}\right)}{\left(d + e x\right)^{4}}\, dx"," ",0,"Integral((f + g*x)**n*(a + 2*c*d*x + c*e*x**2)/(d + e*x)**4, x)","F",0
813,-2,0,0,0.000000," ","integrate((e*x+d)**m*(g*x+f)**n*(c*e*x**2+2*c*d*x+a),x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
814,1,420,0,9.516447," ","integrate((c*x**2+b*x+a)/(e*x+d)/(g*x+f),x)","\frac{c x}{e g} + \frac{\left(a g^{2} - b f g + c f^{2}\right) \log{\left(x + \frac{a d e g^{2} + a e^{2} f g - 2 b d e f g + c d^{2} f g + c d e f^{2} - \frac{d^{2} e g \left(a g^{2} - b f g + c f^{2}\right)}{d g - e f} + \frac{2 d e^{2} f \left(a g^{2} - b f g + c f^{2}\right)}{d g - e f} - \frac{e^{3} f^{2} \left(a g^{2} - b f g + c f^{2}\right)}{g \left(d g - e f\right)}}{2 a e^{2} g^{2} - b d e g^{2} - b e^{2} f g + c d^{2} g^{2} + c e^{2} f^{2}} \right)}}{g^{2} \left(d g - e f\right)} - \frac{\left(a e^{2} - b d e + c d^{2}\right) \log{\left(x + \frac{a d e g^{2} + a e^{2} f g - 2 b d e f g + c d^{2} f g + c d e f^{2} + \frac{d^{2} g^{3} \left(a e^{2} - b d e + c d^{2}\right)}{e \left(d g - e f\right)} - \frac{2 d f g^{2} \left(a e^{2} - b d e + c d^{2}\right)}{d g - e f} + \frac{e f^{2} g \left(a e^{2} - b d e + c d^{2}\right)}{d g - e f}}{2 a e^{2} g^{2} - b d e g^{2} - b e^{2} f g + c d^{2} g^{2} + c e^{2} f^{2}} \right)}}{e^{2} \left(d g - e f\right)}"," ",0,"c*x/(e*g) + (a*g**2 - b*f*g + c*f**2)*log(x + (a*d*e*g**2 + a*e**2*f*g - 2*b*d*e*f*g + c*d**2*f*g + c*d*e*f**2 - d**2*e*g*(a*g**2 - b*f*g + c*f**2)/(d*g - e*f) + 2*d*e**2*f*(a*g**2 - b*f*g + c*f**2)/(d*g - e*f) - e**3*f**2*(a*g**2 - b*f*g + c*f**2)/(g*(d*g - e*f)))/(2*a*e**2*g**2 - b*d*e*g**2 - b*e**2*f*g + c*d**2*g**2 + c*e**2*f**2))/(g**2*(d*g - e*f)) - (a*e**2 - b*d*e + c*d**2)*log(x + (a*d*e*g**2 + a*e**2*f*g - 2*b*d*e*f*g + c*d**2*f*g + c*d*e*f**2 + d**2*g**3*(a*e**2 - b*d*e + c*d**2)/(e*(d*g - e*f)) - 2*d*f*g**2*(a*e**2 - b*d*e + c*d**2)/(d*g - e*f) + e*f**2*g*(a*e**2 - b*d*e + c*d**2)/(d*g - e*f))/(2*a*e**2*g**2 - b*d*e*g**2 - b*e**2*f*g + c*d**2*g**2 + c*e**2*f**2))/(e**2*(d*g - e*f))","B",0
815,-1,0,0,0.000000," ","integrate((c*x**2+b*x+a)**2/(e*x+d)/(g*x+f),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
816,-1,0,0,0.000000," ","integrate((c*x**2+b*x+a)**3/(e*x+d)/(g*x+f),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
817,-1,0,0,0.000000," ","integrate(1/(e*x+d)/(g*x+f)/(c*x**2+b*x+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
818,-1,0,0,0.000000," ","integrate(1/(e*x+d)/(g*x+f)/(c*x**2+b*x+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
819,1,1544,0,164.697463," ","integrate((e*x+d)**3*(c*x**2+b*x+a)/(g*x+f)**(1/2),x)","\begin{cases} \frac{- \frac{2 a d^{3} f}{\sqrt{f + g x}} - 2 a d^{3} \left(- \frac{f}{\sqrt{f + g x}} - \sqrt{f + g x}\right) - \frac{6 a d^{2} e f \left(- \frac{f}{\sqrt{f + g x}} - \sqrt{f + g x}\right)}{g} - \frac{6 a d^{2} e \left(\frac{f^{2}}{\sqrt{f + g x}} + 2 f \sqrt{f + g x} - \frac{\left(f + g x\right)^{\frac{3}{2}}}{3}\right)}{g} - \frac{6 a d e^{2} f \left(\frac{f^{2}}{\sqrt{f + g x}} + 2 f \sqrt{f + g x} - \frac{\left(f + g x\right)^{\frac{3}{2}}}{3}\right)}{g^{2}} - \frac{6 a d e^{2} \left(- \frac{f^{3}}{\sqrt{f + g x}} - 3 f^{2} \sqrt{f + g x} + f \left(f + g x\right)^{\frac{3}{2}} - \frac{\left(f + g x\right)^{\frac{5}{2}}}{5}\right)}{g^{2}} - \frac{2 a e^{3} f \left(- \frac{f^{3}}{\sqrt{f + g x}} - 3 f^{2} \sqrt{f + g x} + f \left(f + g x\right)^{\frac{3}{2}} - \frac{\left(f + g x\right)^{\frac{5}{2}}}{5}\right)}{g^{3}} - \frac{2 a e^{3} \left(\frac{f^{4}}{\sqrt{f + g x}} + 4 f^{3} \sqrt{f + g x} - 2 f^{2} \left(f + g x\right)^{\frac{3}{2}} + \frac{4 f \left(f + g x\right)^{\frac{5}{2}}}{5} - \frac{\left(f + g x\right)^{\frac{7}{2}}}{7}\right)}{g^{3}} - \frac{2 b d^{3} f \left(- \frac{f}{\sqrt{f + g x}} - \sqrt{f + g x}\right)}{g} - \frac{2 b d^{3} \left(\frac{f^{2}}{\sqrt{f + g x}} + 2 f \sqrt{f + g x} - \frac{\left(f + g x\right)^{\frac{3}{2}}}{3}\right)}{g} - \frac{6 b d^{2} e f \left(\frac{f^{2}}{\sqrt{f + g x}} + 2 f \sqrt{f + g x} - \frac{\left(f + g x\right)^{\frac{3}{2}}}{3}\right)}{g^{2}} - \frac{6 b d^{2} e \left(- \frac{f^{3}}{\sqrt{f + g x}} - 3 f^{2} \sqrt{f + g x} + f \left(f + g x\right)^{\frac{3}{2}} - \frac{\left(f + g x\right)^{\frac{5}{2}}}{5}\right)}{g^{2}} - \frac{6 b d e^{2} f \left(- \frac{f^{3}}{\sqrt{f + g x}} - 3 f^{2} \sqrt{f + g x} + f \left(f + g x\right)^{\frac{3}{2}} - \frac{\left(f + g x\right)^{\frac{5}{2}}}{5}\right)}{g^{3}} - \frac{6 b d e^{2} \left(\frac{f^{4}}{\sqrt{f + g x}} + 4 f^{3} \sqrt{f + g x} - 2 f^{2} \left(f + g x\right)^{\frac{3}{2}} + \frac{4 f \left(f + g x\right)^{\frac{5}{2}}}{5} - \frac{\left(f + g x\right)^{\frac{7}{2}}}{7}\right)}{g^{3}} - \frac{2 b e^{3} f \left(\frac{f^{4}}{\sqrt{f + g x}} + 4 f^{3} \sqrt{f + g x} - 2 f^{2} \left(f + g x\right)^{\frac{3}{2}} + \frac{4 f \left(f + g x\right)^{\frac{5}{2}}}{5} - \frac{\left(f + g x\right)^{\frac{7}{2}}}{7}\right)}{g^{4}} - \frac{2 b e^{3} \left(- \frac{f^{5}}{\sqrt{f + g x}} - 5 f^{4} \sqrt{f + g x} + \frac{10 f^{3} \left(f + g x\right)^{\frac{3}{2}}}{3} - 2 f^{2} \left(f + g x\right)^{\frac{5}{2}} + \frac{5 f \left(f + g x\right)^{\frac{7}{2}}}{7} - \frac{\left(f + g x\right)^{\frac{9}{2}}}{9}\right)}{g^{4}} - \frac{2 c d^{3} f \left(\frac{f^{2}}{\sqrt{f + g x}} + 2 f \sqrt{f + g x} - \frac{\left(f + g x\right)^{\frac{3}{2}}}{3}\right)}{g^{2}} - \frac{2 c d^{3} \left(- \frac{f^{3}}{\sqrt{f + g x}} - 3 f^{2} \sqrt{f + g x} + f \left(f + g x\right)^{\frac{3}{2}} - \frac{\left(f + g x\right)^{\frac{5}{2}}}{5}\right)}{g^{2}} - \frac{6 c d^{2} e f \left(- \frac{f^{3}}{\sqrt{f + g x}} - 3 f^{2} \sqrt{f + g x} + f \left(f + g x\right)^{\frac{3}{2}} - \frac{\left(f + g x\right)^{\frac{5}{2}}}{5}\right)}{g^{3}} - \frac{6 c d^{2} e \left(\frac{f^{4}}{\sqrt{f + g x}} + 4 f^{3} \sqrt{f + g x} - 2 f^{2} \left(f + g x\right)^{\frac{3}{2}} + \frac{4 f \left(f + g x\right)^{\frac{5}{2}}}{5} - \frac{\left(f + g x\right)^{\frac{7}{2}}}{7}\right)}{g^{3}} - \frac{6 c d e^{2} f \left(\frac{f^{4}}{\sqrt{f + g x}} + 4 f^{3} \sqrt{f + g x} - 2 f^{2} \left(f + g x\right)^{\frac{3}{2}} + \frac{4 f \left(f + g x\right)^{\frac{5}{2}}}{5} - \frac{\left(f + g x\right)^{\frac{7}{2}}}{7}\right)}{g^{4}} - \frac{6 c d e^{2} \left(- \frac{f^{5}}{\sqrt{f + g x}} - 5 f^{4} \sqrt{f + g x} + \frac{10 f^{3} \left(f + g x\right)^{\frac{3}{2}}}{3} - 2 f^{2} \left(f + g x\right)^{\frac{5}{2}} + \frac{5 f \left(f + g x\right)^{\frac{7}{2}}}{7} - \frac{\left(f + g x\right)^{\frac{9}{2}}}{9}\right)}{g^{4}} - \frac{2 c e^{3} f \left(- \frac{f^{5}}{\sqrt{f + g x}} - 5 f^{4} \sqrt{f + g x} + \frac{10 f^{3} \left(f + g x\right)^{\frac{3}{2}}}{3} - 2 f^{2} \left(f + g x\right)^{\frac{5}{2}} + \frac{5 f \left(f + g x\right)^{\frac{7}{2}}}{7} - \frac{\left(f + g x\right)^{\frac{9}{2}}}{9}\right)}{g^{5}} - \frac{2 c e^{3} \left(\frac{f^{6}}{\sqrt{f + g x}} + 6 f^{5} \sqrt{f + g x} - 5 f^{4} \left(f + g x\right)^{\frac{3}{2}} + 4 f^{3} \left(f + g x\right)^{\frac{5}{2}} - \frac{15 f^{2} \left(f + g x\right)^{\frac{7}{2}}}{7} + \frac{2 f \left(f + g x\right)^{\frac{9}{2}}}{3} - \frac{\left(f + g x\right)^{\frac{11}{2}}}{11}\right)}{g^{5}}}{g} & \text{for}\: g \neq 0 \\\frac{a d^{3} x + \frac{c e^{3} x^{6}}{6} + \frac{x^{5} \left(b e^{3} + 3 c d e^{2}\right)}{5} + \frac{x^{4} \left(a e^{3} + 3 b d e^{2} + 3 c d^{2} e\right)}{4} + \frac{x^{3} \left(3 a d e^{2} + 3 b d^{2} e + c d^{3}\right)}{3} + \frac{x^{2} \left(3 a d^{2} e + b d^{3}\right)}{2}}{\sqrt{f}} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((-2*a*d**3*f/sqrt(f + g*x) - 2*a*d**3*(-f/sqrt(f + g*x) - sqrt(f + g*x)) - 6*a*d**2*e*f*(-f/sqrt(f + g*x) - sqrt(f + g*x))/g - 6*a*d**2*e*(f**2/sqrt(f + g*x) + 2*f*sqrt(f + g*x) - (f + g*x)**(3/2)/3)/g - 6*a*d*e**2*f*(f**2/sqrt(f + g*x) + 2*f*sqrt(f + g*x) - (f + g*x)**(3/2)/3)/g**2 - 6*a*d*e**2*(-f**3/sqrt(f + g*x) - 3*f**2*sqrt(f + g*x) + f*(f + g*x)**(3/2) - (f + g*x)**(5/2)/5)/g**2 - 2*a*e**3*f*(-f**3/sqrt(f + g*x) - 3*f**2*sqrt(f + g*x) + f*(f + g*x)**(3/2) - (f + g*x)**(5/2)/5)/g**3 - 2*a*e**3*(f**4/sqrt(f + g*x) + 4*f**3*sqrt(f + g*x) - 2*f**2*(f + g*x)**(3/2) + 4*f*(f + g*x)**(5/2)/5 - (f + g*x)**(7/2)/7)/g**3 - 2*b*d**3*f*(-f/sqrt(f + g*x) - sqrt(f + g*x))/g - 2*b*d**3*(f**2/sqrt(f + g*x) + 2*f*sqrt(f + g*x) - (f + g*x)**(3/2)/3)/g - 6*b*d**2*e*f*(f**2/sqrt(f + g*x) + 2*f*sqrt(f + g*x) - (f + g*x)**(3/2)/3)/g**2 - 6*b*d**2*e*(-f**3/sqrt(f + g*x) - 3*f**2*sqrt(f + g*x) + f*(f + g*x)**(3/2) - (f + g*x)**(5/2)/5)/g**2 - 6*b*d*e**2*f*(-f**3/sqrt(f + g*x) - 3*f**2*sqrt(f + g*x) + f*(f + g*x)**(3/2) - (f + g*x)**(5/2)/5)/g**3 - 6*b*d*e**2*(f**4/sqrt(f + g*x) + 4*f**3*sqrt(f + g*x) - 2*f**2*(f + g*x)**(3/2) + 4*f*(f + g*x)**(5/2)/5 - (f + g*x)**(7/2)/7)/g**3 - 2*b*e**3*f*(f**4/sqrt(f + g*x) + 4*f**3*sqrt(f + g*x) - 2*f**2*(f + g*x)**(3/2) + 4*f*(f + g*x)**(5/2)/5 - (f + g*x)**(7/2)/7)/g**4 - 2*b*e**3*(-f**5/sqrt(f + g*x) - 5*f**4*sqrt(f + g*x) + 10*f**3*(f + g*x)**(3/2)/3 - 2*f**2*(f + g*x)**(5/2) + 5*f*(f + g*x)**(7/2)/7 - (f + g*x)**(9/2)/9)/g**4 - 2*c*d**3*f*(f**2/sqrt(f + g*x) + 2*f*sqrt(f + g*x) - (f + g*x)**(3/2)/3)/g**2 - 2*c*d**3*(-f**3/sqrt(f + g*x) - 3*f**2*sqrt(f + g*x) + f*(f + g*x)**(3/2) - (f + g*x)**(5/2)/5)/g**2 - 6*c*d**2*e*f*(-f**3/sqrt(f + g*x) - 3*f**2*sqrt(f + g*x) + f*(f + g*x)**(3/2) - (f + g*x)**(5/2)/5)/g**3 - 6*c*d**2*e*(f**4/sqrt(f + g*x) + 4*f**3*sqrt(f + g*x) - 2*f**2*(f + g*x)**(3/2) + 4*f*(f + g*x)**(5/2)/5 - (f + g*x)**(7/2)/7)/g**3 - 6*c*d*e**2*f*(f**4/sqrt(f + g*x) + 4*f**3*sqrt(f + g*x) - 2*f**2*(f + g*x)**(3/2) + 4*f*(f + g*x)**(5/2)/5 - (f + g*x)**(7/2)/7)/g**4 - 6*c*d*e**2*(-f**5/sqrt(f + g*x) - 5*f**4*sqrt(f + g*x) + 10*f**3*(f + g*x)**(3/2)/3 - 2*f**2*(f + g*x)**(5/2) + 5*f*(f + g*x)**(7/2)/7 - (f + g*x)**(9/2)/9)/g**4 - 2*c*e**3*f*(-f**5/sqrt(f + g*x) - 5*f**4*sqrt(f + g*x) + 10*f**3*(f + g*x)**(3/2)/3 - 2*f**2*(f + g*x)**(5/2) + 5*f*(f + g*x)**(7/2)/7 - (f + g*x)**(9/2)/9)/g**5 - 2*c*e**3*(f**6/sqrt(f + g*x) + 6*f**5*sqrt(f + g*x) - 5*f**4*(f + g*x)**(3/2) + 4*f**3*(f + g*x)**(5/2) - 15*f**2*(f + g*x)**(7/2)/7 + 2*f*(f + g*x)**(9/2)/3 - (f + g*x)**(11/2)/11)/g**5)/g, Ne(g, 0)), ((a*d**3*x + c*e**3*x**6/6 + x**5*(b*e**3 + 3*c*d*e**2)/5 + x**4*(a*e**3 + 3*b*d*e**2 + 3*c*d**2*e)/4 + x**3*(3*a*d*e**2 + 3*b*d**2*e + c*d**3)/3 + x**2*(3*a*d**2*e + b*d**3)/2)/sqrt(f), True))","A",0
820,1,1001,0,105.538911," ","integrate((e*x+d)**2*(c*x**2+b*x+a)/(g*x+f)**(1/2),x)","\begin{cases} \frac{- \frac{2 a d^{2} f}{\sqrt{f + g x}} - 2 a d^{2} \left(- \frac{f}{\sqrt{f + g x}} - \sqrt{f + g x}\right) - \frac{4 a d e f \left(- \frac{f}{\sqrt{f + g x}} - \sqrt{f + g x}\right)}{g} - \frac{4 a d e \left(\frac{f^{2}}{\sqrt{f + g x}} + 2 f \sqrt{f + g x} - \frac{\left(f + g x\right)^{\frac{3}{2}}}{3}\right)}{g} - \frac{2 a e^{2} f \left(\frac{f^{2}}{\sqrt{f + g x}} + 2 f \sqrt{f + g x} - \frac{\left(f + g x\right)^{\frac{3}{2}}}{3}\right)}{g^{2}} - \frac{2 a e^{2} \left(- \frac{f^{3}}{\sqrt{f + g x}} - 3 f^{2} \sqrt{f + g x} + f \left(f + g x\right)^{\frac{3}{2}} - \frac{\left(f + g x\right)^{\frac{5}{2}}}{5}\right)}{g^{2}} - \frac{2 b d^{2} f \left(- \frac{f}{\sqrt{f + g x}} - \sqrt{f + g x}\right)}{g} - \frac{2 b d^{2} \left(\frac{f^{2}}{\sqrt{f + g x}} + 2 f \sqrt{f + g x} - \frac{\left(f + g x\right)^{\frac{3}{2}}}{3}\right)}{g} - \frac{4 b d e f \left(\frac{f^{2}}{\sqrt{f + g x}} + 2 f \sqrt{f + g x} - \frac{\left(f + g x\right)^{\frac{3}{2}}}{3}\right)}{g^{2}} - \frac{4 b d e \left(- \frac{f^{3}}{\sqrt{f + g x}} - 3 f^{2} \sqrt{f + g x} + f \left(f + g x\right)^{\frac{3}{2}} - \frac{\left(f + g x\right)^{\frac{5}{2}}}{5}\right)}{g^{2}} - \frac{2 b e^{2} f \left(- \frac{f^{3}}{\sqrt{f + g x}} - 3 f^{2} \sqrt{f + g x} + f \left(f + g x\right)^{\frac{3}{2}} - \frac{\left(f + g x\right)^{\frac{5}{2}}}{5}\right)}{g^{3}} - \frac{2 b e^{2} \left(\frac{f^{4}}{\sqrt{f + g x}} + 4 f^{3} \sqrt{f + g x} - 2 f^{2} \left(f + g x\right)^{\frac{3}{2}} + \frac{4 f \left(f + g x\right)^{\frac{5}{2}}}{5} - \frac{\left(f + g x\right)^{\frac{7}{2}}}{7}\right)}{g^{3}} - \frac{2 c d^{2} f \left(\frac{f^{2}}{\sqrt{f + g x}} + 2 f \sqrt{f + g x} - \frac{\left(f + g x\right)^{\frac{3}{2}}}{3}\right)}{g^{2}} - \frac{2 c d^{2} \left(- \frac{f^{3}}{\sqrt{f + g x}} - 3 f^{2} \sqrt{f + g x} + f \left(f + g x\right)^{\frac{3}{2}} - \frac{\left(f + g x\right)^{\frac{5}{2}}}{5}\right)}{g^{2}} - \frac{4 c d e f \left(- \frac{f^{3}}{\sqrt{f + g x}} - 3 f^{2} \sqrt{f + g x} + f \left(f + g x\right)^{\frac{3}{2}} - \frac{\left(f + g x\right)^{\frac{5}{2}}}{5}\right)}{g^{3}} - \frac{4 c d e \left(\frac{f^{4}}{\sqrt{f + g x}} + 4 f^{3} \sqrt{f + g x} - 2 f^{2} \left(f + g x\right)^{\frac{3}{2}} + \frac{4 f \left(f + g x\right)^{\frac{5}{2}}}{5} - \frac{\left(f + g x\right)^{\frac{7}{2}}}{7}\right)}{g^{3}} - \frac{2 c e^{2} f \left(\frac{f^{4}}{\sqrt{f + g x}} + 4 f^{3} \sqrt{f + g x} - 2 f^{2} \left(f + g x\right)^{\frac{3}{2}} + \frac{4 f \left(f + g x\right)^{\frac{5}{2}}}{5} - \frac{\left(f + g x\right)^{\frac{7}{2}}}{7}\right)}{g^{4}} - \frac{2 c e^{2} \left(- \frac{f^{5}}{\sqrt{f + g x}} - 5 f^{4} \sqrt{f + g x} + \frac{10 f^{3} \left(f + g x\right)^{\frac{3}{2}}}{3} - 2 f^{2} \left(f + g x\right)^{\frac{5}{2}} + \frac{5 f \left(f + g x\right)^{\frac{7}{2}}}{7} - \frac{\left(f + g x\right)^{\frac{9}{2}}}{9}\right)}{g^{4}}}{g} & \text{for}\: g \neq 0 \\\frac{a d^{2} x + \frac{c e^{2} x^{5}}{5} + \frac{x^{4} \left(b e^{2} + 2 c d e\right)}{4} + \frac{x^{3} \left(a e^{2} + 2 b d e + c d^{2}\right)}{3} + \frac{x^{2} \left(2 a d e + b d^{2}\right)}{2}}{\sqrt{f}} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((-2*a*d**2*f/sqrt(f + g*x) - 2*a*d**2*(-f/sqrt(f + g*x) - sqrt(f + g*x)) - 4*a*d*e*f*(-f/sqrt(f + g*x) - sqrt(f + g*x))/g - 4*a*d*e*(f**2/sqrt(f + g*x) + 2*f*sqrt(f + g*x) - (f + g*x)**(3/2)/3)/g - 2*a*e**2*f*(f**2/sqrt(f + g*x) + 2*f*sqrt(f + g*x) - (f + g*x)**(3/2)/3)/g**2 - 2*a*e**2*(-f**3/sqrt(f + g*x) - 3*f**2*sqrt(f + g*x) + f*(f + g*x)**(3/2) - (f + g*x)**(5/2)/5)/g**2 - 2*b*d**2*f*(-f/sqrt(f + g*x) - sqrt(f + g*x))/g - 2*b*d**2*(f**2/sqrt(f + g*x) + 2*f*sqrt(f + g*x) - (f + g*x)**(3/2)/3)/g - 4*b*d*e*f*(f**2/sqrt(f + g*x) + 2*f*sqrt(f + g*x) - (f + g*x)**(3/2)/3)/g**2 - 4*b*d*e*(-f**3/sqrt(f + g*x) - 3*f**2*sqrt(f + g*x) + f*(f + g*x)**(3/2) - (f + g*x)**(5/2)/5)/g**2 - 2*b*e**2*f*(-f**3/sqrt(f + g*x) - 3*f**2*sqrt(f + g*x) + f*(f + g*x)**(3/2) - (f + g*x)**(5/2)/5)/g**3 - 2*b*e**2*(f**4/sqrt(f + g*x) + 4*f**3*sqrt(f + g*x) - 2*f**2*(f + g*x)**(3/2) + 4*f*(f + g*x)**(5/2)/5 - (f + g*x)**(7/2)/7)/g**3 - 2*c*d**2*f*(f**2/sqrt(f + g*x) + 2*f*sqrt(f + g*x) - (f + g*x)**(3/2)/3)/g**2 - 2*c*d**2*(-f**3/sqrt(f + g*x) - 3*f**2*sqrt(f + g*x) + f*(f + g*x)**(3/2) - (f + g*x)**(5/2)/5)/g**2 - 4*c*d*e*f*(-f**3/sqrt(f + g*x) - 3*f**2*sqrt(f + g*x) + f*(f + g*x)**(3/2) - (f + g*x)**(5/2)/5)/g**3 - 4*c*d*e*(f**4/sqrt(f + g*x) + 4*f**3*sqrt(f + g*x) - 2*f**2*(f + g*x)**(3/2) + 4*f*(f + g*x)**(5/2)/5 - (f + g*x)**(7/2)/7)/g**3 - 2*c*e**2*f*(f**4/sqrt(f + g*x) + 4*f**3*sqrt(f + g*x) - 2*f**2*(f + g*x)**(3/2) + 4*f*(f + g*x)**(5/2)/5 - (f + g*x)**(7/2)/7)/g**4 - 2*c*e**2*(-f**5/sqrt(f + g*x) - 5*f**4*sqrt(f + g*x) + 10*f**3*(f + g*x)**(3/2)/3 - 2*f**2*(f + g*x)**(5/2) + 5*f*(f + g*x)**(7/2)/7 - (f + g*x)**(9/2)/9)/g**4)/g, Ne(g, 0)), ((a*d**2*x + c*e**2*x**5/5 + x**4*(b*e**2 + 2*c*d*e)/4 + x**3*(a*e**2 + 2*b*d*e + c*d**2)/3 + x**2*(2*a*d*e + b*d**2)/2)/sqrt(f), True))","A",0
