1,1,1231,0,22.933556," ","integrate((e*x+d)**2*(C*x**2+B*x+A)*(-e**2*x**2+d**2)**(1/2),x)","A 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 A 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) + A 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) + B 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 B 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) + B 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) + C 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 C 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) + C 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,"A*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*A*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)) + A*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)) + B*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*B*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)) + B*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)) + C*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*C*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)) + C*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
2,1,670,0,12.771402," ","integrate((e*x+d)*(C*x**2+B*x+A)*(-e**2*x**2+d**2)**(1/2),x)","A d \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) + A 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) + B d \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) + B 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) + C 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) + C 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,"A*d*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)) + A*e*Piecewise((x**2*sqrt(d**2)/2, Eq(e**2, 0)), (-(d**2 - e**2*x**2)**(3/2)/(3*e**2), True)) + B*d*Piecewise((x**2*sqrt(d**2)/2, Eq(e**2, 0)), (-(d**2 - e**2*x**2)**(3/2)/(3*e**2), True)) + B*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)) + C*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)) + C*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
3,1,343,0,7.107684," ","integrate((C*x**2+B*x+A)*(-e**2*x**2+d**2)**(1/2),x)","A \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) + B \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) + C \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,"A*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)) + B*Piecewise((x**2*sqrt(d**2)/2, Eq(e**2, 0)), (-(d**2 - e**2*x**2)**(3/2)/(3*e**2), True)) + C*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
4,0,0,0,0.000000," ","integrate((C*x**2+B*x+A)*(-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)} \left(A + B x + C x^{2}\right)}{d + e x}\, dx"," ",0,"Integral(sqrt(-(-d + e*x)*(d + e*x))*(A + B*x + C*x**2)/(d + e*x), x)","F",0
5,0,0,0,0.000000," ","integrate((C*x**2+B*x+A)*(-e**2*x**2+d**2)**(1/2)/(e*x+d)**2,x)","\int \frac{\sqrt{- \left(- d + e x\right) \left(d + e x\right)} \left(A + B x + C x^{2}\right)}{\left(d + e x\right)^{2}}\, dx"," ",0,"Integral(sqrt(-(-d + e*x)*(d + e*x))*(A + B*x + C*x**2)/(d + e*x)**2, x)","F",0
6,0,0,0,0.000000," ","integrate((C*x**2+B*x+A)*(-e**2*x**2+d**2)**(1/2)/(e*x+d)**3,x)","\int \frac{\sqrt{- \left(- d + e x\right) \left(d + e x\right)} \left(A + B x + C x^{2}\right)}{\left(d + e x\right)^{3}}\, dx"," ",0,"Integral(sqrt(-(-d + e*x)*(d + e*x))*(A + B*x + C*x**2)/(d + e*x)**3, x)","F",0
7,0,0,0,0.000000," ","integrate((C*x**2+B*x+A)*(-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(A + B x + C x^{2}\right)}{\left(d + e x\right)^{4}}\, dx"," ",0,"Integral(sqrt(-(-d + e*x)*(d + e*x))*(A + B*x + C*x**2)/(d + e*x)**4, x)","F",0
8,0,0,0,0.000000," ","integrate((C*x**2+B*x+A)*(-e**2*x**2+d**2)**(1/2)/(e*x+d)**5,x)","\int \frac{\sqrt{- \left(- d + e x\right) \left(d + e x\right)} \left(A + B x + C x^{2}\right)}{\left(d + e x\right)^{5}}\, dx"," ",0,"Integral(sqrt(-(-d + e*x)*(d + e*x))*(A + B*x + C*x**2)/(d + e*x)**5, x)","F",0
9,-1,0,0,0.000000," ","integrate((C*x**2+B*x+A)*(-e**2*x**2+d**2)**(1/2)/(e*x+d)**6,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
10,1,1268,0,24.442861," ","integrate((e*x+d)**3*(C*x**2+B*x+A)/(-e**2*x**2+d**2)**(1/2),x)","A d^{3} \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) + 3 A d^{2} 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) + 3 A d 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) + A e^{3} \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) + B d^{3} \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) + 3 B d^{2} 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) + 3 B d 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) + B e^{3} \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) + C d^{3} \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) + 3 C d^{2} 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) + 3 C d 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) + C e^{3} \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,"A*d**3*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))) + 3*A*d**2*e*Piecewise((x**2/(2*sqrt(d**2)), Eq(e**2, 0)), (-sqrt(d**2 - e**2*x**2)/e**2, True)) + 3*A*d*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*e**3*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)) + B*d**3*Piecewise((x**2/(2*sqrt(d**2)), Eq(e**2, 0)), (-sqrt(d**2 - e**2*x**2)/e**2, True)) + 3*B*d**2*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)) + 3*B*d*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)) + B*e**3*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*d**3*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)) + 3*C*d**2*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)) + 3*C*d*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*e**3*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
11,1,891,0,18.031834," ","integrate((e*x+d)**2*(C*x**2+B*x+A)/(-e**2*x**2+d**2)**(1/2),x)","A 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 A 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) + A 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) + B 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 B 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) + B 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) + C 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 C 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) + C 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,"A*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*A*d*e*Piecewise((x**2/(2*sqrt(d**2)), Eq(e**2, 0)), (-sqrt(d**2 - e**2*x**2)/e**2, True)) + A*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)) + B*d**2*Piecewise((x**2/(2*sqrt(d**2)), Eq(e**2, 0)), (-sqrt(d**2 - e**2*x**2)/e**2, True)) + 2*B*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)) + B*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)) + C*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*C*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)) + C*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))","A",0
12,1,484,0,10.171508," ","integrate((e*x+d)*(C*x**2+B*x+A)/(-e**2*x**2+d**2)**(1/2),x)","A d \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) + A 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) + B d \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) + B 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) + C 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) + C 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,"A*d*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))) + A*e*Piecewise((x**2/(2*sqrt(d**2)), Eq(e**2, 0)), (-sqrt(d**2 - e**2*x**2)/e**2, True)) + B*d*Piecewise((x**2/(2*sqrt(d**2)), Eq(e**2, 0)), (-sqrt(d**2 - e**2*x**2)/e**2, True)) + B*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)) + C*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)) + C*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))","A",0
13,1,262,0,4.560304," ","integrate((C*x**2+B*x+A)/(-e**2*x**2+d**2)**(1/2),x)","A \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) + B \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) + C \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,"A*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))) + B*Piecewise((x**2/(2*sqrt(d**2)), Eq(e**2, 0)), (-sqrt(d**2 - e**2*x**2)/e**2, True)) + C*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
14,0,0,0,0.000000," ","integrate((C*x**2+B*x+A)/(e*x+d)/(-e**2*x**2+d**2)**(1/2),x)","\int \frac{A + B x + C x^{2}}{\sqrt{- \left(- d + e x\right) \left(d + e x\right)} \left(d + e x\right)}\, dx"," ",0,"Integral((A + B*x + C*x**2)/(sqrt(-(-d + e*x)*(d + e*x))*(d + e*x)), x)","F",0
15,0,0,0,0.000000," ","integrate((C*x**2+B*x+A)/(e*x+d)**2/(-e**2*x**2+d**2)**(1/2),x)","\int \frac{A + B x + C x^{2}}{\sqrt{- \left(- d + e x\right) \left(d + e x\right)} \left(d + e x\right)^{2}}\, dx"," ",0,"Integral((A + B*x + C*x**2)/(sqrt(-(-d + e*x)*(d + e*x))*(d + e*x)**2), x)","F",0
16,0,0,0,0.000000," ","integrate((C*x**2+B*x+A)/(e*x+d)**3/(-e**2*x**2+d**2)**(1/2),x)","\int \frac{A + B x + C x^{2}}{\sqrt{- \left(- d + e x\right) \left(d + e x\right)} \left(d + e x\right)^{3}}\, dx"," ",0,"Integral((A + B*x + C*x**2)/(sqrt(-(-d + e*x)*(d + e*x))*(d + e*x)**3), x)","F",0
17,0,0,0,0.000000," ","integrate((C*x**2+B*x+A)/(e*x+d)**4/(-e**2*x**2+d**2)**(1/2),x)","\int \frac{A + B x + C x^{2}}{\sqrt{- \left(- d + e x\right) \left(d + e x\right)} \left(d + e x\right)^{4}}\, dx"," ",0,"Integral((A + B*x + C*x**2)/(sqrt(-(-d + e*x)*(d + e*x))*(d + e*x)**4), x)","F",0
18,1,257,0,0.116738," ","integrate((e*x+d)**3*(c*x**2+a)*(C*x**2+B*x+A),x)","A a d^{3} x + \frac{C c e^{3} x^{8}}{8} + x^{7} \left(\frac{B c e^{3}}{7} + \frac{3 C c d e^{2}}{7}\right) + x^{6} \left(\frac{A c e^{3}}{6} + \frac{B c d e^{2}}{2} + \frac{C a e^{3}}{6} + \frac{C c d^{2} e}{2}\right) + x^{5} \left(\frac{3 A c d e^{2}}{5} + \frac{B a e^{3}}{5} + \frac{3 B c d^{2} e}{5} + \frac{3 C a d e^{2}}{5} + \frac{C c d^{3}}{5}\right) + x^{4} \left(\frac{A a e^{3}}{4} + \frac{3 A c d^{2} e}{4} + \frac{3 B a d e^{2}}{4} + \frac{B c d^{3}}{4} + \frac{3 C a d^{2} e}{4}\right) + x^{3} \left(A a d e^{2} + \frac{A c d^{3}}{3} + B a d^{2} e + \frac{C a d^{3}}{3}\right) + x^{2} \left(\frac{3 A a d^{2} e}{2} + \frac{B a d^{3}}{2}\right)"," ",0,"A*a*d**3*x + C*c*e**3*x**8/8 + x**7*(B*c*e**3/7 + 3*C*c*d*e**2/7) + x**6*(A*c*e**3/6 + B*c*d*e**2/2 + C*a*e**3/6 + C*c*d**2*e/2) + x**5*(3*A*c*d*e**2/5 + B*a*e**3/5 + 3*B*c*d**2*e/5 + 3*C*a*d*e**2/5 + C*c*d**3/5) + x**4*(A*a*e**3/4 + 3*A*c*d**2*e/4 + 3*B*a*d*e**2/4 + B*c*d**3/4 + 3*C*a*d**2*e/4) + x**3*(A*a*d*e**2 + A*c*d**3/3 + B*a*d**2*e + C*a*d**3/3) + x**2*(3*A*a*d**2*e/2 + B*a*d**3/2)","A",0
19,1,173,0,0.095321," ","integrate((e*x+d)**2*(c*x**2+a)*(C*x**2+B*x+A),x)","A a d^{2} x + \frac{C c e^{2} x^{7}}{7} + x^{6} \left(\frac{B c e^{2}}{6} + \frac{C c d e}{3}\right) + x^{5} \left(\frac{A c e^{2}}{5} + \frac{2 B c d e}{5} + \frac{C a e^{2}}{5} + \frac{C c d^{2}}{5}\right) + x^{4} \left(\frac{A c d e}{2} + \frac{B a e^{2}}{4} + \frac{B c d^{2}}{4} + \frac{C a d e}{2}\right) + x^{3} \left(\frac{A a e^{2}}{3} + \frac{A c d^{2}}{3} + \frac{2 B a d e}{3} + \frac{C a d^{2}}{3}\right) + x^{2} \left(A a d e + \frac{B a d^{2}}{2}\right)"," ",0,"A*a*d**2*x + C*c*e**2*x**7/7 + x**6*(B*c*e**2/6 + C*c*d*e/3) + x**5*(A*c*e**2/5 + 2*B*c*d*e/5 + C*a*e**2/5 + C*c*d**2/5) + x**4*(A*c*d*e/2 + B*a*e**2/4 + B*c*d**2/4 + C*a*d*e/2) + x**3*(A*a*e**2/3 + A*c*d**2/3 + 2*B*a*d*e/3 + C*a*d**2/3) + x**2*(A*a*d*e + B*a*d**2/2)","A",0
20,1,97,0,0.082181," ","integrate((e*x+d)*(c*x**2+a)*(C*x**2+B*x+A),x)","A a d x + \frac{C c e x^{6}}{6} + x^{5} \left(\frac{B c e}{5} + \frac{C c d}{5}\right) + x^{4} \left(\frac{A c e}{4} + \frac{B c d}{4} + \frac{C a e}{4}\right) + x^{3} \left(\frac{A c d}{3} + \frac{B a e}{3} + \frac{C a d}{3}\right) + x^{2} \left(\frac{A a e}{2} + \frac{B a d}{2}\right)"," ",0,"A*a*d*x + C*c*e*x**6/6 + x**5*(B*c*e/5 + C*c*d/5) + x**4*(A*c*e/4 + B*c*d/4 + C*a*e/4) + x**3*(A*c*d/3 + B*a*e/3 + C*a*d/3) + x**2*(A*a*e/2 + B*a*d/2)","A",0
21,1,42,0,0.071663," ","integrate((c*x**2+a)*(C*x**2+B*x+A),x)","A a x + \frac{B a x^{2}}{2} + \frac{B c x^{4}}{4} + \frac{C c x^{5}}{5} + x^{3} \left(\frac{A c}{3} + \frac{C a}{3}\right)"," ",0,"A*a*x + B*a*x**2/2 + B*c*x**4/4 + C*c*x**5/5 + x**3*(A*c/3 + C*a/3)","A",0
22,1,148,0,0.638297," ","integrate((c*x**2+a)*(C*x**2+B*x+A)/(e*x+d),x)","\frac{C c x^{4}}{4 e} + x^{3} \left(\frac{B c}{3 e} - \frac{C c d}{3 e^{2}}\right) + x^{2} \left(\frac{A c}{2 e} - \frac{B c d}{2 e^{2}} + \frac{C a}{2 e} + \frac{C c d^{2}}{2 e^{3}}\right) + x \left(- \frac{A c d}{e^{2}} + \frac{B a}{e} + \frac{B c d^{2}}{e^{3}} - \frac{C a d}{e^{2}} - \frac{C c d^{3}}{e^{4}}\right) + \frac{\left(a e^{2} + c d^{2}\right) \left(A e^{2} - B d e + C d^{2}\right) \log{\left(d + e x \right)}}{e^{5}}"," ",0,"C*c*x**4/(4*e) + x**3*(B*c/(3*e) - C*c*d/(3*e**2)) + x**2*(A*c/(2*e) - B*c*d/(2*e**2) + C*a/(2*e) + C*c*d**2/(2*e**3)) + x*(-A*c*d/e**2 + B*a/e + B*c*d**2/e**3 - C*a*d/e**2 - C*c*d**3/e**4) + (a*e**2 + c*d**2)*(A*e**2 - B*d*e + C*d**2)*log(d + e*x)/e**5","A",0