821,1,549,0,55.827856," ","integrate((e*x+d)*(c*x**2+b*x+a)/(g*x+f)**(1/2),x)","\begin{cases} \frac{- \frac{2 a d f}{\sqrt{f + g x}} - 2 a d \left(- \frac{f}{\sqrt{f + g x}} - \sqrt{f + g x}\right) - \frac{2 a e f \left(- \frac{f}{\sqrt{f + g x}} - \sqrt{f + g x}\right)}{g} - \frac{2 a e \left(\frac{f^{2}}{\sqrt{f + g x}} + 2 f \sqrt{f + g x} - \frac{\left(f + g x\right)^{\frac{3}{2}}}{3}\right)}{g} - \frac{2 b d f \left(- \frac{f}{\sqrt{f + g x}} - \sqrt{f + g x}\right)}{g} - \frac{2 b d \left(\frac{f^{2}}{\sqrt{f + g x}} + 2 f \sqrt{f + g x} - \frac{\left(f + g x\right)^{\frac{3}{2}}}{3}\right)}{g} - \frac{2 b e f \left(\frac{f^{2}}{\sqrt{f + g x}} + 2 f \sqrt{f + g x} - \frac{\left(f + g x\right)^{\frac{3}{2}}}{3}\right)}{g^{2}} - \frac{2 b e \left(- \frac{f^{3}}{\sqrt{f + g x}} - 3 f^{2} \sqrt{f + g x} + f \left(f + g x\right)^{\frac{3}{2}} - \frac{\left(f + g x\right)^{\frac{5}{2}}}{5}\right)}{g^{2}} - \frac{2 c d f \left(\frac{f^{2}}{\sqrt{f + g x}} + 2 f \sqrt{f + g x} - \frac{\left(f + g x\right)^{\frac{3}{2}}}{3}\right)}{g^{2}} - \frac{2 c d \left(- \frac{f^{3}}{\sqrt{f + g x}} - 3 f^{2} \sqrt{f + g x} + f \left(f + g x\right)^{\frac{3}{2}} - \frac{\left(f + g x\right)^{\frac{5}{2}}}{5}\right)}{g^{2}} - \frac{2 c e f \left(- \frac{f^{3}}{\sqrt{f + g x}} - 3 f^{2} \sqrt{f + g x} + f \left(f + g x\right)^{\frac{3}{2}} - \frac{\left(f + g x\right)^{\frac{5}{2}}}{5}\right)}{g^{3}} - \frac{2 c e \left(\frac{f^{4}}{\sqrt{f + g x}} + 4 f^{3} \sqrt{f + g x} - 2 f^{2} \left(f + g x\right)^{\frac{3}{2}} + \frac{4 f \left(f + g x\right)^{\frac{5}{2}}}{5} - \frac{\left(f + g x\right)^{\frac{7}{2}}}{7}\right)}{g^{3}}}{g} & \text{for}\: g \neq 0 \\\frac{a d x + \frac{c e x^{4}}{4} + \frac{x^{3} \left(b e + c d\right)}{3} + \frac{x^{2} \left(a e + b d\right)}{2}}{\sqrt{f}} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((-2*a*d*f/sqrt(f + g*x) - 2*a*d*(-f/sqrt(f + g*x) - sqrt(f + g*x)) - 2*a*e*f*(-f/sqrt(f + g*x) - sqrt(f + g*x))/g - 2*a*e*(f**2/sqrt(f + g*x) + 2*f*sqrt(f + g*x) - (f + g*x)**(3/2)/3)/g - 2*b*d*f*(-f/sqrt(f + g*x) - sqrt(f + g*x))/g - 2*b*d*(f**2/sqrt(f + g*x) + 2*f*sqrt(f + g*x) - (f + g*x)**(3/2)/3)/g - 2*b*e*f*(f**2/sqrt(f + g*x) + 2*f*sqrt(f + g*x) - (f + g*x)**(3/2)/3)/g**2 - 2*b*e*(-f**3/sqrt(f + g*x) - 3*f**2*sqrt(f + g*x) + f*(f + g*x)**(3/2) - (f + g*x)**(5/2)/5)/g**2 - 2*c*d*f*(f**2/sqrt(f + g*x) + 2*f*sqrt(f + g*x) - (f + g*x)**(3/2)/3)/g**2 - 2*c*d*(-f**3/sqrt(f + g*x) - 3*f**2*sqrt(f + g*x) + f*(f + g*x)**(3/2) - (f + g*x)**(5/2)/5)/g**2 - 2*c*e*f*(-f**3/sqrt(f + g*x) - 3*f**2*sqrt(f + g*x) + f*(f + g*x)**(3/2) - (f + g*x)**(5/2)/5)/g**3 - 2*c*e*(f**4/sqrt(f + g*x) + 4*f**3*sqrt(f + g*x) - 2*f**2*(f + g*x)**(3/2) + 4*f*(f + g*x)**(5/2)/5 - (f + g*x)**(7/2)/7)/g**3)/g, Ne(g, 0)), ((a*d*x + c*e*x**4/4 + x**3*(b*e + c*d)/3 + x**2*(a*e + b*d)/2)/sqrt(f), True))","A",0
822,1,223,0,10.865450," ","integrate((c*x**2+b*x+a)/(g*x+f)**(1/2),x)","\begin{cases} \frac{- \frac{2 a f}{\sqrt{f + g x}} - 2 a \left(- \frac{f}{\sqrt{f + g x}} - \sqrt{f + g x}\right) - \frac{2 b f \left(- \frac{f}{\sqrt{f + g x}} - \sqrt{f + g x}\right)}{g} - \frac{2 b \left(\frac{f^{2}}{\sqrt{f + g x}} + 2 f \sqrt{f + g x} - \frac{\left(f + g x\right)^{\frac{3}{2}}}{3}\right)}{g} - \frac{2 c f \left(\frac{f^{2}}{\sqrt{f + g x}} + 2 f \sqrt{f + g x} - \frac{\left(f + g x\right)^{\frac{3}{2}}}{3}\right)}{g^{2}} - \frac{2 c \left(- \frac{f^{3}}{\sqrt{f + g x}} - 3 f^{2} \sqrt{f + g x} + f \left(f + g x\right)^{\frac{3}{2}} - \frac{\left(f + g x\right)^{\frac{5}{2}}}{5}\right)}{g^{2}}}{g} & \text{for}\: g \neq 0 \\\frac{a x + \frac{b x^{2}}{2} + \frac{c x^{3}}{3}}{\sqrt{f}} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((-2*a*f/sqrt(f + g*x) - 2*a*(-f/sqrt(f + g*x) - sqrt(f + g*x)) - 2*b*f*(-f/sqrt(f + g*x) - sqrt(f + g*x))/g - 2*b*(f**2/sqrt(f + g*x) + 2*f*sqrt(f + g*x) - (f + g*x)**(3/2)/3)/g - 2*c*f*(f**2/sqrt(f + g*x) + 2*f*sqrt(f + g*x) - (f + g*x)**(3/2)/3)/g**2 - 2*c*(-f**3/sqrt(f + g*x) - 3*f**2*sqrt(f + g*x) + f*(f + g*x)**(3/2) - (f + g*x)**(5/2)/5)/g**2)/g, Ne(g, 0)), ((a*x + b*x**2/2 + c*x**3/3)/sqrt(f), True))","A",0
823,1,112,0,37.628982," ","integrate((c*x**2+b*x+a)/(e*x+d)/(g*x+f)**(1/2),x)","\frac{2 c \left(f + g x\right)^{\frac{3}{2}}}{3 e g^{2}} - \frac{2 \left(a e^{2} - b d e + c d^{2}\right) \operatorname{atan}{\left(\frac{1}{\sqrt{\frac{e}{d g - e f}} \sqrt{f + g x}} \right)}}{e^{2} \sqrt{\frac{e}{d g - e f}} \left(d g - e f\right)} + \frac{2 \sqrt{f + g x} \left(b e g - c d g - c e f\right)}{e^{2} g^{2}}"," ",0,"2*c*(f + g*x)**(3/2)/(3*e*g**2) - 2*(a*e**2 - b*d*e + c*d**2)*atan(1/(sqrt(e/(d*g - e*f))*sqrt(f + g*x)))/(e**2*sqrt(e/(d*g - e*f))*(d*g - e*f)) + 2*sqrt(f + g*x)*(b*e*g - c*d*g - c*e*f)/(e**2*g**2)","A",0
824,-1,0,0,0.000000," ","integrate((c*x**2+b*x+a)/(e*x+d)**2/(g*x+f)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
825,-1,0,0,0.000000," ","integrate((c*x**2+b*x+a)/(e*x+d)**3/(g*x+f)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
826,1,452,0,158.555252," ","integrate((e*x+d)**3*(c*x**2+b*x+a)/(g*x+f)**(3/2),x)","\frac{2 c e^{3} \left(f + g x\right)^{\frac{9}{2}}}{9 g^{6}} + \frac{\left(f + g x\right)^{\frac{7}{2}} \left(2 b e^{3} g + 6 c d e^{2} g - 10 c e^{3} f\right)}{7 g^{6}} + \frac{\left(f + g x\right)^{\frac{5}{2}} \left(2 a e^{3} g^{2} + 6 b d e^{2} g^{2} - 8 b e^{3} f g + 6 c d^{2} e g^{2} - 24 c d e^{2} f g + 20 c e^{3} f^{2}\right)}{5 g^{6}} + \frac{\left(f + g x\right)^{\frac{3}{2}} \left(6 a d e^{2} g^{3} - 6 a e^{3} f g^{2} + 6 b d^{2} e g^{3} - 18 b d e^{2} f g^{2} + 12 b e^{3} f^{2} g + 2 c d^{3} g^{3} - 18 c d^{2} e f g^{2} + 36 c d e^{2} f^{2} g - 20 c e^{3} f^{3}\right)}{3 g^{6}} + \frac{\sqrt{f + g x} \left(6 a d^{2} e g^{4} - 12 a d e^{2} f g^{3} + 6 a e^{3} f^{2} g^{2} + 2 b d^{3} g^{4} - 12 b d^{2} e f g^{3} + 18 b d e^{2} f^{2} g^{2} - 8 b e^{3} f^{3} g - 4 c d^{3} f g^{3} + 18 c d^{2} e f^{2} g^{2} - 24 c d e^{2} f^{3} g + 10 c e^{3} f^{4}\right)}{g^{6}} - \frac{2 \left(d g - e f\right)^{3} \left(a g^{2} - b f g + c f^{2}\right)}{g^{6} \sqrt{f + g x}}"," ",0,"2*c*e**3*(f + g*x)**(9/2)/(9*g**6) + (f + g*x)**(7/2)*(2*b*e**3*g + 6*c*d*e**2*g - 10*c*e**3*f)/(7*g**6) + (f + g*x)**(5/2)*(2*a*e**3*g**2 + 6*b*d*e**2*g**2 - 8*b*e**3*f*g + 6*c*d**2*e*g**2 - 24*c*d*e**2*f*g + 20*c*e**3*f**2)/(5*g**6) + (f + g*x)**(3/2)*(6*a*d*e**2*g**3 - 6*a*e**3*f*g**2 + 6*b*d**2*e*g**3 - 18*b*d*e**2*f*g**2 + 12*b*e**3*f**2*g + 2*c*d**3*g**3 - 18*c*d**2*e*f*g**2 + 36*c*d*e**2*f**2*g - 20*c*e**3*f**3)/(3*g**6) + sqrt(f + g*x)*(6*a*d**2*e*g**4 - 12*a*d*e**2*f*g**3 + 6*a*e**3*f**2*g**2 + 2*b*d**3*g**4 - 12*b*d**2*e*f*g**3 + 18*b*d*e**2*f**2*g**2 - 8*b*e**3*f**3*g - 4*c*d**3*f*g**3 + 18*c*d**2*e*f**2*g**2 - 24*c*d*e**2*f**3*g + 10*c*e**3*f**4)/g**6 - 2*(d*g - e*f)**3*(a*g**2 - b*f*g + c*f**2)/(g**6*sqrt(f + g*x))","A",0
827,1,272,0,79.486740," ","integrate((e*x+d)**2*(c*x**2+b*x+a)/(g*x+f)**(3/2),x)","\frac{2 c e^{2} \left(f + g x\right)^{\frac{7}{2}}}{7 g^{5}} + \frac{\left(f + g x\right)^{\frac{5}{2}} \left(2 b e^{2} g + 4 c d e g - 8 c e^{2} f\right)}{5 g^{5}} + \frac{\left(f + g x\right)^{\frac{3}{2}} \left(2 a e^{2} g^{2} + 4 b d e g^{2} - 6 b e^{2} f g + 2 c d^{2} g^{2} - 12 c d e f g + 12 c e^{2} f^{2}\right)}{3 g^{5}} + \frac{\sqrt{f + g x} \left(4 a d e g^{3} - 4 a e^{2} f g^{2} + 2 b d^{2} g^{3} - 8 b d e f g^{2} + 6 b e^{2} f^{2} g - 4 c d^{2} f g^{2} + 12 c d e f^{2} g - 8 c e^{2} f^{3}\right)}{g^{5}} - \frac{2 \left(d g - e f\right)^{2} \left(a g^{2} - b f g + c f^{2}\right)}{g^{5} \sqrt{f + g x}}"," ",0,"2*c*e**2*(f + g*x)**(7/2)/(7*g**5) + (f + g*x)**(5/2)*(2*b*e**2*g + 4*c*d*e*g - 8*c*e**2*f)/(5*g**5) + (f + g*x)**(3/2)*(2*a*e**2*g**2 + 4*b*d*e*g**2 - 6*b*e**2*f*g + 2*c*d**2*g**2 - 12*c*d*e*f*g + 12*c*e**2*f**2)/(3*g**5) + sqrt(f + g*x)*(4*a*d*e*g**3 - 4*a*e**2*f*g**2 + 2*b*d**2*g**3 - 8*b*d*e*f*g**2 + 6*b*e**2*f**2*g - 4*c*d**2*f*g**2 + 12*c*d*e*f**2*g - 8*c*e**2*f**3)/g**5 - 2*(d*g - e*f)**2*(a*g**2 - b*f*g + c*f**2)/(g**5*sqrt(f + g*x))","A",0
828,1,141,0,34.525463," ","integrate((e*x+d)*(c*x**2+b*x+a)/(g*x+f)**(3/2),x)","\frac{2 c e \left(f + g x\right)^{\frac{5}{2}}}{5 g^{4}} + \frac{\left(f + g x\right)^{\frac{3}{2}} \left(2 b e g + 2 c d g - 6 c e f\right)}{3 g^{4}} + \frac{\sqrt{f + g x} \left(2 a e g^{2} + 2 b d g^{2} - 4 b e f g - 4 c d f g + 6 c e f^{2}\right)}{g^{4}} - \frac{2 \left(d g - e f\right) \left(a g^{2} - b f g + c f^{2}\right)}{g^{4} \sqrt{f + g x}}"," ",0,"2*c*e*(f + g*x)**(5/2)/(5*g**4) + (f + g*x)**(3/2)*(2*b*e*g + 2*c*d*g - 6*c*e*f)/(3*g**4) + sqrt(f + g*x)*(2*a*e*g**2 + 2*b*d*g**2 - 4*b*e*f*g - 4*c*d*f*g + 6*c*e*f**2)/g**4 - 2*(d*g - e*f)*(a*g**2 - b*f*g + c*f**2)/(g**4*sqrt(f + g*x))","A",0
829,1,70,0,13.121125," ","integrate((c*x**2+b*x+a)/(g*x+f)**(3/2),x)","\frac{2 c \left(f + g x\right)^{\frac{3}{2}}}{3 g^{3}} + \frac{\sqrt{f + g x} \left(2 b g - 4 c f\right)}{g^{3}} - \frac{2 \left(a g^{2} - b f g + c f^{2}\right)}{g^{3} \sqrt{f + g x}}"," ",0,"2*c*(f + g*x)**(3/2)/(3*g**3) + sqrt(f + g*x)*(2*b*g - 4*c*f)/g**3 - 2*(a*g**2 - b*f*g + c*f**2)/(g**3*sqrt(f + g*x))","A",0
830,1,116,0,52.234028," ","integrate((c*x**2+b*x+a)/(e*x+d)/(g*x+f)**(3/2),x)","\frac{2 c \sqrt{f + g x}}{e g^{2}} - \frac{2 \left(a g^{2} - b f g + c f^{2}\right)}{g^{2} \sqrt{f + g x} \left(d g - e f\right)} - \frac{2 \left(a e^{2} - b d e + c d^{2}\right) \operatorname{atan}{\left(\frac{\sqrt{f + g x}}{\sqrt{\frac{d g - e f}{e}}} \right)}}{e^{2} \sqrt{\frac{d g - e f}{e}} \left(d g - e f\right)}"," ",0,"2*c*sqrt(f + g*x)/(e*g**2) - 2*(a*g**2 - b*f*g + c*f**2)/(g**2*sqrt(f + g*x)*(d*g - e*f)) - 2*(a*e**2 - b*d*e + c*d**2)*atan(sqrt(f + g*x)/sqrt((d*g - e*f)/e))/(e**2*sqrt((d*g - e*f)/e)*(d*g - e*f))","A",0
831,-1,0,0,0.000000," ","integrate((c*x**2+b*x+a)/(e*x+d)**2/(g*x+f)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
832,-1,0,0,0.000000," ","integrate((c*x**2+b*x+a)/(e*x+d)**3/(g*x+f)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
833,0,0,0,0.000000," ","integrate((-1+x)**(1/2)*(1+x)**(1/2)/(-x**2+x+1),x)","- \int \frac{\sqrt{x - 1} \sqrt{x + 1}}{x^{2} - x - 1}\, dx"," ",0,"-Integral(sqrt(x - 1)*sqrt(x + 1)/(x**2 - x - 1), x)","F",0
834,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)/(e*x+d)**(1/2)/(g*x+f)**(1/2),x)","\int \frac{a + b x + c x^{2}}{\sqrt{d + e x} \sqrt{f + g x}}\, dx"," ",0,"Integral((a + b*x + c*x**2)/(sqrt(d + e*x)*sqrt(f + g*x)), x)","F",0
835,-1,0,0,0.000000," ","integrate((e*x+d)**(3/2)*(c*x**2+b*x+a)/(g*x+f)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
836,-1,0,0,0.000000," ","integrate((e*x+d)**(1/2)*(c*x**2+b*x+a)/(g*x+f)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
837,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)/(e*x+d)**(1/2)/(g*x+f)**(1/2),x)","\int \frac{a + b x + c x^{2}}{\sqrt{d + e x} \sqrt{f + g x}}\, dx"," ",0,"Integral((a + b*x + c*x**2)/(sqrt(d + e*x)*sqrt(f + g*x)), x)","F",0
838,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)/(e*x+d)**(3/2)/(g*x+f)**(1/2),x)","\int \frac{a + b x + c x^{2}}{\left(d + e x\right)^{\frac{3}{2}} \sqrt{f + g x}}\, dx"," ",0,"Integral((a + b*x + c*x**2)/((d + e*x)**(3/2)*sqrt(f + g*x)), x)","F",0
839,-1,0,0,0.000000," ","integrate((c*x**2+b*x+a)/(e*x+d)**(5/2)/(g*x+f)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
840,-1,0,0,0.000000," ","integrate((c*x**2+b*x+a)/(e*x+d)**(7/2)/(g*x+f)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
841,-1,0,0,0.000000," ","integrate((c*x**2+b*x+a)/(e*x+d)**(9/2)/(g*x+f)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
842,0,0,0,0.000000," ","integrate((e*x+d)**(1/2)*(c*x**2+b*x+a)/(f*x+e)**(3/2),x)","\int \frac{\sqrt{d + e x} \left(a + b x + c x^{2}\right)}{\left(e + f x\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(sqrt(d + e*x)*(a + b*x + c*x**2)/(e + f*x)**(3/2), x)","F",0
843,-1,0,0,0.000000," ","integrate((e*x+d)**(3/2)*(8*e**2*x**2+20*d*e*x+15*d**2)/(b*x+a)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
844,-1,0,0,0.000000," ","integrate((e*x+d)**(1/2)*(8*e**2*x**2+20*d*e*x+15*d**2)/(b*x+a)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
845,0,0,0,0.000000," ","integrate((8*e**2*x**2+20*d*e*x+15*d**2)/(e*x+d)**(1/2)/(b*x+a)**(1/2),x)","\int \frac{15 d^{2} + 20 d e x + 8 e^{2} x^{2}}{\sqrt{a + b x} \sqrt{d + e x}}\, dx"," ",0,"Integral((15*d**2 + 20*d*e*x + 8*e**2*x**2)/(sqrt(a + b*x)*sqrt(d + e*x)), x)","F",0
846,0,0,0,0.000000," ","integrate((8*e**2*x**2+20*d*e*x+15*d**2)/(e*x+d)**(3/2)/(b*x+a)**(1/2),x)","\int \frac{15 d^{2} + 20 d e x + 8 e^{2} x^{2}}{\sqrt{a + b x} \left(d + e x\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((15*d**2 + 20*d*e*x + 8*e**2*x**2)/(sqrt(a + b*x)*(d + e*x)**(3/2)), x)","F",0
847,-1,0,0,0.000000," ","integrate((8*e**2*x**2+20*d*e*x+15*d**2)/(e*x+d)**(5/2)/(b*x+a)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
848,-1,0,0,0.000000," ","integrate((8*e**2*x**2+20*d*e*x+15*d**2)/(e*x+d)**(7/2)/(b*x+a)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
849,-1,0,0,0.000000," ","integrate((8*e**2*x**2+20*d*e*x+15*d**2)/(e*x+d)**(9/2)/(b*x+a)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
850,-1,0,0,0.000000," ","integrate((e*x+d)**(3/2)/(c*x**2+b*x+a)/(g*x+f)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
851,0,0,0,0.000000," ","integrate((e*x+d)**(1/2)/(c*x**2+b*x+a)/(g*x+f)**(1/2),x)","\int \frac{\sqrt{d + e x}}{\sqrt{f + g x} \left(a + b x + c x^{2}\right)}\, dx"," ",0,"Integral(sqrt(d + e*x)/(sqrt(f + g*x)*(a + b*x + c*x**2)), x)","F",0
852,0,0,0,0.000000," ","integrate(1/(e*x+d)**(1/2)/(c*x**2+b*x+a)/(g*x+f)**(1/2),x)","\int \frac{1}{\sqrt{d + e x} \sqrt{f + g x} \left(a + b x + c x^{2}\right)}\, dx"," ",0,"Integral(1/(sqrt(d + e*x)*sqrt(f + g*x)*(a + b*x + c*x**2)), x)","F",0
853,0,0,0,0.000000," ","integrate(1/(e*x+d)**(3/2)/(c*x**2+b*x+a)/(g*x+f)**(1/2),x)","\int \frac{1}{\left(d + e x\right)^{\frac{3}{2}} \sqrt{f + g x} \left(a + b x + c x^{2}\right)}\, dx"," ",0,"Integral(1/((d + e*x)**(3/2)*sqrt(f + g*x)*(a + b*x + c*x**2)), x)","F",0
854,0,0,0,0.000000," ","integrate((g*x+f)**3*(c*x**2+b*x+a)**(1/2)/(e*x+d),x)","\int \frac{\left(f + g x\right)^{3} \sqrt{a + b x + c x^{2}}}{d + e x}\, dx"," ",0,"Integral((f + g*x)**3*sqrt(a + b*x + c*x**2)/(d + e*x), x)","F",0
855,0,0,0,0.000000," ","integrate((g*x+f)**2*(c*x**2+b*x+a)**(1/2)/(e*x+d),x)","\int \frac{\left(f + g x\right)^{2} \sqrt{a + b x + c x^{2}}}{d + e x}\, dx"," ",0,"Integral((f + g*x)**2*sqrt(a + b*x + c*x**2)/(d + e*x), x)","F",0
856,0,0,0,0.000000," ","integrate((g*x+f)*(c*x**2+b*x+a)**(1/2)/(e*x+d),x)","\int \frac{\left(f + g x\right) \sqrt{a + b x + c x^{2}}}{d + e x}\, dx"," ",0,"Integral((f + g*x)*sqrt(a + b*x + c*x**2)/(d + e*x), x)","F",0
857,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(1/2)/(e*x+d),x)","\int \frac{\sqrt{a + b x + c x^{2}}}{d + e x}\, dx"," ",0,"Integral(sqrt(a + b*x + c*x**2)/(d + e*x), x)","F",0