23,1,185,0,1.256647," ","integrate((c*x**2+a)*(C*x**2+B*x+A)/(e*x+d)**2,x)","\frac{C c x^{3}}{3 e^{2}} + x^{2} \left(\frac{B c}{2 e^{2}} - \frac{C c d}{e^{3}}\right) + x \left(\frac{A c}{e^{2}} - \frac{2 B c d}{e^{3}} + \frac{C a}{e^{2}} + \frac{3 C c d^{2}}{e^{4}}\right) + \frac{- A a e^{4} - A c d^{2} e^{2} + B a d e^{3} + B c d^{3} e - C a d^{2} e^{2} - C c d^{4}}{d e^{5} + e^{6} x} - \frac{\left(2 A c d e^{2} - B a e^{3} - 3 B c d^{2} e + 2 C a d e^{2} + 4 C c d^{3}\right) \log{\left(d + e x \right)}}{e^{5}}"," ",0,"C*c*x**3/(3*e**2) + x**2*(B*c/(2*e**2) - C*c*d/e**3) + x*(A*c/e**2 - 2*B*c*d/e**3 + C*a/e**2 + 3*C*c*d**2/e**4) + (-A*a*e**4 - A*c*d**2*e**2 + B*a*d*e**3 + B*c*d**3*e - C*a*d**2*e**2 - C*c*d**4)/(d*e**5 + e**6*x) - (2*A*c*d*e**2 - B*a*e**3 - 3*B*c*d**2*e + 2*C*a*d*e**2 + 4*C*c*d**3)*log(d + e*x)/e**5","A",0
24,1,206,0,5.287649," ","integrate((c*x**2+a)*(C*x**2+B*x+A)/(e*x+d)**3,x)","\frac{C c x^{2}}{2 e^{3}} + x \left(\frac{B c}{e^{3}} - \frac{3 C c d}{e^{4}}\right) + \frac{- A a e^{4} + 3 A c d^{2} e^{2} - B a d e^{3} - 5 B c d^{3} e + 3 C a d^{2} e^{2} + 7 C c d^{4} + x \left(4 A c d e^{3} - 2 B a e^{4} - 6 B c d^{2} e^{2} + 4 C a d e^{3} + 8 C c d^{3} e\right)}{2 d^{2} e^{5} + 4 d e^{6} x + 2 e^{7} x^{2}} + \frac{\left(A c e^{2} - 3 B c d e + C a e^{2} + 6 C c d^{2}\right) \log{\left(d + e x \right)}}{e^{5}}"," ",0,"C*c*x**2/(2*e**3) + x*(B*c/e**3 - 3*C*c*d/e**4) + (-A*a*e**4 + 3*A*c*d**2*e**2 - B*a*d*e**3 - 5*B*c*d**3*e + 3*C*a*d**2*e**2 + 7*C*c*d**4 + x*(4*A*c*d*e**3 - 2*B*a*e**4 - 6*B*c*d**2*e**2 + 4*C*a*d*e**3 + 8*C*c*d**3*e))/(2*d**2*e**5 + 4*d*e**6*x + 2*e**7*x**2) + (A*c*e**2 - 3*B*c*d*e + C*a*e**2 + 6*C*c*d**2)*log(d + e*x)/e**5","A",0
25,1,445,0,0.133671," ","integrate((e*x+d)**3*(c*x**2+a)**2*(C*x**2+B*x+A),x)","A a^{2} d^{3} x + \frac{C c^{2} e^{3} x^{10}}{10} + x^{9} \left(\frac{B c^{2} e^{3}}{9} + \frac{C c^{2} d e^{2}}{3}\right) + x^{8} \left(\frac{A c^{2} e^{3}}{8} + \frac{3 B c^{2} d e^{2}}{8} + \frac{C a c e^{3}}{4} + \frac{3 C c^{2} d^{2} e}{8}\right) + x^{7} \left(\frac{3 A c^{2} d e^{2}}{7} + \frac{2 B a c e^{3}}{7} + \frac{3 B c^{2} d^{2} e}{7} + \frac{6 C a c d e^{2}}{7} + \frac{C c^{2} d^{3}}{7}\right) + x^{6} \left(\frac{A a c e^{3}}{3} + \frac{A c^{2} d^{2} e}{2} + B a c d e^{2} + \frac{B c^{2} d^{3}}{6} + \frac{C a^{2} e^{3}}{6} + C a c d^{2} e\right) + x^{5} \left(\frac{6 A a c d e^{2}}{5} + \frac{A c^{2} d^{3}}{5} + \frac{B a^{2} e^{3}}{5} + \frac{6 B a c d^{2} e}{5} + \frac{3 C a^{2} d e^{2}}{5} + \frac{2 C a c d^{3}}{5}\right) + x^{4} \left(\frac{A a^{2} e^{3}}{4} + \frac{3 A a c d^{2} e}{2} + \frac{3 B a^{2} d e^{2}}{4} + \frac{B a c d^{3}}{2} + \frac{3 C a^{2} d^{2} e}{4}\right) + x^{3} \left(A a^{2} d e^{2} + \frac{2 A a c d^{3}}{3} + B a^{2} d^{2} e + \frac{C a^{2} d^{3}}{3}\right) + x^{2} \left(\frac{3 A a^{2} d^{2} e}{2} + \frac{B a^{2} d^{3}}{2}\right)"," ",0,"A*a**2*d**3*x + C*c**2*e**3*x**10/10 + x**9*(B*c**2*e**3/9 + C*c**2*d*e**2/3) + x**8*(A*c**2*e**3/8 + 3*B*c**2*d*e**2/8 + C*a*c*e**3/4 + 3*C*c**2*d**2*e/8) + x**7*(3*A*c**2*d*e**2/7 + 2*B*a*c*e**3/7 + 3*B*c**2*d**2*e/7 + 6*C*a*c*d*e**2/7 + C*c**2*d**3/7) + x**6*(A*a*c*e**3/3 + A*c**2*d**2*e/2 + B*a*c*d*e**2 + B*c**2*d**3/6 + C*a**2*e**3/6 + C*a*c*d**2*e) + x**5*(6*A*a*c*d*e**2/5 + A*c**2*d**3/5 + B*a**2*e**3/5 + 6*B*a*c*d**2*e/5 + 3*C*a**2*d*e**2/5 + 2*C*a*c*d**3/5) + x**4*(A*a**2*e**3/4 + 3*A*a*c*d**2*e/2 + 3*B*a**2*d*e**2/4 + B*a*c*d**3/2 + 3*C*a**2*d**2*e/4) + x**3*(A*a**2*d*e**2 + 2*A*a*c*d**3/3 + B*a**2*d**2*e + C*a**2*d**3/3) + x**2*(3*A*a**2*d**2*e/2 + B*a**2*d**3/2)","A",0
26,1,311,0,0.124164," ","integrate((e*x+d)**2*(c*x**2+a)**2*(C*x**2+B*x+A),x)","A a^{2} d^{2} x + \frac{C c^{2} e^{2} x^{9}}{9} + x^{8} \left(\frac{B c^{2} e^{2}}{8} + \frac{C c^{2} d e}{4}\right) + x^{7} \left(\frac{A c^{2} e^{2}}{7} + \frac{2 B c^{2} d e}{7} + \frac{2 C a c e^{2}}{7} + \frac{C c^{2} d^{2}}{7}\right) + x^{6} \left(\frac{A c^{2} d e}{3} + \frac{B a c e^{2}}{3} + \frac{B c^{2} d^{2}}{6} + \frac{2 C a c d e}{3}\right) + x^{5} \left(\frac{2 A a c e^{2}}{5} + \frac{A c^{2} d^{2}}{5} + \frac{4 B a c d e}{5} + \frac{C a^{2} e^{2}}{5} + \frac{2 C a c d^{2}}{5}\right) + x^{4} \left(A a c d e + \frac{B a^{2} e^{2}}{4} + \frac{B a c d^{2}}{2} + \frac{C a^{2} d e}{2}\right) + x^{3} \left(\frac{A a^{2} e^{2}}{3} + \frac{2 A a c d^{2}}{3} + \frac{2 B a^{2} d e}{3} + \frac{C a^{2} d^{2}}{3}\right) + x^{2} \left(A a^{2} d e + \frac{B a^{2} d^{2}}{2}\right)"," ",0,"A*a**2*d**2*x + C*c**2*e**2*x**9/9 + x**8*(B*c**2*e**2/8 + C*c**2*d*e/4) + x**7*(A*c**2*e**2/7 + 2*B*c**2*d*e/7 + 2*C*a*c*e**2/7 + C*c**2*d**2/7) + x**6*(A*c**2*d*e/3 + B*a*c*e**2/3 + B*c**2*d**2/6 + 2*C*a*c*d*e/3) + x**5*(2*A*a*c*e**2/5 + A*c**2*d**2/5 + 4*B*a*c*d*e/5 + C*a**2*e**2/5 + 2*C*a*c*d**2/5) + x**4*(A*a*c*d*e + B*a**2*e**2/4 + B*a*c*d**2/2 + C*a**2*d*e/2) + x**3*(A*a**2*e**2/3 + 2*A*a*c*d**2/3 + 2*B*a**2*d*e/3 + C*a**2*d**2/3) + x**2*(A*a**2*d*e + B*a**2*d**2/2)","A",0
27,1,180,0,0.097363," ","integrate((e*x+d)*(c*x**2+a)**2*(C*x**2+B*x+A),x)","A a^{2} d x + \frac{C c^{2} e x^{8}}{8} + x^{7} \left(\frac{B c^{2} e}{7} + \frac{C c^{2} d}{7}\right) + x^{6} \left(\frac{A c^{2} e}{6} + \frac{B c^{2} d}{6} + \frac{C a c e}{3}\right) + x^{5} \left(\frac{A c^{2} d}{5} + \frac{2 B a c e}{5} + \frac{2 C a c d}{5}\right) + x^{4} \left(\frac{A a c e}{2} + \frac{B a c d}{2} + \frac{C a^{2} e}{4}\right) + x^{3} \left(\frac{2 A a c d}{3} + \frac{B a^{2} e}{3} + \frac{C a^{2} d}{3}\right) + x^{2} \left(\frac{A a^{2} e}{2} + \frac{B a^{2} d}{2}\right)"," ",0,"A*a**2*d*x + C*c**2*e*x**8/8 + x**7*(B*c**2*e/7 + C*c**2*d/7) + x**6*(A*c**2*e/6 + B*c**2*d/6 + C*a*c*e/3) + x**5*(A*c**2*d/5 + 2*B*a*c*e/5 + 2*C*a*c*d/5) + x**4*(A*a*c*e/2 + B*a*c*d/2 + C*a**2*e/4) + x**3*(2*A*a*c*d/3 + B*a**2*e/3 + C*a**2*d/3) + x**2*(A*a**2*e/2 + B*a**2*d/2)","A",0
28,1,83,0,0.081100," ","integrate((c*x**2+a)**2*(C*x**2+B*x+A),x)","A a^{2} x + \frac{B a^{2} x^{2}}{2} + \frac{B a c x^{4}}{2} + \frac{B c^{2} x^{6}}{6} + \frac{C c^{2} x^{7}}{7} + x^{5} \left(\frac{A c^{2}}{5} + \frac{2 C a c}{5}\right) + x^{3} \left(\frac{2 A a c}{3} + \frac{C a^{2}}{3}\right)"," ",0,"A*a**2*x + B*a**2*x**2/2 + B*a*c*x**4/2 + B*c**2*x**6/6 + C*c**2*x**7/7 + x**5*(A*c**2/5 + 2*C*a*c/5) + x**3*(2*A*a*c/3 + C*a**2/3)","A",0
29,1,359,0,0.936695," ","integrate((c*x**2+a)**2*(C*x**2+B*x+A)/(e*x+d),x)","\frac{C c^{2} x^{6}}{6 e} + x^{5} \left(\frac{B c^{2}}{5 e} - \frac{C c^{2} d}{5 e^{2}}\right) + x^{4} \left(\frac{A c^{2}}{4 e} - \frac{B c^{2} d}{4 e^{2}} + \frac{C a c}{2 e} + \frac{C c^{2} d^{2}}{4 e^{3}}\right) + x^{3} \left(- \frac{A c^{2} d}{3 e^{2}} + \frac{2 B a c}{3 e} + \frac{B c^{2} d^{2}}{3 e^{3}} - \frac{2 C a c d}{3 e^{2}} - \frac{C c^{2} d^{3}}{3 e^{4}}\right) + x^{2} \left(\frac{A a c}{e} + \frac{A c^{2} d^{2}}{2 e^{3}} - \frac{B a c d}{e^{2}} - \frac{B c^{2} d^{3}}{2 e^{4}} + \frac{C a^{2}}{2 e} + \frac{C a c d^{2}}{e^{3}} + \frac{C c^{2} d^{4}}{2 e^{5}}\right) + x \left(- \frac{2 A a c d}{e^{2}} - \frac{A c^{2} d^{3}}{e^{4}} + \frac{B a^{2}}{e} + \frac{2 B a c d^{2}}{e^{3}} + \frac{B c^{2} d^{4}}{e^{5}} - \frac{C a^{2} d}{e^{2}} - \frac{2 C a c d^{3}}{e^{4}} - \frac{C c^{2} d^{5}}{e^{6}}\right) + \frac{\left(a e^{2} + c d^{2}\right)^{2} \left(A e^{2} - B d e + C d^{2}\right) \log{\left(d + e x \right)}}{e^{7}}"," ",0,"C*c**2*x**6/(6*e) + x**5*(B*c**2/(5*e) - C*c**2*d/(5*e**2)) + x**4*(A*c**2/(4*e) - B*c**2*d/(4*e**2) + C*a*c/(2*e) + C*c**2*d**2/(4*e**3)) + x**3*(-A*c**2*d/(3*e**2) + 2*B*a*c/(3*e) + B*c**2*d**2/(3*e**3) - 2*C*a*c*d/(3*e**2) - C*c**2*d**3/(3*e**4)) + x**2*(A*a*c/e + A*c**2*d**2/(2*e**3) - B*a*c*d/e**2 - B*c**2*d**3/(2*e**4) + C*a**2/(2*e) + C*a*c*d**2/e**3 + C*c**2*d**4/(2*e**5)) + x*(-2*A*a*c*d/e**2 - A*c**2*d**3/e**4 + B*a**2/e + 2*B*a*c*d**2/e**3 + B*c**2*d**4/e**5 - C*a**2*d/e**2 - 2*C*a*c*d**3/e**4 - C*c**2*d**5/e**6) + (a*e**2 + c*d**2)**2*(A*e**2 - B*d*e + C*d**2)*log(d + e*x)/e**7","A",0
30,1,416,0,2.785055," ","integrate((c*x**2+a)**2*(C*x**2+B*x+A)/(e*x+d)**2,x)","\frac{C c^{2} x^{5}}{5 e^{2}} + x^{4} \left(\frac{B c^{2}}{4 e^{2}} - \frac{C c^{2} d}{2 e^{3}}\right) + x^{3} \left(\frac{A c^{2}}{3 e^{2}} - \frac{2 B c^{2} d}{3 e^{3}} + \frac{2 C a c}{3 e^{2}} + \frac{C c^{2} d^{2}}{e^{4}}\right) + x^{2} \left(- \frac{A c^{2} d}{e^{3}} + \frac{B a c}{e^{2}} + \frac{3 B c^{2} d^{2}}{2 e^{4}} - \frac{2 C a c d}{e^{3}} - \frac{2 C c^{2} d^{3}}{e^{5}}\right) + x \left(\frac{2 A a c}{e^{2}} + \frac{3 A c^{2} d^{2}}{e^{4}} - \frac{4 B a c d}{e^{3}} - \frac{4 B c^{2} d^{3}}{e^{5}} + \frac{C a^{2}}{e^{2}} + \frac{6 C a c d^{2}}{e^{4}} + \frac{5 C c^{2} d^{4}}{e^{6}}\right) + \frac{- A a^{2} e^{6} - 2 A a c d^{2} e^{4} - A c^{2} d^{4} e^{2} + B a^{2} d e^{5} + 2 B a c d^{3} e^{3} + B c^{2} d^{5} e - C a^{2} d^{2} e^{4} - 2 C a c d^{4} e^{2} - C c^{2} d^{6}}{d e^{7} + e^{8} x} - \frac{\left(a e^{2} + c d^{2}\right) \left(4 A c d e^{2} - B a e^{3} - 5 B c d^{2} e + 2 C a d e^{2} + 6 C c d^{3}\right) \log{\left(d + e x \right)}}{e^{7}}"," ",0,"C*c**2*x**5/(5*e**2) + x**4*(B*c**2/(4*e**2) - C*c**2*d/(2*e**3)) + x**3*(A*c**2/(3*e**2) - 2*B*c**2*d/(3*e**3) + 2*C*a*c/(3*e**2) + C*c**2*d**2/e**4) + x**2*(-A*c**2*d/e**3 + B*a*c/e**2 + 3*B*c**2*d**2/(2*e**4) - 2*C*a*c*d/e**3 - 2*C*c**2*d**3/e**5) + x*(2*A*a*c/e**2 + 3*A*c**2*d**2/e**4 - 4*B*a*c*d/e**3 - 4*B*c**2*d**3/e**5 + C*a**2/e**2 + 6*C*a*c*d**2/e**4 + 5*C*c**2*d**4/e**6) + (-A*a**2*e**6 - 2*A*a*c*d**2*e**4 - A*c**2*d**4*e**2 + B*a**2*d*e**5 + 2*B*a*c*d**3*e**3 + B*c**2*d**5*e - C*a**2*d**2*e**4 - 2*C*a*c*d**4*e**2 - C*c**2*d**6)/(d*e**7 + e**8*x) - (a*e**2 + c*d**2)*(4*A*c*d*e**2 - B*a*e**3 - 5*B*c*d**2*e + 2*C*a*d*e**2 + 6*C*c*d**3)*log(d + e*x)/e**7","A",0
31,1,474,0,14.200161," ","integrate((c*x**2+a)**2*(C*x**2+B*x+A)/(e*x+d)**3,x)","\frac{C c^{2} x^{4}}{4 e^{3}} + x^{3} \left(\frac{B c^{2}}{3 e^{3}} - \frac{C c^{2} d}{e^{4}}\right) + x^{2} \left(\frac{A c^{2}}{2 e^{3}} - \frac{3 B c^{2} d}{2 e^{4}} + \frac{C a c}{e^{3}} + \frac{3 C c^{2} d^{2}}{e^{5}}\right) + x \left(- \frac{3 A c^{2} d}{e^{4}} + \frac{2 B a c}{e^{3}} + \frac{6 B c^{2} d^{2}}{e^{5}} - \frac{6 C a c d}{e^{4}} - \frac{10 C c^{2} d^{3}}{e^{6}}\right) + \frac{- A a^{2} e^{6} + 6 A a c d^{2} e^{4} + 7 A c^{2} d^{4} e^{2} - B a^{2} d e^{5} - 10 B a c d^{3} e^{3} - 9 B c^{2} d^{5} e + 3 C a^{2} d^{2} e^{4} + 14 C a c d^{4} e^{2} + 11 C c^{2} d^{6} + x \left(8 A a c d e^{5} + 8 A c^{2} d^{3} e^{3} - 2 B a^{2} e^{6} - 12 B a c d^{2} e^{4} - 10 B c^{2} d^{4} e^{2} + 4 C a^{2} d e^{5} + 16 C a c d^{3} e^{3} + 12 C c^{2} d^{5} e\right)}{2 d^{2} e^{7} + 4 d e^{8} x + 2 e^{9} x^{2}} + \frac{\left(2 A a c e^{4} + 6 A c^{2} d^{2} e^{2} - 6 B a c d e^{3} - 10 B c^{2} d^{3} e + C a^{2} e^{4} + 12 C a c d^{2} e^{2} + 15 C c^{2} d^{4}\right) \log{\left(d + e x \right)}}{e^{7}}"," ",0,"C*c**2*x**4/(4*e**3) + x**3*(B*c**2/(3*e**3) - C*c**2*d/e**4) + x**2*(A*c**2/(2*e**3) - 3*B*c**2*d/(2*e**4) + C*a*c/e**3 + 3*C*c**2*d**2/e**5) + x*(-3*A*c**2*d/e**4 + 2*B*a*c/e**3 + 6*B*c**2*d**2/e**5 - 6*C*a*c*d/e**4 - 10*C*c**2*d**3/e**6) + (-A*a**2*e**6 + 6*A*a*c*d**2*e**4 + 7*A*c**2*d**4*e**2 - B*a**2*d*e**5 - 10*B*a*c*d**3*e**3 - 9*B*c**2*d**5*e + 3*C*a**2*d**2*e**4 + 14*C*a*c*d**4*e**2 + 11*C*c**2*d**6 + x*(8*A*a*c*d*e**5 + 8*A*c**2*d**3*e**3 - 2*B*a**2*e**6 - 12*B*a*c*d**2*e**4 - 10*B*c**2*d**4*e**2 + 4*C*a**2*d*e**5 + 16*C*a*c*d**3*e**3 + 12*C*c**2*d**5*e))/(2*d**2*e**7 + 4*d*e**8*x + 2*e**9*x**2) + (2*A*a*c*e**4 + 6*A*c**2*d**2*e**2 - 6*B*a*c*d*e**3 - 10*B*c**2*d**3*e + C*a**2*e**4 + 12*C*a*c*d**2*e**2 + 15*C*c**2*d**4)*log(d + e*x)/e**7","A",0
32,1,646,0,0.161378," ","integrate((e*x+d)**3*(c*x**2+a)**3*(C*x**2+B*x+A),x)","A a^{3} d^{3} x + \frac{C c^{3} e^{3} x^{12}}{12} + x^{11} \left(\frac{B c^{3} e^{3}}{11} + \frac{3 C c^{3} d e^{2}}{11}\right) + x^{10} \left(\frac{A c^{3} e^{3}}{10} + \frac{3 B c^{3} d e^{2}}{10} + \frac{3 C a c^{2} e^{3}}{10} + \frac{3 C c^{3} d^{2} e}{10}\right) + x^{9} \left(\frac{A c^{3} d e^{2}}{3} + \frac{B a c^{2} e^{3}}{3} + \frac{B c^{3} d^{2} e}{3} + C a c^{2} d e^{2} + \frac{C c^{3} d^{3}}{9}\right) + x^{8} \left(\frac{3 A a c^{2} e^{3}}{8} + \frac{3 A c^{3} d^{2} e}{8} + \frac{9 B a c^{2} d e^{2}}{8} + \frac{B c^{3} d^{3}}{8} + \frac{3 C a^{2} c e^{3}}{8} + \frac{9 C a c^{2} d^{2} e}{8}\right) + x^{7} \left(\frac{9 A a c^{2} d e^{2}}{7} + \frac{A c^{3} d^{3}}{7} + \frac{3 B a^{2} c e^{3}}{7} + \frac{9 B a c^{2} d^{2} e}{7} + \frac{9 C a^{2} c d e^{2}}{7} + \frac{3 C a c^{2} d^{3}}{7}\right) + x^{6} \left(\frac{A a^{2} c e^{3}}{2} + \frac{3 A a c^{2} d^{2} e}{2} + \frac{3 B a^{2} c d e^{2}}{2} + \frac{B a c^{2} d^{3}}{2} + \frac{C a^{3} e^{3}}{6} + \frac{3 C a^{2} c d^{2} e}{2}\right) + x^{5} \left(\frac{9 A a^{2} c d e^{2}}{5} + \frac{3 A a c^{2} d^{3}}{5} + \frac{B a^{3} e^{3}}{5} + \frac{9 B a^{2} c d^{2} e}{5} + \frac{3 C a^{3} d e^{2}}{5} + \frac{3 C a^{2} c d^{3}}{5}\right) + x^{4} \left(\frac{A a^{3} e^{3}}{4} + \frac{9 A a^{2} c d^{2} e}{4} + \frac{3 B a^{3} d e^{2}}{4} + \frac{3 B a^{2} c d^{3}}{4} + \frac{3 C a^{3} d^{2} e}{4}\right) + x^{3} \left(A a^{3} d e^{2} + A a^{2} c d^{3} + B a^{3} d^{2} e + \frac{C a^{3} d^{3}}{3}\right) + x^{2} \left(\frac{3 A a^{3} d^{2} e}{2} + \frac{B a^{3} d^{3}}{2}\right)"," ",0,"A*a**3*d**3*x + C*c**3*e**3*x**12/12 + x**11*(B*c**3*e**3/11 + 3*C*c**3*d*e**2/11) + x**10*(A*c**3*e**3/10 + 3*B*c**3*d*e**2/10 + 3*C*a*c**2*e**3/10 + 3*C*c**3*d**2*e/10) + x**9*(A*c**3*d*e**2/3 + B*a*c**2*e**3/3 + B*c**3*d**2*e/3 + C*a*c**2*d*e**2 + C*c**3*d**3/9) + x**8*(3*A*a*c**2*e**3/8 + 3*A*c**3*d**2*e/8 + 9*B*a*c**2*d*e**2/8 + B*c**3*d**3/8 + 3*C*a**2*c*e**3/8 + 9*C*a*c**2*d**2*e/8) + x**7*(9*A*a*c**2*d*e**2/7 + A*c**3*d**3/7 + 3*B*a**2*c*e**3/7 + 9*B*a*c**2*d**2*e/7 + 9*C*a**2*c*d*e**2/7 + 3*C*a*c**2*d**3/7) + x**6*(A*a**2*c*e**3/2 + 3*A*a*c**2*d**2*e/2 + 3*B*a**2*c*d*e**2/2 + B*a*c**2*d**3/2 + C*a**3*e**3/6 + 3*C*a**2*c*d**2*e/2) + x**5*(9*A*a**2*c*d*e**2/5 + 3*A*a*c**2*d**3/5 + B*a**3*e**3/5 + 9*B*a**2*c*d**2*e/5 + 3*C*a**3*d*e**2/5 + 3*C*a**2*c*d**3/5) + x**4*(A*a**3*e**3/4 + 9*A*a**2*c*d**2*e/4 + 3*B*a**3*d*e**2/4 + 3*B*a**2*c*d**3/4 + 3*C*a**3*d**2*e/4) + x**3*(A*a**3*d*e**2 + A*a**2*c*d**3 + B*a**3*d**2*e + C*a**3*d**3/3) + x**2*(3*A*a**3*d**2*e/2 + B*a**3*d**3/2)","A",0
33,1,447,0,0.147123," ","integrate((e*x+d)**2*(c*x**2+a)**3*(C*x**2+B*x+A),x)","A a^{3} d^{2} x + \frac{C c^{3} e^{2} x^{11}}{11} + x^{10} \left(\frac{B c^{3} e^{2}}{10} + \frac{C c^{3} d e}{5}\right) + x^{9} \left(\frac{A c^{3} e^{2}}{9} + \frac{2 B c^{3} d e}{9} + \frac{C a c^{2} e^{2}}{3} + \frac{C c^{3} d^{2}}{9}\right) + x^{8} \left(\frac{A c^{3} d e}{4} + \frac{3 B a c^{2} e^{2}}{8} + \frac{B c^{3} d^{2}}{8} + \frac{3 C a c^{2} d e}{4}\right) + x^{7} \left(\frac{3 A a c^{2} e^{2}}{7} + \frac{A c^{3} d^{2}}{7} + \frac{6 B a c^{2} d e}{7} + \frac{3 C a^{2} c e^{2}}{7} + \frac{3 C a c^{2} d^{2}}{7}\right) + x^{6} \left(A a c^{2} d e + \frac{B a^{2} c e^{2}}{2} + \frac{B a c^{2} d^{2}}{2} + C a^{2} c d e\right) + x^{5} \left(\frac{3 A a^{2} c e^{2}}{5} + \frac{3 A a c^{2} d^{2}}{5} + \frac{6 B a^{2} c d e}{5} + \frac{C a^{3} e^{2}}{5} + \frac{3 C a^{2} c d^{2}}{5}\right) + x^{4} \left(\frac{3 A a^{2} c d e}{2} + \frac{B a^{3} e^{2}}{4} + \frac{3 B a^{2} c d^{2}}{4} + \frac{C a^{3} d e}{2}\right) + x^{3} \left(\frac{A a^{3} e^{2}}{3} + A a^{2} c d^{2} + \frac{2 B a^{3} d e}{3} + \frac{C a^{3} d^{2}}{3}\right) + x^{2} \left(A a^{3} d e + \frac{B a^{3} d^{2}}{2}\right)"," ",0,"A*a**3*d**2*x + C*c**3*e**2*x**11/11 + x**10*(B*c**3*e**2/10 + C*c**3*d*e/5) + x**9*(A*c**3*e**2/9 + 2*B*c**3*d*e/9 + C*a*c**2*e**2/3 + C*c**3*d**2/9) + x**8*(A*c**3*d*e/4 + 3*B*a*c**2*e**2/8 + B*c**3*d**2/8 + 3*C*a*c**2*d*e/4) + x**7*(3*A*a*c**2*e**2/7 + A*c**3*d**2/7 + 6*B*a*c**2*d*e/7 + 3*C*a**2*c*e**2/7 + 3*C*a*c**2*d**2/7) + x**6*(A*a*c**2*d*e + B*a**2*c*e**2/2 + B*a*c**2*d**2/2 + C*a**2*c*d*e) + x**5*(3*A*a**2*c*e**2/5 + 3*A*a*c**2*d**2/5 + 6*B*a**2*c*d*e/5 + C*a**3*e**2/5 + 3*C*a**2*c*d**2/5) + x**4*(3*A*a**2*c*d*e/2 + B*a**3*e**2/4 + 3*B*a**2*c*d**2/4 + C*a**3*d*e/2) + x**3*(A*a**3*e**2/3 + A*a**2*c*d**2 + 2*B*a**3*d*e/3 + C*a**3*d**2/3) + x**2*(A*a**3*d*e + B*a**3*d**2/2)","A",0
34,1,265,0,0.114147," ","integrate((e*x+d)*(c*x**2+a)**3*(C*x**2+B*x+A),x)","A a^{3} d x + \frac{C c^{3} e x^{10}}{10} + x^{9} \left(\frac{B c^{3} e}{9} + \frac{C c^{3} d}{9}\right) + x^{8} \left(\frac{A c^{3} e}{8} + \frac{B c^{3} d}{8} + \frac{3 C a c^{2} e}{8}\right) + x^{7} \left(\frac{A c^{3} d}{7} + \frac{3 B a c^{2} e}{7} + \frac{3 C a c^{2} d}{7}\right) + x^{6} \left(\frac{A a c^{2} e}{2} + \frac{B a c^{2} d}{2} + \frac{C a^{2} c e}{2}\right) + x^{5} \left(\frac{3 A a c^{2} d}{5} + \frac{3 B a^{2} c e}{5} + \frac{3 C a^{2} c d}{5}\right) + x^{4} \left(\frac{3 A a^{2} c e}{4} + \frac{3 B a^{2} c d}{4} + \frac{C a^{3} e}{4}\right) + x^{3} \left(A a^{2} c d + \frac{B a^{3} e}{3} + \frac{C a^{3} d}{3}\right) + x^{2} \left(\frac{A a^{3} e}{2} + \frac{B a^{3} d}{2}\right)"," ",0,"A*a**3*d*x + C*c**3*e*x**10/10 + x**9*(B*c**3*e/9 + C*c**3*d/9) + x**8*(A*c**3*e/8 + B*c**3*d/8 + 3*C*a*c**2*e/8) + x**7*(A*c**3*d/7 + 3*B*a*c**2*e/7 + 3*C*a*c**2*d/7) + x**6*(A*a*c**2*e/2 + B*a*c**2*d/2 + C*a**2*c*e/2) + x**5*(3*A*a*c**2*d/5 + 3*B*a**2*c*e/5 + 3*C*a**2*c*d/5) + x**4*(3*A*a**2*c*e/4 + 3*B*a**2*c*d/4 + C*a**3*e/4) + x**3*(A*a**2*c*d + B*a**3*e/3 + C*a**3*d/3) + x**2*(A*a**3*e/2 + B*a**3*d/2)","A",0
35,1,122,0,0.086498," ","integrate((c*x**2+a)**3*(C*x**2+B*x+A),x)","A a^{3} x + \frac{B a^{3} x^{2}}{2} + \frac{3 B a^{2} c x^{4}}{4} + \frac{B a c^{2} x^{6}}{2} + \frac{B c^{3} x^{8}}{8} + \frac{C c^{3} x^{9}}{9} + x^{7} \left(\frac{A c^{3}}{7} + \frac{3 C a c^{2}}{7}\right) + x^{5} \left(\frac{3 A a c^{2}}{5} + \frac{3 C a^{2} c}{5}\right) + x^{3} \left(A a^{2} c + \frac{C a^{3}}{3}\right)"," ",0,"A*a**3*x + B*a**3*x**2/2 + 3*B*a**2*c*x**4/4 + B*a*c**2*x**6/2 + B*c**3*x**8/8 + C*c**3*x**9/9 + x**7*(A*c**3/7 + 3*C*a*c**2/7) + x**5*(3*A*a*c**2/5 + 3*C*a**2*c/5) + x**3*(A*a**2*c + C*a**3/3)","A",0
36,1,685,0,1.466981," ","integrate((c*x**2+a)**3*(C*x**2+B*x+A)/(e*x+d),x)","\frac{C c^{3} x^{8}}{8 e} + x^{7} \left(\frac{B c^{3}}{7 e} - \frac{C c^{3} d}{7 e^{2}}\right) + x^{6} \left(\frac{A c^{3}}{6 e} - \frac{B c^{3} d}{6 e^{2}} + \frac{C a c^{2}}{2 e} + \frac{C c^{3} d^{2}}{6 e^{3}}\right) + x^{5} \left(- \frac{A c^{3} d}{5 e^{2}} + \frac{3 B a c^{2}}{5 e} + \frac{B c^{3} d^{2}}{5 e^{3}} - \frac{3 C a c^{2} d}{5 e^{2}} - \frac{C c^{3} d^{3}}{5 e^{4}}\right) + x^{4} \left(\frac{3 A a c^{2}}{4 e} + \frac{A c^{3} d^{2}}{4 e^{3}} - \frac{3 B a c^{2} d}{4 e^{2}} - \frac{B c^{3} d^{3}}{4 e^{4}} + \frac{3 C a^{2} c}{4 e} + \frac{3 C a c^{2} d^{2}}{4 e^{3}} + \frac{C c^{3} d^{4}}{4 e^{5}}\right) + x^{3} \left(- \frac{A a c^{2} d}{e^{2}} - \frac{A c^{3} d^{3}}{3 e^{4}} + \frac{B a^{2} c}{e} + \frac{B a c^{2} d^{2}}{e^{3}} + \frac{B c^{3} d^{4}}{3 e^{5}} - \frac{C a^{2} c d}{e^{2}} - \frac{C a c^{2} d^{3}}{e^{4}} - \frac{C c^{3} d^{5}}{3 e^{6}}\right) + x^{2} \left(\frac{3 A a^{2} c}{2 e} + \frac{3 A a c^{2} d^{2}}{2 e^{3}} + \frac{A c^{3} d^{4}}{2 e^{5}} - \frac{3 B a^{2} c d}{2 e^{2}} - \frac{3 B a c^{2} d^{3}}{2 e^{4}} - \frac{B c^{3} d^{5}}{2 e^{6}} + \frac{C a^{3}}{2 e} + \frac{3 C a^{2} c d^{2}}{2 e^{3}} + \frac{3 C a c^{2} d^{4}}{2 e^{5}} + \frac{C c^{3} d^{6}}{2 e^{7}}\right) + x \left(- \frac{3 A a^{2} c d}{e^{2}} - \frac{3 A a c^{2} d^{3}}{e^{4}} - \frac{A c^{3} d^{5}}{e^{6}} + \frac{B a^{3}}{e} + \frac{3 B a^{2} c d^{2}}{e^{3}} + \frac{3 B a c^{2} d^{4}}{e^{5}} + \frac{B c^{3} d^{6}}{e^{7}} - \frac{C a^{3} d}{e^{2}} - \frac{3 C a^{2} c d^{3}}{e^{4}} - \frac{3 C a c^{2} d^{5}}{e^{6}} - \frac{C c^{3} d^{7}}{e^{8}}\right) + \frac{\left(a e^{2} + c d^{2}\right)^{3} \left(A e^{2} - B d e + C d^{2}\right) \log{\left(d + e x \right)}}{e^{9}}"," ",0,"C*c**3*x**8/(8*e) + x**7*(B*c**3/(7*e) - C*c**3*d/(7*e**2)) + x**6*(A*c**3/(6*e) - B*c**3*d/(6*e**2) + C*a*c**2/(2*e) + C*c**3*d**2/(6*e**3)) + x**5*(-A*c**3*d/(5*e**2) + 3*B*a*c**2/(5*e) + B*c**3*d**2/(5*e**3) - 3*C*a*c**2*d/(5*e**2) - C*c**3*d**3/(5*e**4)) + x**4*(3*A*a*c**2/(4*e) + A*c**3*d**2/(4*e**3) - 3*B*a*c**2*d/(4*e**2) - B*c**3*d**3/(4*e**4) + 3*C*a**2*c/(4*e) + 3*C*a*c**2*d**2/(4*e**3) + C*c**3*d**4/(4*e**5)) + x**3*(-A*a*c**2*d/e**2 - A*c**3*d**3/(3*e**4) + B*a**2*c/e + B*a*c**2*d**2/e**3 + B*c**3*d**4/(3*e**5) - C*a**2*c*d/e**2 - C*a*c**2*d**3/e**4 - C*c**3*d**5/(3*e**6)) + x**2*(3*A*a**2*c/(2*e) + 3*A*a*c**2*d**2/(2*e**3) + A*c**3*d**4/(2*e**5) - 3*B*a**2*c*d/(2*e**2) - 3*B*a*c**2*d**3/(2*e**4) - B*c**3*d**5/(2*e**6) + C*a**3/(2*e) + 3*C*a**2*c*d**2/(2*e**3) + 3*C*a*c**2*d**4/(2*e**5) + C*c**3*d**6/(2*e**7)) + x*(-3*A*a**2*c*d/e**2 - 3*A*a*c**2*d**3/e**4 - A*c**3*d**5/e**6 + B*a**3/e + 3*B*a**2*c*d**2/e**3 + 3*B*a*c**2*d**4/e**5 + B*c**3*d**6/e**7 - C*a**3*d/e**2 - 3*C*a**2*c*d**3/e**4 - 3*C*a*c**2*d**5/e**6 - C*c**3*d**7/e**8) + (a*e**2 + c*d**2)**3*(A*e**2 - B*d*e + C*d**2)*log(d + e*x)/e**9","A",0
37,1,748,0,4.949326," ","integrate((c*x**2+a)**3*(C*x**2+B*x+A)/(e*x+d)**2,x)","\frac{C c^{3} x^{7}}{7 e^{2}} + x^{6} \left(\frac{B c^{3}}{6 e^{2}} - \frac{C c^{3} d}{3 e^{3}}\right) + x^{5} \left(\frac{A c^{3}}{5 e^{2}} - \frac{2 B c^{3} d}{5 e^{3}} + \frac{3 C a c^{2}}{5 e^{2}} + \frac{3 C c^{3} d^{2}}{5 e^{4}}\right) + x^{4} \left(- \frac{A c^{3} d}{2 e^{3}} + \frac{3 B a c^{2}}{4 e^{2}} + \frac{3 B c^{3} d^{2}}{4 e^{4}} - \frac{3 C a c^{2} d}{2 e^{3}} - \frac{C c^{3} d^{3}}{e^{5}}\right) + x^{3} \left(\frac{A a c^{2}}{e^{2}} + \frac{A c^{3} d^{2}}{e^{4}} - \frac{2 B a c^{2} d}{e^{3}} - \frac{4 B c^{3} d^{3}}{3 e^{5}} + \frac{C a^{2} c}{e^{2}} + \frac{3 C a c^{2} d^{2}}{e^{4}} + \frac{5 C c^{3} d^{4}}{3 e^{6}}\right) + x^{2} \left(- \frac{3 A a c^{2} d}{e^{3}} - \frac{2 A c^{3} d^{3}}{e^{5}} + \frac{3 B a^{2} c}{2 e^{2}} + \frac{9 B a c^{2} d^{2}}{2 e^{4}} + \frac{5 B c^{3} d^{4}}{2 e^{6}} - \frac{3 C a^{2} c d}{e^{3}} - \frac{6 C a c^{2} d^{3}}{e^{5}} - \frac{3 C c^{3} d^{5}}{e^{7}}\right) + x \left(\frac{3 A a^{2} c}{e^{2}} + \frac{9 A a c^{2} d^{2}}{e^{4}} + \frac{5 A c^{3} d^{4}}{e^{6}} - \frac{6 B a^{2} c d}{e^{3}} - \frac{12 B a c^{2} d^{3}}{e^{5}} - \frac{6 B c^{3} d^{5}}{e^{7}} + \frac{C a^{3}}{e^{2}} + \frac{9 C a^{2} c d^{2}}{e^{4}} + \frac{15 C a c^{2} d^{4}}{e^{6}} + \frac{7 C c^{3} d^{6}}{e^{8}}\right) + \frac{- A a^{3} e^{8} - 3 A a^{2} c d^{2} e^{6} - 3 A a c^{2} d^{4} e^{4} - A c^{3} d^{6} e^{2} + B a^{3} d e^{7} + 3 B a^{2} c d^{3} e^{5} + 3 B a c^{2} d^{5} e^{3} + B c^{3} d^{7} e - C a^{3} d^{2} e^{6} - 3 C a^{2} c d^{4} e^{4} - 3 C a c^{2} d^{6} e^{2} - C c^{3} d^{8}}{d e^{9} + e^{10} x} - \frac{\left(a e^{2} + c d^{2}\right)^{2} \left(6 A c d e^{2} - B a e^{3} - 7 B c d^{2} e + 2 C a d e^{2} + 8 C c d^{3}\right) \log{\left(d + e x \right)}}{e^{9}}"," ",0,"C*c**3*x**7/(7*e**2) + x**6*(B*c**3/(6*e**2) - C*c**3*d/(3*e**3)) + x**5*(A*c**3/(5*e**2) - 2*B*c**3*d/(5*e**3) + 3*C*a*c**2/(5*e**2) + 3*C*c**3*d**2/(5*e**4)) + x**4*(-A*c**3*d/(2*e**3) + 3*B*a*c**2/(4*e**2) + 3*B*c**3*d**2/(4*e**4) - 3*C*a*c**2*d/(2*e**3) - C*c**3*d**3/e**5) + x**3*(A*a*c**2/e**2 + A*c**3*d**2/e**4 - 2*B*a*c**2*d/e**3 - 4*B*c**3*d**3/(3*e**5) + C*a**2*c/e**2 + 3*C*a*c**2*d**2/e**4 + 5*C*c**3*d**4/(3*e**6)) + x**2*(-3*A*a*c**2*d/e**3 - 2*A*c**3*d**3/e**5 + 3*B*a**2*c/(2*e**2) + 9*B*a*c**2*d**2/(2*e**4) + 5*B*c**3*d**4/(2*e**6) - 3*C*a**2*c*d/e**3 - 6*C*a*c**2*d**3/e**5 - 3*C*c**3*d**5/e**7) + x*(3*A*a**2*c/e**2 + 9*A*a*c**2*d**2/e**4 + 5*A*c**3*d**4/e**6 - 6*B*a**2*c*d/e**3 - 12*B*a*c**2*d**3/e**5 - 6*B*c**3*d**5/e**7 + C*a**3/e**2 + 9*C*a**2*c*d**2/e**4 + 15*C*a*c**2*d**4/e**6 + 7*C*c**3*d**6/e**8) + (-A*a**3*e**8 - 3*A*a**2*c*d**2*e**6 - 3*A*a*c**2*d**4*e**4 - A*c**3*d**6*e**2 + B*a**3*d*e**7 + 3*B*a**2*c*d**3*e**5 + 3*B*a*c**2*d**5*e**3 + B*c**3*d**7*e - C*a**3*d**2*e**6 - 3*C*a**2*c*d**4*e**4 - 3*C*a*c**2*d**6*e**2 - C*c**3*d**8)/(d*e**9 + e**10*x) - (a*e**2 + c*d**2)**2*(6*A*c*d*e**2 - B*a*e**3 - 7*B*c*d**2*e + 2*C*a*d*e**2 + 8*C*c*d**3)*log(d + e*x)/e**9","A",0
38,1,816,0,25.278669," ","integrate((c*x**2+a)**3*(C*x**2+B*x+A)/(e*x+d)**3,x)","\frac{C c^{3} x^{6}}{6 e^{3}} + x^{5} \left(\frac{B c^{3}}{5 e^{3}} - \frac{3 C c^{3} d}{5 e^{4}}\right) + x^{4} \left(\frac{A c^{3}}{4 e^{3}} - \frac{3 B c^{3} d}{4 e^{4}} + \frac{3 C a c^{2}}{4 e^{3}} + \frac{3 C c^{3} d^{2}}{2 e^{5}}\right) + x^{3} \left(- \frac{A c^{3} d}{e^{4}} + \frac{B a c^{2}}{e^{3}} + \frac{2 B c^{3} d^{2}}{e^{5}} - \frac{3 C a c^{2} d}{e^{4}} - \frac{10 C c^{3} d^{3}}{3 e^{6}}\right) + x^{2} \left(\frac{3 A a c^{2}}{2 e^{3}} + \frac{3 A c^{3} d^{2}}{e^{5}} - \frac{9 B a c^{2} d}{2 e^{4}} - \frac{5 B c^{3} d^{3}}{e^{6}} + \frac{3 C a^{2} c}{2 e^{3}} + \frac{9 C a c^{2} d^{2}}{e^{5}} + \frac{15 C c^{3} d^{4}}{2 e^{7}}\right) + x \left(- \frac{9 A a c^{2} d}{e^{4}} - \frac{10 A c^{3} d^{3}}{e^{6}} + \frac{3 B a^{2} c}{e^{3}} + \frac{18 B a c^{2} d^{2}}{e^{5}} + \frac{15 B c^{3} d^{4}}{e^{7}} - \frac{9 C a^{2} c d}{e^{4}} - \frac{30 C a c^{2} d^{3}}{e^{6}} - \frac{21 C c^{3} d^{5}}{e^{8}}\right) + \frac{- A a^{3} e^{8} + 9 A a^{2} c d^{2} e^{6} + 21 A a c^{2} d^{4} e^{4} + 11 A c^{3} d^{6} e^{2} - B a^{3} d e^{7} - 15 B a^{2} c d^{3} e^{5} - 27 B a c^{2} d^{5} e^{3} - 13 B c^{3} d^{7} e + 3 C a^{3} d^{2} e^{6} + 21 C a^{2} c d^{4} e^{4} + 33 C a c^{2} d^{6} e^{2} + 15 C c^{3} d^{8} + x \left(12 A a^{2} c d e^{7} + 24 A a c^{2} d^{3} e^{5} + 12 A c^{3} d^{5} e^{3} - 2 B a^{3} e^{8} - 18 B a^{2} c d^{2} e^{6} - 30 B a c^{2} d^{4} e^{4} - 14 B c^{3} d^{6} e^{2} + 4 C a^{3} d e^{7} + 24 C a^{2} c d^{3} e^{5} + 36 C a c^{2} d^{5} e^{3} + 16 C c^{3} d^{7} e\right)}{2 d^{2} e^{9} + 4 d e^{10} x + 2 e^{11} x^{2}} + \frac{\left(a e^{2} + c d^{2}\right) \left(3 A a c e^{4} + 15 A c^{2} d^{2} e^{2} - 9 B a c d e^{3} - 21 B c^{2} d^{3} e + C a^{2} e^{4} + 17 C a c d^{2} e^{2} + 28 C c^{2} d^{4}\right) \log{\left(d + e x \right)}}{e^{9}}"," ",0,"C*c**3*x**6/(6*e**3) + x**5*(B*c**3/(5*e**3) - 3*C*c**3*d/(5*e**4)) + x**4*(A*c**3/(4*e**3) - 3*B*c**3*d/(4*e**4) + 3*C*a*c**2/(4*e**3) + 3*C*c**3*d**2/(2*e**5)) + x**3*(-A*c**3*d/e**4 + B*a*c**2/e**3 + 2*B*c**3*d**2/e**5 - 3*C*a*c**2*d/e**4 - 10*C*c**3*d**3/(3*e**6)) + x**2*(3*A*a*c**2/(2*e**3) + 3*A*c**3*d**2/e**5 - 9*B*a*c**2*d/(2*e**4) - 5*B*c**3*d**3/e**6 + 3*C*a**2*c/(2*e**3) + 9*C*a*c**2*d**2/e**5 + 15*C*c**3*d**4/(2*e**7)) + x*(-9*A*a*c**2*d/e**4 - 10*A*c**3*d**3/e**6 + 3*B*a**2*c/e**3 + 18*B*a*c**2*d**2/e**5 + 15*B*c**3*d**4/e**7 - 9*C*a**2*c*d/e**4 - 30*C*a*c**2*d**3/e**6 - 21*C*c**3*d**5/e**8) + (-A*a**3*e**8 + 9*A*a**2*c*d**2*e**6 + 21*A*a*c**2*d**4*e**4 + 11*A*c**3*d**6*e**2 - B*a**3*d*e**7 - 15*B*a**2*c*d**3*e**5 - 27*B*a*c**2*d**5*e**3 - 13*B*c**3*d**7*e + 3*C*a**3*d**2*e**6 + 21*C*a**2*c*d**4*e**4 + 33*C*a*c**2*d**6*e**2 + 15*C*c**3*d**8 + x*(12*A*a**2*c*d*e**7 + 24*A*a*c**2*d**3*e**5 + 12*A*c**3*d**5*e**3 - 2*B*a**3*e**8 - 18*B*a**2*c*d**2*e**6 - 30*B*a*c**2*d**4*e**4 - 14*B*c**3*d**6*e**2 + 4*C*a**3*d*e**7 + 24*C*a**2*c*d**3*e**5 + 36*C*a*c**2*d**5*e**3 + 16*C*c**3*d**7*e))/(2*d**2*e**9 + 4*d*e**10*x + 2*e**11*x**2) + (a*e**2 + c*d**2)*(3*A*a*c*e**4 + 15*A*c**2*d**2*e**2 - 9*B*a*c*d*e**3 - 21*B*c**2*d**3*e + C*a**2*e**4 + 17*C*a*c*d**2*e**2 + 28*C*c**2*d**4)*log(d + e*x)/e**9","A",0