858,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(1/2)/(e*x+d)/(g*x+f),x)","\int \frac{\sqrt{a + b x + c x^{2}}}{\left(d + e x\right) \left(f + g x\right)}\, dx"," ",0,"Integral(sqrt(a + b*x + c*x**2)/((d + e*x)*(f + g*x)), x)","F",0
859,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(1/2)/(e*x+d)/(g*x+f)**2,x)","\int \frac{\sqrt{a + b x + c x^{2}}}{\left(d + e x\right) \left(f + g x\right)^{2}}\, dx"," ",0,"Integral(sqrt(a + b*x + c*x**2)/((d + e*x)*(f + g*x)**2), x)","F",0
860,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(1/2)/(e*x+d)/(g*x+f)**3,x)","\int \frac{\sqrt{a + b x + c x^{2}}}{\left(d + e x\right) \left(f + g x\right)^{3}}\, dx"," ",0,"Integral(sqrt(a + b*x + c*x**2)/((d + e*x)*(f + g*x)**3), x)","F",0
861,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(1/2)/(e*x+d)/(g*x+f)**4,x)","\int \frac{\sqrt{a + b x + c x^{2}}}{\left(d + e x\right) \left(f + g x\right)^{4}}\, dx"," ",0,"Integral(sqrt(a + b*x + c*x**2)/((d + e*x)*(f + g*x)**4), x)","F",0
862,0,0,0,0.000000," ","integrate((g*x+f)**3*(c*x**2+b*x+a)**(3/2)/(e*x+d),x)","\int \frac{\left(f + g x\right)^{3} \left(a + b x + c x^{2}\right)^{\frac{3}{2}}}{d + e x}\, dx"," ",0,"Integral((f + g*x)**3*(a + b*x + c*x**2)**(3/2)/(d + e*x), x)","F",0
863,0,0,0,0.000000," ","integrate((g*x+f)**2*(c*x**2+b*x+a)**(3/2)/(e*x+d),x)","\int \frac{\left(f + g x\right)^{2} \left(a + b x + c x^{2}\right)^{\frac{3}{2}}}{d + e x}\, dx"," ",0,"Integral((f + g*x)**2*(a + b*x + c*x**2)**(3/2)/(d + e*x), x)","F",0
864,0,0,0,0.000000," ","integrate((g*x+f)*(c*x**2+b*x+a)**(3/2)/(e*x+d),x)","\int \frac{\left(f + g x\right) \left(a + b x + c x^{2}\right)^{\frac{3}{2}}}{d + e x}\, dx"," ",0,"Integral((f + g*x)*(a + b*x + c*x**2)**(3/2)/(d + e*x), x)","F",0
865,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(3/2)/(e*x+d),x)","\int \frac{\left(a + b x + c x^{2}\right)^{\frac{3}{2}}}{d + e x}\, dx"," ",0,"Integral((a + b*x + c*x**2)**(3/2)/(d + e*x), x)","F",0
866,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(3/2)/(e*x+d)/(g*x+f),x)","\int \frac{\left(a + b x + c x^{2}\right)^{\frac{3}{2}}}{\left(d + e x\right) \left(f + g x\right)}\, dx"," ",0,"Integral((a + b*x + c*x**2)**(3/2)/((d + e*x)*(f + g*x)), x)","F",0
867,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(3/2)/(e*x+d)/(g*x+f)**2,x)","\int \frac{\left(a + b x + c x^{2}\right)^{\frac{3}{2}}}{\left(d + e x\right) \left(f + g x\right)^{2}}\, dx"," ",0,"Integral((a + b*x + c*x**2)**(3/2)/((d + e*x)*(f + g*x)**2), x)","F",0
868,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(3/2)/(e*x+d)/(g*x+f)**3,x)","\int \frac{\left(a + b x + c x^{2}\right)^{\frac{3}{2}}}{\left(d + e x\right) \left(f + g x\right)^{3}}\, dx"," ",0,"Integral((a + b*x + c*x**2)**(3/2)/((d + e*x)*(f + g*x)**3), x)","F",0
869,-1,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(5/2)/(e*x+d)/(g*x+f),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
870,0,0,0,0.000000," ","integrate((g*x+f)**4/(e*x+d)/(c*x**2+b*x+a)**(1/2),x)","\int \frac{\left(f + g x\right)^{4}}{\left(d + e x\right) \sqrt{a + b x + c x^{2}}}\, dx"," ",0,"Integral((f + g*x)**4/((d + e*x)*sqrt(a + b*x + c*x**2)), x)","F",0
871,0,0,0,0.000000," ","integrate((g*x+f)**3/(e*x+d)/(c*x**2+b*x+a)**(1/2),x)","\int \frac{\left(f + g x\right)^{3}}{\left(d + e x\right) \sqrt{a + b x + c x^{2}}}\, dx"," ",0,"Integral((f + g*x)**3/((d + e*x)*sqrt(a + b*x + c*x**2)), x)","F",0
872,0,0,0,0.000000," ","integrate((g*x+f)**2/(e*x+d)/(c*x**2+b*x+a)**(1/2),x)","\int \frac{\left(f + g x\right)^{2}}{\left(d + e x\right) \sqrt{a + b x + c x^{2}}}\, dx"," ",0,"Integral((f + g*x)**2/((d + e*x)*sqrt(a + b*x + c*x**2)), x)","F",0
873,0,0,0,0.000000," ","integrate((g*x+f)/(e*x+d)/(c*x**2+b*x+a)**(1/2),x)","\int \frac{f + g x}{\left(d + e x\right) \sqrt{a + b x + c x^{2}}}\, dx"," ",0,"Integral((f + g*x)/((d + e*x)*sqrt(a + b*x + c*x**2)), x)","F",0
874,0,0,0,0.000000," ","integrate(1/(e*x+d)/(c*x**2+b*x+a)**(1/2),x)","\int \frac{1}{\left(d + e x\right) \sqrt{a + b x + c x^{2}}}\, dx"," ",0,"Integral(1/((d + e*x)*sqrt(a + b*x + c*x**2)), x)","F",0
875,0,0,0,0.000000," ","integrate(1/(e*x+d)/(g*x+f)/(c*x**2+b*x+a)**(1/2),x)","\int \frac{1}{\left(d + e x\right) \left(f + g x\right) \sqrt{a + b x + c x^{2}}}\, dx"," ",0,"Integral(1/((d + e*x)*(f + g*x)*sqrt(a + b*x + c*x**2)), x)","F",0
876,0,0,0,0.000000," ","integrate(1/(e*x+d)/(g*x+f)**2/(c*x**2+b*x+a)**(1/2),x)","\int \frac{1}{\left(d + e x\right) \left(f + g x\right)^{2} \sqrt{a + b x + c x^{2}}}\, dx"," ",0,"Integral(1/((d + e*x)*(f + g*x)**2*sqrt(a + b*x + c*x**2)), x)","F",0
877,0,0,0,0.000000," ","integrate(1/(e*x+d)/(g*x+f)**3/(c*x**2+b*x+a)**(1/2),x)","\int \frac{1}{\left(d + e x\right) \left(f + g x\right)^{3} \sqrt{a + b x + c x^{2}}}\, dx"," ",0,"Integral(1/((d + e*x)*(f + g*x)**3*sqrt(a + b*x + c*x**2)), x)","F",0
878,0,0,0,0.000000," ","integrate((g*x+f)**4/(e*x+d)/(c*x**2+b*x+a)**(3/2),x)","\int \frac{\left(f + g x\right)^{4}}{\left(d + e x\right) \left(a + b x + c x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((f + g*x)**4/((d + e*x)*(a + b*x + c*x**2)**(3/2)), x)","F",0
879,0,0,0,0.000000," ","integrate((g*x+f)**3/(e*x+d)/(c*x**2+b*x+a)**(3/2),x)","\int \frac{\left(f + g x\right)^{3}}{\left(d + e x\right) \left(a + b x + c x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((f + g*x)**3/((d + e*x)*(a + b*x + c*x**2)**(3/2)), x)","F",0
880,0,0,0,0.000000," ","integrate((g*x+f)**2/(e*x+d)/(c*x**2+b*x+a)**(3/2),x)","\int \frac{\left(f + g x\right)^{2}}{\left(d + e x\right) \left(a + b x + c x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((f + g*x)**2/((d + e*x)*(a + b*x + c*x**2)**(3/2)), x)","F",0
881,0,0,0,0.000000," ","integrate((g*x+f)/(e*x+d)/(c*x**2+b*x+a)**(3/2),x)","\int \frac{f + g x}{\left(d + e x\right) \left(a + b x + c x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((f + g*x)/((d + e*x)*(a + b*x + c*x**2)**(3/2)), x)","F",0
882,0,0,0,0.000000," ","integrate(1/(e*x+d)/(c*x**2+b*x+a)**(3/2),x)","\int \frac{1}{\left(d + e x\right) \left(a + b x + c x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/((d + e*x)*(a + b*x + c*x**2)**(3/2)), x)","F",0
883,0,0,0,0.000000," ","integrate(1/(e*x+d)/(g*x+f)/(c*x**2+b*x+a)**(3/2),x)","\int \frac{1}{\left(d + e x\right) \left(f + g x\right) \left(a + b x + c x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/((d + e*x)*(f + g*x)*(a + b*x + c*x**2)**(3/2)), x)","F",0
884,0,0,0,0.000000," ","integrate(1/(e*x+d)/(g*x+f)**2/(c*x**2+b*x+a)**(3/2),x)","\int \frac{1}{\left(d + e x\right) \left(f + g x\right)^{2} \left(a + b x + c x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/((d + e*x)*(f + g*x)**2*(a + b*x + c*x**2)**(3/2)), x)","F",0
885,0,0,0,0.000000," ","integrate(1/(e*x+d)/(g*x+f)**3/(c*x**2+b*x+a)**(3/2),x)","\int \frac{1}{\left(d + e x\right) \left(f + g x\right)^{3} \left(a + b x + c x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/((d + e*x)*(f + g*x)**3*(a + b*x + c*x**2)**(3/2)), x)","F",0
886,0,0,0,0.000000," ","integrate((e*x+d)**3*(g*x+f)**(1/2)*(c*x**2+b*x+a)**(1/2),x)","\int \left(d + e x\right)^{3} \sqrt{f + g x} \sqrt{a + b x + c x^{2}}\, dx"," ",0,"Integral((d + e*x)**3*sqrt(f + g*x)*sqrt(a + b*x + c*x**2), x)","F",0
887,0,0,0,0.000000," ","integrate((e*x+d)**2*(g*x+f)**(1/2)*(c*x**2+b*x+a)**(1/2),x)","\int \left(d + e x\right)^{2} \sqrt{f + g x} \sqrt{a + b x + c x^{2}}\, dx"," ",0,"Integral((d + e*x)**2*sqrt(f + g*x)*sqrt(a + b*x + c*x**2), x)","F",0
888,0,0,0,0.000000," ","integrate((e*x+d)*(g*x+f)**(1/2)*(c*x**2+b*x+a)**(1/2),x)","\int \left(d + e x\right) \sqrt{f + g x} \sqrt{a + b x + c x^{2}}\, dx"," ",0,"Integral((d + e*x)*sqrt(f + g*x)*sqrt(a + b*x + c*x**2), x)","F",0
889,0,0,0,0.000000," ","integrate((g*x+f)**(1/2)*(c*x**2+b*x+a)**(1/2),x)","\int \sqrt{f + g x} \sqrt{a + b x + c x^{2}}\, dx"," ",0,"Integral(sqrt(f + g*x)*sqrt(a + b*x + c*x**2), x)","F",0
890,0,0,0,0.000000," ","integrate((g*x+f)**(1/2)*(c*x**2+b*x+a)**(1/2)/(e*x+d),x)","\int \frac{\sqrt{f + g x} \sqrt{a + b x + c x^{2}}}{d + e x}\, dx"," ",0,"Integral(sqrt(f + g*x)*sqrt(a + b*x + c*x**2)/(d + e*x), x)","F",0
891,0,0,0,0.000000," ","integrate((g*x+f)**(1/2)*(c*x**2+b*x+a)**(1/2)/(e*x+d)**2,x)","\int \frac{\sqrt{f + g x} \sqrt{a + b x + c x^{2}}}{\left(d + e x\right)^{2}}\, dx"," ",0,"Integral(sqrt(f + g*x)*sqrt(a + b*x + c*x**2)/(d + e*x)**2, x)","F",0
892,-1,0,0,0.000000," ","integrate((g*x+f)**(1/2)*(c*x**2+b*x+a)**(1/2)/(e*x+d)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
893,-1,0,0,0.000000," ","integrate((e*x+d)**3*(c*x**2+b*x+a)**(1/2)/(g*x+f)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
894,-1,0,0,0.000000," ","integrate((e*x+d)**2*(c*x**2+b*x+a)**(1/2)/(g*x+f)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
895,0,0,0,0.000000," ","integrate((e*x+d)*(c*x**2+b*x+a)**(1/2)/(g*x+f)**(1/2),x)","\int \frac{\left(d + e x\right) \sqrt{a + b x + c x^{2}}}{\sqrt{f + g x}}\, dx"," ",0,"Integral((d + e*x)*sqrt(a + b*x + c*x**2)/sqrt(f + g*x), x)","F",0
896,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(1/2)/(g*x+f)**(1/2),x)","\int \frac{\sqrt{a + b x + c x^{2}}}{\sqrt{f + g x}}\, dx"," ",0,"Integral(sqrt(a + b*x + c*x**2)/sqrt(f + g*x), x)","F",0
897,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(1/2)/(e*x+d)/(g*x+f)**(1/2),x)","\int \frac{\sqrt{a + b x + c x^{2}}}{\left(d + e x\right) \sqrt{f + g x}}\, dx"," ",0,"Integral(sqrt(a + b*x + c*x**2)/((d + e*x)*sqrt(f + g*x)), x)","F",0
898,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(1/2)/(e*x+d)**2/(g*x+f)**(1/2),x)","\int \frac{\sqrt{a + b x + c x^{2}}}{\left(d + e x\right)^{2} \sqrt{f + g x}}\, dx"," ",0,"Integral(sqrt(a + b*x + c*x**2)/((d + e*x)**2*sqrt(f + g*x)), x)","F",0
899,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(1/2)/(e*x+d)**3/(g*x+f)**(1/2),x)","\int \frac{\sqrt{a + b x + c x^{2}}}{\left(d + e x\right)^{3} \sqrt{f + g x}}\, dx"," ",0,"Integral(sqrt(a + b*x + c*x**2)/((d + e*x)**3*sqrt(f + g*x)), x)","F",0
900,0,0,0,0.000000," ","integrate((e*x+d)**3*(g*x+f)**(1/2)/(c*x**2+b*x+a)**(1/2),x)","\int \frac{\left(d + e x\right)^{3} \sqrt{f + g x}}{\sqrt{a + b x + c x^{2}}}\, dx"," ",0,"Integral((d + e*x)**3*sqrt(f + g*x)/sqrt(a + b*x + c*x**2), x)","F",0
901,0,0,0,0.000000," ","integrate((e*x+d)**2*(g*x+f)**(1/2)/(c*x**2+b*x+a)**(1/2),x)","\int \frac{\left(d + e x\right)^{2} \sqrt{f + g x}}{\sqrt{a + b x + c x^{2}}}\, dx"," ",0,"Integral((d + e*x)**2*sqrt(f + g*x)/sqrt(a + b*x + c*x**2), x)","F",0
902,0,0,0,0.000000," ","integrate((e*x+d)*(g*x+f)**(1/2)/(c*x**2+b*x+a)**(1/2),x)","\int \frac{\left(d + e x\right) \sqrt{f + g x}}{\sqrt{a + b x + c x^{2}}}\, dx"," ",0,"Integral((d + e*x)*sqrt(f + g*x)/sqrt(a + b*x + c*x**2), x)","F",0
903,0,0,0,0.000000," ","integrate((g*x+f)**(1/2)/(c*x**2+b*x+a)**(1/2),x)","\int \frac{\sqrt{f + g x}}{\sqrt{a + b x + c x^{2}}}\, dx"," ",0,"Integral(sqrt(f + g*x)/sqrt(a + b*x + c*x**2), x)","F",0
904,0,0,0,0.000000," ","integrate((g*x+f)**(1/2)/(e*x+d)/(c*x**2+b*x+a)**(1/2),x)","\int \frac{\sqrt{f + g x}}{\left(d + e x\right) \sqrt{a + b x + c x^{2}}}\, dx"," ",0,"Integral(sqrt(f + g*x)/((d + e*x)*sqrt(a + b*x + c*x**2)), x)","F",0
905,0,0,0,0.000000," ","integrate((g*x+f)**(1/2)/(e*x+d)**2/(c*x**2+b*x+a)**(1/2),x)","\int \frac{\sqrt{f + g x}}{\left(d + e x\right)^{2} \sqrt{a + b x + c x^{2}}}\, dx"," ",0,"Integral(sqrt(f + g*x)/((d + e*x)**2*sqrt(a + b*x + c*x**2)), x)","F",0
906,-1,0,0,0.000000," ","integrate((g*x+f)**(1/2)/(e*x+d)**3/(c*x**2+b*x+a)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
907,0,0,0,0.000000," ","integrate((g*x+f)**(3/2)/(e*x+d)/(c*x**2+b*x+a)**(1/2),x)","\int \frac{\left(f + g x\right)^{\frac{3}{2}}}{\left(d + e x\right) \sqrt{a + b x + c x^{2}}}\, dx"," ",0,"Integral((f + g*x)**(3/2)/((d + e*x)*sqrt(a + b*x + c*x**2)), x)","F",0
908,0,0,0,0.000000," ","integrate((g*x+f)**(5/2)/(e*x+d)/(c*x**2+b*x+a)**(1/2),x)","\int \frac{\left(f + g x\right)^{\frac{5}{2}}}{\left(d + e x\right) \sqrt{a + b x + c x^{2}}}\, dx"," ",0,"Integral((f + g*x)**(5/2)/((d + e*x)*sqrt(a + b*x + c*x**2)), x)","F",0
909,0,0,0,0.000000," ","integrate((e*x+d)**3/(g*x+f)**(1/2)/(c*x**2+b*x+a)**(1/2),x)","\int \frac{\left(d + e x\right)^{3}}{\sqrt{f + g x} \sqrt{a + b x + c x^{2}}}\, dx"," ",0,"Integral((d + e*x)**3/(sqrt(f + g*x)*sqrt(a + b*x + c*x**2)), x)","F",0
910,0,0,0,0.000000," ","integrate((e*x+d)**2/(g*x+f)**(1/2)/(c*x**2+b*x+a)**(1/2),x)","\int \frac{\left(d + e x\right)^{2}}{\sqrt{f + g x} \sqrt{a + b x + c x^{2}}}\, dx"," ",0,"Integral((d + e*x)**2/(sqrt(f + g*x)*sqrt(a + b*x + c*x**2)), x)","F",0
911,0,0,0,0.000000," ","integrate((e*x+d)/(g*x+f)**(1/2)/(c*x**2+b*x+a)**(1/2),x)","\int \frac{d + e x}{\sqrt{f + g x} \sqrt{a + b x + c x^{2}}}\, dx"," ",0,"Integral((d + e*x)/(sqrt(f + g*x)*sqrt(a + b*x + c*x**2)), x)","F",0
912,0,0,0,0.000000," ","integrate(1/(g*x+f)**(1/2)/(c*x**2+b*x+a)**(1/2),x)","\int \frac{1}{\sqrt{f + g x} \sqrt{a + b x + c x^{2}}}\, dx"," ",0,"Integral(1/(sqrt(f + g*x)*sqrt(a + b*x + c*x**2)), x)","F",0
913,0,0,0,0.000000," ","integrate(1/(e*x+d)/(g*x+f)**(1/2)/(c*x**2+b*x+a)**(1/2),x)","\int \frac{1}{\left(d + e x\right) \sqrt{f + g x} \sqrt{a + b x + c x^{2}}}\, dx"," ",0,"Integral(1/((d + e*x)*sqrt(f + g*x)*sqrt(a + b*x + c*x**2)), x)","F",0
914,0,0,0,0.000000," ","integrate(1/(e*x+d)**2/(g*x+f)**(1/2)/(c*x**2+b*x+a)**(1/2),x)","\int \frac{1}{\left(d + e x\right)^{2} \sqrt{f + g x} \sqrt{a + b x + c x^{2}}}\, dx"," ",0,"Integral(1/((d + e*x)**2*sqrt(f + g*x)*sqrt(a + b*x + c*x**2)), x)","F",0
915,0,0,0,0.000000," ","integrate(1/(e*x+d)**3/(g*x+f)**(1/2)/(c*x**2+b*x+a)**(1/2),x)","\int \frac{1}{\left(d + e x\right)^{3} \sqrt{f + g x} \sqrt{a + b x + c x^{2}}}\, dx"," ",0,"Integral(1/((d + e*x)**3*sqrt(f + g*x)*sqrt(a + b*x + c*x**2)), x)","F",0
916,0,0,0,0.000000," ","integrate(1/(e*x+d)/(g*x+f)**(3/2)/(c*x**2+b*x+a)**(1/2),x)","\int \frac{1}{\left(d + e x\right) \left(f + g x\right)^{\frac{3}{2}} \sqrt{a + b x + c x^{2}}}\, dx"," ",0,"Integral(1/((d + e*x)*(f + g*x)**(3/2)*sqrt(a + b*x + c*x**2)), x)","F",0
917,0,0,0,0.000000," ","integrate(1/(e*x+d)/(g*x+f)**(5/2)/(c*x**2+b*x+a)**(1/2),x)","\int \frac{1}{\left(d + e x\right) \left(f + g x\right)^{\frac{5}{2}} \sqrt{a + b x + c x^{2}}}\, dx"," ",0,"Integral(1/((d + e*x)*(f + g*x)**(5/2)*sqrt(a + b*x + c*x**2)), x)","F",0
918,0,0,0,0.000000," ","integrate((e*x+d)**(1/2)/(g*x+f)**(1/2)/(c*x**2+b*x+a)**(1/2),x)","\int \frac{\sqrt{d + e x}}{\sqrt{f + g x} \sqrt{a + b x + c x^{2}}}\, dx"," ",0,"Integral(sqrt(d + e*x)/(sqrt(f + g*x)*sqrt(a + b*x + c*x**2)), x)","F",0
919,0,0,0,0.000000," ","integrate(1/(e*x+d)**(1/2)/(g*x+f)**(1/2)/(c*x**2+b*x+a)**(1/2),x)","\int \frac{1}{\sqrt{d + e x} \sqrt{f + g x} \sqrt{a + b x + c x^{2}}}\, dx"," ",0,"Integral(1/(sqrt(d + e*x)*sqrt(f + g*x)*sqrt(a + b*x + c*x**2)), x)","F",0