39,1,73,0,0.367661," ","integrate((b*x**2+a)*(3*b*d*x**2+4*b*c*x-a*d)/(d*x+c)**2,x)","- \frac{b^{2} c x^{2}}{d^{2}} + \frac{b^{2} x^{3}}{d} + x \left(\frac{2 a b}{d} + \frac{b^{2} c^{2}}{d^{3}}\right) + \frac{a^{2} d^{4} + 2 a b c^{2} d^{2} + b^{2} c^{4}}{c d^{4} + d^{5} x}"," ",0,"-b**2*c*x**2/d**2 + b**2*x**3/d + x*(2*a*b/d + b**2*c**2/d**3) + (a**2*d**4 + 2*a*b*c**2*d**2 + b**2*c**4)/(c*d**4 + d**5*x)","B",0
40,1,73,0,0.366982," ","integrate((b*x**2+a)*(-a*d+b*x*(3*d*x+4*c))/(d*x+c)**2,x)","- \frac{b^{2} c x^{2}}{d^{2}} + \frac{b^{2} x^{3}}{d} + x \left(\frac{2 a b}{d} + \frac{b^{2} c^{2}}{d^{3}}\right) + \frac{a^{2} d^{4} + 2 a b c^{2} d^{2} + b^{2} c^{4}}{c d^{4} + d^{5} x}"," ",0,"-b**2*c*x**2/d**2 + b**2*x**3/d + x*(2*a*b/d + b**2*c**2/d**3) + (a**2*d**4 + 2*a*b*c**2*d**2 + b**2*c**4)/(c*d**4 + d**5*x)","B",0
41,1,153,0,0.587153," ","integrate((b*x**2+a)**2*(5*b*d*x**2+6*b*c*x-a*d)/(d*x+c)**2,x)","- \frac{b^{3} c x^{4}}{d^{2}} + \frac{b^{3} x^{5}}{d} + x^{3} \left(\frac{3 a b^{2}}{d} + \frac{b^{3} c^{2}}{d^{3}}\right) + x^{2} \left(- \frac{3 a b^{2} c}{d^{2}} - \frac{b^{3} c^{3}}{d^{4}}\right) + x \left(\frac{3 a^{2} b}{d} + \frac{3 a b^{2} c^{2}}{d^{3}} + \frac{b^{3} c^{4}}{d^{5}}\right) + \frac{a^{3} d^{6} + 3 a^{2} b c^{2} d^{4} + 3 a b^{2} c^{4} d^{2} + b^{3} c^{6}}{c d^{6} + d^{7} x}"," ",0,"-b**3*c*x**4/d**2 + b**3*x**5/d + x**3*(3*a*b**2/d + b**3*c**2/d**3) + x**2*(-3*a*b**2*c/d**2 - b**3*c**3/d**4) + x*(3*a**2*b/d + 3*a*b**2*c**2/d**3 + b**3*c**4/d**5) + (a**3*d**6 + 3*a**2*b*c**2*d**4 + 3*a*b**2*c**4*d**2 + b**3*c**6)/(c*d**6 + d**7*x)","B",0
42,1,153,0,0.610377," ","integrate((b*x**2+a)**2*(-a*d+b*x*(5*d*x+6*c))/(d*x+c)**2,x)","- \frac{b^{3} c x^{4}}{d^{2}} + \frac{b^{3} x^{5}}{d} + x^{3} \left(\frac{3 a b^{2}}{d} + \frac{b^{3} c^{2}}{d^{3}}\right) + x^{2} \left(- \frac{3 a b^{2} c}{d^{2}} - \frac{b^{3} c^{3}}{d^{4}}\right) + x \left(\frac{3 a^{2} b}{d} + \frac{3 a b^{2} c^{2}}{d^{3}} + \frac{b^{3} c^{4}}{d^{5}}\right) + \frac{a^{3} d^{6} + 3 a^{2} b c^{2} d^{4} + 3 a b^{2} c^{4} d^{2} + b^{3} c^{6}}{c d^{6} + d^{7} x}"," ",0,"-b**3*c*x**4/d**2 + b**3*x**5/d + x**3*(3*a*b**2/d + b**3*c**2/d**3) + x**2*(-3*a*b**2*c/d**2 - b**3*c**3/d**4) + x*(3*a**2*b/d + 3*a*b**2*c**2/d**3 + b**3*c**4/d**5) + (a**3*d**6 + 3*a**2*b*c**2*d**4 + 3*a*b**2*c**4*d**2 + b**3*c**6)/(c*d**6 + d**7*x)","B",0
43,1,1008,0,5.462061," ","integrate((e*x+d)**3*(C*x**2+B*x+A)/(c*x**2+a),x)","\frac{C e^{3} x^{4}}{4 c} + x^{3} \left(\frac{B e^{3}}{3 c} + \frac{C d e^{2}}{c}\right) + x^{2} \left(\frac{A e^{3}}{2 c} + \frac{3 B d e^{2}}{2 c} - \frac{C a e^{3}}{2 c^{2}} + \frac{3 C d^{2} e}{2 c}\right) + x \left(\frac{3 A d e^{2}}{c} - \frac{B a e^{3}}{c^{2}} + \frac{3 B d^{2} e}{c} - \frac{3 C a d e^{2}}{c^{2}} + \frac{C d^{3}}{c}\right) + \left(\frac{- A a c e^{3} + 3 A c^{2} d^{2} e - 3 B a c d e^{2} + B c^{2} d^{3} + C a^{2} e^{3} - 3 C a c d^{2} e}{2 c^{3}} - \frac{\sqrt{- a c^{7}} \left(- 3 A a c d e^{2} + A c^{2} d^{3} + B a^{2} e^{3} - 3 B a c d^{2} e + 3 C a^{2} d e^{2} - C a c d^{3}\right)}{2 a c^{6}}\right) \log{\left(x + \frac{A a^{2} c e^{3} - 3 A a c^{2} d^{2} e + 3 B a^{2} c d e^{2} - B a c^{2} d^{3} - C a^{3} e^{3} + 3 C a^{2} c d^{2} e + 2 a c^{3} \left(\frac{- A a c e^{3} + 3 A c^{2} d^{2} e - 3 B a c d e^{2} + B c^{2} d^{3} + C a^{2} e^{3} - 3 C a c d^{2} e}{2 c^{3}} - \frac{\sqrt{- a c^{7}} \left(- 3 A a c d e^{2} + A c^{2} d^{3} + B a^{2} e^{3} - 3 B a c d^{2} e + 3 C a^{2} d e^{2} - C a c d^{3}\right)}{2 a c^{6}}\right)}{- 3 A a c^{2} d e^{2} + A c^{3} d^{3} + B a^{2} c e^{3} - 3 B a c^{2} d^{2} e + 3 C a^{2} c d e^{2} - C a c^{2} d^{3}} \right)} + \left(\frac{- A a c e^{3} + 3 A c^{2} d^{2} e - 3 B a c d e^{2} + B c^{2} d^{3} + C a^{2} e^{3} - 3 C a c d^{2} e}{2 c^{3}} + \frac{\sqrt{- a c^{7}} \left(- 3 A a c d e^{2} + A c^{2} d^{3} + B a^{2} e^{3} - 3 B a c d^{2} e + 3 C a^{2} d e^{2} - C a c d^{3}\right)}{2 a c^{6}}\right) \log{\left(x + \frac{A a^{2} c e^{3} - 3 A a c^{2} d^{2} e + 3 B a^{2} c d e^{2} - B a c^{2} d^{3} - C a^{3} e^{3} + 3 C a^{2} c d^{2} e + 2 a c^{3} \left(\frac{- A a c e^{3} + 3 A c^{2} d^{2} e - 3 B a c d e^{2} + B c^{2} d^{3} + C a^{2} e^{3} - 3 C a c d^{2} e}{2 c^{3}} + \frac{\sqrt{- a c^{7}} \left(- 3 A a c d e^{2} + A c^{2} d^{3} + B a^{2} e^{3} - 3 B a c d^{2} e + 3 C a^{2} d e^{2} - C a c d^{3}\right)}{2 a c^{6}}\right)}{- 3 A a c^{2} d e^{2} + A c^{3} d^{3} + B a^{2} c e^{3} - 3 B a c^{2} d^{2} e + 3 C a^{2} c d e^{2} - C a c^{2} d^{3}} \right)}"," ",0,"C*e**3*x**4/(4*c) + x**3*(B*e**3/(3*c) + C*d*e**2/c) + x**2*(A*e**3/(2*c) + 3*B*d*e**2/(2*c) - C*a*e**3/(2*c**2) + 3*C*d**2*e/(2*c)) + x*(3*A*d*e**2/c - B*a*e**3/c**2 + 3*B*d**2*e/c - 3*C*a*d*e**2/c**2 + C*d**3/c) + ((-A*a*c*e**3 + 3*A*c**2*d**2*e - 3*B*a*c*d*e**2 + B*c**2*d**3 + C*a**2*e**3 - 3*C*a*c*d**2*e)/(2*c**3) - sqrt(-a*c**7)*(-3*A*a*c*d*e**2 + A*c**2*d**3 + B*a**2*e**3 - 3*B*a*c*d**2*e + 3*C*a**2*d*e**2 - C*a*c*d**3)/(2*a*c**6))*log(x + (A*a**2*c*e**3 - 3*A*a*c**2*d**2*e + 3*B*a**2*c*d*e**2 - B*a*c**2*d**3 - C*a**3*e**3 + 3*C*a**2*c*d**2*e + 2*a*c**3*((-A*a*c*e**3 + 3*A*c**2*d**2*e - 3*B*a*c*d*e**2 + B*c**2*d**3 + C*a**2*e**3 - 3*C*a*c*d**2*e)/(2*c**3) - sqrt(-a*c**7)*(-3*A*a*c*d*e**2 + A*c**2*d**3 + B*a**2*e**3 - 3*B*a*c*d**2*e + 3*C*a**2*d*e**2 - C*a*c*d**3)/(2*a*c**6)))/(-3*A*a*c**2*d*e**2 + A*c**3*d**3 + B*a**2*c*e**3 - 3*B*a*c**2*d**2*e + 3*C*a**2*c*d*e**2 - C*a*c**2*d**3)) + ((-A*a*c*e**3 + 3*A*c**2*d**2*e - 3*B*a*c*d*e**2 + B*c**2*d**3 + C*a**2*e**3 - 3*C*a*c*d**2*e)/(2*c**3) + sqrt(-a*c**7)*(-3*A*a*c*d*e**2 + A*c**2*d**3 + B*a**2*e**3 - 3*B*a*c*d**2*e + 3*C*a**2*d*e**2 - C*a*c*d**3)/(2*a*c**6))*log(x + (A*a**2*c*e**3 - 3*A*a*c**2*d**2*e + 3*B*a**2*c*d*e**2 - B*a*c**2*d**3 - C*a**3*e**3 + 3*C*a**2*c*d**2*e + 2*a*c**3*((-A*a*c*e**3 + 3*A*c**2*d**2*e - 3*B*a*c*d*e**2 + B*c**2*d**3 + C*a**2*e**3 - 3*C*a*c*d**2*e)/(2*c**3) + sqrt(-a*c**7)*(-3*A*a*c*d*e**2 + A*c**2*d**3 + B*a**2*e**3 - 3*B*a*c*d**2*e + 3*C*a**2*d*e**2 - C*a*c*d**3)/(2*a*c**6)))/(-3*A*a*c**2*d*e**2 + A*c**3*d**3 + B*a**2*c*e**3 - 3*B*a*c**2*d**2*e + 3*C*a**2*c*d*e**2 - C*a*c**2*d**3))","B",0
44,1,638,0,3.150473," ","integrate((e*x+d)**2*(C*x**2+B*x+A)/(c*x**2+a),x)","\frac{C e^{2} x^{3}}{3 c} + x^{2} \left(\frac{B e^{2}}{2 c} + \frac{C d e}{c}\right) + x \left(\frac{A e^{2}}{c} + \frac{2 B d e}{c} - \frac{C a e^{2}}{c^{2}} + \frac{C d^{2}}{c}\right) + \left(- \frac{- 2 A c d e + B a e^{2} - B c d^{2} + 2 C a d e}{2 c^{2}} - \frac{\sqrt{- a c^{5}} \left(- A a c e^{2} + A c^{2} d^{2} - 2 B a c d e + C a^{2} e^{2} - C a c d^{2}\right)}{2 a c^{5}}\right) \log{\left(x + \frac{- 2 A a c d e + B a^{2} e^{2} - B a c d^{2} + 2 C a^{2} d e + 2 a c^{2} \left(- \frac{- 2 A c d e + B a e^{2} - B c d^{2} + 2 C a d e}{2 c^{2}} - \frac{\sqrt{- a c^{5}} \left(- A a c e^{2} + A c^{2} d^{2} - 2 B a c d e + C a^{2} e^{2} - C a c d^{2}\right)}{2 a c^{5}}\right)}{- A a c e^{2} + A c^{2} d^{2} - 2 B a c d e + C a^{2} e^{2} - C a c d^{2}} \right)} + \left(- \frac{- 2 A c d e + B a e^{2} - B c d^{2} + 2 C a d e}{2 c^{2}} + \frac{\sqrt{- a c^{5}} \left(- A a c e^{2} + A c^{2} d^{2} - 2 B a c d e + C a^{2} e^{2} - C a c d^{2}\right)}{2 a c^{5}}\right) \log{\left(x + \frac{- 2 A a c d e + B a^{2} e^{2} - B a c d^{2} + 2 C a^{2} d e + 2 a c^{2} \left(- \frac{- 2 A c d e + B a e^{2} - B c d^{2} + 2 C a d e}{2 c^{2}} + \frac{\sqrt{- a c^{5}} \left(- A a c e^{2} + A c^{2} d^{2} - 2 B a c d e + C a^{2} e^{2} - C a c d^{2}\right)}{2 a c^{5}}\right)}{- A a c e^{2} + A c^{2} d^{2} - 2 B a c d e + C a^{2} e^{2} - C a c d^{2}} \right)}"," ",0,"C*e**2*x**3/(3*c) + x**2*(B*e**2/(2*c) + C*d*e/c) + x*(A*e**2/c + 2*B*d*e/c - C*a*e**2/c**2 + C*d**2/c) + (-(-2*A*c*d*e + B*a*e**2 - B*c*d**2 + 2*C*a*d*e)/(2*c**2) - sqrt(-a*c**5)*(-A*a*c*e**2 + A*c**2*d**2 - 2*B*a*c*d*e + C*a**2*e**2 - C*a*c*d**2)/(2*a*c**5))*log(x + (-2*A*a*c*d*e + B*a**2*e**2 - B*a*c*d**2 + 2*C*a**2*d*e + 2*a*c**2*(-(-2*A*c*d*e + B*a*e**2 - B*c*d**2 + 2*C*a*d*e)/(2*c**2) - sqrt(-a*c**5)*(-A*a*c*e**2 + A*c**2*d**2 - 2*B*a*c*d*e + C*a**2*e**2 - C*a*c*d**2)/(2*a*c**5)))/(-A*a*c*e**2 + A*c**2*d**2 - 2*B*a*c*d*e + C*a**2*e**2 - C*a*c*d**2)) + (-(-2*A*c*d*e + B*a*e**2 - B*c*d**2 + 2*C*a*d*e)/(2*c**2) + sqrt(-a*c**5)*(-A*a*c*e**2 + A*c**2*d**2 - 2*B*a*c*d*e + C*a**2*e**2 - C*a*c*d**2)/(2*a*c**5))*log(x + (-2*A*a*c*d*e + B*a**2*e**2 - B*a*c*d**2 + 2*C*a**2*d*e + 2*a*c**2*(-(-2*A*c*d*e + B*a*e**2 - B*c*d**2 + 2*C*a*d*e)/(2*c**2) + sqrt(-a*c**5)*(-A*a*c*e**2 + A*c**2*d**2 - 2*B*a*c*d*e + C*a**2*e**2 - C*a*c*d**2)/(2*a*c**5)))/(-A*a*c*e**2 + A*c**2*d**2 - 2*B*a*c*d*e + C*a**2*e**2 - C*a*c*d**2))","B",0
45,1,337,0,1.659722," ","integrate((e*x+d)*(C*x**2+B*x+A)/(c*x**2+a),x)","\frac{C e x^{2}}{2 c} + x \left(\frac{B e}{c} + \frac{C d}{c}\right) + \left(- \frac{- A c e - B c d + C a e}{2 c^{2}} - \frac{\sqrt{- a c^{5}} \left(- A c d + B a e + C a d\right)}{2 a c^{4}}\right) \log{\left(x + \frac{A a c e + B a c d - C a^{2} e - 2 a c^{2} \left(- \frac{- A c e - B c d + C a e}{2 c^{2}} - \frac{\sqrt{- a c^{5}} \left(- A c d + B a e + C a d\right)}{2 a c^{4}}\right)}{- A c^{2} d + B a c e + C a c d} \right)} + \left(- \frac{- A c e - B c d + C a e}{2 c^{2}} + \frac{\sqrt{- a c^{5}} \left(- A c d + B a e + C a d\right)}{2 a c^{4}}\right) \log{\left(x + \frac{A a c e + B a c d - C a^{2} e - 2 a c^{2} \left(- \frac{- A c e - B c d + C a e}{2 c^{2}} + \frac{\sqrt{- a c^{5}} \left(- A c d + B a e + C a d\right)}{2 a c^{4}}\right)}{- A c^{2} d + B a c e + C a c d} \right)}"," ",0,"C*e*x**2/(2*c) + x*(B*e/c + C*d/c) + (-(-A*c*e - B*c*d + C*a*e)/(2*c**2) - sqrt(-a*c**5)*(-A*c*d + B*a*e + C*a*d)/(2*a*c**4))*log(x + (A*a*c*e + B*a*c*d - C*a**2*e - 2*a*c**2*(-(-A*c*e - B*c*d + C*a*e)/(2*c**2) - sqrt(-a*c**5)*(-A*c*d + B*a*e + C*a*d)/(2*a*c**4)))/(-A*c**2*d + B*a*c*e + C*a*c*d)) + (-(-A*c*e - B*c*d + C*a*e)/(2*c**2) + sqrt(-a*c**5)*(-A*c*d + B*a*e + C*a*d)/(2*a*c**4))*log(x + (A*a*c*e + B*a*c*d - C*a**2*e - 2*a*c**2*(-(-A*c*e - B*c*d + C*a*e)/(2*c**2) + sqrt(-a*c**5)*(-A*c*d + B*a*e + C*a*d)/(2*a*c**4)))/(-A*c**2*d + B*a*c*e + C*a*c*d))","B",0
46,1,156,0,0.486203," ","integrate((C*x**2+B*x+A)/(c*x**2+a),x)","\frac{C x}{c} + \left(\frac{B}{2 c} - \frac{\sqrt{- a c^{3}} \left(- A c + C a\right)}{2 a c^{3}}\right) \log{\left(x + \frac{B a - 2 a c \left(\frac{B}{2 c} - \frac{\sqrt{- a c^{3}} \left(- A c + C a\right)}{2 a c^{3}}\right)}{- A c + C a} \right)} + \left(\frac{B}{2 c} + \frac{\sqrt{- a c^{3}} \left(- A c + C a\right)}{2 a c^{3}}\right) \log{\left(x + \frac{B a - 2 a c \left(\frac{B}{2 c} + \frac{\sqrt{- a c^{3}} \left(- A c + C a\right)}{2 a c^{3}}\right)}{- A c + C a} \right)}"," ",0,"C*x/c + (B/(2*c) - sqrt(-a*c**3)*(-A*c + C*a)/(2*a*c**3))*log(x + (B*a - 2*a*c*(B/(2*c) - sqrt(-a*c**3)*(-A*c + C*a)/(2*a*c**3)))/(-A*c + C*a)) + (B/(2*c) + sqrt(-a*c**3)*(-A*c + C*a)/(2*a*c**3))*log(x + (B*a - 2*a*c*(B/(2*c) + sqrt(-a*c**3)*(-A*c + C*a)/(2*a*c**3)))/(-A*c + C*a))","B",0
47,-1,0,0,0.000000," ","integrate((C*x**2+B*x+A)/(e*x+d)/(c*x**2+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
48,-1,0,0,0.000000," ","integrate((C*x**2+B*x+A)/(e*x+d)**2/(c*x**2+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
49,-1,0,0,0.000000," ","integrate((C*x**2+B*x+A)/(e*x+d)**3/(c*x**2+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
50,1,952,0,34.457251," ","integrate((e*x+d)**3*(C*x**2+B*x+A)/(c*x**2+a)**2,x)","\frac{C e^{3} x^{2}}{2 c^{2}} + x \left(\frac{B e^{3}}{c^{2}} + \frac{3 C d e^{2}}{c^{2}}\right) + \left(- \frac{e \left(- A c e^{2} - 3 B c d e + 2 C a e^{2} - 3 C c d^{2}\right)}{2 c^{3}} - \frac{\sqrt{- a^{3} c^{7}} \left(- 3 A a c d e^{2} - A c^{2} d^{3} + 3 B a^{2} e^{3} - 3 B a c d^{2} e + 9 C a^{2} d e^{2} - C a c d^{3}\right)}{4 a^{3} c^{6}}\right) \log{\left(x + \frac{2 A a^{2} c e^{3} + 6 B a^{2} c d e^{2} - 4 C a^{3} e^{3} + 6 C a^{2} c d^{2} e - 4 a^{2} c^{3} \left(- \frac{e \left(- A c e^{2} - 3 B c d e + 2 C a e^{2} - 3 C c d^{2}\right)}{2 c^{3}} - \frac{\sqrt{- a^{3} c^{7}} \left(- 3 A a c d e^{2} - A c^{2} d^{3} + 3 B a^{2} e^{3} - 3 B a c d^{2} e + 9 C a^{2} d e^{2} - C a c d^{3}\right)}{4 a^{3} c^{6}}\right)}{- 3 A a c^{2} d e^{2} - A c^{3} d^{3} + 3 B a^{2} c e^{3} - 3 B a c^{2} d^{2} e + 9 C a^{2} c d e^{2} - C a c^{2} d^{3}} \right)} + \left(- \frac{e \left(- A c e^{2} - 3 B c d e + 2 C a e^{2} - 3 C c d^{2}\right)}{2 c^{3}} + \frac{\sqrt{- a^{3} c^{7}} \left(- 3 A a c d e^{2} - A c^{2} d^{3} + 3 B a^{2} e^{3} - 3 B a c d^{2} e + 9 C a^{2} d e^{2} - C a c d^{3}\right)}{4 a^{3} c^{6}}\right) \log{\left(x + \frac{2 A a^{2} c e^{3} + 6 B a^{2} c d e^{2} - 4 C a^{3} e^{3} + 6 C a^{2} c d^{2} e - 4 a^{2} c^{3} \left(- \frac{e \left(- A c e^{2} - 3 B c d e + 2 C a e^{2} - 3 C c d^{2}\right)}{2 c^{3}} + \frac{\sqrt{- a^{3} c^{7}} \left(- 3 A a c d e^{2} - A c^{2} d^{3} + 3 B a^{2} e^{3} - 3 B a c d^{2} e + 9 C a^{2} d e^{2} - C a c d^{3}\right)}{4 a^{3} c^{6}}\right)}{- 3 A a c^{2} d e^{2} - A c^{3} d^{3} + 3 B a^{2} c e^{3} - 3 B a c^{2} d^{2} e + 9 C a^{2} c d e^{2} - C a c^{2} d^{3}} \right)} + \frac{A a^{2} c e^{3} - 3 A a c^{2} d^{2} e + 3 B a^{2} c d e^{2} - B a c^{2} d^{3} - C a^{3} e^{3} + 3 C a^{2} c d^{2} e + x \left(- 3 A a c^{2} d e^{2} + A c^{3} d^{3} + B a^{2} c e^{3} - 3 B a c^{2} d^{2} e + 3 C a^{2} c d e^{2} - C a c^{2} d^{3}\right)}{2 a^{2} c^{3} + 2 a c^{4} x^{2}}"," ",0,"C*e**3*x**2/(2*c**2) + x*(B*e**3/c**2 + 3*C*d*e**2/c**2) + (-e*(-A*c*e**2 - 3*B*c*d*e + 2*C*a*e**2 - 3*C*c*d**2)/(2*c**3) - sqrt(-a**3*c**7)*(-3*A*a*c*d*e**2 - A*c**2*d**3 + 3*B*a**2*e**3 - 3*B*a*c*d**2*e + 9*C*a**2*d*e**2 - C*a*c*d**3)/(4*a**3*c**6))*log(x + (2*A*a**2*c*e**3 + 6*B*a**2*c*d*e**2 - 4*C*a**3*e**3 + 6*C*a**2*c*d**2*e - 4*a**2*c**3*(-e*(-A*c*e**2 - 3*B*c*d*e + 2*C*a*e**2 - 3*C*c*d**2)/(2*c**3) - sqrt(-a**3*c**7)*(-3*A*a*c*d*e**2 - A*c**2*d**3 + 3*B*a**2*e**3 - 3*B*a*c*d**2*e + 9*C*a**2*d*e**2 - C*a*c*d**3)/(4*a**3*c**6)))/(-3*A*a*c**2*d*e**2 - A*c**3*d**3 + 3*B*a**2*c*e**3 - 3*B*a*c**2*d**2*e + 9*C*a**2*c*d*e**2 - C*a*c**2*d**3)) + (-e*(-A*c*e**2 - 3*B*c*d*e + 2*C*a*e**2 - 3*C*c*d**2)/(2*c**3) + sqrt(-a**3*c**7)*(-3*A*a*c*d*e**2 - A*c**2*d**3 + 3*B*a**2*e**3 - 3*B*a*c*d**2*e + 9*C*a**2*d*e**2 - C*a*c*d**3)/(4*a**3*c**6))*log(x + (2*A*a**2*c*e**3 + 6*B*a**2*c*d*e**2 - 4*C*a**3*e**3 + 6*C*a**2*c*d**2*e - 4*a**2*c**3*(-e*(-A*c*e**2 - 3*B*c*d*e + 2*C*a*e**2 - 3*C*c*d**2)/(2*c**3) + sqrt(-a**3*c**7)*(-3*A*a*c*d*e**2 - A*c**2*d**3 + 3*B*a**2*e**3 - 3*B*a*c*d**2*e + 9*C*a**2*d*e**2 - C*a*c*d**3)/(4*a**3*c**6)))/(-3*A*a*c**2*d*e**2 - A*c**3*d**3 + 3*B*a**2*c*e**3 - 3*B*a*c**2*d**2*e + 9*C*a**2*c*d*e**2 - C*a*c**2*d**3)) + (A*a**2*c*e**3 - 3*A*a*c**2*d**2*e + 3*B*a**2*c*d*e**2 - B*a*c**2*d**3 - C*a**3*e**3 + 3*C*a**2*c*d**2*e + x*(-3*A*a*c**2*d*e**2 + A*c**3*d**3 + B*a**2*c*e**3 - 3*B*a*c**2*d**2*e + 3*C*a**2*c*d*e**2 - C*a*c**2*d**3))/(2*a**2*c**3 + 2*a*c**4*x**2)","B",0
51,1,593,0,18.398074," ","integrate((e*x+d)**2*(C*x**2+B*x+A)/(c*x**2+a)**2,x)","\frac{C e^{2} x}{c^{2}} + \left(\frac{e \left(B e + 2 C d\right)}{2 c^{2}} - \frac{\sqrt{- a^{3} c^{5}} \left(- A a c e^{2} - A c^{2} d^{2} - 2 B a c d e + 3 C a^{2} e^{2} - C a c d^{2}\right)}{4 a^{3} c^{5}}\right) \log{\left(x + \frac{2 B a^{2} e^{2} + 4 C a^{2} d e - 4 a^{2} c^{2} \left(\frac{e \left(B e + 2 C d\right)}{2 c^{2}} - \frac{\sqrt{- a^{3} c^{5}} \left(- A a c e^{2} - A c^{2} d^{2} - 2 B a c d e + 3 C a^{2} e^{2} - C a c d^{2}\right)}{4 a^{3} c^{5}}\right)}{- A a c e^{2} - A c^{2} d^{2} - 2 B a c d e + 3 C a^{2} e^{2} - C a c d^{2}} \right)} + \left(\frac{e \left(B e + 2 C d\right)}{2 c^{2}} + \frac{\sqrt{- a^{3} c^{5}} \left(- A a c e^{2} - A c^{2} d^{2} - 2 B a c d e + 3 C a^{2} e^{2} - C a c d^{2}\right)}{4 a^{3} c^{5}}\right) \log{\left(x + \frac{2 B a^{2} e^{2} + 4 C a^{2} d e - 4 a^{2} c^{2} \left(\frac{e \left(B e + 2 C d\right)}{2 c^{2}} + \frac{\sqrt{- a^{3} c^{5}} \left(- A a c e^{2} - A c^{2} d^{2} - 2 B a c d e + 3 C a^{2} e^{2} - C a c d^{2}\right)}{4 a^{3} c^{5}}\right)}{- A a c e^{2} - A c^{2} d^{2} - 2 B a c d e + 3 C a^{2} e^{2} - C a c d^{2}} \right)} + \frac{- 2 A a c d e + B a^{2} e^{2} - B a c d^{2} + 2 C a^{2} d e + x \left(- A a c e^{2} + A c^{2} d^{2} - 2 B a c d e + C a^{2} e^{2} - C a c d^{2}\right)}{2 a^{2} c^{2} + 2 a c^{3} x^{2}}"," ",0,"C*e**2*x/c**2 + (e*(B*e + 2*C*d)/(2*c**2) - sqrt(-a**3*c**5)*(-A*a*c*e**2 - A*c**2*d**2 - 2*B*a*c*d*e + 3*C*a**2*e**2 - C*a*c*d**2)/(4*a**3*c**5))*log(x + (2*B*a**2*e**2 + 4*C*a**2*d*e - 4*a**2*c**2*(e*(B*e + 2*C*d)/(2*c**2) - sqrt(-a**3*c**5)*(-A*a*c*e**2 - A*c**2*d**2 - 2*B*a*c*d*e + 3*C*a**2*e**2 - C*a*c*d**2)/(4*a**3*c**5)))/(-A*a*c*e**2 - A*c**2*d**2 - 2*B*a*c*d*e + 3*C*a**2*e**2 - C*a*c*d**2)) + (e*(B*e + 2*C*d)/(2*c**2) + sqrt(-a**3*c**5)*(-A*a*c*e**2 - A*c**2*d**2 - 2*B*a*c*d*e + 3*C*a**2*e**2 - C*a*c*d**2)/(4*a**3*c**5))*log(x + (2*B*a**2*e**2 + 4*C*a**2*d*e - 4*a**2*c**2*(e*(B*e + 2*C*d)/(2*c**2) + sqrt(-a**3*c**5)*(-A*a*c*e**2 - A*c**2*d**2 - 2*B*a*c*d*e + 3*C*a**2*e**2 - C*a*c*d**2)/(4*a**3*c**5)))/(-A*a*c*e**2 - A*c**2*d**2 - 2*B*a*c*d*e + 3*C*a**2*e**2 - C*a*c*d**2)) + (-2*A*a*c*d*e + B*a**2*e**2 - B*a*c*d**2 + 2*C*a**2*d*e + x*(-A*a*c*e**2 + A*c**2*d**2 - 2*B*a*c*d*e + C*a**2*e**2 - C*a*c*d**2))/(2*a**2*c**2 + 2*a*c**3*x**2)","B",0
52,1,318,0,6.410664," ","integrate((e*x+d)*(C*x**2+B*x+A)/(c*x**2+a)**2,x)","\left(\frac{C e}{2 c^{2}} - \frac{\sqrt{- a^{3} c^{5}} \left(A c d + B a e + C a d\right)}{4 a^{3} c^{4}}\right) \log{\left(x + \frac{- 2 C a^{2} e + 4 a^{2} c^{2} \left(\frac{C e}{2 c^{2}} - \frac{\sqrt{- a^{3} c^{5}} \left(A c d + B a e + C a d\right)}{4 a^{3} c^{4}}\right)}{A c^{2} d + B a c e + C a c d} \right)} + \left(\frac{C e}{2 c^{2}} + \frac{\sqrt{- a^{3} c^{5}} \left(A c d + B a e + C a d\right)}{4 a^{3} c^{4}}\right) \log{\left(x + \frac{- 2 C a^{2} e + 4 a^{2} c^{2} \left(\frac{C e}{2 c^{2}} + \frac{\sqrt{- a^{3} c^{5}} \left(A c d + B a e + C a d\right)}{4 a^{3} c^{4}}\right)}{A c^{2} d + B a c e + C a c d} \right)} + \frac{- A a c e - B a c d + C a^{2} e + x \left(A c^{2} d - B a c e - C a c d\right)}{2 a^{2} c^{2} + 2 a c^{3} x^{2}}"," ",0,"(C*e/(2*c**2) - sqrt(-a**3*c**5)*(A*c*d + B*a*e + C*a*d)/(4*a**3*c**4))*log(x + (-2*C*a**2*e + 4*a**2*c**2*(C*e/(2*c**2) - sqrt(-a**3*c**5)*(A*c*d + B*a*e + C*a*d)/(4*a**3*c**4)))/(A*c**2*d + B*a*c*e + C*a*c*d)) + (C*e/(2*c**2) + sqrt(-a**3*c**5)*(A*c*d + B*a*e + C*a*d)/(4*a**3*c**4))*log(x + (-2*C*a**2*e + 4*a**2*c**2*(C*e/(2*c**2) + sqrt(-a**3*c**5)*(A*c*d + B*a*e + C*a*d)/(4*a**3*c**4)))/(A*c**2*d + B*a*c*e + C*a*c*d)) + (-A*a*c*e - B*a*c*d + C*a**2*e + x*(A*c**2*d - B*a*c*e - C*a*c*d))/(2*a**2*c**2 + 2*a*c**3*x**2)","B",0
53,1,116,0,0.654328," ","integrate((C*x**2+B*x+A)/(c*x**2+a)**2,x)","- \frac{\sqrt{- \frac{1}{a^{3} c^{3}}} \left(A c + C a\right) \log{\left(- a^{2} c \sqrt{- \frac{1}{a^{3} c^{3}}} + x \right)}}{4} + \frac{\sqrt{- \frac{1}{a^{3} c^{3}}} \left(A c + C a\right) \log{\left(a^{2} c \sqrt{- \frac{1}{a^{3} c^{3}}} + x \right)}}{4} + \frac{- B a + x \left(A c - C a\right)}{2 a^{2} c + 2 a c^{2} x^{2}}"," ",0,"-sqrt(-1/(a**3*c**3))*(A*c + C*a)*log(-a**2*c*sqrt(-1/(a**3*c**3)) + x)/4 + sqrt(-1/(a**3*c**3))*(A*c + C*a)*log(a**2*c*sqrt(-1/(a**3*c**3)) + x)/4 + (-B*a + x*(A*c - C*a))/(2*a**2*c + 2*a*c**2*x**2)","A",0
54,-1,0,0,0.000000," ","integrate((C*x**2+B*x+A)/(e*x+d)/(c*x**2+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
55,-1,0,0,0.000000," ","integrate((C*x**2+B*x+A)/(e*x+d)**2/(c*x**2+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
56,-1,0,0,0.000000," ","integrate((C*x**2+B*x+A)/(e*x+d)**3/(c*x**2+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
57,-1,0,0,0.000000," ","integrate((e*x+d)**3*(C*x**2+B*x+A)/(c*x**2+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
58,1,391,0,141.178870," ","integrate((e*x+d)**2*(C*x**2+B*x+A)/(c*x**2+a)**3,x)","- \frac{\sqrt{- \frac{1}{a^{5} c^{5}}} \left(A a c e^{2} + 3 A c^{2} d^{2} + 2 B a c d e + 3 C a^{2} e^{2} + C a c d^{2}\right) \log{\left(- a^{3} c^{2} \sqrt{- \frac{1}{a^{5} c^{5}}} + x \right)}}{16} + \frac{\sqrt{- \frac{1}{a^{5} c^{5}}} \left(A a c e^{2} + 3 A c^{2} d^{2} + 2 B a c d e + 3 C a^{2} e^{2} + C a c d^{2}\right) \log{\left(a^{3} c^{2} \sqrt{- \frac{1}{a^{5} c^{5}}} + x \right)}}{16} + \frac{- 4 A a^{2} c d e - 2 B a^{3} e^{2} - 2 B a^{2} c d^{2} - 4 C a^{3} d e + x^{3} \left(A a c^{2} e^{2} + 3 A c^{3} d^{2} + 2 B a c^{2} d e - 5 C a^{2} c e^{2} + C a c^{2} d^{2}\right) + x^{2} \left(- 4 B a^{2} c e^{2} - 8 C a^{2} c d e\right) + x \left(- A a^{2} c e^{2} + 5 A a c^{2} d^{2} - 2 B a^{2} c d e - 3 C a^{3} e^{2} - C a^{2} c d^{2}\right)}{8 a^{4} c^{2} + 16 a^{3} c^{3} x^{2} + 8 a^{2} c^{4} x^{4}}"," ",0,"-sqrt(-1/(a**5*c**5))*(A*a*c*e**2 + 3*A*c**2*d**2 + 2*B*a*c*d*e + 3*C*a**2*e**2 + C*a*c*d**2)*log(-a**3*c**2*sqrt(-1/(a**5*c**5)) + x)/16 + sqrt(-1/(a**5*c**5))*(A*a*c*e**2 + 3*A*c**2*d**2 + 2*B*a*c*d*e + 3*C*a**2*e**2 + C*a*c*d**2)*log(a**3*c**2*sqrt(-1/(a**5*c**5)) + x)/16 + (-4*A*a**2*c*d*e - 2*B*a**3*e**2 - 2*B*a**2*c*d**2 - 4*C*a**3*d*e + x**3*(A*a*c**2*e**2 + 3*A*c**3*d**2 + 2*B*a*c**2*d*e - 5*C*a**2*c*e**2 + C*a*c**2*d**2) + x**2*(-4*B*a**2*c*e**2 - 8*C*a**2*c*d*e) + x*(-A*a**2*c*e**2 + 5*A*a*c**2*d**2 - 2*B*a**2*c*d*e - 3*C*a**3*e**2 - C*a**2*c*d**2))/(8*a**4*c**2 + 16*a**3*c**3*x**2 + 8*a**2*c**4*x**4)","B",0
59,1,240,0,32.420124," ","integrate((e*x+d)*(C*x**2+B*x+A)/(c*x**2+a)**3,x)","- \frac{\sqrt{- \frac{1}{a^{5} c^{3}}} \left(3 A c d + B a e + C a d\right) \log{\left(- a^{3} c \sqrt{- \frac{1}{a^{5} c^{3}}} + x \right)}}{16} + \frac{\sqrt{- \frac{1}{a^{5} c^{3}}} \left(3 A c d + B a e + C a d\right) \log{\left(a^{3} c \sqrt{- \frac{1}{a^{5} c^{3}}} + x \right)}}{16} + \frac{- 2 A a^{2} c e - 2 B a^{2} c d - 2 C a^{3} e - 4 C a^{2} c e x^{2} + x^{3} \left(3 A c^{3} d + B a c^{2} e + C a c^{2} d\right) + x \left(5 A a c^{2} d - B a^{2} c e - C a^{2} c d\right)}{8 a^{4} c^{2} + 16 a^{3} c^{3} x^{2} + 8 a^{2} c^{4} x^{4}}"," ",0,"-sqrt(-1/(a**5*c**3))*(3*A*c*d + B*a*e + C*a*d)*log(-a**3*c*sqrt(-1/(a**5*c**3)) + x)/16 + sqrt(-1/(a**5*c**3))*(3*A*c*d + B*a*e + C*a*d)*log(a**3*c*sqrt(-1/(a**5*c**3)) + x)/16 + (-2*A*a**2*c*e - 2*B*a**2*c*d - 2*C*a**3*e - 4*C*a**2*c*e*x**2 + x**3*(3*A*c**3*d + B*a*c**2*e + C*a*c**2*d) + x*(5*A*a*c**2*d - B*a**2*c*e - C*a**2*c*d))/(8*a**4*c**2 + 16*a**3*c**3*x**2 + 8*a**2*c**4*x**4)","A",0
60,1,156,0,1.233771," ","integrate((C*x**2+B*x+A)/(c*x**2+a)**3,x)","- \frac{\sqrt{- \frac{1}{a^{5} c^{3}}} \left(3 A c + C a\right) \log{\left(- a^{3} c \sqrt{- \frac{1}{a^{5} c^{3}}} + x \right)}}{16} + \frac{\sqrt{- \frac{1}{a^{5} c^{3}}} \left(3 A c + C a\right) \log{\left(a^{3} c \sqrt{- \frac{1}{a^{5} c^{3}}} + x \right)}}{16} + \frac{- 2 B a^{2} + x^{3} \left(3 A c^{2} + C a c\right) + x \left(5 A a c - C a^{2}\right)}{8 a^{4} c + 16 a^{3} c^{2} x^{2} + 8 a^{2} c^{3} x^{4}}"," ",0,"-sqrt(-1/(a**5*c**3))*(3*A*c + C*a)*log(-a**3*c*sqrt(-1/(a**5*c**3)) + x)/16 + sqrt(-1/(a**5*c**3))*(3*A*c + C*a)*log(a**3*c*sqrt(-1/(a**5*c**3)) + x)/16 + (-2*B*a**2 + x**3*(3*A*c**2 + C*a*c) + x*(5*A*a*c - C*a**2))/(8*a**4*c + 16*a**3*c**2*x**2 + 8*a**2*c**3*x**4)","A",0
61,-1,0,0,0.000000," ","integrate((C*x**2+B*x+A)/(e*x+d)/(c*x**2+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
62,-1,0,0,0.000000," ","integrate((C*x**2+B*x+A)/(e*x+d)**2/(c*x**2+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
63,-1,0,0,0.000000," ","integrate((C*x**2+B*x+A)/(e*x+d)**3/(c*x**2+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
64,-1,0,0,0.000000," ","integrate((e*x+d)**4*(C*x**2+B*x+A)/(c*x**2+a)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
65,-1,0,0,0.000000," ","integrate((e*x+d)**3*(C*x**2+B*x+A)/(c*x**2+a)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
66,-1,0,0,0.000000," ","integrate((e*x+d)**2*(C*x**2+B*x+A)/(c*x**2+a)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