920,1,15757,0,14.704751," ","integrate((e*x+d)**m*(g*x+f)**2*(c*x**2+b*x+a),x)","\begin{cases} d^{m} \left(a f^{2} x + a f g x^{2} + \frac{a g^{2} x^{3}}{3} + \frac{b f^{2} x^{2}}{2} + \frac{2 b f g x^{3}}{3} + \frac{b g^{2} x^{4}}{4} + \frac{c f^{2} x^{3}}{3} + \frac{c f g x^{4}}{2} + \frac{c g^{2} x^{5}}{5}\right) & \text{for}\: e = 0 \\- \frac{a d^{2} e^{2} g^{2}}{12 d^{4} e^{5} + 48 d^{3} e^{6} x + 72 d^{2} e^{7} x^{2} + 48 d e^{8} x^{3} + 12 e^{9} x^{4}} - \frac{2 a d e^{3} f g}{12 d^{4} e^{5} + 48 d^{3} e^{6} x + 72 d^{2} e^{7} x^{2} + 48 d e^{8} x^{3} + 12 e^{9} x^{4}} - \frac{4 a d e^{3} g^{2} x}{12 d^{4} e^{5} + 48 d^{3} e^{6} x + 72 d^{2} e^{7} x^{2} + 48 d e^{8} x^{3} + 12 e^{9} x^{4}} - \frac{3 a e^{4} f^{2}}{12 d^{4} e^{5} + 48 d^{3} e^{6} x + 72 d^{2} e^{7} x^{2} + 48 d e^{8} x^{3} + 12 e^{9} x^{4}} - \frac{8 a e^{4} f g x}{12 d^{4} e^{5} + 48 d^{3} e^{6} x + 72 d^{2} e^{7} x^{2} + 48 d e^{8} x^{3} + 12 e^{9} x^{4}} - \frac{6 a e^{4} g^{2} x^{2}}{12 d^{4} e^{5} + 48 d^{3} e^{6} x + 72 d^{2} e^{7} x^{2} + 48 d e^{8} x^{3} + 12 e^{9} x^{4}} - \frac{3 b d^{3} e g^{2}}{12 d^{4} e^{5} + 48 d^{3} e^{6} x + 72 d^{2} e^{7} x^{2} + 48 d e^{8} x^{3} + 12 e^{9} x^{4}} - \frac{2 b d^{2} e^{2} f g}{12 d^{4} e^{5} + 48 d^{3} e^{6} x + 72 d^{2} e^{7} x^{2} + 48 d e^{8} x^{3} + 12 e^{9} x^{4}} - \frac{12 b d^{2} e^{2} g^{2} x}{12 d^{4} e^{5} + 48 d^{3} e^{6} x + 72 d^{2} e^{7} x^{2} + 48 d e^{8} x^{3} + 12 e^{9} x^{4}} - \frac{b d e^{3} f^{2}}{12 d^{4} e^{5} + 48 d^{3} e^{6} x + 72 d^{2} e^{7} x^{2} + 48 d e^{8} x^{3} + 12 e^{9} x^{4}} - \frac{8 b d e^{3} f g x}{12 d^{4} e^{5} + 48 d^{3} e^{6} x + 72 d^{2} e^{7} x^{2} + 48 d e^{8} x^{3} + 12 e^{9} x^{4}} - \frac{18 b d e^{3} g^{2} x^{2}}{12 d^{4} e^{5} + 48 d^{3} e^{6} x + 72 d^{2} e^{7} x^{2} + 48 d e^{8} x^{3} + 12 e^{9} x^{4}} - \frac{4 b e^{4} f^{2} x}{12 d^{4} e^{5} + 48 d^{3} e^{6} x + 72 d^{2} e^{7} x^{2} + 48 d e^{8} x^{3} + 12 e^{9} x^{4}} - \frac{12 b e^{4} f g x^{2}}{12 d^{4} e^{5} + 48 d^{3} e^{6} x + 72 d^{2} e^{7} x^{2} + 48 d e^{8} x^{3} + 12 e^{9} x^{4}} - \frac{12 b e^{4} g^{2} x^{3}}{12 d^{4} e^{5} + 48 d^{3} e^{6} x + 72 d^{2} e^{7} x^{2} + 48 d e^{8} x^{3} + 12 e^{9} x^{4}} + \frac{12 c d^{4} g^{2} \log{\left(\frac{d}{e} + x \right)}}{12 d^{4} e^{5} + 48 d^{3} e^{6} x + 72 d^{2} e^{7} x^{2} + 48 d e^{8} x^{3} + 12 e^{9} x^{4}} + \frac{25 c d^{4} g^{2}}{12 d^{4} e^{5} + 48 d^{3} e^{6} x + 72 d^{2} e^{7} x^{2} + 48 d e^{8} x^{3} + 12 e^{9} x^{4}} - \frac{6 c d^{3} e f g}{12 d^{4} e^{5} + 48 d^{3} e^{6} x + 72 d^{2} e^{7} x^{2} + 48 d e^{8} x^{3} + 12 e^{9} x^{4}} + \frac{48 c d^{3} e g^{2} x \log{\left(\frac{d}{e} + x \right)}}{12 d^{4} e^{5} + 48 d^{3} e^{6} x + 72 d^{2} e^{7} x^{2} + 48 d e^{8} x^{3} + 12 e^{9} x^{4}} + \frac{88 c d^{3} e g^{2} x}{12 d^{4} e^{5} + 48 d^{3} e^{6} x + 72 d^{2} e^{7} x^{2} + 48 d e^{8} x^{3} + 12 e^{9} x^{4}} - \frac{c d^{2} e^{2} f^{2}}{12 d^{4} e^{5} + 48 d^{3} e^{6} x + 72 d^{2} e^{7} x^{2} + 48 d e^{8} x^{3} + 12 e^{9} x^{4}} - \frac{24 c d^{2} e^{2} f g x}{12 d^{4} e^{5} + 48 d^{3} e^{6} x + 72 d^{2} e^{7} x^{2} + 48 d e^{8} x^{3} + 12 e^{9} x^{4}} + \frac{72 c d^{2} e^{2} g^{2} x^{2} \log{\left(\frac{d}{e} + x \right)}}{12 d^{4} e^{5} + 48 d^{3} e^{6} x + 72 d^{2} e^{7} x^{2} + 48 d e^{8} x^{3} + 12 e^{9} x^{4}} + \frac{108 c d^{2} e^{2} g^{2} x^{2}}{12 d^{4} e^{5} + 48 d^{3} e^{6} x + 72 d^{2} e^{7} x^{2} + 48 d e^{8} x^{3} + 12 e^{9} x^{4}} - \frac{4 c d e^{3} f^{2} x}{12 d^{4} e^{5} + 48 d^{3} e^{6} x + 72 d^{2} e^{7} x^{2} + 48 d e^{8} x^{3} + 12 e^{9} x^{4}} - \frac{36 c d e^{3} f g x^{2}}{12 d^{4} e^{5} + 48 d^{3} e^{6} x + 72 d^{2} e^{7} x^{2} + 48 d e^{8} x^{3} + 12 e^{9} x^{4}} + \frac{48 c d e^{3} g^{2} x^{3} \log{\left(\frac{d}{e} + x \right)}}{12 d^{4} e^{5} + 48 d^{3} e^{6} x + 72 d^{2} e^{7} x^{2} + 48 d e^{8} x^{3} + 12 e^{9} x^{4}} + \frac{48 c d e^{3} g^{2} x^{3}}{12 d^{4} e^{5} + 48 d^{3} e^{6} x + 72 d^{2} e^{7} x^{2} + 48 d e^{8} x^{3} + 12 e^{9} x^{4}} - \frac{6 c e^{4} f^{2} x^{2}}{12 d^{4} e^{5} + 48 d^{3} e^{6} x + 72 d^{2} e^{7} x^{2} + 48 d e^{8} x^{3} + 12 e^{9} x^{4}} - \frac{24 c e^{4} f g x^{3}}{12 d^{4} e^{5} + 48 d^{3} e^{6} x + 72 d^{2} e^{7} x^{2} + 48 d e^{8} x^{3} + 12 e^{9} x^{4}} + \frac{12 c e^{4} g^{2} x^{4} \log{\left(\frac{d}{e} + x \right)}}{12 d^{4} e^{5} + 48 d^{3} e^{6} x + 72 d^{2} e^{7} x^{2} + 48 d e^{8} x^{3} + 12 e^{9} x^{4}} & \text{for}\: m = -5 \\- \frac{2 a d^{2} e^{2} g^{2}}{6 d^{3} e^{5} + 18 d^{2} e^{6} x + 18 d e^{7} x^{2} + 6 e^{8} x^{3}} - \frac{2 a d e^{3} f g}{6 d^{3} e^{5} + 18 d^{2} e^{6} x + 18 d e^{7} x^{2} + 6 e^{8} x^{3}} - \frac{6 a d e^{3} g^{2} x}{6 d^{3} e^{5} + 18 d^{2} e^{6} x + 18 d e^{7} x^{2} + 6 e^{8} x^{3}} - \frac{2 a e^{4} f^{2}}{6 d^{3} e^{5} + 18 d^{2} e^{6} x + 18 d e^{7} x^{2} + 6 e^{8} x^{3}} - \frac{6 a e^{4} f g x}{6 d^{3} e^{5} + 18 d^{2} e^{6} x + 18 d e^{7} x^{2} + 6 e^{8} x^{3}} - \frac{6 a e^{4} g^{2} x^{2}}{6 d^{3} e^{5} + 18 d^{2} e^{6} x + 18 d e^{7} x^{2} + 6 e^{8} x^{3}} + \frac{6 b d^{3} e g^{2} \log{\left(\frac{d}{e} + x \right)}}{6 d^{3} e^{5} + 18 d^{2} e^{6} x + 18 d e^{7} x^{2} + 6 e^{8} x^{3}} + \frac{11 b d^{3} e g^{2}}{6 d^{3} e^{5} + 18 d^{2} e^{6} x + 18 d e^{7} x^{2} + 6 e^{8} x^{3}} - \frac{4 b d^{2} e^{2} f g}{6 d^{3} e^{5} + 18 d^{2} e^{6} x + 18 d e^{7} x^{2} + 6 e^{8} x^{3}} + \frac{18 b d^{2} e^{2} g^{2} x \log{\left(\frac{d}{e} + x \right)}}{6 d^{3} e^{5} + 18 d^{2} e^{6} x + 18 d e^{7} x^{2} + 6 e^{8} x^{3}} + \frac{27 b d^{2} e^{2} g^{2} x}{6 d^{3} e^{5} + 18 d^{2} e^{6} x + 18 d e^{7} x^{2} + 6 e^{8} x^{3}} - \frac{b d e^{3} f^{2}}{6 d^{3} e^{5} + 18 d^{2} e^{6} x + 18 d e^{7} x^{2} + 6 e^{8} x^{3}} - \frac{12 b d e^{3} f g x}{6 d^{3} e^{5} + 18 d^{2} e^{6} x + 18 d e^{7} x^{2} + 6 e^{8} x^{3}} + \frac{18 b d e^{3} g^{2} x^{2} \log{\left(\frac{d}{e} + x \right)}}{6 d^{3} e^{5} + 18 d^{2} e^{6} x + 18 d e^{7} x^{2} + 6 e^{8} x^{3}} + \frac{18 b d e^{3} g^{2} x^{2}}{6 d^{3} e^{5} + 18 d^{2} e^{6} x + 18 d e^{7} x^{2} + 6 e^{8} x^{3}} - \frac{3 b e^{4} f^{2} x}{6 d^{3} e^{5} + 18 d^{2} e^{6} x + 18 d e^{7} x^{2} + 6 e^{8} x^{3}} - \frac{12 b e^{4} f g x^{2}}{6 d^{3} e^{5} + 18 d^{2} e^{6} x + 18 d e^{7} x^{2} + 6 e^{8} x^{3}} + \frac{6 b e^{4} g^{2} x^{3} \log{\left(\frac{d}{e} + x \right)}}{6 d^{3} e^{5} + 18 d^{2} e^{6} x + 18 d e^{7} x^{2} + 6 e^{8} x^{3}} - \frac{24 c d^{4} g^{2} \log{\left(\frac{d}{e} + x \right)}}{6 d^{3} e^{5} + 18 d^{2} e^{6} x + 18 d e^{7} x^{2} + 6 e^{8} x^{3}} - \frac{44 c d^{4} g^{2}}{6 d^{3} e^{5} + 18 d^{2} e^{6} x + 18 d e^{7} x^{2} + 6 e^{8} x^{3}} + \frac{12 c d^{3} e f g \log{\left(\frac{d}{e} + x \right)}}{6 d^{3} e^{5} + 18 d^{2} e^{6} x + 18 d e^{7} x^{2} + 6 e^{8} x^{3}} + \frac{22 c d^{3} e f g}{6 d^{3} e^{5} + 18 d^{2} e^{6} x + 18 d e^{7} x^{2} + 6 e^{8} x^{3}} - \frac{72 c d^{3} e g^{2} x \log{\left(\frac{d}{e} + x \right)}}{6 d^{3} e^{5} + 18 d^{2} e^{6} x + 18 d e^{7} x^{2} + 6 e^{8} x^{3}} - \frac{108 c d^{3} e g^{2} x}{6 d^{3} e^{5} + 18 d^{2} e^{6} x + 18 d e^{7} x^{2} + 6 e^{8} x^{3}} - \frac{2 c d^{2} e^{2} f^{2}}{6 d^{3} e^{5} + 18 d^{2} e^{6} x + 18 d e^{7} x^{2} + 6 e^{8} x^{3}} + \frac{36 c d^{2} e^{2} f g x \log{\left(\frac{d}{e} + x \right)}}{6 d^{3} e^{5} + 18 d^{2} e^{6} x + 18 d e^{7} x^{2} + 6 e^{8} x^{3}} + \frac{54 c d^{2} e^{2} f g x}{6 d^{3} e^{5} + 18 d^{2} e^{6} x + 18 d e^{7} x^{2} + 6 e^{8} x^{3}} - \frac{72 c d^{2} e^{2} g^{2} x^{2} \log{\left(\frac{d}{e} + x \right)}}{6 d^{3} e^{5} + 18 d^{2} e^{6} x + 18 d e^{7} x^{2} + 6 e^{8} x^{3}} - \frac{72 c d^{2} e^{2} g^{2} x^{2}}{6 d^{3} e^{5} + 18 d^{2} e^{6} x + 18 d e^{7} x^{2} + 6 e^{8} x^{3}} - \frac{6 c d e^{3} f^{2} x}{6 d^{3} e^{5} + 18 d^{2} e^{6} x + 18 d e^{7} x^{2} + 6 e^{8} x^{3}} + \frac{36 c d e^{3} f g x^{2} \log{\left(\frac{d}{e} + x \right)}}{6 d^{3} e^{5} + 18 d^{2} e^{6} x + 18 d e^{7} x^{2} + 6 e^{8} x^{3}} + \frac{36 c d e^{3} f g x^{2}}{6 d^{3} e^{5} + 18 d^{2} e^{6} x + 18 d e^{7} x^{2} + 6 e^{8} x^{3}} - \frac{24 c d e^{3} g^{2} x^{3} \log{\left(\frac{d}{e} + x \right)}}{6 d^{3} e^{5} + 18 d^{2} e^{6} x + 18 d e^{7} x^{2} + 6 e^{8} x^{3}} - \frac{6 c e^{4} f^{2} x^{2}}{6 d^{3} e^{5} + 18 d^{2} e^{6} x + 18 d e^{7} x^{2} + 6 e^{8} x^{3}} + \frac{12 c e^{4} f g x^{3} \log{\left(\frac{d}{e} + x \right)}}{6 d^{3} e^{5} + 18 d^{2} e^{6} x + 18 d e^{7} x^{2} + 6 e^{8} x^{3}} + \frac{6 c e^{4} g^{2} x^{4}}{6 d^{3} e^{5} + 18 d^{2} e^{6} x + 18 d e^{7} x^{2} + 6 e^{8} x^{3}} & \text{for}\: m = -4 \\\frac{2 a d^{2} e^{2} g^{2} \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} + \frac{3 a d^{2} e^{2} g^{2}}{2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} - \frac{2 a d e^{3} f g}{2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} + \frac{4 a d e^{3} g^{2} x \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} + \frac{4 a d e^{3} g^{2} x}{2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} - \frac{a e^{4} f^{2}}{2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} - \frac{4 a e^{4} f g x}{2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} + \frac{2 a e^{4} g^{2} x^{2} \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} - \frac{6 b d^{3} e g^{2} \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} - \frac{9 b d^{3} e g^{2}}{2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} + \frac{4 b d^{2} e^{2} f g \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} + \frac{6 b d^{2} e^{2} f g}{2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} - \frac{12 b d^{2} e^{2} g^{2} x \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} - \frac{12 b d^{2} e^{2} g^{2} x}{2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} - \frac{b d e^{3} f^{2}}{2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} + \frac{8 b d e^{3} f g x \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} + \frac{8 b d e^{3} f g x}{2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} - \frac{6 b d e^{3} g^{2} x^{2} \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} - \frac{2 b e^{4} f^{2} x}{2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} + \frac{4 b e^{4} f g x^{2} \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} + \frac{2 b e^{4} g^{2} x^{3}}{2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} + \frac{12 c d^{4} g^{2} \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} + \frac{18 c d^{4} g^{2}}{2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} - \frac{12 c d^{3} e f g \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} - \frac{18 c d^{3} e f g}{2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} + \frac{24 c d^{3} e g^{2} x \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} + \frac{24 c d^{3} e g^{2} x}{2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} + \frac{2 c d^{2} e^{2} f^{2} \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} + \frac{3 c d^{2} e^{2} f^{2}}{2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} - \frac{24 c d^{2} e^{2} f g x \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} - \frac{24 c d^{2} e^{2} f g x}{2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} + \frac{12 c d^{2} e^{2} g^{2} x^{2} \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} + \frac{4 c d e^{3} f^{2} x \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} + \frac{4 c d e^{3} f^{2} x}{2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} - \frac{12 c d e^{3} f g x^{2} \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} - \frac{4 c d e^{3} g^{2} x^{3}}{2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} + \frac{2 c e^{4} f^{2} x^{2} \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} + \frac{4 c e^{4} f g x^{3}}{2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} + \frac{c e^{4} g^{2} x^{4}}{2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} & \text{for}\: m = -3 \\- \frac{12 a d^{2} e^{2} g^{2} \log{\left(\frac{d}{e} + x \right)}}{6 d e^{5} + 6 e^{6} x} - \frac{12 a d^{2} e^{2} g^{2}}{6 d e^{5} + 6 e^{6} x} + \frac{12 a d e^{3} f g \log{\left(\frac{d}{e} + x \right)}}{6 d e^{5} + 6 e^{6} x} + \frac{12 a d e^{3} f g}{6 d e^{5} + 6 e^{6} x} - \frac{12 a d e^{3} g^{2} x \log{\left(\frac{d}{e} + x \right)}}{6 d e^{5} + 6 e^{6} x} - \frac{6 a e^{4} f^{2}}{6 d e^{5} + 6 e^{6} x} + \frac{12 a e^{4} f g x \log{\left(\frac{d}{e} + x \right)}}{6 d e^{5} + 6 e^{6} x} + \frac{6 a e^{4} g^{2} x^{2}}{6 d e^{5} + 6 e^{6} x} + \frac{18 b d^{3} e g^{2} \log{\left(\frac{d}{e} + x \right)}}{6 d e^{5} + 6 e^{6} x} + \frac{18 b d^{3} e g^{2}}{6 d e^{5} + 6 e^{6} x} - \frac{24 b d^{2} e^{2} f g \log{\left(\frac{d}{e} + x \right)}}{6 d e^{5} + 6 e^{6} x} - \frac{24 b d^{2} e^{2} f g}{6 d e^{5} + 6 e^{6} x} + \frac{18 b d^{2} e^{2} g^{2} x \log{\left(\frac{d}{e} + x \right)}}{6 d e^{5} + 6 e^{6} x} + \frac{6 b d e^{3} f^{2} \log{\left(\frac{d}{e} + x \right)}}{6 d e^{5} + 6 e^{6} x} + \frac{6 b d e^{3} f^{2}}{6 d e^{5} + 6 e^{6} x} - \frac{24 b d e^{3} f g x \log{\left(\frac{d}{e} + x \right)}}{6 d e^{5} + 6 e^{6} x} - \frac{9 b d e^{3} g^{2} x^{2}}{6 d e^{5} + 6 e^{6} x} + \frac{6 b e^{4} f^{2} x \log{\left(\frac{d}{e} + x \right)}}{6 d e^{5} + 6 e^{6} x} + \frac{12 b e^{4} f g x^{2}}{6 d e^{5} + 6 e^{6} x} + \frac{3 b e^{4} g^{2} x^{3}}{6 d e^{5} + 6 e^{6} x} - \frac{24 c d^{4} g^{2} \log{\left(\frac{d}{e} + x \right)}}{6 d e^{5} + 6 e^{6} x} - \frac{24 c d^{4} g^{2}}{6 d e^{5} + 6 e^{6} x} + \frac{36 c d^{3} e f g \log{\left(\frac{d}{e} + x \right)}}{6 d e^{5} + 6 e^{6} x} + \frac{36 c d^{3} e f g}{6 d e^{5} + 6 e^{6} x} - \frac{24 c d^{3} e g^{2} x \log{\left(\frac{d}{e} + x \right)}}{6 d e^{5} + 6 e^{6} x} - \frac{12 c d^{2} e^{2} f^{2} \log{\left(\frac{d}{e} + x \right)}}{6 d e^{5} + 6 e^{6} x} - \frac{12 c d^{2} e^{2} f^{2}}{6 d e^{5} + 6 e^{6} x} + \frac{36 c d^{2} e^{2} f g x \log{\left(\frac{d}{e} + x \right)}}{6 d e^{5} + 6 e^{6} x} + \frac{12 c d^{2} e^{2} g^{2} x^{2}}{6 d e^{5} + 6 e^{6} x} - \frac{12 c d e^{3} f^{2} x \log{\left(\frac{d}{e} + x \right)}}{6 d e^{5} + 6 e^{6} x} - \frac{18 c d e^{3} f g x^{2}}{6 d e^{5} + 6 e^{6} x} - \frac{4 c d e^{3} g^{2} x^{3}}{6 d e^{5} + 6 e^{6} x} + \frac{6 c e^{4} f^{2} x^{2}}{6 d e^{5} + 6 e^{6} x} + \frac{6 c e^{4} f g x^{3}}{6 d e^{5} + 6 e^{6} x} + \frac{2 c e^{4} g^{2} x^{4}}{6 d e^{5} + 6 e^{6} x} & \text{for}\: m = -2 \\\frac{a d^{2} g^{2} \log{\left(\frac{d}{e} + x \right)}}{e^{3}} - \frac{2 a d f g \log{\left(\frac{d}{e} + x \right)}}{e^{2}} - \frac{a d g^{2} x}{e^{2}} + \frac{a f^{2} \log{\left(\frac{d}{e} + x \right)}}{e} + \frac{2 a f g x}{e} + \frac{a g^{2} x^{2}}{2 e} - \frac{b d^{3} g^{2} \log{\left(\frac{d}{e} + x \right)}}{e^{4}} + \frac{2 b d^{2} f g \log{\left(\frac{d}{e} + x \right)}}{e^{3}} + \frac{b d^{2} g^{2} x}{e^{3}} - \frac{b d f^{2} \log{\left(\frac{d}{e} + x \right)}}{e^{2}} - \frac{2 b d f g x}{e^{2}} - \frac{b d g^{2} x^{2}}{2 e^{2}} + \frac{b f^{2} x}{e} + \frac{b f g x^{2}}{e} + \frac{b g^{2} x^{3}}{3 e} + \frac{c d^{4} g^{2} \log{\left(\frac{d}{e} + x \right)}}{e^{5}} - \frac{2 c d^{3} f g \log{\left(\frac{d}{e} + x \right)}}{e^{4}} - \frac{c d^{3} g^{2} x}{e^{4}} + \frac{c d^{2} f^{2} \log{\left(\frac{d}{e} + x \right)}}{e^{3}} + \frac{2 c d^{2} f g x}{e^{3}} + \frac{c d^{2} g^{2} x^{2}}{2 e^{3}} - \frac{c d f^{2} x}{e^{2}} - \frac{c d f