67,1,298,0,139.971387," ","integrate((e*x+d)*(C*x**2+B*x+A)/(c*x**2+a)**4,x)","- \frac{\sqrt{- \frac{1}{a^{7} c^{3}}} \left(5 A c d + B a e + C a d\right) \log{\left(- a^{4} c \sqrt{- \frac{1}{a^{7} c^{3}}} + x \right)}}{32} + \frac{\sqrt{- \frac{1}{a^{7} c^{3}}} \left(5 A c d + B a e + C a d\right) \log{\left(a^{4} c \sqrt{- \frac{1}{a^{7} c^{3}}} + x \right)}}{32} + \frac{- 8 A a^{3} c e - 8 B a^{3} c d - 4 C a^{4} e - 12 C a^{3} c e x^{2} + x^{5} \left(15 A c^{4} d + 3 B a c^{3} e + 3 C a c^{3} d\right) + x^{3} \left(40 A a c^{3} d + 8 B a^{2} c^{2} e + 8 C a^{2} c^{2} d\right) + x \left(33 A a^{2} c^{2} d - 3 B a^{3} c e - 3 C a^{3} c d\right)}{48 a^{6} c^{2} + 144 a^{5} c^{3} x^{2} + 144 a^{4} c^{4} x^{4} + 48 a^{3} c^{5} x^{6}}"," ",0,"-sqrt(-1/(a**7*c**3))*(5*A*c*d + B*a*e + C*a*d)*log(-a**4*c*sqrt(-1/(a**7*c**3)) + x)/32 + sqrt(-1/(a**7*c**3))*(5*A*c*d + B*a*e + C*a*d)*log(a**4*c*sqrt(-1/(a**7*c**3)) + x)/32 + (-8*A*a**3*c*e - 8*B*a**3*c*d - 4*C*a**4*e - 12*C*a**3*c*e*x**2 + x**5*(15*A*c**4*d + 3*B*a*c**3*e + 3*C*a*c**3*d) + x**3*(40*A*a*c**3*d + 8*B*a**2*c**2*e + 8*C*a**2*c**2*d) + x*(33*A*a**2*c**2*d - 3*B*a**3*c*e - 3*C*a**3*c*d))/(48*a**6*c**2 + 144*a**5*c**3*x**2 + 144*a**4*c**4*x**4 + 48*a**3*c**5*x**6)","A",0
68,1,196,0,2.078443," ","integrate((C*x**2+B*x+A)/(c*x**2+a)**4,x)","- \frac{\sqrt{- \frac{1}{a^{7} c^{3}}} \left(5 A c + C a\right) \log{\left(- a^{4} c \sqrt{- \frac{1}{a^{7} c^{3}}} + x \right)}}{32} + \frac{\sqrt{- \frac{1}{a^{7} c^{3}}} \left(5 A c + C a\right) \log{\left(a^{4} c \sqrt{- \frac{1}{a^{7} c^{3}}} + x \right)}}{32} + \frac{- 8 B a^{3} + x^{5} \left(15 A c^{3} + 3 C a c^{2}\right) + x^{3} \left(40 A a c^{2} + 8 C a^{2} c\right) + x \left(33 A a^{2} c - 3 C a^{3}\right)}{48 a^{6} c + 144 a^{5} c^{2} x^{2} + 144 a^{4} c^{3} x^{4} + 48 a^{3} c^{4} x^{6}}"," ",0,"-sqrt(-1/(a**7*c**3))*(5*A*c + C*a)*log(-a**4*c*sqrt(-1/(a**7*c**3)) + x)/32 + sqrt(-1/(a**7*c**3))*(5*A*c + C*a)*log(a**4*c*sqrt(-1/(a**7*c**3)) + x)/32 + (-8*B*a**3 + x**5*(15*A*c**3 + 3*C*a*c**2) + x**3*(40*A*a*c**2 + 8*C*a**2*c) + x*(33*A*a**2*c - 3*C*a**3))/(48*a**6*c + 144*a**5*c**2*x**2 + 144*a**4*c**3*x**4 + 48*a**3*c**4*x**6)","A",0
69,1,29,0,0.129465," ","integrate(x**3*(x**2+x+1)/(x**2+1)**2,x)","\frac{x^{2}}{2} + x + \frac{x}{2 x^{2} + 2} - \frac{\log{\left(x^{2} + 1 \right)}}{2} - \frac{3 \operatorname{atan}{\left(x \right)}}{2}"," ",0,"x**2/2 + x + x/(2*x**2 + 2) - log(x**2 + 1)/2 - 3*atan(x)/2","A",0
70,1,20,0,0.123711," ","integrate(x**2*(x**2+x+1)/(x**2+1)**2,x)","x + \frac{\log{\left(x^{2} + 1 \right)}}{2} - \operatorname{atan}{\left(x \right)} + \frac{1}{2 x^{2} + 2}"," ",0,"x + log(x**2 + 1)/2 - atan(x) + 1/(2*x**2 + 2)","A",0
71,1,20,0,0.127409," ","integrate(x*(x**2+x+1)/(x**2+1)**2,x)","- \frac{x}{2 x^{2} + 2} + \frac{\log{\left(x^{2} + 1 \right)}}{2} + \frac{\operatorname{atan}{\left(x \right)}}{2}"," ",0,"-x/(2*x**2 + 2) + log(x**2 + 1)/2 + atan(x)/2","A",0
72,1,10,0,0.113673," ","integrate((x**2+x+1)/(x**2+1)**2,x)","\operatorname{atan}{\left(x \right)} - \frac{1}{2 x^{2} + 2}"," ",0,"atan(x) - 1/(2*x**2 + 2)","A",0
73,1,24,0,0.158979," ","integrate((x**2+x+1)/x/(x**2+1)**2,x)","\frac{x}{2 x^{2} + 2} + \log{\left(x \right)} - \frac{\log{\left(x^{2} + 1 \right)}}{2} + \frac{\operatorname{atan}{\left(x \right)}}{2}"," ",0,"x/(2*x**2 + 2) + log(x) - log(x**2 + 1)/2 + atan(x)/2","A",0
74,1,31,0,0.161027," ","integrate((x**2+x+1)/x**2/(x**2+1)**2,x)","\log{\left(x \right)} - \frac{\log{\left(x^{2} + 1 \right)}}{2} - \operatorname{atan}{\left(x \right)} + \frac{- 2 x^{2} + x - 2}{2 x^{3} + 2 x}"," ",0,"log(x) - log(x**2 + 1)/2 - atan(x) + (-2*x**2 + x - 2)/(2*x**3 + 2*x)","A",0
75,1,42,0,0.176198," ","integrate((x**2+x+1)/x**3/(x**2+1)**2,x)","- \log{\left(x \right)} + \frac{\log{\left(x^{2} + 1 \right)}}{2} - \frac{3 \operatorname{atan}{\left(x \right)}}{2} + \frac{- 3 x^{3} - x^{2} - 2 x - 1}{2 x^{4} + 2 x^{2}}"," ",0,"-log(x) + log(x**2 + 1)/2 - 3*atan(x)/2 + (-3*x**3 - x**2 - 2*x - 1)/(2*x**4 + 2*x**2)","A",0
76,1,8,0,0.115005," ","integrate((x**2+2*x+1)/(x**2+1)**2,x)","\operatorname{atan}{\left(x \right)} - \frac{1}{x^{2} + 1}"," ",0,"atan(x) - 1/(x**2 + 1)","A",0
77,1,20,0,0.127007," ","integrate((3*x**2+12*x+2)/(x**2+4)**2,x)","\frac{- 5 x - 24}{4 x^{2} + 16} + \frac{7 \operatorname{atan}{\left(\frac{x}{2} \right)}}{8}"," ",0,"(-5*x - 24)/(4*x**2 + 16) + 7*atan(x/2)/8","A",0
78,1,1088,0,28.367146," ","integrate((h*x+g)**3*(f*x**2+e*x+d)*(c*x**2+a)**(1/2),x)","- \frac{a^{\frac{5}{2}} e h^{3} x}{16 c^{2} \sqrt{1 + \frac{c x^{2}}{a}}} - \frac{3 a^{\frac{5}{2}} f g h^{2} x}{16 c^{2} \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{3 a^{\frac{3}{2}} d g h^{2} x}{8 c \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{3 a^{\frac{3}{2}} e g^{2} h x}{8 c \sqrt{1 + \frac{c x^{2}}{a}}} - \frac{a^{\frac{3}{2}} e h^{3} x^{3}}{48 c \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{a^{\frac{3}{2}} f g^{3} x}{8 c \sqrt{1 + \frac{c x^{2}}{a}}} - \frac{a^{\frac{3}{2}} f g h^{2} x^{3}}{16 c \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{\sqrt{a} d g^{3} x \sqrt{1 + \frac{c x^{2}}{a}}}{2} + \frac{9 \sqrt{a} d g h^{2} x^{3}}{8 \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{9 \sqrt{a} e g^{2} h x^{3}}{8 \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{5 \sqrt{a} e h^{3} x^{5}}{24 \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{3 \sqrt{a} f g^{3} x^{3}}{8 \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{5 \sqrt{a} f g h^{2} x^{5}}{8 \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{a^{3} e h^{3} \operatorname{asinh}{\left(\frac{\sqrt{c} x}{\sqrt{a}} \right)}}{16 c^{\frac{5}{2}}} + \frac{3 a^{3} f g h^{2} \operatorname{asinh}{\left(\frac{\sqrt{c} x}{\sqrt{a}} \right)}}{16 c^{\frac{5}{2}}} - \frac{3 a^{2} d g h^{2} \operatorname{asinh}{\left(\frac{\sqrt{c} x}{\sqrt{a}} \right)}}{8 c^{\frac{3}{2}}} - \frac{3 a^{2} e g^{2} h \operatorname{asinh}{\left(\frac{\sqrt{c} x}{\sqrt{a}} \right)}}{8 c^{\frac{3}{2}}} - \frac{a^{2} f g^{3} \operatorname{asinh}{\left(\frac{\sqrt{c} x}{\sqrt{a}} \right)}}{8 c^{\frac{3}{2}}} + \frac{a d g^{3} \operatorname{asinh}{\left(\frac{\sqrt{c} x}{\sqrt{a}} \right)}}{2 \sqrt{c}} + 3 d g^{2} h \left(\begin{cases} \frac{\sqrt{a} x^{2}}{2} & \text{for}\: c = 0 \\\frac{\left(a + c x^{2}\right)^{\frac{3}{2}}}{3 c} & \text{otherwise} \end{cases}\right) + d h^{3} \left(\begin{cases} - \frac{2 a^{2} \sqrt{a + c x^{2}}}{15 c^{2}} + \frac{a x^{2} \sqrt{a + c x^{2}}}{15 c} + \frac{x^{4} \sqrt{a + c x^{2}}}{5} & \text{for}\: c \neq 0 \\\frac{\sqrt{a} x^{4}}{4} & \text{otherwise} \end{cases}\right) + e g^{3} \left(\begin{cases} \frac{\sqrt{a} x^{2}}{2} & \text{for}\: c = 0 \\\frac{\left(a + c x^{2}\right)^{\frac{3}{2}}}{3 c} & \text{otherwise} \end{cases}\right) + 3 e g h^{2} \left(\begin{cases} - \frac{2 a^{2} \sqrt{a + c x^{2}}}{15 c^{2}} + \frac{a x^{2} \sqrt{a + c x^{2}}}{15 c} + \frac{x^{4} \sqrt{a + c x^{2}}}{5} & \text{for}\: c \neq 0 \\\frac{\sqrt{a} x^{4}}{4} & \text{otherwise} \end{cases}\right) + 3 f g^{2} h \left(\begin{cases} - \frac{2 a^{2} \sqrt{a + c x^{2}}}{15 c^{2}} + \frac{a x^{2} \sqrt{a + c x^{2}}}{15 c} + \frac{x^{4} \sqrt{a + c x^{2}}}{5} & \text{for}\: c \neq 0 \\\frac{\sqrt{a} x^{4}}{4} & \text{otherwise} \end{cases}\right) + f h^{3} \left(\begin{cases} \frac{8 a^{3} \sqrt{a + c x^{2}}}{105 c^{3}} - \frac{4 a^{2} x^{2} \sqrt{a + c x^{2}}}{105 c^{2}} + \frac{a x^{4} \sqrt{a + c x^{2}}}{35 c} + \frac{x^{6} \sqrt{a + c x^{2}}}{7} & \text{for}\: c \neq 0 \\\frac{\sqrt{a} x^{6}}{6} & \text{otherwise} \end{cases}\right) + \frac{3 c d g h^{2} x^{5}}{4 \sqrt{a} \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{3 c e g^{2} h x^{5}}{4 \sqrt{a} \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{c e h^{3} x^{7}}{6 \sqrt{a} \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{c f g^{3} x^{5}}{4 \sqrt{a} \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{c f g h^{2} x^{7}}{2 \sqrt{a} \sqrt{1 + \frac{c x^{2}}{a}}}"," ",0,"-a**(5/2)*e*h**3*x/(16*c**2*sqrt(1 + c*x**2/a)) - 3*a**(5/2)*f*g*h**2*x/(16*c**2*sqrt(1 + c*x**2/a)) + 3*a**(3/2)*d*g*h**2*x/(8*c*sqrt(1 + c*x**2/a)) + 3*a**(3/2)*e*g**2*h*x/(8*c*sqrt(1 + c*x**2/a)) - a**(3/2)*e*h**3*x**3/(48*c*sqrt(1 + c*x**2/a)) + a**(3/2)*f*g**3*x/(8*c*sqrt(1 + c*x**2/a)) - a**(3/2)*f*g*h**2*x**3/(16*c*sqrt(1 + c*x**2/a)) + sqrt(a)*d*g**3*x*sqrt(1 + c*x**2/a)/2 + 9*sqrt(a)*d*g*h**2*x**3/(8*sqrt(1 + c*x**2/a)) + 9*sqrt(a)*e*g**2*h*x**3/(8*sqrt(1 + c*x**2/a)) + 5*sqrt(a)*e*h**3*x**5/(24*sqrt(1 + c*x**2/a)) + 3*sqrt(a)*f*g**3*x**3/(8*sqrt(1 + c*x**2/a)) + 5*sqrt(a)*f*g*h**2*x**5/(8*sqrt(1 + c*x**2/a)) + a**3*e*h**3*asinh(sqrt(c)*x/sqrt(a))/(16*c**(5/2)) + 3*a**3*f*g*h**2*asinh(sqrt(c)*x/sqrt(a))/(16*c**(5/2)) - 3*a**2*d*g*h**2*asinh(sqrt(c)*x/sqrt(a))/(8*c**(3/2)) - 3*a**2*e*g**2*h*asinh(sqrt(c)*x/sqrt(a))/(8*c**(3/2)) - a**2*f*g**3*asinh(sqrt(c)*x/sqrt(a))/(8*c**(3/2)) + a*d*g**3*asinh(sqrt(c)*x/sqrt(a))/(2*sqrt(c)) + 3*d*g**2*h*Piecewise((sqrt(a)*x**2/2, Eq(c, 0)), ((a + c*x**2)**(3/2)/(3*c), True)) + d*h**3*Piecewise((-2*a**2*sqrt(a + c*x**2)/(15*c**2) + a*x**2*sqrt(a + c*x**2)/(15*c) + x**4*sqrt(a + c*x**2)/5, Ne(c, 0)), (sqrt(a)*x**4/4, True)) + e*g**3*Piecewise((sqrt(a)*x**2/2, Eq(c, 0)), ((a + c*x**2)**(3/2)/(3*c), True)) + 3*e*g*h**2*Piecewise((-2*a**2*sqrt(a + c*x**2)/(15*c**2) + a*x**2*sqrt(a + c*x**2)/(15*c) + x**4*sqrt(a + c*x**2)/5, Ne(c, 0)), (sqrt(a)*x**4/4, True)) + 3*f*g**2*h*Piecewise((-2*a**2*sqrt(a + c*x**2)/(15*c**2) + a*x**2*sqrt(a + c*x**2)/(15*c) + x**4*sqrt(a + c*x**2)/5, Ne(c, 0)), (sqrt(a)*x**4/4, True)) + f*h**3*Piecewise((8*a**3*sqrt(a + c*x**2)/(105*c**3) - 4*a**2*x**2*sqrt(a + c*x**2)/(105*c**2) + a*x**4*sqrt(a + c*x**2)/(35*c) + x**6*sqrt(a + c*x**2)/7, Ne(c, 0)), (sqrt(a)*x**6/6, True)) + 3*c*d*g*h**2*x**5/(4*sqrt(a)*sqrt(1 + c*x**2/a)) + 3*c*e*g**2*h*x**5/(4*sqrt(a)*sqrt(1 + c*x**2/a)) + c*e*h**3*x**7/(6*sqrt(a)*sqrt(1 + c*x**2/a)) + c*f*g**3*x**5/(4*sqrt(a)*sqrt(1 + c*x**2/a)) + c*f*g*h**2*x**7/(2*sqrt(a)*sqrt(1 + c*x**2/a))","A",0
79,1,738,0,21.000687," ","integrate((h*x+g)**2*(f*x**2+e*x+d)*(c*x**2+a)**(1/2),x)","- \frac{a^{\frac{5}{2}} f h^{2} x}{16 c^{2} \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{a^{\frac{3}{2}} d h^{2} x}{8 c \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{a^{\frac{3}{2}} e g h x}{4 c \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{a^{\frac{3}{2}} f g^{2} x}{8 c \sqrt{1 + \frac{c x^{2}}{a}}} - \frac{a^{\frac{3}{2}} f h^{2} x^{3}}{48 c \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{\sqrt{a} d g^{2} x \sqrt{1 + \frac{c x^{2}}{a}}}{2} + \frac{3 \sqrt{a} d h^{2} x^{3}}{8 \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{3 \sqrt{a} e g h x^{3}}{4 \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{3 \sqrt{a} f g^{2} x^{3}}{8 \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{5 \sqrt{a} f h^{2} x^{5}}{24 \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{a^{3} f h^{2} \operatorname{asinh}{\left(\frac{\sqrt{c} x}{\sqrt{a}} \right)}}{16 c^{\frac{5}{2}}} - \frac{a^{2} d h^{2} \operatorname{asinh}{\left(\frac{\sqrt{c} x}{\sqrt{a}} \right)}}{8 c^{\frac{3}{2}}} - \frac{a^{2} e g h \operatorname{asinh}{\left(\frac{\sqrt{c} x}{\sqrt{a}} \right)}}{4 c^{\frac{3}{2}}} - \frac{a^{2} f g^{2} \operatorname{asinh}{\left(\frac{\sqrt{c} x}{\sqrt{a}} \right)}}{8 c^{\frac{3}{2}}} + \frac{a d g^{2} \operatorname{asinh}{\left(\frac{\sqrt{c} x}{\sqrt{a}} \right)}}{2 \sqrt{c}} + 2 d g h \left(\begin{cases} \frac{\sqrt{a} x^{2}}{2} & \text{for}\: c = 0 \\\frac{\left(a + c x^{2}\right)^{\frac{3}{2}}}{3 c} & \text{otherwise} \end{cases}\right) + e g^{2} \left(\begin{cases} \frac{\sqrt{a} x^{2}}{2} & \text{for}\: c = 0 \\\frac{\left(a + c x^{2}\right)^{\frac{3}{2}}}{3 c} & \text{otherwise} \end{cases}\right) + e h^{2} \left(\begin{cases} - \frac{2 a^{2} \sqrt{a + c x^{2}}}{15 c^{2}} + \frac{a x^{2} \sqrt{a + c x^{2}}}{15 c} + \frac{x^{4} \sqrt{a + c x^{2}}}{5} & \text{for}\: c \neq 0 \\\frac{\sqrt{a} x^{4}}{4} & \text{otherwise} \end{cases}\right) + 2 f g h \left(\begin{cases} - \frac{2 a^{2} \sqrt{a + c x^{2}}}{15 c^{2}} + \frac{a x^{2} \sqrt{a + c x^{2}}}{15 c} + \frac{x^{4} \sqrt{a + c x^{2}}}{5} & \text{for}\: c \neq 0 \\\frac{\sqrt{a} x^{4}}{4} & \text{otherwise} \end{cases}\right) + \frac{c d h^{2} x^{5}}{4 \sqrt{a} \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{c e g h x^{5}}{2 \sqrt{a} \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{c f g^{2} x^{5}}{4 \sqrt{a} \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{c f h^{2} x^{7}}{6 \sqrt{a} \sqrt{1 + \frac{c x^{2}}{a}}}"," ",0,"-a**(5/2)*f*h**2*x/(16*c**2*sqrt(1 + c*x**2/a)) + a**(3/2)*d*h**2*x/(8*c*sqrt(1 + c*x**2/a)) + a**(3/2)*e*g*h*x/(4*c*sqrt(1 + c*x**2/a)) + a**(3/2)*f*g**2*x/(8*c*sqrt(1 + c*x**2/a)) - a**(3/2)*f*h**2*x**3/(48*c*sqrt(1 + c*x**2/a)) + sqrt(a)*d*g**2*x*sqrt(1 + c*x**2/a)/2 + 3*sqrt(a)*d*h**2*x**3/(8*sqrt(1 + c*x**2/a)) + 3*sqrt(a)*e*g*h*x**3/(4*sqrt(1 + c*x**2/a)) + 3*sqrt(a)*f*g**2*x**3/(8*sqrt(1 + c*x**2/a)) + 5*sqrt(a)*f*h**2*x**5/(24*sqrt(1 + c*x**2/a)) + a**3*f*h**2*asinh(sqrt(c)*x/sqrt(a))/(16*c**(5/2)) - a**2*d*h**2*asinh(sqrt(c)*x/sqrt(a))/(8*c**(3/2)) - a**2*e*g*h*asinh(sqrt(c)*x/sqrt(a))/(4*c**(3/2)) - a**2*f*g**2*asinh(sqrt(c)*x/sqrt(a))/(8*c**(3/2)) + a*d*g**2*asinh(sqrt(c)*x/sqrt(a))/(2*sqrt(c)) + 2*d*g*h*Piecewise((sqrt(a)*x**2/2, Eq(c, 0)), ((a + c*x**2)**(3/2)/(3*c), True)) + e*g**2*Piecewise((sqrt(a)*x**2/2, Eq(c, 0)), ((a + c*x**2)**(3/2)/(3*c), True)) + e*h**2*Piecewise((-2*a**2*sqrt(a + c*x**2)/(15*c**2) + a*x**2*sqrt(a + c*x**2)/(15*c) + x**4*sqrt(a + c*x**2)/5, Ne(c, 0)), (sqrt(a)*x**4/4, True)) + 2*f*g*h*Piecewise((-2*a**2*sqrt(a + c*x**2)/(15*c**2) + a*x**2*sqrt(a + c*x**2)/(15*c) + x**4*sqrt(a + c*x**2)/5, Ne(c, 0)), (sqrt(a)*x**4/4, True)) + c*d*h**2*x**5/(4*sqrt(a)*sqrt(1 + c*x**2/a)) + c*e*g*h*x**5/(2*sqrt(a)*sqrt(1 + c*x**2/a)) + c*f*g**2*x**5/(4*sqrt(a)*sqrt(1 + c*x**2/a)) + c*f*h**2*x**7/(6*sqrt(a)*sqrt(1 + c*x**2/a))","A",0