g x^{2}}{e^{2}} - \frac{c d g^{2} x^{3}}{3 e^{2}} + \frac{c f^{2} x^{2}}{2 e} + \frac{2 c f g x^{3}}{3 e} + \frac{c g^{2} x^{4}}{4 e} & \text{for}\: m = -1 \\\frac{2 a d^{3} e^{2} g^{2} m^{2} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{18 a d^{3} e^{2} g^{2} m \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{40 a d^{3} e^{2} g^{2} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} - \frac{2 a d^{2} e^{3} f g m^{3} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} - \frac{24 a d^{2} e^{3} f g m^{2} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} - \frac{94 a d^{2} e^{3} f g m \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} - \frac{120 a d^{2} e^{3} f g \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} - \frac{2 a d^{2} e^{3} g^{2} m^{3} x \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} - \frac{18 a d^{2} e^{3} g^{2} m^{2} x \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} - \frac{40 a d^{2} e^{3} g^{2} m x \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{a d e^{4} f^{2} m^{4} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{14 a d e^{4} f^{2} m^{3} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{71 a d e^{4} f^{2} m^{2} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{154 a d e^{4} f^{2} m \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{120 a d e^{4} f^{2} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{2 a d e^{4} f g m^{4} x \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{24 a d e^{4} f g m^{3} x \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{94 a d e^{4} f g m^{2} x \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{120 a d e^{4} f g m x \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{a d e^{4} g^{2} m^{4} x^{2} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{10 a d e^{4} g^{2} m^{3} x^{2} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{29 a d e^{4} g^{2} m^{2} x^{2} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{20 a d e^{4} g^{2} m x^{2} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{a e^{5} f^{2} m^{4} x \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{14 a e^{5} f^{2} m^{3} x \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{71 a e^{5} f^{2} m^{2} x \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{154 a e^{5} f^{2} m x \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{120 a e^{5} f^{2} x \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{2 a e^{5} f g m^{4} x^{2} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{26 a e^{5} f g m^{3} x^{2} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{118 a e^{5} f g m^{2} x^{2} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{214 a e^{5} f g m x^{2} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{120 a e^{5} f g x^{2} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{a e^{5} g^{2} m^{4} x^{3} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{12 a e^{5} g^{2} m^{3} x^{3} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{49 a e^{5} g^{2} m^{2} x^{3} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{78 a e^{5} g^{2} m x^{3} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{40 a e^{5} g^{2} x^{3} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} - \frac{6 b d^{4} e g^{2} m \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} - \frac{30 b d^{4} e g^{2} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{4 b d^{3} e^{2} f g m^{2} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{36 b d^{3} e^{2} f g m \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{80 b d^{3} e^{2} f g \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{6 b d^{3} e^{2} g^{2} m^{2} x \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{30 b d^{3} e^{2} g^{2} m x \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} - \frac{b d^{2} e^{3} f^{2} m^{3} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} - \frac{12 b d^{2} e^{3} f^{2} m^{2} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} - \frac{47 b d^{2} e^{3} f^{2} m \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} - \frac{60 b d^{2} e^{3} f^{2} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} - \frac{4 b d^{2} e^{3} f g m^{3} x \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} - \frac{36 b d^{2} e^{3} f g m^{2} x \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} - \frac{80 b d^{2} e^{3} f g m x \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} - \frac{3 b d^{2} e^{3} g^{2} m^{3} x^{2} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} - \frac{18 b d^{2} e^{3} g^{2} m^{2} x^{2} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} - \frac{15 b d^{2} e^{3} g^{2} m x^{2} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{b d e^{4} f^{2} m^{4} x \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{12 b d e^{4} f^{2} m^{3} x \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{47 b d e^{4} f^{2} m^{2} x \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{60 b d e^{4} f^{2} m x \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{2 b d e^{4} f g m^{4} x^{2} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{20 b d e^{4} f g m^{3} x^{2} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{58 b d e^{4} f g m^{2} x^{2} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{40 b d e^{4} f g m x^{2} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{b d e^{4} g^{2} m^{4} x^{3} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{8 b d e^{4} g^{2} m^{3} x^{3} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{17 b d e^{4} g^{2} m^{2} x^{3} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{10 b d e^{4} g^{2} m x^{3} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{b e^{5} f^{2} m^{4} x^{2} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{13 b e^{5} f^{2} m^{3} x^{2} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{59 b e^{5} f^{2} m^{2} x^{2} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{107 b e^{5} f^{2} m x^{2} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{60 b e^{5} f^{2} x^{2} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{2 b e^{5} f g m^{4} x^{3} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{24 b e^{5} f g m^{3} x^{3} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{98 b e^{5} f g m^{2} x^{3} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{156 b e^{5} f g m x^{3} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{80 b e^{5} f g x^{3} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{b e^{5} g^{2} m^{4} x^{4} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{11 b e^{5} g^{2} m^{3} x^{4} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{41 b e^{5} g^{2} m^{2} x^{4} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{61 b e^{5} g^{2} m x^{4} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{30 b e^{5} g^{2} x^{4} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{24 c d^{5} g^{2} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} - \frac{12 c d^{4} e f g m \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} - \frac{60 c d^{4} e f g \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} - \frac{24 c d^{4} e g^{2} m x \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{2 c d^{3} e^{2} f^{2} m^{2} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{18 c d^{3} e^{2} f^{2} m \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{40 c d^{3} e^{2} f^{2} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{12 c d^{3} e^{2} f g m^{2} x \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{60 c d^{3} e^{2} f g m x \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{12 c d^{3} e^{2} g^{2} m^{2} x^{2} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{12 c d^{3} e^{2} g^{2} m x^{2} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} - \frac{2 c d^{2} e^{3} f^{2} m^{3} x \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} - \frac{18 c d^{2} e^{3} f^{2} m^{2} x \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} - \frac{40 c d^{2} e^{3} f^{2} m x \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} - \frac{6 c d^{2} e^{3} f g m^{3} x^{2} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} - \frac{36 c d^{2} e^{3} f g m^{2} x^{2} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} - \frac{30 c d^{2} e^{3} f g m x^{2} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} - \frac{4 c d^{2} e^{3} g^{2} m^{3} x^{3} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} - \frac{12 c d^{2} e^{3} g^{2} m^{2} x^{3} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} - \frac{8 c d^{2} e^{3} g^{2} m x^{3} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{c d e^{4} f^{2} m^{4} x^{2} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{10 c d e^{4} f^{2} m^{3} x^{2} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{29 c d e^{4} f^{2} m^{2} x^{2} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{20 c d e^{4} f^{2} m x^{2} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{2 c d e^{4} f g m^{4} x^{3} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{16 c d e^{4} f g m^{3} x^{3} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{34 c d e^{4} f g m^{2} x^{3} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{20 c d e^{4} f g m x^{3} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{c d e^{4} g^{2} m^{4} x^{4} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{6 c d e^{4} g^{2} m^{3} x^{4} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{11 c d e^{4} g^{2} m^{2} x^{4} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{6 c d e^{4} g^{2} m x^{4} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{c e^{5} f^{2} m^{4} x^{3} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{12 c e^{5} f^{2} m^{3} x^{3} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{49 c e^{5} f^{2} m^{2} x^{3} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{78 c e^{5} f^{2} m x^{3} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{40 c e^{5} f^{2} x^{3} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{2 c e^{5} f g m^{4} x^{4} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{22 c e^{5} f g m^{3} x^{4} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{82 c e^{5} f g m^{2} x^{4} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{122 c e^{5} f g m x^{4} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{60 c e^{5} f g x^{4} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{c e^{5} g^{2} m^{4} x^{5} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{10 c e^{5} g^{2} m^{3} x^{5} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{35 c e^{5} g^{2} m^{2} x^{5} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{50 c e^{5} g^{2} m x^{5} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} + \frac{24 c e^{5} g^{2} x^{5} \left(d + e x\right)^{m}}{e^{5} m^{5} + 15 e^{5} m^{4} + 85 e^{5} m^{3} + 225 e^{5} m^{2} + 274 e^{5} m + 120 e^{5}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((d**m*(a*f**2*x + a*f*g*x**2 + a*g**2*x**3/3 + b*f**2*x**2/2 + 2*b*f*g*x**3/3 + b*g**2*x**4/4 + c*f**2*x**3/3 + c*f*g*x**4/2 + c*g**2*x**5/5), Eq(e, 0)), (-a*d**2*e**2*g**2/(12*d**4*e**5 + 48*d**3*e**6*x + 72*d**2*e**7*x**2 + 48*d*e**8*x**3 + 12*e**9*x**4) - 2*a*d*e**3*f*g/(12*d**4*e**5 + 48*d**3*e**6*x + 72*d**2*e**7*x**2 + 48*d*e**8*x**3 + 12*e**9*x**4) - 4*a*d*e**3*g**2*x/(12*d**4*e**5 + 48*d**3*e**6*x + 72*d**2*e**7*x**2 + 48*d*e**8*x**3 + 12*e**9*x**4) - 3*a*e**4*f**2/(12*d**4*e**5 + 48*d**3*e**6*x + 72*d**2*e**7*x**2 + 48*d*e**8*x**3 + 12*e**9*x**4) - 8*a*e**4*f*g*x/(12*d**4*e**5 + 48*d**3*e**6*x + 72*d**2*e**7*x**2 + 48*d*e**8*x**3 + 12*e**9*x**4) - 6*a*e**4*g**2*x**2/(12*d**4*e**5 + 48*d**3*e**6*x + 72*d**2*e**7*x**2 + 48*d*e**8*x**3 + 12*e**9*x**4) - 3*b*d**3*e*g**2/(12*d**4*e**5 + 48*d**3*e**6*x + 72*d**2*e**7*x**2 + 48*d*e**8*x**3 + 12*e**9*x**4) - 2*b*d**2*e**2*f*g/(12*d**4*e**5 + 48*d**3*e**6*x + 72*d**2*e**7*x**2 + 48*d*e**8*x**3 + 12*e**9*x**4) - 12*b*d**2*e**2*g**2*x/(12*d**4*e**5 + 48*d**3*e**6*x + 72*d**2*e**7*x**2 + 48*d*e**8*x**3 + 12*e**9*x**4) - b*d*e**3*f**2/(12*d**4*e**5 + 48*d**3*e**6*x + 72*d**2*e**7*x**2 + 48*d*e**8*x**3 + 12*e**9*x**4) - 8*b*d*e**3*f*g*x/(12*d**4*e**5 + 48*d**3*e**6*x + 72*d**2*e**7*x**2 + 48*d*e**8*x**3 + 12*e**9*x**4) - 18*b*d*e**3*g**2*x**2/(12*d**4*e**5 + 48*d**3*e**6*x + 72*d**2*e**7*x**2 + 48*d*e**8*x**3 + 12*e**9*x**4) - 4*b*e**4*f**2*x/(12*d**4*e**5 + 48*d**3*e**6*x + 72*d**2*e**7*x**2 + 48*d*e**8*x**3 + 12*e**9*x**4) - 12*b*e**4*f*g*x**2/(12*d**4*e**5 + 48*d**3*e**6*x + 72*d**2*e**7*x**2 + 48*d*e**8*x**3 + 12*e**9*x**4) - 12*b*e**4*g**2*x**3/(12*d**4*e**5 + 48*d**3*e**6*x + 72*d**2*e**7*x**2 + 48*d*e**8*x**3 + 12*e**9*x**4) + 12*c*d**4*g**2*log(d/e + x)/(12*d**4*e**5 + 48*d**3*e**6*x + 72*d**2*e**7*x**2 + 48*d*e**8*x**3 + 12*e**9*x**4) + 25*c*d**4*g**2/(12*d**4*e**5 + 48*d**3*e**6*x + 72*d**2*e**7*x**2 + 48*d*e**8*x**3 + 12*e**9*x**4) - 6*c*d**3*e*f*g/(12*d**4*e**5 + 48*d**3*e**6*x + 72*d**2*e**7*x**2 + 48*d*e**8*x**3 + 12*e**9*x**4) + 48*c*d**3*e*g**2*x*log(d/e + x)/(12*d**4*e**5 + 48*d**3*e**6*x + 72*d**2*e**7*x**2 + 48*d*e**8*x**3 + 12*e**9*x**4) + 88*c*d**3*e*g**2*x/(12*d**4*e**5 + 48*d**3*e**6*x + 72*d**2*e**7*x**2 + 48*d*e**8*x**3 + 12*e**9*x**4) - c*d**2*e**2*f**2/(12*d**4*e**5 + 48*d**3*e**6*x + 72*d**2*e**7*x**2 + 48*d*e**8*x**3 + 12*e**9*x**4) - 24*c*d**2*e**2*f*g*x/(12*d**4*e**5 + 48*d**3*e**6*x + 72*d**2*e**7*x**2 + 48*d*e**8*x**3 + 12*e**9*x**4) + 72*c*d**2*e**2*g**2*x**2*log(d/e + x)/(12*d**4*e**5 + 48*d**3*e**6*x + 72*d**2*e**7*x**2 + 48*d*e**8*x**3 + 12*e**9*x**4) + 108*c*d**2*e**2*g**2*x**2/(12*d**4*e**5 + 48*d**3*e**6*x + 72*d**2*e**7*x**2 + 48*d*e**8*x**3 + 12*e**9*x**4) - 4*c*d*e**3*f**2*x/(12*d**4*e**5 + 48*d**3*e**6*x + 72*d**2*e**7*x**2 + 48*d*e**8*x**3 + 12*e**9*x**4) - 36*c*d*e**3*f*g*x**2/(12*d**4*e**5 + 48*d**3*e**6*x + 72*d**2*e**7*x**2 + 48*d*e**8*x**3 + 12*e**9*x**4) + 48*c*d*e**3*g**2*x**3*log(d/e + x)/(12*d**4*e**5 + 48*d**3*e**6*x + 72*d**2*e**7*x**2 + 48*d*e**8*x**3 + 12*e**9*x**4) + 48*c*d*e**3*g**2*x**3/(12*d**4*e**5 + 48*d**3*e**6*x + 72*d**2*e**7*x**2 + 48*d*e**8*x**3 + 12*e**9*x**4) - 6*c*e**4*f**2*x**2/(12*d**4*e**5 + 48*d**3*e**6*x + 72*d**2*e**7*x**2 + 48*d*e**8*x**3 + 12*e**9*x**4) - 24*c*e**4*f*g*x**3/(12*d**4*e**5 + 48*d**3*e**6*x + 72*d**2*e**7*x**2 + 48*d*e**8*x**3 + 12*e**9*x**4) + 12*c*e**4*g**2*x**4*log(d/e + x)/(12*d**4*e**5 + 48*d**3*e**6*x + 72*d**2*e**7*x**2 + 48*d*e**8*x**3 + 12*e**9*x**4), Eq(m, -5)), (-2*a*d**2*e**2*g**2/(6*d**3*e**5 + 18*d**2*e**6*x + 18*d*e**7*x**2 + 6*e**8*x**3) - 2*a*d*e**3*f*g/(6*d**3*e**5 + 18*d**2*e**6*x + 18*d*e**7*x**2 + 6*e**8*x**3) - 6*a*d*e**3*g**2*x/(6*d**3*e**5 + 18*d**2*e**6*x + 18*d*e**7*x**2 + 6*e**8*x**3) - 2*a*e**4*f**2/(6*d**3*e**5 + 18*d**2*e**6*x + 18*d*e**7*x**2 + 6*e**8*x**3) - 6*a*e**4*f*g*x/(6*d**3*e**5 + 18*d**2*e**6*x + 18*d*e**7*x**2 + 6*e**8*x**3) - 6*a*e**4*g**2*x**2/(6*d**3*e**5 + 18*d**2*e**6*x + 18*d*e**7*x**2 + 6*e**8*x**3) + 6*b*d**3*e*g**2*log(d/e + x)/(6*d**3*e**5 + 18*d**2*e**6*x + 18*d*e**7*x**2 + 6*e**8*x**3) + 11*b*d**3*e*g**2/(6*d**3*e**5 + 18*d**2*e**6*x + 18*d*e**7*x**2 + 6*e**8*x**3) - 4*b*d**2*e**2*f*g/(6*d**3*e**5 + 18*d**2*e**6*x + 18*d*e**7*x**2 + 6*e**8*x**3) + 18*b*d**2*e**2*g**2*x*log(d/e + x)/(6*d**3*e**5 + 18*d**2*e**6*x + 18*d*e**7*x**2 + 6*e**8*x**3) + 27*b*d**2*e**2*g**2*x/(6*d**3*e**5 + 18*d**2*e**6*x + 18*d*e**7*x**2 + 6*e**8*x**3) - b*d*e**3*f**2/(6*d**3*e**5 + 18*d**2*e**6*x + 18*d*e**7*x**2 + 6*e**8*x**3) - 12*b*d*e**3*f*g*x/(6*d**3*e**5 + 18*d**2*e**6*x + 18*d*e**7*x**2 + 6*e**8*x**3) + 18*b*d*e**3*g**2*x**2*log(d/e + x)/(6*d**3*e**5 + 18*d**2*e**6*x + 18*d*e**7*x**2 + 6*e**8*x**3) + 18*b*d*e**3*g**2*x**2/(6*d**3*e**5 + 18*d**2*e**6*x + 18*d*e**7*x**2 + 6*e**8*x**3) - 3*b*e**4*f**2*x/(6*d**3*e**5 + 18*d**2*e**6*x + 18*d*e**7*x**2 + 6*e**8*x**3) - 12*b*e**4*f*g*x**2/(6*d**3*e**5 + 18*d**2*e**6*x + 18*d*e**7*x**2 + 6*e**8*x**3) + 6*b*e**4*g**2*x**3*log(d/e + x)/(6*d**3*e**5 + 18*d**2*e**6*x + 18*d*e**7*x**2 + 6*e**8*x**3) - 24*c*d**4*g**2*log(d/e + x)/(6*d**3*e**5 + 18*d**2*e**6*x + 18*d*e**7*x**2 + 6*e**8*x**3) - 44*c*d**4*g**2/(6*d**3*e**5 + 18*d**2*e**6*x + 18*d*e**7*x**2 + 6*e**8*x**3) + 12*c*d**3*e*f*g*log(d/e + x)/(6*d**3*e**5 + 18*d**2*e**6*x + 18*d*e**7*x**2 + 6*e**8*x**3) + 22*c*d**3*e*f*g/(6*d**3*e**5 + 18*d**2*e**6*x + 18*d*e**7*x**2 + 6*e**8*x**3) - 72*c*d**3*e*g**2*x*log(d/e + x)/(6*d**3*e**5 + 18*d**2*e**6*x + 18*d*e**7*x**2 + 6*e**8*x**3) - 108*c*d**3*e*g**2*x/(6*d**3*e**5 + 18*d**2*e**6*x + 18*d*e**7*x**2 + 6*e**8*x**3) - 2*c*d**2*e**2*f**2/(6*d**3*e**5 + 18*d**2*e**6*x + 18*d*e**7*x**2 + 6*e**8*x**3) + 36*c*d**2*e**2*f*g*x*log(d/e + x)/(6*d**3*e**5 + 18*d**2*e**6*x + 18*d*e**7*x**2 + 6*e**8*x**3) + 54*c*d**2*e**2*f*g*x/(6*d**3*e**5 + 18*d**2*e**6*x + 18*d*e**7*x**2 + 6*e**8*x**3) - 72*c*d**2*e**2*g**2*x**2*log(d/e + x)/(6*d**3*e**5 + 18*d**2*e**6*x + 18*d*e**7*x**2 + 6*e**8*x**3) - 72*c*d**2*e**2*g**2*x**2/(6*d**3*e**5 + 18*d**2*e**6*x + 18*d*e**7*x**2 + 6*e**8*x**3) - 6*c*d*e**3*f**2*x/(6*d**3*e**5 + 18*d**2*e**6*x + 18*d*e**7*x**2 + 6*e**8*x**3) + 36*c*d*e**3*f*g*x**2*log(d/e + x)/(6*d**3*e**5 + 18*d**2*e**6*x + 18*d*e**7*x**2 + 6*e**8*x**3) + 36*c*d*e**3*f*g*x**2/(6*d**3*e**5 + 18*d**2*e**6*x + 18*d*e**7*x**2 + 6*e**8*x**3) - 24*c*d*e**3*g**2*x**3*log(d/e + x)/(6*d**3*e**5 + 18*d**2*e**6*x + 18*d*e**7*x**2 + 6*e**8*x**3) - 6*c*e**4*f**2*x**2/(6*d**3*e**5 + 18*d**2*e**6*x + 18*d*e**7*x**2 + 6*e**8*x**3) + 12*c*e**4*f*g*x**3*log(d/e + x)/(6*d**3*e**5 + 18*d**2*e**6*x + 18*d*e**7*x**2 + 6*e**8*x**3) + 6*c*e**4*g**2*x**4/(6*d**3*e**5 + 18*d**2*e**6*x + 18*d*e**7*x**2 + 6*e**8*x**3), Eq(m, -4)), (2*a*d**2*e**2*g**2*log(d/e + x)/(2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) + 3*a*d**2*e**2*g**2/(2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) - 2*a*d*e**3*f*g/(2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) + 4*a*d*e**3*g**2*x*log(d/e + x)/(2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) + 4*a*d*e**3*g**2*x/(2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) - a*e**4*f**2/(2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) - 4*a*e**4*f*g*x/(2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) + 2*a*e**4*g**2*x**2*log(d/e + x)/(2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) - 6*b*d**3*e*g**2*log(d/e + x)/(2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) - 9*b*d**3*e*g**2/(2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) + 4*b*d**2*e**2*f*g*log(d/e + x)/(2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) + 6*b*d**2*e**2*f*g/(2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) - 12*b*d**2*e**2*g**2*x*log(d/e + x)/(2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) - 12*b*d**2*e**2*g**2*x/(2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) - b*d*e**3*f**2/(2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) + 8*b*d*e**3*f*g*x*log(d/e + x)/(2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) + 8*b*d*e**3*f*g*x/(2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) - 6*b*d*e**3*g**2*x**2*log(d/e + x)/(2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) - 2*b*e**4*f**2*x/(2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) + 4*b*e**4*f*g*x**2*log(d/e + x)/(2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) + 2*b*e**4*g**2*x**3/(2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) + 12*c*d**4*g**2*log(d/e + x)/(2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) + 18*c*d**4*g**2/(2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) - 12*c*d**3*e*f*g*log(d/e + x)/(2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) - 18*c*d**3*e*f*g/(2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) + 24*c*d**3*e*g**2*x*log(d/e + x)/(2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) + 24*c*d**3*e*g**2*x/(2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) + 2*c*d**2*e**2*f**2*log(d/e + x)/(2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) + 3*c*d**2*e**2*f**2/(2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) - 24*c*d**2*e**2*f*g*x*log(d/e + x)/(2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) - 24*c*d**2*e**2*f*g*x/(2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) + 12*c*d**2*e**2*g**2*x**2*log(d/e + x)/(2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) + 4*c*d*e**3*f**2*x*log(d/e + x)/(2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) + 4*c*d*e**3*f**2*x/(2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) - 12*c*d*e**3*f*g*x**2*log(d/e + x)/(2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) - 4*c*d*e**3*g**2*x**3/(2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) + 2*c*e**4*f**2*x**2*log(d/e + x)/(2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) + 4*c*e**4*f*g*x**3/(2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) + c*e**4*g**2*x**4/(2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2), Eq(m, -3)), (-12*a*d**2*e**2*g**2*log(d/e + x)/(6*d*e**5 + 6*e**6*x) - 12*a*d**2*e**2*g**2/(6*d*e**5 + 6*e**6*x) + 12*a*d*e**3*f*g*log(d/e + x)/(6*d*e**5 + 6*e**6*x) + 12*a*d*e**3*f*g/(6*d*e**5 + 6*e**6*x) - 12*a*d*e**3*g**2*x*log(d/e + x)/(6*d*e**5 + 6*e**6*x) - 6*a*e**4*f**2/(6*d*e**5 + 6*e**6*x) + 12*a*e**4*f*g*x*log(d/e + x)/(6*d*e**5 + 6*e**6*x) + 6*a*e**4*g**2*x**2/(6*d*e**5 + 6*e**6*x) + 18*b*d**3*e*g**2*log(d/e + x)/(6*d*e**5 + 6*e**6*x) + 18*b*d**3*e*g**2/(6*d*e**5 + 6*e**6*x) - 24*b*d**2*e**2*f*g*log(d/e + x)/(6*d*e**5 + 6*e**6*x) - 24*b*d**2*e**2*f*g/(6*d*e**5 + 6*e**6*x) + 18*b*d**2*e**2*g**2*x*log(d/e + x)/(6*d*e**5 + 6*e**6*x) + 6*b*d*e**3*f**2*log(d/e + x)/(6*d*e**5 + 6*e**6*x) + 6*b*d*e**3*f**2/(6*d*e**5 + 6*e**6*x) - 24*b*d*e**3*f*g*x*log(d/e + x)/(6*d*e**5 + 6*e**6*x) - 9*b*d*e**3*g**2*x**2/(6*d*e**5 + 6*e**6*x) + 6*b*e**4*f**2*x*log(d/e + x)/(6*d*e**5 + 6*e**6*x) + 12*b*e**4*f*g*x**2/(6*d*e**5 + 6*e**6*x) + 3*b*e**4*g**2*x**3/(6*d*e**5 + 6*e**6*x) - 24*c*d**4*g**2*log(d/e + x)/(6*d*e**5 + 6*e**6*x) - 24*c*d**4*g**2/(6*d*e**5 + 6*e**6*x) + 36*c*d**3*e*f*g*log(d/e + x)/(6*d*e**5 + 6*e**6*x) + 36*c*d**3*e*f*g/(6*d*e**5 + 6*e**6*x) - 24*c*d**3*e*g**2*x*log(d/e + x)/(6*d*e**5 + 6*e**6*x) - 12*c*d**2*e**2*f**2*log(d/e + x)/(6*d*e**5 + 6*e**6*x) - 12*c*d**2*e**2*f**2/(6*d*e**5 + 6*e**6*x) + 36*c*d**2*e**2*f*g*x*log(d/e + x)/(6*d*e**5 + 6*e**6*x) + 12*c*d**2*e**2*g**2*x**2/(6*d*e**5 + 6*e**6*x) - 12*c*d*e**3*f**2*x*log(d/e + x)/(6*d*e**5 + 6*e**6*x) - 18*c*d*e**3*f*g*x**2/(6*d*e**5 + 6*e**6*x) - 4*c*d*e**3*g**2*x**3/(6*d*e**5 + 6*e**6*x) + 6*c*e**4*f**2*x**2/(6*d*e**5 + 6*e**6*x) + 6*c*e**4*f*g*x**3/(6*d*e**5 + 6*e**6*x) + 2*c*e**4*g**2*x**4/(6*d*e**5 + 6*e**6*x), Eq(m, -2)), (a*d**2*g**2*log(d/e + x)/e**3 - 2*a*d*f*g*log(d/e + x)/e**2 - a*d*g**2*x/e**2 + a*f**2*log(d/e + x)/e + 2*a*f*g*x/e + a*g**2*x**2/(2*e) - b*d**3*g**2*log(d/e + x)/e**4 + 2*b*d**2*f*g*log(d/e + x)/e**3 + b*d**2*g**2*x/e**3 - b*d*f**2*log(d/e + x)/e**2 - 2*b*d*f*g*x/e**2 - b*d*g**2*x**2/(2*e**2) + b*f**2*x/e + b*f*g*x**2/e + b*g**2*x**3/(3*e) + c*d**4*g**2*log(d/e + x)/e**5 - 2*c*d**3*f*g*log(d/e + x)/e**4 - c*d**3*g**2*x/e**4 + c*d**2*f**2*log(d/e + x)/e**3 + 2*c*d**2*f*g*x/e**3 + c*d**2*g**2*x**2/(2*e**3) - c*d*f**2*x/e**2 - c*d*f*g*x**2/e**2 - c*d*g**2*x**3/(3*e**2) + c*f**2*x**2/(2*e) + 2*c*f*g*x**3/(3*e) + c*g**2*x**4/(4*e), Eq(m, -1)), (2*a*d**3*e**2*g**2*m**2*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 18*a*d**3*e**2*g**2*m*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 40*a*d**3*e**2*g**2*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) - 2*a*d**2*e**3*f*g*m**3*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) - 24*a*d**2*e**3*f*g*m**2*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) - 94*a*d**2*e**3*f*g*m*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) - 120*a*d**2*e**3*f*g*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) - 2*a*d**2*e**3*g**2*m**3*x*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) - 18*a*d**2*e**3*g**2*m**2*x*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) - 40*a*d**2*e**3*g**2*m*x*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + a*d*e**4*f**2*m**4*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 14*a*d*e**4*f**2*m**3*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 71*a*d*e**4*f**2*m**2*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 154*a*d*e**4*f**2*m*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 120*a*d*e**4*f**2*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 2*a*d*e**4*f*g*m**4*x*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 24*a*d*e**4*f*g*m**3*x*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 94*a*d*e**4*f*g*m**2*x*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 120*a*d*e**4*f*g*m*x*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + a*d*e**4*g**2*m**4*x**2*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 10*a*d*e**4*g**2*m**3*x**2*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 29*a*d*e**4*g**2*m**2*x**2*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 20*a*d*e**4*g**2*m*x**2*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + a*e**5*f**2*m**4*x*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 14*a*e**5*f**2*m**3*x*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 71*a*e**5*f**2*m**2*x*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 154*a*e**5*f**2*m*x*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 120*a*e**5*f**2*x*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 2*a*e**5*f*g*m**4*x**2*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 26*a*e**5*f*g*m**3*x**2*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 118*a*e**5*f*g*m**2*x**2*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 214*a*e**5*f*g*m*x**2*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 120*a*e**5*f*g*x**2*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + a*e**5*g**2*m**4*x**3*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 12*a*e**5*g**2*m**3*x**3*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 49*a*e**5*g**2*m**2*x**3*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 78*a*e**5*g**2*m*x**3*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 40*a*e**5*g**2*x**3*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) - 6*b*d**4*e*g**2*m*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) - 30*b*d**4*e*g**2*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 4*b*d**3*e**2*f*g*m**2*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 36*b*d**3*e**2*f*g*m*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 80*b*d**3*e**2*f*g*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 6*b*d**3*e**2*g**2*m**2*x*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 30*b*d**3*e**2*g**2*m*x*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) - b*d**2*e**3*f**2*m**3*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) - 12*b*d**2*e**3*f**2*m**2*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) - 47*b*d**2*e**3*f**2*m*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) - 60*b*d**2*e**3*f**2*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) - 4*b*d**2*e**3*f*g*m**3*x*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) - 36*b*d**2*e**3*f*g*m**2*x*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) - 80*b*d**2*e**3*f*g*m*x*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) - 3*b*d**2*e**3*g**2*m**3*x**2*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) - 18*b*d**2*e**3*g**2*m**2*x**2*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) - 15*b*d**2*e**3*g**2*m*x**2*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + b*d*e**4*f**2*m**4*x*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 12*b*d*e**4*f**2*m**3*x*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 47*b*d*e**4*f**2*m**2*x*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 60*b*d*e**4*f**2*m*x*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 2*b*d*e**4*f*g*m**4*x**2*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 20*b*d*e**4*f*g*m**3*x**2*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 58*b*d*e**4*f*g*m**2*x**2*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 40*b*d*e**4*f*g*m*x**2*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + b*d*e**4*g**2*m**4*x**3*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 8*b*d*e**4*g**2*m**3*x**3*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 17*b*d*e**4*g**2*m**2*x**3*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 10*b*d*e**4*g**2*m*x**3*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + b*e**5*f**2*m**4*x**2*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 13*b*e**5*f**2*m**3*x**2*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 59*b*e**5*f**2*m**2*x**2*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 107*b*e**5*f**2*m*x**2*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 60*b*e**5*f**2*x**2*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 2*b*e**5*f*g*m**4*x**3*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 24*b*e**5*f*g*m**3*x**3*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 98*b*e**5*f*g*m**2*x**3*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 156*b*e**5*f*g*m*x**3*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 80*b*e**5*f*g*x**3*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + b*e**5*g**2*m**4*x**4*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 11*b*e**5*g**2*m**3*x**4*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 41*b*e**5*g**2*m**2*x**4*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 61*b*e**5*g**2*m*x**4*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 30*b*e**5*g**2*x**4*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 24*c*d**5*g**2*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) - 12*c*d**4*e*f*g*m*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) - 60*c*d**4*e*f*g*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) - 24*c*d**4*e*g**2*m*x*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 2*c*d**3*e**2*f**2*m**2*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 18*c*d**3*e**2*f**2*m*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 40*c*d**3*e**2*f**2*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 12*c*d**3*e**2*f*g*m**2*x*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 60*c*d**3*e**2*f*g*m*x*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 12*c*d**3*e**2*g**2*m**2*x**2*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 12*c*d**3*e**2*g**2*m*x**2*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) - 2*c*d**2*e**3*f**2*m**3*x*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) - 18*c*d**2*e**3*f**2*m**2*x*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) - 40*c*d**2*e**3*f**2*m*x*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) - 6*c*d**2*e**3*f*g*m**3*x**2*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) - 36*c*d**2*e**3*f*g*m**2*x**2*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) - 30*c*d**2*e**3*f*g*m*x**2*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) - 4*c*d**2*e**3*g**2*m**3*x**3*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) - 12*c*d**2*e**3*g**2*m**2*x**3*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) - 8*c*d**2*e**3*g**2*m*x**3*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + c*d*e**4*f**2*m**4*x**2*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 10*c*d*e**4*f**2*m**3*x**2*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 29*c*d*e**4*f**2*m**2*x**2*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 20*c*d*e**4*f**2*m*x**2*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 2*c*d*e**4*f*g*m**4*x**3*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 16*c*d*e**4*f*g*m**3*x**3*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 34*c*d*e**4*f*g*m**2*x**3*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 20*c*d*e**4*f*g*m*x**3*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + c*d*e**4*g**2*m**4*x**4*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 6*c*d*e**4*g**2*m**3*x**4*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 11*c*d*e**4*g**2*m**2*x**4*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 6*c*d*e**4*g**2*m*x**4*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + c*e**5*f**2*m**4*x**3*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 12*c*e**5*f**2*m**3*x**3*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 49*c*e**5*f**2*m**2*x**3*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 78*c*e**5*f**2*m*x**3*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 40*c*e**5*f**2*x**3*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 2*c*e**5*f*g*m**4*x**4*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 22*c*e**5*f*g*m**3*x**4*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 82*c*e**5*f*g*m**2*x**4*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 122*c*e**5*f*g*m*x**4*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 60*c*e**5*f*g*x**4*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + c*e**5*g**2*m**4*x**5*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 10*c*e**5*g**2*m**3*x**5*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 35*c*e**5*g**2*m**2*x**5*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 50*c*e**5*g**2*m*x**5*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5) + 24*c*e**5*g**2*x**5*(d + e*x)**m/(e**5*m**5 + 15*e**5*m**4 + 85*e**5*m**3 + 225*e**5*m**2 + 274*e**5*m + 120*e**5), True))","A",0
921,1,5930,0,5.863416," ","integrate((e*x+d)**m*(g*x+f)*(c*x**2+b*x+a),x)","\begin{cases} d^{m} \left(a f x + \frac{a g x^{2}}{2} + \frac{b f x^{2}}{2} + \frac{b g x^{3}}{3} + \frac{c f x^{3}}{3} + \frac{c g x^{4}}{4}\right) & \text{for}\: e = 0 \\- \frac{a d e^{2} g}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} - \frac{2 a e^{3} f}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} - \frac{3 a e^{3} g x}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} - \frac{2 b d^{2} e g}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} - \frac{b d e^{2} f}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} - \frac{6 b d e^{2} g x}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} - \frac{3 b e^{3} f x}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} - \frac{6 b e^{3} g x^{2}}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} + \frac{6 c d^{3} g \log{\left(\frac{d}{e} + x \right)}}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} + \frac{11 c d^{3} g}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} - \frac{2 c d^{2} e f}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} + \frac{18 c d^{2} e g x \log{\left(\frac{d}{e} + x \right)}}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} + \frac{27 c d^{2} e g x}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} - \frac{6 c d e^{2} f x}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} + \frac{18 c d e^{2} g x^{2} \log{\left(\frac{d}{e} + x \right)}}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} + \frac{18 c d e^{2} g x^{2}}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} - \frac{6 c e^{3} f x^{2}}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} + \frac{6 c e^{3} g x^{3} \log{\left(\frac{d}{e} + x \right)}}{6 d^{3} e^{4} + 18 d^{2} e^{5} x + 18 d e^{6} x^{2} + 6 e^{7} x^{3}} & \text{for}\: m = -4 \\- \frac{a d e^{2} g}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} - \frac{a e^{3} f}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} - \frac{2 a e^{3} g x}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} + \frac{2 b d^{2} e g \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} + \frac{3 b d^{2} e g}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} - \frac{b d e^{2} f}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} + \frac{4 b d e^{2} g x \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} + \frac{4 b d e^{2} g x}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} - \frac{2 b e^{3} f x}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} + \frac{2 b e^{3} g x^{2} \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} - \frac{6 c d^{3} g \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} - \frac{9 c d^{3} g}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} + \frac{2 c d^{2} e f \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} + \frac{3 c d^{2} e f}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} - \frac{12 c d^{2} e g x \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} - \frac{12 c d^{2} e g x}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} + \frac{4 c d e^{2} f x \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} + \frac{4 c d e^{2} f x}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} - \frac{6 c d e^{2} g x^{2} \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} + \frac{2 c e^{3} f x^{2} \log{\left(\frac{d}{e} + x \right)}}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} + \frac{2 c e^{3} g x^{3}}{2 d^{2} e^{4} + 4 d e^{5} x + 2 e^{6} x^{2}} & \text{for}\: m = -3 \\\frac{2 a d e^{2} g \log{\left(\frac{d}{e} + x \right)}}{2 d e^{4} + 2 e^{5} x} + \frac{2 a d e^{2} g}{2 d e^{4} + 2 e^{5} x} - \frac{2 a e^{3} f}{2 d e^{4} + 2 e^{5} x} + \frac{2 a e^{3} g x \log{\left(\frac{d}{e} + x \right)}}{2 d e^{4} + 2 e^{5} x} - \frac{4 b d^{2} e g \log{\left(\frac{d}{e} + x \right)}}{2 d e^{4} + 2 e^{5} x} - \frac{4 b d^{2} e g}{2 d e^{4} + 2 e^{5} x} + \frac{2 b d e^{2} f \log{\left(\frac{d}{e} + x \right)}}{2 d e^{4} + 2 e^{5} x} + \frac{2 b d e^{2} f}{2 d e^{4} + 2 e^{5} x} - \frac{4 b d e^{2} g x \log{\left(\frac{d}{e} + x \right)}}{2 d e^{4} + 2 e^{5} x} + \frac{2 b e^{3} f x \log{\left(\frac{d}{e} + x \right)}}{2 d e^{4} + 2 e^{5} x} + \frac{2 b e^{3} g x^{2}}{2 d e^{4} + 2 e^{5} x} + \frac{6 c d^{3} g \log{\left(\frac{d}{e} + x \right)}}{2 d e^{4} + 2 e^{5} x} + \frac{6 c d^{3} g}{2 d e^{4} + 2 e^{5} x} - \frac{4 c d^{2} e f \log{\left(\frac{d}{e} + x \right)}}{2 d e^{4} + 2 e^{5} x} - \frac{4 c d^{2} e f}{2 d e^{4} + 2 e^{5} x} + \frac{6 c d^{2} e g x \log{\left(\frac{d}{e} + x \right)}}{2 d e^{4} + 2 e^{5} x} - \frac{4 c d e^{2} f x \log{\left(\frac{d}{e} + x \right)}}{2 d e^{4} + 2 e^{5} x} - \frac{3 c d e^{2} g x^{2}}{2 d e^{4} + 2 e^{5} x} + \frac{2 c e^{3} f x^{2}}{2 d e^{4} + 2 e^{5} x} + \frac{c e^{3} g x^{3}}{2 d e^{4} + 2 e^{5} x} & \text{for}\: m = -2 \\- \frac{a d g \log{\left(\frac{d}{e} + x \right)}}{e^{2}} + \frac{a f \log{\left(\frac{d}{e} + x \right)}}{e} + \frac{a g x}{e} + \frac{b d^{2} g \log{\left(\frac{d}{e} + x \right)}}{e^{3}} - \frac{b d f \log{\left(\frac{d}{e} + x \right)}}{e^{2}} - \frac{b d g x}{e^{2}} + \frac{b f x}{e} + \frac{b g x^{2}}{2 e} - \frac{c d^{3} g \log{\left(\frac{d}{e} + x \right)}}{e^{4}} + \frac{c d^{2} f \log{\left(\frac{d}{e} + x \right)}}{e^{3}} + \frac{c d^{2} g x}{e^{3}} - \frac{c d f x}{e^{2}} - \frac{c d g x^{2}}{2 e^{2}} + \frac{c f x^{2}}{2 e} + \frac{c g x^{3}}{3 e} & \text{for}\: m = -1 \\- \frac{a d^{2} e^{2} g m^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} - \frac{7 a d^{2} e^{2} g m \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} - \frac{12 a d^{2} e^{2} g \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{a d e^{3} f m^{3} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{9 a d e^{3} f m^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{26 a d e^{3} f m \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{24 a d e^{3} f \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{a d e^{3} g m^{3} x \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{7 a d e^{3} g m^{2} x \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{12 a d e^{3} g m x \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{a e^{4} f m^{3} x \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{9 a e^{4} f m^{2} x \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{26 a e^{4} f m x \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{24 a e^{4} f x \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{a e^{4} g m^{3} x^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{8 a e^{4} g m^{2} x^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{19 a e^{4} g m x^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{12 a e^{4} g x^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{2 b d^{3} e g m \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{8 b d^{3} e g \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} - \frac{b d^{2} e^{2} f m^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} - \frac{7 b d^{2} e^{2} f m \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} - \frac{12 b d^{2} e^{2} f \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} - \frac{2 b d^{2} e^{2} g m^{2} x \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} - \frac{8 b d^{2} e^{2} g m x \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{b d e^{3} f m^{3} x \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{7 b d e^{3} f m^{2} x \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{12 b d e^{3} f m x \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{b d e^{3} g m^{3} x^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{5 b d e^{3} g m^{2} x^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{4 b d e^{3} g m x^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{b e^{4} f m^{3} x^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{8 b e^{4} f m^{2} x^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{19 b e^{4} f m x^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{12 b e^{4} f x^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{b e^{4} g m^{3} x^{3} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{7 b e^{4} g m^{2} x^{3} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{14 b e^{4} g m x^{3} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{8 b e^{4} g x^{3} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} - \frac{6 c d^{4} g \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{2 c d^{3} e f m \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{8 c d^{3} e f \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{6 c d^{3} e g m x \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} - \frac{2 c d^{2} e^{2} f m^{2} x \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} - \frac{8 c d^{2} e^{2} f m x \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} - \frac{3 c d^{2} e^{2} g m^{2} x^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} - \frac{3 c d^{2} e^{2} g m x^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{c d e^{3} f m^{3} x^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{5 c d e^{3} f m^{2} x^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{4 c d e^{3} f m x^{2} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{c d e^{3} g m^{3} x^{3} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{3 c d e^{3} g m^{2} x^{3} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{2 c d e^{3} g m x^{3} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{c e^{4} f m^{3} x^{3} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{7 c e^{4} f m^{2} x^{3} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{14 c e^{4} f m x^{3} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{8 c e^{4} f x^{3} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{c e^{4} g m^{3} x^{4} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{6 c e^{4} g m^{2} x^{4} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{11 c e^{4} g m x^{4} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} + \frac{6 c e^{4} g x^{4} \left(d + e x\right)^{m}}{e^{4} m^{4} + 10 e^{4} m^{3} + 35 e^{4} m^{2} + 50 e^{4} m + 24 e^{4}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((d**m*(a*f*x + a*g*x**2/2 + b*f*x**2/2 + b*g*x**3/3 + c*f*x**3/3 + c*g*x**4/4), Eq(e, 0)), (-a*d*e**2*g/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) - 2*a*e**3*f/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) - 3*a*e**3*g*x/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) - 2*b*d**2*e*g/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) - b*d*e**2*f/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) - 6*b*d*e**2*g*x/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) - 3*b*e**3*f*x/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) - 6*b*e**3*g*x**2/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) + 6*c*d**3*g*log(d/e + x)/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) + 11*c*d**3*g/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) - 2*c*d**2*e*f/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) + 18*c*d**2*e*g*x*log(d/e + x)/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) + 27*c*d**2*e*g*x/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) - 6*c*d*e**2*f*x/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) + 18*c*d*e**2*g*x**2*log(d/e + x)/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) + 18*c*d*e**2*g*x**2/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) - 6*c*e**3*f*x**2/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3) + 6*c*e**3*g*x**3*log(d/e + x)/(6*d**3*e**4 + 18*d**2*e**5*x + 18*d*e**6*x**2 + 6*e**7*x**3), Eq(m, -4)), (-a*d*e**2*g/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) - a*e**3*f/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) - 2*a*e**3*g*x/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) + 2*b*d**2*e*g*log(d/e + x)/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) + 3*b*d**2*e*g/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) - b*d*e**2*f/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) + 4*b*d*e**2*g*x*log(d/e + x)/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) + 4*b*d*e**2*g*x/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) - 2*b*e**3*f*x/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) + 2*b*e**3*g*x**2*log(d/e + x)/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) - 6*c*d**3*g*log(d/e + x)/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) - 9*c*d**3*g/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) + 2*c*d**2*e*f*log(d/e + x)/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) + 3*c*d**2*e*f/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) - 12*c*d**2*e*g*x*log(d/e + x)/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) - 12*c*d**2*e*g*x/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) + 4*c*d*e**2*f*x*log(d/e + x)/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) + 4*c*d*e**2*f*x/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) - 6*c*d*e**2*g*x**2*log(d/e + x)/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) + 2*c*e**3*f*x**2*log(d/e + x)/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2) + 2*c*e**3*g*x**3/(2*d**2*e**4 + 4*d*e**5*x + 2*e**6*x**2), Eq(m, -3)), (2*a*d*e**2*g*log(d/e + x)/(2*d*e**4 + 2*e**5*x) + 2*a*d*e**2*g/(2*d*e**4 + 2*e**5*x) - 2*a*e**3*f/(2*d*e**4 + 2*e**5*x) + 2*a*e**3*g*x*log(d/e + x)/(2*d*e**4 + 2*e**5*x) - 4*b*d**2*e*g*log(d/e + x)/(2*d*e**4 + 2*e**5*x) - 4*b*d**2*e*g/(2*d*e**4 + 2*e**5*x) + 2*b*d*e**2*f*log(d/e + x)/(2*d*e**4 + 2*e**5*x) + 2*b*d*e**2*f/(2*d*e**4 + 2*e**5*x) - 4*b*d*e**2*g*x*log(d/e + x)/(2*d*e**4 + 2*e**5*x) + 2*b*e**3*f*x*log(d/e + x)/(2*d*e**4 + 2*e**5*x) + 2*b*e**3*g*x**2/(2*d*e**4 + 2*e**5*x) + 6*c*d**3*g*log(d/e + x)/(2*d*e**4 + 2*e**5*x) + 6*c*d**3*g/(2*d*e**4 + 2*e**5*x) - 4*c*d**2*e*f*log(d/e + x)/(2*d*e**4 + 2*e**5*x) - 4*c*d**2*e*f/(2*d*e**4 + 2*e**5*x) + 6*c*d**2*e*g*x*log(d/e + x)/(2*d*e**4 + 2*e**5*x) - 4*c*d*e**2*f*x*log(d/e + x)/(2*d*e**4 + 2*e**5*x) - 3*c*d*e**2*g*x**2/(2*d*e**4 + 2*e**5*x) + 2*c*e**3*f*x**2/(2*d*e**4 + 2*e**5*x) + c*e**3*g*x**3/(2*d*e**4 + 2*e**5*x), Eq(m, -2)), (-a*d*g*log(d/e + x)/e**2 + a*f*log(d/e + x)/e + a*g*x/e + b*d**2*g*log(d/e + x)/e**3 - b*d*f*log(d/e + x)/e**2 - b*d*g*x/e**2 + b*f*x/e + b*g*x**2/(2*e) - c*d**3*g*log(d/e + x)/e**4 + c*d**2*f*log(d/e + x)/e**3 + c*d**2*g*x/e**3 - c*d*f*x/e**2 - c*d*g*x**2/(2*e**2) + c*f*x**2/(2*e) + c*g*x**3/(3*e), Eq(m, -1)), (-a*d**2*e**2*g*m**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) - 7*a*d**2*e**2*g*m*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) - 12*a*d**2*e**2*g*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + a*d*e**3*f*m**3*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 9*a*d*e**3*f*m**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 26*a*d*e**3*f*m*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 24*a*d*e**3*f*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + a*d*e**3*g*m**3*x*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 7*a*d*e**3*g*m**2*x*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 12*a*d*e**3*g*m*x*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + a*e**4*f*m**3*x*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 9*a*e**4*f*m**2*x*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 26*a*e**4*f*m*x*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 24*a*e**4*f*x*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + a*e**4*g*m**3*x**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 8*a*e**4*g*m**2*x**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 19*a*e**4*g*m*x**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 12*a*e**4*g*x**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 2*b*d**3*e*g*m*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 8*b*d**3*e*g*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) - b*d**2*e**2*f*m**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) - 7*b*d**2*e**2*f*m*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) - 12*b*d**2*e**2*f*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) - 2*b*d**2*e**2*g*m**2*x*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) - 8*b*d**2*e**2*g*m*x*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + b*d*e**3*f*m**3*x*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 7*b*d*e**3*f*m**2*x*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 12*b*d*e**3*f*m*x*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + b*d*e**3*g*m**3*x**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 5*b*d*e**3*g*m**2*x**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 4*b*d*e**3*g*m*x**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + b*e**4*f*m**3*x**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 8*b*e**4*f*m**2*x**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 19*b*e**4*f*m*x**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 12*b*e**4*f*x**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + b*e**4*g*m**3*x**3*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 7*b*e**4*g*m**2*x**3*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 14*b*e**4*g*m*x**3*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 8*b*e**4*g*x**3*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) - 6*c*d**4*g*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 2*c*d**3*e*f*m*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 8*c*d**3*e*f*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 6*c*d**3*e*g*m*x*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) - 2*c*d**2*e**2*f*m**2*x*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) - 8*c*d**2*e**2*f*m*x*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) - 3*c*d**2*e**2*g*m**2*x**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) - 3*c*d**2*e**2*g*m*x**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + c*d*e**3*f*m**3*x**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 5*c*d*e**3*f*m**2*x**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 4*c*d*e**3*f*m*x**2*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + c*d*e**3*g*m**3*x**3*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 3*c*d*e**3*g*m**2*x**3*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 2*c*d*e**3*g*m*x**3*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + c*e**4*f*m**3*x**3*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 7*c*e**4*f*m**2*x**3*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 14*c*e**4*f*m*x**3*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 8*c*e**4*f*x**3*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + c*e**4*g*m**3*x**4*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 6*c*e**4*g*m**2*x**4*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 11*c*e**4*g*m*x**4*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4) + 6*c*e**4*g*x**4*(d + e*x)**m/(e**4*m**4 + 10*e**4*m**3 + 35*e**4*m**2 + 50*e**4*m + 24*e**4), True))","A",0
922,0,0,0,0.000000," ","integrate((e*x+d)**m*(c*x**2+b*x+a)/(g*x+f),x)","\int \frac{\left(d + e x\right)^{m} \left(a + b x + c x^{2}\right)}{f + g x}\, dx"," ",0,"Integral((d + e*x)**m*(a + b*x + c*x**2)/(f + g*x), x)","F",0
923,-2,0,0,0.000000," ","integrate((e*x+d)**m*(c*x**2+b*x+a)/(g*x+f)**2,x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
924,0,0,0,0.000000," ","integrate((e*x+d)**m*(c*x**2+b*x+a)/(g*x+f)**3,x)","\int \frac{\left(d + e x\right)^{m} \left(a + b x + c x^{2}\right)}{\left(f + g x\right)^{3}}\, dx"," ",0,"Integral((d + e*x)**m*(a + b*x + c*x**2)/(f + g*x)**3, x)","F",0
925,-1,0,0,0.000000," ","integrate((e*x+d)**m*(g*x+f)**2*(c*x**2+b*x+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
926,-1,0,0,0.000000," ","integrate((e*x+d)**m*(g*x+f)*(c*x**2+b*x+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
927,0,0,0,0.000000," ","integrate((e*x+d)**m*(c*x**2+b*x+a)**2/(g*x+f),x)","\int \frac{\left(d + e x\right)^{m} \left(a + b x + c x^{2}\right)^{2}}{f + g x}\, dx"," ",0,"Integral((d + e*x)**m*(a + b*x + c*x**2)**2/(f + g*x), x)","F",0
928,-2,0,0,0.000000," ","integrate((e*x+d)**m*(c*x**2+b*x+a)**2/(g*x+f)**2,x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
929,0,0,0,0.000000," ","integrate((e*x+d)**m*(c*x**2+b*x+a)**2/(g*x+f)**3,x)","\int \frac{\left(d + e x\right)^{m} \left(a + b x + c x^{2}\right)^{2}}{\left(f + g x\right)^{3}}\, dx"," ",0,"Integral((d + e*x)**m*(a + b*x + c*x**2)**2/(f + g*x)**3, x)","F",0
930,0,0,0,0.000000," ","integrate((2+3*x)**4*(1+4*x)**m/(3*x**2-5*x+1),x)","\int \frac{\left(3 x + 2\right)^{4} \left(4 x + 1\right)^{m}}{3 x^{2} - 5 x + 1}\, dx"," ",0,"Integral((3*x + 2)**4*(4*x + 1)**m/(3*x**2 - 5*x + 1), x)","F",0
931,0,0,0,0.000000," ","integrate((2+3*x)**3*(1+4*x)**m/(3*x**2-5*x+1),x)","\int \frac{\left(3 x + 2\right)^{3} \left(4 x + 1\right)^{m}}{3 x^{2} - 5 x + 1}\, dx"," ",0,"Integral((3*x + 2)**3*(4*x + 1)**m/(3*x**2 - 5*x + 1), x)","F",0
932,0,0,0,0.000000," ","integrate((2+3*x)**2*(1+4*x)**m/(3*x**2-5*x+1),x)","\int \frac{\left(3 x + 2\right)^{2} \left(4 x + 1\right)^{m}}{3 x^{2} - 5 x + 1}\, dx"," ",0,"Integral((3*x + 2)**2*(4*x + 1)**m/(3*x**2 - 5*x + 1), x)","F",0
933,0,0,0,0.000000," ","integrate((2+3*x)*(1+4*x)**m/(3*x**2-5*x+1),x)","\int \frac{\left(3 x + 2\right) \left(4 x + 1\right)^{m}}{3 x^{2} - 5 x + 1}\, dx"," ",0,"Integral((3*x + 2)*(4*x + 1)**m/(3*x**2 - 5*x + 1), x)","F",0
934,0,0,0,0.000000," ","integrate((1+4*x)**m/(3*x**2-5*x+1),x)","\int \frac{\left(4 x + 1\right)^{m}}{3 x^{2} - 5 x + 1}\, dx"," ",0,"Integral((4*x + 1)**m/(3*x**2 - 5*x + 1), x)","F",0
935,0,0,0,0.000000," ","integrate((1+4*x)**m/(2+3*x)/(3*x**2-5*x+1),x)","\int \frac{\left(4 x + 1\right)^{m}}{\left(3 x + 2\right) \left(3 x^{2} - 5 x + 1\right)}\, dx"," ",0,"Integral((4*x + 1)**m/((3*x + 2)*(3*x**2 - 5*x + 1)), x)","F",0
936,0,0,0,0.000000," ","integrate((1+4*x)**m/(2+3*x)**2/(3*x**2-5*x+1),x)","\int \frac{\left(4 x + 1\right)^{m}}{\left(3 x + 2\right)^{2} \left(3 x^{2} - 5 x + 1\right)}\, dx"," ",0,"Integral((4*x + 1)**m/((3*x + 2)**2*(3*x**2 - 5*x + 1)), x)","F",0
937,0,0,0,0.000000," ","integrate((2+3*x)**4*(1+4*x)**m/(3*x**2-5*x+1)**2,x)","\int \frac{\left(3 x + 2\right)^{4} \left(4 x + 1\right)^{m}}{\left(3 x^{2} - 5 x + 1\right)^{2}}\, dx"," ",0,"Integral((3*x + 2)**4*(4*x + 1)**m/(3*x**2 - 5*x + 1)**2, x)","F",0
938,0,0,0,0.000000," ","integrate((2+3*x)**3*(1+4*x)**m/(3*x**2-5*x+1)**2,x)","\int \frac{\left(3 x + 2\right)^{3} \left(4 x + 1\right)^{m}}{\left(3 x^{2} - 5 x + 1\right)^{2}}\, dx"," ",0,"Integral((3*x + 2)**3*(4*x + 1)**m/(3*x**2 - 5*x + 1)**2, x)","F",0
939,0,0,0,0.000000," ","integrate((2+3*x)**2*(1+4*x)**m/(3*x**2-5*x+1)**2,x)","\int \frac{\left(3 x + 2\right)^{2} \left(4 x + 1\right)^{m}}{\left(3 x^{2} - 5 x + 1\right)^{2}}\, dx"," ",0,"Integral((3*x + 2)**2*(4*x + 1)**m/(3*x**2 - 5*x + 1)**2, x)","F",0
940,0,0,0,0.000000," ","integrate((2+3*x)*(1+4*x)**m/(3*x**2-5*x+1)**2,x)","\int \frac{\left(3 x + 2\right) \left(4 x + 1\right)^{m}}{\left(3 x^{2} - 5 x + 1\right)^{2}}\, dx"," ",0,"Integral((3*x + 2)*(4*x + 1)**m/(3*x**2 - 5*x + 1)**2, x)","F",0
941,0,0,0,0.000000," ","integrate((1+4*x)**m/(3*x**2-5*x+1)**2,x)","\int \frac{\left(4 x + 1\right)^{m}}{\left(3 x^{2} - 5 x + 1\right)^{2}}\, dx"," ",0,"Integral((4*x + 1)**m/(3*x**2 - 5*x + 1)**2, x)","F",0
942,0,0,0,0.000000," ","integrate((1+4*x)**m/(2+3*x)/(3*x**2-5*x+1)**2,x)","\int \frac{\left(4 x + 1\right)^{m}}{\left(3 x + 2\right) \left(3 x^{2} - 5 x + 1\right)^{2}}\, dx"," ",0,"Integral((4*x + 1)**m/((3*x + 2)*(3*x**2 - 5*x + 1)**2), x)","F",0
943,0,0,0,0.000000," ","integrate((1+4*x)**m/(2+3*x)**2/(3*x**2-5*x+1)**2,x)","\int \frac{\left(4 x + 1\right)^{m}}{\left(3 x + 2\right)^{2} \left(3 x^{2} - 5 x + 1\right)^{2}}\, dx"," ",0,"Integral((4*x + 1)**m/((3*x + 2)**2*(3*x**2 - 5*x + 1)**2), x)","F",0
944,-2,0,0,0.000000," ","integrate((e*x+d)**m*(c*x**2+b*x+a)/(f*x+e)**(3/2),x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
945,0,0,0,0.000000," ","integrate((e*x+d)**m*(g*x+f)**2*(c*x**2+b*x+a)**(1/2),x)","\int \left(d + e x\right)^{m} \left(f + g x\right)^{2} \sqrt{a + b x + c x^{2}}\, dx"," ",0,"Integral((d + e*x)**m*(f + g*x)**2*sqrt(a + b*x + c*x**2), x)","F",0
946,0,0,0,0.000000," ","integrate((e*x+d)**m*(g*x+f)*(c*x**2+b*x+a)**(1/2),x)","\int \left(d + e x\right)^{m} \left(f + g x\right) \sqrt{a + b x + c x^{2}}\, dx"," ",0,"Integral((d + e*x)**m*(f + g*x)*sqrt(a + b*x + c*x**2), x)","F",0
947,0,0,0,0.000000," ","integrate((e*x+d)**m*(c*x**2+b*x+a)**(1/2),x)","\int \left(d + e x\right)^{m} \sqrt{a + b x + c x^{2}}\, dx"," ",0,"Integral((d + e*x)**m*sqrt(a + b*x + c*x**2), x)","F",0
948,0,0,0,0.000000," ","integrate((e*x+d)**m*(c*x**2+b*x+a)**(1/2)/(g*x+f),x)","\int \frac{\left(d + e x\right)^{m} \sqrt{a + b x + c x^{2}}}{f + g x}\, dx"," ",0,"Integral((d + e*x)**m*sqrt(a + b*x + c*x**2)/(f + g*x), x)","F",0
949,0,0,0,0.000000," ","integrate((e*x+d)**m*(g*x+f)**2/(c*x**2+b*x+a)**(1/2),x)","\int \frac{\left(d + e x\right)^{m} \left(f + g x\right)^{2}}{\sqrt{a + b x + c x^{2}}}\, dx"," ",0,"Integral((d + e*x)**m*(f + g*x)**2/sqrt(a + b*x + c*x**2), x)","F",0
950,0,0,0,0.000000," ","integrate((e*x+d)**m*(g*x+f)/(c*x**2+b*x+a)**(1/2),x)","\int \frac{\left(d + e x\right)^{m} \left(f + g x\right)}{\sqrt{a + b x + c x^{2}}}\, dx"," ",0,"Integral((d + e*x)**m*(f + g*x)/sqrt(a + b*x + c*x**2), x)","F",0
951,0,0,0,0.000000," ","integrate((e*x+d)**m/(c*x**2+b*x+a)**(1/2),x)","\int \frac{\left(d + e x\right)^{m}}{\sqrt{a + b x + c x^{2}}}\, dx"," ",0,"Integral((d + e*x)**m/sqrt(a + b*x + c*x**2), x)","F",0
952,0,0,0,0.000000," ","integrate((e*x+d)**m/(g*x+f)/(c*x**2+b*x+a)**(1/2),x)","\int \frac{\left(d + e x\right)^{m}}{\left(f + g x\right) \sqrt{a + b x + c x^{2}}}\, dx"," ",0,"Integral((d + e*x)**m/((f + g*x)*sqrt(a + b*x + c*x**2)), x)","F",0
953,-2,0,0,0.000000," ","integrate((e*x+d)**m*(g*x+f)**n*(c*x**2+b*x+a),x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
954,-1,0,0,0.000000," ","integrate((e*x+d)**m*(g*x+f)**2*(c*x**2+b*x+a)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
955,-1,0,0,0.000000," ","integrate((e*x+d)**m*(g*x+f)*(c*x**2+b*x+a)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
956,-1,0,0,0.000000," ","integrate((e*x+d)**m*(c*x**2+b*x+a)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
957,-1,0,0,0.000000," ","integrate((e*x+d)**m*(c*x**2+b*x+a)**p/(g*x+f),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
958,0,0,0,0.000000," ","integrate(1/x**2/(1-1/c**2/x**2)**(1/2)/(e*x+d)**(1/2),x)","\int \frac{1}{x^{2} \sqrt{- \left(-1 + \frac{1}{c x}\right) \left(1 + \frac{1}{c x}\right)} \sqrt{d + e x}}\, dx"," ",0,"Integral(1/(x**2*sqrt(-(-1 + 1/(c*x))*(1 + 1/(c*x)))*sqrt(d + e*x)), x)","F",0