80,1,384,0,11.876010," ","integrate((h*x+g)*(f*x**2+e*x+d)*(c*x**2+a)**(1/2),x)","\frac{a^{\frac{3}{2}} e h x}{8 c \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{a^{\frac{3}{2}} f g x}{8 c \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{\sqrt{a} d g x \sqrt{1 + \frac{c x^{2}}{a}}}{2} + \frac{3 \sqrt{a} e h x^{3}}{8 \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{3 \sqrt{a} f g x^{3}}{8 \sqrt{1 + \frac{c x^{2}}{a}}} - \frac{a^{2} e h \operatorname{asinh}{\left(\frac{\sqrt{c} x}{\sqrt{a}} \right)}}{8 c^{\frac{3}{2}}} - \frac{a^{2} f g \operatorname{asinh}{\left(\frac{\sqrt{c} x}{\sqrt{a}} \right)}}{8 c^{\frac{3}{2}}} + \frac{a d g \operatorname{asinh}{\left(\frac{\sqrt{c} x}{\sqrt{a}} \right)}}{2 \sqrt{c}} + d h \left(\begin{cases} \frac{\sqrt{a} x^{2}}{2} & \text{for}\: c = 0 \\\frac{\left(a + c x^{2}\right)^{\frac{3}{2}}}{3 c} & \text{otherwise} \end{cases}\right) + e g \left(\begin{cases} \frac{\sqrt{a} x^{2}}{2} & \text{for}\: c = 0 \\\frac{\left(a + c x^{2}\right)^{\frac{3}{2}}}{3 c} & \text{otherwise} \end{cases}\right) + f h \left(\begin{cases} - \frac{2 a^{2} \sqrt{a + c x^{2}}}{15 c^{2}} + \frac{a x^{2} \sqrt{a + c x^{2}}}{15 c} + \frac{x^{4} \sqrt{a + c x^{2}}}{5} & \text{for}\: c \neq 0 \\\frac{\sqrt{a} x^{4}}{4} & \text{otherwise} \end{cases}\right) + \frac{c e h x^{5}}{4 \sqrt{a} \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{c f g x^{5}}{4 \sqrt{a} \sqrt{1 + \frac{c x^{2}}{a}}}"," ",0,"a**(3/2)*e*h*x/(8*c*sqrt(1 + c*x**2/a)) + a**(3/2)*f*g*x/(8*c*sqrt(1 + c*x**2/a)) + sqrt(a)*d*g*x*sqrt(1 + c*x**2/a)/2 + 3*sqrt(a)*e*h*x**3/(8*sqrt(1 + c*x**2/a)) + 3*sqrt(a)*f*g*x**3/(8*sqrt(1 + c*x**2/a)) - a**2*e*h*asinh(sqrt(c)*x/sqrt(a))/(8*c**(3/2)) - a**2*f*g*asinh(sqrt(c)*x/sqrt(a))/(8*c**(3/2)) + a*d*g*asinh(sqrt(c)*x/sqrt(a))/(2*sqrt(c)) + d*h*Piecewise((sqrt(a)*x**2/2, Eq(c, 0)), ((a + c*x**2)**(3/2)/(3*c), True)) + e*g*Piecewise((sqrt(a)*x**2/2, Eq(c, 0)), ((a + c*x**2)**(3/2)/(3*c), True)) + f*h*Piecewise((-2*a**2*sqrt(a + c*x**2)/(15*c**2) + a*x**2*sqrt(a + c*x**2)/(15*c) + x**4*sqrt(a + c*x**2)/5, Ne(c, 0)), (sqrt(a)*x**4/4, True)) + c*e*h*x**5/(4*sqrt(a)*sqrt(1 + c*x**2/a)) + c*f*g*x**5/(4*sqrt(a)*sqrt(1 + c*x**2/a))","A",0
81,1,170,0,6.903165," ","integrate((f*x**2+e*x+d)*(c*x**2+a)**(1/2),x)","\frac{a^{\frac{3}{2}} f x}{8 c \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{\sqrt{a} d x \sqrt{1 + \frac{c x^{2}}{a}}}{2} + \frac{3 \sqrt{a} f x^{3}}{8 \sqrt{1 + \frac{c x^{2}}{a}}} - \frac{a^{2} f \operatorname{asinh}{\left(\frac{\sqrt{c} x}{\sqrt{a}} \right)}}{8 c^{\frac{3}{2}}} + \frac{a d \operatorname{asinh}{\left(\frac{\sqrt{c} x}{\sqrt{a}} \right)}}{2 \sqrt{c}} + e \left(\begin{cases} \frac{\sqrt{a} x^{2}}{2} & \text{for}\: c = 0 \\\frac{\left(a + c x^{2}\right)^{\frac{3}{2}}}{3 c} & \text{otherwise} \end{cases}\right) + \frac{c f x^{5}}{4 \sqrt{a} \sqrt{1 + \frac{c x^{2}}{a}}}"," ",0,"a**(3/2)*f*x/(8*c*sqrt(1 + c*x**2/a)) + sqrt(a)*d*x*sqrt(1 + c*x**2/a)/2 + 3*sqrt(a)*f*x**3/(8*sqrt(1 + c*x**2/a)) - a**2*f*asinh(sqrt(c)*x/sqrt(a))/(8*c**(3/2)) + a*d*asinh(sqrt(c)*x/sqrt(a))/(2*sqrt(c)) + e*Piecewise((sqrt(a)*x**2/2, Eq(c, 0)), ((a + c*x**2)**(3/2)/(3*c), True)) + c*f*x**5/(4*sqrt(a)*sqrt(1 + c*x**2/a))","A",0
82,0,0,0,0.000000," ","integrate((f*x**2+e*x+d)*(c*x**2+a)**(1/2)/(h*x+g),x)","\int \frac{\sqrt{a + c x^{2}} \left(d + e x + f x^{2}\right)}{g + h x}\, dx"," ",0,"Integral(sqrt(a + c*x**2)*(d + e*x + f*x**2)/(g + h*x), x)","F",0
83,0,0,0,0.000000," ","integrate((f*x**2+e*x+d)*(c*x**2+a)**(1/2)/(h*x+g)**2,x)","\int \frac{\sqrt{a + c x^{2}} \left(d + e x + f x^{2}\right)}{\left(g + h x\right)^{2}}\, dx"," ",0,"Integral(sqrt(a + c*x**2)*(d + e*x + f*x**2)/(g + h*x)**2, x)","F",0
84,0,0,0,0.000000," ","integrate((f*x**2+e*x+d)*(c*x**2+a)**(1/2)/(h*x+g)**3,x)","\int \frac{\sqrt{a + c x^{2}} \left(d + e x + f x^{2}\right)}{\left(g + h x\right)^{3}}\, dx"," ",0,"Integral(sqrt(a + c*x**2)*(d + e*x + f*x**2)/(g + h*x)**3, x)","F",0
85,0,0,0,0.000000," ","integrate((f*x**2+e*x+d)*(c*x**2+a)**(1/2)/(h*x+g)**4,x)","\int \frac{\sqrt{a + c x^{2}} \left(d + e x + f x^{2}\right)}{\left(g + h x\right)^{4}}\, dx"," ",0,"Integral(sqrt(a + c*x**2)*(d + e*x + f*x**2)/(g + h*x)**4, x)","F",0
86,0,0,0,0.000000," ","integrate((f*x**2+e*x+d)*(c*x**2+a)**(1/2)/(h*x+g)**5,x)","\int \frac{\sqrt{a + c x^{2}} \left(d + e x + f x^{2}\right)}{\left(g + h x\right)^{5}}\, dx"," ",0,"Integral(sqrt(a + c*x**2)*(d + e*x + f*x**2)/(g + h*x)**5, x)","F",0
87,-1,0,0,0.000000," ","integrate((f*x**2+e*x+d)*(c*x**2+a)**(1/2)/(h*x+g)**6,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
88,1,1916,0,72.413768," ","integrate((h*x+g)**3*(c*x**2+a)**(3/2)*(f*x**2+e*x+d),x)","- \frac{3 a^{\frac{7}{2}} e h^{3} x}{128 c^{2} \sqrt{1 + \frac{c x^{2}}{a}}} - \frac{9 a^{\frac{7}{2}} f g h^{2} x}{128 c^{2} \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{3 a^{\frac{5}{2}} d g h^{2} x}{16 c \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{3 a^{\frac{5}{2}} e g^{2} h x}{16 c \sqrt{1 + \frac{c x^{2}}{a}}} - \frac{a^{\frac{5}{2}} e h^{3} x^{3}}{128 c \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{a^{\frac{5}{2}} f g^{3} x}{16 c \sqrt{1 + \frac{c x^{2}}{a}}} - \frac{3 a^{\frac{5}{2}} f g h^{2} x^{3}}{128 c \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{a^{\frac{3}{2}} d g^{3} x \sqrt{1 + \frac{c x^{2}}{a}}}{2} + \frac{a^{\frac{3}{2}} d g^{3} x}{8 \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{17 a^{\frac{3}{2}} d g h^{2} x^{3}}{16 \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{17 a^{\frac{3}{2}} e g^{2} h x^{3}}{16 \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{13 a^{\frac{3}{2}} e h^{3} x^{5}}{64 \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{17 a^{\frac{3}{2}} f g^{3} x^{3}}{48 \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{39 a^{\frac{3}{2}} f g h^{2} x^{5}}{64 \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{3 \sqrt{a} c d g^{3} x^{3}}{8 \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{11 \sqrt{a} c d g h^{2} x^{5}}{8 \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{11 \sqrt{a} c e g^{2} h x^{5}}{8 \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{5 \sqrt{a} c e h^{3} x^{7}}{16 \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{11 \sqrt{a} c f g^{3} x^{5}}{24 \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{15 \sqrt{a} c f g h^{2} x^{7}}{16 \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{3 a^{4} e h^{3} \operatorname{asinh}{\left(\frac{\sqrt{c} x}{\sqrt{a}} \right)}}{128 c^{\frac{5}{2}}} + \frac{9 a^{4} f g h^{2} \operatorname{asinh}{\left(\frac{\sqrt{c} x}{\sqrt{a}} \right)}}{128 c^{\frac{5}{2}}} - \frac{3 a^{3} d g h^{2} \operatorname{asinh}{\left(\frac{\sqrt{c} x}{\sqrt{a}} \right)}}{16 c^{\frac{3}{2}}} - \frac{3 a^{3} e g^{2} h \operatorname{asinh}{\left(\frac{\sqrt{c} x}{\sqrt{a}} \right)}}{16 c^{\frac{3}{2}}} - \frac{a^{3} f g^{3} \operatorname{asinh}{\left(\frac{\sqrt{c} x}{\sqrt{a}} \right)}}{16 c^{\frac{3}{2}}} + \frac{3 a^{2} d g^{3} \operatorname{asinh}{\left(\frac{\sqrt{c} x}{\sqrt{a}} \right)}}{8 \sqrt{c}} + 3 a d g^{2} h \left(\begin{cases} \frac{\sqrt{a} x^{2}}{2} & \text{for}\: c = 0 \\\frac{\left(a + c x^{2}\right)^{\frac{3}{2}}}{3 c} & \text{otherwise} \end{cases}\right) + a d h^{3} \left(\begin{cases} - \frac{2 a^{2} \sqrt{a + c x^{2}}}{15 c^{2}} + \frac{a x^{2} \sqrt{a + c x^{2}}}{15 c} + \frac{x^{4} \sqrt{a + c x^{2}}}{5} & \text{for}\: c \neq 0 \\\frac{\sqrt{a} x^{4}}{4} & \text{otherwise} \end{cases}\right) + a e g^{3} \left(\begin{cases} \frac{\sqrt{a} x^{2}}{2} & \text{for}\: c = 0 \\\frac{\left(a + c x^{2}\right)^{\frac{3}{2}}}{3 c} & \text{otherwise} \end{cases}\right) + 3 a e g h^{2} \left(\begin{cases} - \frac{2 a^{2} \sqrt{a + c x^{2}}}{15 c^{2}} + \frac{a x^{2} \sqrt{a + c x^{2}}}{15 c} + \frac{x^{4} \sqrt{a + c x^{2}}}{5} & \text{for}\: c \neq 0 \\\frac{\sqrt{a} x^{4}}{4} & \text{otherwise} \end{cases}\right) + 3 a f g^{2} h \left(\begin{cases} - \frac{2 a^{2} \sqrt{a + c x^{2}}}{15 c^{2}} + \frac{a x^{2} \sqrt{a + c x^{2}}}{15 c} + \frac{x^{4} \sqrt{a + c x^{2}}}{5} & \text{for}\: c \neq 0 \\\frac{\sqrt{a} x^{4}}{4} & \text{otherwise} \end{cases}\right) + a f h^{3} \left(\begin{cases} \frac{8 a^{3} \sqrt{a + c x^{2}}}{105 c^{3}} - \frac{4 a^{2} x^{2} \sqrt{a + c x^{2}}}{105 c^{2}} + \frac{a x^{4} \sqrt{a + c x^{2}}}{35 c} + \frac{x^{6} \sqrt{a + c x^{2}}}{7} & \text{for}\: c \neq 0 \\\frac{\sqrt{a} x^{6}}{6} & \text{otherwise} \end{cases}\right) + 3 c d g^{2} h \left(\begin{cases} - \frac{2 a^{2} \sqrt{a + c x^{2}}}{15 c^{2}} + \frac{a x^{2} \sqrt{a + c x^{2}}}{15 c} + \frac{x^{4} \sqrt{a + c x^{2}}}{5} & \text{for}\: c \neq 0 \\\frac{\sqrt{a} x^{4}}{4} & \text{otherwise} \end{cases}\right) + c d h^{3} \left(\begin{cases} \frac{8 a^{3} \sqrt{a + c x^{2}}}{105 c^{3}} - \frac{4 a^{2} x^{2} \sqrt{a + c x^{2}}}{105 c^{2}} + \frac{a x^{4} \sqrt{a + c x^{2}}}{35 c} + \frac{x^{6} \sqrt{a + c x^{2}}}{7} & \text{for}\: c \neq 0 \\\frac{\sqrt{a} x^{6}}{6} & \text{otherwise} \end{cases}\right) + c e g^{3} \left(\begin{cases} - \frac{2 a^{2} \sqrt{a + c x^{2}}}{15 c^{2}} + \frac{a x^{2} \sqrt{a + c x^{2}}}{15 c} + \frac{x^{4} \sqrt{a + c x^{2}}}{5} & \text{for}\: c \neq 0 \\\frac{\sqrt{a} x^{4}}{4} & \text{otherwise} \end{cases}\right) + 3 c e g h^{2} \left(\begin{cases} \frac{8 a^{3} \sqrt{a + c x^{2}}}{105 c^{3}} - \frac{4 a^{2} x^{2} \sqrt{a + c x^{2}}}{105 c^{2}} + \frac{a x^{4} \sqrt{a + c x^{2}}}{35 c} + \frac{x^{6} \sqrt{a + c x^{2}}}{7} & \text{for}\: c \neq 0 \\\frac{\sqrt{a} x^{6}}{6} & \text{otherwise} \end{cases}\right) + 3 c f g^{2} h \left(\begin{cases} \frac{8 a^{3} \sqrt{a + c x^{2}}}{105 c^{3}} - \frac{4 a^{2} x^{2} \sqrt{a + c x^{2}}}{105 c^{2}} + \frac{a x^{4} \sqrt{a + c x^{2}}}{35 c} + \frac{x^{6} \sqrt{a + c x^{2}}}{7} & \text{for}\: c \neq 0 \\\frac{\sqrt{a} x^{6}}{6} & \text{otherwise} \end{cases}\right) + c f h^{3} \left(\begin{cases} - \frac{16 a^{4} \sqrt{a + c x^{2}}}{315 c^{4}} + \frac{8 a^{3} x^{2} \sqrt{a + c x^{2}}}{315 c^{3}} - \frac{2 a^{2} x^{4} \sqrt{a + c x^{2}}}{105 c^{2}} + \frac{a x^{6} \sqrt{a + c x^{2}}}{63 c} + \frac{x^{8} \sqrt{a + c x^{2}}}{9} & \text{for}\: c \neq 0 \\\frac{\sqrt{a} x^{8}}{8} & \text{otherwise} \end{cases}\right) + \frac{c^{2} d g^{3} x^{5}}{4 \sqrt{a} \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{c^{2} d g h^{2} x^{7}}{2 \sqrt{a} \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{c^{2} e g^{2} h x^{7}}{2 \sqrt{a} \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{c^{2} e h^{3} x^{9}}{8 \sqrt{a} \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{c^{2} f g^{3} x^{7}}{6 \sqrt{a} \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{3 c^{2} f g h^{2} x^{9}}{8 \sqrt{a} \sqrt{1 + \frac{c x^{2}}{a}}}"," ",0,"-3*a**(7/2)*e*h**3*x/(128*c**2*sqrt(1 + c*x**2/a)) - 9*a**(7/2)*f*g*h**2*x/(128*c**2*sqrt(1 + c*x**2/a)) + 3*a**(5/2)*d*g*h**2*x/(16*c*sqrt(1 + c*x**2/a)) + 3*a**(5/2)*e*g**2*h*x/(16*c*sqrt(1 + c*x**2/a)) - a**(5/2)*e*h**3*x**3/(128*c*sqrt(1 + c*x**2/a)) + a**(5/2)*f*g**3*x/(16*c*sqrt(1 + c*x**2/a)) - 3*a**(5/2)*f*g*h**2*x**3/(128*c*sqrt(1 + c*x**2/a)) + a**(3/2)*d*g**3*x*sqrt(1 + c*x**2/a)/2 + a**(3/2)*d*g**3*x/(8*sqrt(1 + c*x**2/a)) + 17*a**(3/2)*d*g*h**2*x**3/(16*sqrt(1 + c*x**2/a)) + 17*a**(3/2)*e*g**2*h*x**3/(16*sqrt(1 + c*x**2/a)) + 13*a**(3/2)*e*h**3*x**5/(64*sqrt(1 + c*x**2/a)) + 17*a**(3/2)*f*g**3*x**3/(48*sqrt(1 + c*x**2/a)) + 39*a**(3/2)*f*g*h**2*x**5/(64*sqrt(1 + c*x**2/a)) + 3*sqrt(a)*c*d*g**3*x**3/(8*sqrt(1 + c*x**2/a)) + 11*sqrt(a)*c*d*g*h**2*x**5/(8*sqrt(1 + c*x**2/a)) + 11*sqrt(a)*c*e*g**2*h*x**5/(8*sqrt(1 + c*x**2/a)) + 5*sqrt(a)*c*e*h**3*x**7/(16*sqrt(1 + c*x**2/a)) + 11*sqrt(a)*c*f*g**3*x**5/(24*sqrt(1 + c*x**2/a)) + 15*sqrt(a)*c*f*g*h**2*x**7/(16*sqrt(1 + c*x**2/a)) + 3*a**4*e*h**3*asinh(sqrt(c)*x/sqrt(a))/(128*c**(5/2)) + 9*a**4*f*g*h**2*asinh(sqrt(c)*x/sqrt(a))/(128*c**(5/2)) - 3*a**3*d*g*h**2*asinh(sqrt(c)*x/sqrt(a))/(16*c**(3/2)) - 3*a**3*e*g**2*h*asinh(sqrt(c)*x/sqrt(a))/(16*c**(3/2)) - a**3*f*g**3*asinh(sqrt(c)*x/sqrt(a))/(16*c**(3/2)) + 3*a**2*d*g**3*asinh(sqrt(c)*x/sqrt(a))/(8*sqrt(c)) + 3*a*d*g**2*h*Piecewise((sqrt(a)*x**2/2, Eq(c, 0)), ((a + c*x**2)**(3/2)/(3*c), True)) + a*d*h**3*Piecewise((-2*a**2*sqrt(a + c*x**2)/(15*c**2) + a*x**2*sqrt(a + c*x**2)/(15*c) + x**4*sqrt(a + c*x**2)/5, Ne(c, 0)), (sqrt(a)*x**4/4, True)) + a*e*g**3*Piecewise((sqrt(a)*x**2/2, Eq(c, 0)), ((a + c*x**2)**(3/2)/(3*c), True)) + 3*a*e*g*h**2*Piecewise((-2*a**2*sqrt(a + c*x**2)/(15*c**2) + a*x**2*sqrt(a + c*x**2)/(15*c) + x**4*sqrt(a + c*x**2)/5, Ne(c, 0)), (sqrt(a)*x**4/4, True)) + 3*a*f*g**2*h*Piecewise((-2*a**2*sqrt(a + c*x**2)/(15*c**2) + a*x**2*sqrt(a + c*x**2)/(15*c) + x**4*sqrt(a + c*x**2)/5, Ne(c, 0)), (sqrt(a)*x**4/4, True)) + a*f*h**3*Piecewise((8*a**3*sqrt(a + c*x**2)/(105*c**3) - 4*a**2*x**2*sqrt(a + c*x**2)/(105*c**2) + a*x**4*sqrt(a + c*x**2)/(35*c) + x**6*sqrt(a + c*x**2)/7, Ne(c, 0)), (sqrt(a)*x**6/6, True)) + 3*c*d*g**2*h*Piecewise((-2*a**2*sqrt(a + c*x**2)/(15*c**2) + a*x**2*sqrt(a + c*x**2)/(15*c) + x**4*sqrt(a + c*x**2)/5, Ne(c, 0)), (sqrt(a)*x**4/4, True)) + c*d*h**3*Piecewise((8*a**3*sqrt(a + c*x**2)/(105*c**3) - 4*a**2*x**2*sqrt(a + c*x**2)/(105*c**2) + a*x**4*sqrt(a + c*x**2)/(35*c) + x**6*sqrt(a + c*x**2)/7, Ne(c, 0)), (sqrt(a)*x**6/6, True)) + c*e*g**3*Piecewise((-2*a**2*sqrt(a + c*x**2)/(15*c**2) + a*x**2*sqrt(a + c*x**2)/(15*c) + x**4*sqrt(a + c*x**2)/5, Ne(c, 0)), (sqrt(a)*x**4/4, True)) + 3*c*e*g*h**2*Piecewise((8*a**3*sqrt(a + c*x**2)/(105*c**3) - 4*a**2*x**2*sqrt(a + c*x**2)/(105*c**2) + a*x**4*sqrt(a + c*x**2)/(35*c) + x**6*sqrt(a + c*x**2)/7, Ne(c, 0)), (sqrt(a)*x**6/6, True)) + 3*c*f*g**2*h*Piecewise((8*a**3*sqrt(a + c*x**2)/(105*c**3) - 4*a**2*x**2*sqrt(a + c*x**2)/(105*c**2) + a*x**4*sqrt(a + c*x**2)/(35*c) + x**6*sqrt(a + c*x**2)/7, Ne(c, 0)), (sqrt(a)*x**6/6, True)) + c*f*h**3*Piecewise((-16*a**4*sqrt(a + c*x**2)/(315*c**4) + 8*a**3*x**2*sqrt(a + c*x**2)/(315*c**3) - 2*a**2*x**4*sqrt(a + c*x**2)/(105*c**2) + a*x**6*sqrt(a + c*x**2)/(63*c) + x**8*sqrt(a + c*x**2)/9, Ne(c, 0)), (sqrt(a)*x**8/8, True)) + c**2*d*g**3*x**5/(4*sqrt(a)*sqrt(1 + c*x**2/a)) + c**2*d*g*h**2*x**7/(2*sqrt(a)*sqrt(1 + c*x**2/a)) + c**2*e*g**2*h*x**7/(2*sqrt(a)*sqrt(1 + c*x**2/a)) + c**2*e*h**3*x**9/(8*sqrt(a)*sqrt(1 + c*x**2/a)) + c**2*f*g**3*x**7/(6*sqrt(a)*sqrt(1 + c*x**2/a)) + 3*c**2*f*g*h**2*x**9/(8*sqrt(a)*sqrt(1 + c*x**2/a))","A",0
89,1,1304,0,54.496264," ","integrate((h*x+g)**2*(c*x**2+a)**(3/2)*(f*x**2+e*x+d),x)","- \frac{3 a^{\frac{7}{2}} f h^{2} x}{128 c^{2} \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{a^{\frac{5}{2}} d h^{2} x}{16 c \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{a^{\frac{5}{2}} e g h x}{8 c \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{a^{\frac{5}{2}} f g^{2} x}{16 c \sqrt{1 + \frac{c x^{2}}{a}}} - \frac{a^{\frac{5}{2}} f h^{2} x^{3}}{128 c \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{a^{\frac{3}{2}} d g^{2} x \sqrt{1 + \frac{c x^{2}}{a}}}{2} + \frac{a^{\frac{3}{2}} d g^{2} x}{8 \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{17 a^{\frac{3}{2}} d h^{2} x^{3}}{48 \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{17 a^{\frac{3}{2}} e g h x^{3}}{24 \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{17 a^{\frac{3}{2}} f g^{2} x^{3}}{48 \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{13 a^{\frac{3}{2}} f h^{2} x^{5}}{64 \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{3 \sqrt{a} c d g^{2} x^{3}}{8 \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{11 \sqrt{a} c d h^{2} x^{5}}{24 \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{11 \sqrt{a} c e g h x^{5}}{12 \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{11 \sqrt{a} c f g^{2} x^{5}}{24 \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{5 \sqrt{a} c f h^{2} x^{7}}{16 \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{3 a^{4} f h^{2} \operatorname{asinh}{\left(\frac{\sqrt{c} x}{\sqrt{a}} \right)}}{128 c^{\frac{5}{2}}} - \frac{a^{3} d h^{2} \operatorname{asinh}{\left(\frac{\sqrt{c} x}{\sqrt{a}} \right)}}{16 c^{\frac{3}{2}}} - \frac{a^{3} e g h \operatorname{asinh}{\left(\frac{\sqrt{c} x}{\sqrt{a}} \right)}}{8 c^{\frac{3}{2}}} - \frac{a^{3} f g^{2} \operatorname{asinh}{\left(\frac{\sqrt{c} x}{\sqrt{a}} \right)}}{16 c^{\frac{3}{2}}} + \frac{3 a^{2} d g^{2} \operatorname{asinh}{\left(\frac{\sqrt{c} x}{\sqrt{a}} \right)}}{8 \sqrt{c}} + 2 a d g h \left(\begin{cases} \frac{\sqrt{a} x^{2}}{2} & \text{for}\: c = 0 \\\frac{\left(a + c x^{2}\right)^{\frac{3}{2}}}{3 c} & \text{otherwise} \end{cases}\right) + a e g^{2} \left(\begin{cases} \frac{\sqrt{a} x^{2}}{2} & \text{for}\: c = 0 \\\frac{\left(a + c x^{2}\right)^{\frac{3}{2}}}{3 c} & \text{otherwise} \end{cases}\right) + a e h^{2} \left(\begin{cases} - \frac{2 a^{2} \sqrt{a + c x^{2}}}{15 c^{2}} + \frac{a x^{2} \sqrt{a + c x^{2}}}{15 c} + \frac{x^{4} \sqrt{a + c x^{2}}}{5} & \text{for}\: c \neq 0 \\\frac{\sqrt{a} x^{4}}{4} & \text{otherwise} \end{cases}\right) + 2 a f g h \left(\begin{cases} - \frac{2 a^{2} \sqrt{a + c x^{2}}}{15 c^{2}} + \frac{a x^{2} \sqrt{a + c x^{2}}}{15 c} + \frac{x^{4} \sqrt{a + c x^{2}}}{5} & \text{for}\: c \neq 0 \\\frac{\sqrt{a} x^{4}}{4} & \text{otherwise} \end{cases}\right) + 2 c d g h \left(\begin{cases} - \frac{2 a^{2} \sqrt{a + c x^{2}}}{15 c^{2}} + \frac{a x^{2} \sqrt{a + c x^{2}}}{15 c} + \frac{x^{4} \sqrt{a + c x^{2}}}{5} & \text{for}\: c \neq 0 \\\frac{\sqrt{a} x^{4}}{4} & \text{otherwise} \end{cases}\right) + c e g^{2} \left(\begin{cases} - \frac{2 a^{2} \sqrt{a + c x^{2}}}{15 c^{2}} + \frac{a x^{2} \sqrt{a + c x^{2}}}{15 c} + \frac{x^{4} \sqrt{a + c x^{2}}}{5} & \text{for}\: c \neq 0 \\\frac{\sqrt{a} x^{4}}{4} & \text{otherwise} \end{cases}\right) + c e h^{2} \left(\begin{cases} \frac{8 a^{3} \sqrt{a + c x^{2}}}{105 c^{3}} - \frac{4 a^{2} x^{2} \sqrt{a + c x^{2}}}{105 c^{2}} + \frac{a x^{4} \sqrt{a + c x^{2}}}{35 c} + \frac{x^{6} \sqrt{a + c x^{2}}}{7} & \text{for}\: c \neq 0 \\\frac{\sqrt{a} x^{6}}{6} & \text{otherwise} \end{cases}\right) + 2 c f g h \left(\begin{cases} \frac{8 a^{3} \sqrt{a + c x^{2}}}{105 c^{3}} - \frac{4 a^{2} x^{2} \sqrt{a + c x^{2}}}{105 c^{2}} + \frac{a x^{4} \sqrt{a + c x^{2}}}{35 c} + \frac{x^{6} \sqrt{a + c x^{2}}}{7} & \text{for}\: c \neq 0 \\\frac{\sqrt{a} x^{6}}{6} & \text{otherwise} \end{cases}\right) + \frac{c^{2} d g^{2} x^{5}}{4 \sqrt{a} \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{c^{2} d h^{2} x^{7}}{6 \sqrt{a} \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{c^{2} e g h x^{7}}{3 \sqrt{a} \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{c^{2} f g^{2} x^{7}}{6 \sqrt{a} \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{c^{2} f h^{2} x^{9}}{8 \sqrt{a} \sqrt{1 + \frac{c x^{2}}{a}}}"," ",0,"-3*a**(7/2)*f*h**2*x/(128*c**2*sqrt(1 + c*x**2/a)) + a**(5/2)*d*h**2*x/(16*c*sqrt(1 + c*x**2/a)) + a**(5/2)*e*g*h*x/(8*c*sqrt(1 + c*x**2/a)) + a**(5/2)*f*g**2*x/(16*c*sqrt(1 + c*x**2/a)) - a**(5/2)*f*h**2*x**3/(128*c*sqrt(1 + c*x**2/a)) + a**(3/2)*d*g**2*x*sqrt(1 + c*x**2/a)/2 + a**(3/2)*d*g**2*x/(8*sqrt(1 + c*x**2/a)) + 17*a**(3/2)*d*h**2*x**3/(48*sqrt(1 + c*x**2/a)) + 17*a**(3/2)*e*g*h*x**3/(24*sqrt(1 + c*x**2/a)) + 17*a**(3/2)*f*g**2*x**3/(48*sqrt(1 + c*x**2/a)) + 13*a**(3/2)*f*h**2*x**5/(64*sqrt(1 + c*x**2/a)) + 3*sqrt(a)*c*d*g**2*x**3/(8*sqrt(1 + c*x**2/a)) + 11*sqrt(a)*c*d*h**2*x**5/(24*sqrt(1 + c*x**2/a)) + 11*sqrt(a)*c*e*g*h*x**5/(12*sqrt(1 + c*x**2/a)) + 11*sqrt(a)*c*f*g**2*x**5/(24*sqrt(1 + c*x**2/a)) + 5*sqrt(a)*c*f*h**2*x**7/(16*sqrt(1 + c*x**2/a)) + 3*a**4*f*h**2*asinh(sqrt(c)*x/sqrt(a))/(128*c**(5/2)) - a**3*d*h**2*asinh(sqrt(c)*x/sqrt(a))/(16*c**(3/2)) - a**3*e*g*h*asinh(sqrt(c)*x/sqrt(a))/(8*c**(3/2)) - a**3*f*g**2*asinh(sqrt(c)*x/sqrt(a))/(16*c**(3/2)) + 3*a**2*d*g**2*asinh(sqrt(c)*x/sqrt(a))/(8*sqrt(c)) + 2*a*d*g*h*Piecewise((sqrt(a)*x**2/2, Eq(c, 0)), ((a + c*x**2)**(3/2)/(3*c), True)) + a*e*g**2*Piecewise((sqrt(a)*x**2/2, Eq(c, 0)), ((a + c*x**2)**(3/2)/(3*c), True)) + a*e*h**2*Piecewise((-2*a**2*sqrt(a + c*x**2)/(15*c**2) + a*x**2*sqrt(a + c*x**2)/(15*c) + x**4*sqrt(a + c*x**2)/5, Ne(c, 0)), (sqrt(a)*x**4/4, True)) + 2*a*f*g*h*Piecewise((-2*a**2*sqrt(a + c*x**2)/(15*c**2) + a*x**2*sqrt(a + c*x**2)/(15*c) + x**4*sqrt(a + c*x**2)/5, Ne(c, 0)), (sqrt(a)*x**4/4, True)) + 2*c*d*g*h*Piecewise((-2*a**2*sqrt(a + c*x**2)/(15*c**2) + a*x**2*sqrt(a + c*x**2)/(15*c) + x**4*sqrt(a + c*x**2)/5, Ne(c, 0)), (sqrt(a)*x**4/4, True)) + c*e*g**2*Piecewise((-2*a**2*sqrt(a + c*x**2)/(15*c**2) + a*x**2*sqrt(a + c*x**2)/(15*c) + x**4*sqrt(a + c*x**2)/5, Ne(c, 0)), (sqrt(a)*x**4/4, True)) + c*e*h**2*Piecewise((8*a**3*sqrt(a + c*x**2)/(105*c**3) - 4*a**2*x**2*sqrt(a + c*x**2)/(105*c**2) + a*x**4*sqrt(a + c*x**2)/(35*c) + x**6*sqrt(a + c*x**2)/7, Ne(c, 0)), (sqrt(a)*x**6/6, True)) + 2*c*f*g*h*Piecewise((8*a**3*sqrt(a + c*x**2)/(105*c**3) - 4*a**2*x**2*sqrt(a + c*x**2)/(105*c**2) + a*x**4*sqrt(a + c*x**2)/(35*c) + x**6*sqrt(a + c*x**2)/7, Ne(c, 0)), (sqrt(a)*x**6/6, True)) + c**2*d*g**2*x**5/(4*sqrt(a)*sqrt(1 + c*x**2/a)) + c**2*d*h**2*x**7/(6*sqrt(a)*sqrt(1 + c*x**2/a)) + c**2*e*g*h*x**7/(3*sqrt(a)*sqrt(1 + c*x**2/a)) + c**2*f*g**2*x**7/(6*sqrt(a)*sqrt(1 + c*x**2/a)) + c**2*f*h**2*x**9/(8*sqrt(a)*sqrt(1 + c*x**2/a))","A",0
90,1,768,0,27.892791," ","integrate((h*x+g)*(c*x**2+a)**(3/2)*(f*x**2+e*x+d),x)","\frac{a^{\frac{5}{2}} e h x}{16 c \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{a^{\frac{5}{2}} f g x}{16 c \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{a^{\frac{3}{2}} d g x \sqrt{1 + \frac{c x^{2}}{a}}}{2} + \frac{a^{\frac{3}{2}} d g x}{8 \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{17 a^{\frac{3}{2}} e h x^{3}}{48 \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{17 a^{\frac{3}{2}} f g x^{3}}{48 \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{3 \sqrt{a} c d g x^{3}}{8 \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{11 \sqrt{a} c e h x^{5}}{24 \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{11 \sqrt{a} c f g x^{5}}{24 \sqrt{1 + \frac{c x^{2}}{a}}} - \frac{a^{3} e h \operatorname{asinh}{\left(\frac{\sqrt{c} x}{\sqrt{a}} \right)}}{16 c^{\frac{3}{2}}} - \frac{a^{3} f g \operatorname{asinh}{\left(\frac{\sqrt{c} x}{\sqrt{a}} \right)}}{16 c^{\frac{3}{2}}} + \frac{3 a^{2} d g \operatorname{asinh}{\left(\frac{\sqrt{c} x}{\sqrt{a}} \right)}}{8 \sqrt{c}} + a d h \left(\begin{cases} \frac{\sqrt{a} x^{2}}{2} & \text{for}\: c = 0 \\\frac{\left(a + c x^{2}\right)^{\frac{3}{2}}}{3 c} & \text{otherwise} \end{cases}\right) + a e g \left(\begin{cases} \frac{\sqrt{a} x^{2}}{2} & \text{for}\: c = 0 \\\frac{\left(a + c x^{2}\right)^{\frac{3}{2}}}{3 c} & \text{otherwise} \end{cases}\right) + a f h \left(\begin{cases} - \frac{2 a^{2} \sqrt{a + c x^{2}}}{15 c^{2}} + \frac{a x^{2} \sqrt{a + c x^{2}}}{15 c} + \frac{x^{4} \sqrt{a + c x^{2}}}{5} & \text{for}\: c \neq 0 \\\frac{\sqrt{a} x^{4}}{4} & \text{otherwise} \end{cases}\right) + c d h \left(\begin{cases} - \frac{2 a^{2} \sqrt{a + c x^{2}}}{15 c^{2}} + \frac{a x^{2} \sqrt{a + c x^{2}}}{15 c} + \frac{x^{4} \sqrt{a + c x^{2}}}{5} & \text{for}\: c \neq 0 \\\frac{\sqrt{a} x^{4}}{4} & \text{otherwise} \end{cases}\right) + c e g \left(\begin{cases} - \frac{2 a^{2} \sqrt{a + c x^{2}}}{15 c^{2}} + \frac{a x^{2} \sqrt{a + c x^{2}}}{15 c} + \frac{x^{4} \sqrt{a + c x^{2}}}{5} & \text{for}\: c \neq 0 \\\frac{\sqrt{a} x^{4}}{4} & \text{otherwise} \end{cases}\right) + c f h \left(\begin{cases} \frac{8 a^{3} \sqrt{a + c x^{2}}}{105 c^{3}} - \frac{4 a^{2} x^{2} \sqrt{a + c x^{2}}}{105 c^{2}} + \frac{a x^{4} \sqrt{a + c x^{2}}}{35 c} + \frac{x^{6} \sqrt{a + c x^{2}}}{7} & \text{for}\: c \neq 0 \\\frac{\sqrt{a} x^{6}}{6} & \text{otherwise} \end{cases}\right) + \frac{c^{2} d g x^{5}}{4 \sqrt{a} \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{c^{2} e h x^{7}}{6 \sqrt{a} \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{c^{2} f g x^{7}}{6 \sqrt{a} \sqrt{1 + \frac{c x^{2}}{a}}}"," ",0,"a**(5/2)*e*h*x/(16*c*sqrt(1 + c*x**2/a)) + a**(5/2)*f*g*x/(16*c*sqrt(1 + c*x**2/a)) + a**(3/2)*d*g*x*sqrt(1 + c*x**2/a)/2 + a**(3/2)*d*g*x/(8*sqrt(1 + c*x**2/a)) + 17*a**(3/2)*e*h*x**3/(48*sqrt(1 + c*x**2/a)) + 17*a**(3/2)*f*g*x**3/(48*sqrt(1 + c*x**2/a)) + 3*sqrt(a)*c*d*g*x**3/(8*sqrt(1 + c*x**2/a)) + 11*sqrt(a)*c*e*h*x**5/(24*sqrt(1 + c*x**2/a)) + 11*sqrt(a)*c*f*g*x**5/(24*sqrt(1 + c*x**2/a)) - a**3*e*h*asinh(sqrt(c)*x/sqrt(a))/(16*c**(3/2)) - a**3*f*g*asinh(sqrt(c)*x/sqrt(a))/(16*c**(3/2)) + 3*a**2*d*g*asinh(sqrt(c)*x/sqrt(a))/(8*sqrt(c)) + a*d*h*Piecewise((sqrt(a)*x**2/2, Eq(c, 0)), ((a + c*x**2)**(3/2)/(3*c), True)) + a*e*g*Piecewise((sqrt(a)*x**2/2, Eq(c, 0)), ((a + c*x**2)**(3/2)/(3*c), True)) + a*f*h*Piecewise((-2*a**2*sqrt(a + c*x**2)/(15*c**2) + a*x**2*sqrt(a + c*x**2)/(15*c) + x**4*sqrt(a + c*x**2)/5, Ne(c, 0)), (sqrt(a)*x**4/4, True)) + c*d*h*Piecewise((-2*a**2*sqrt(a + c*x**2)/(15*c**2) + a*x**2*sqrt(a + c*x**2)/(15*c) + x**4*sqrt(a + c*x**2)/5, Ne(c, 0)), (sqrt(a)*x**4/4, True)) + c*e*g*Piecewise((-2*a**2*sqrt(a + c*x**2)/(15*c**2) + a*x**2*sqrt(a + c*x**2)/(15*c) + x**4*sqrt(a + c*x**2)/5, Ne(c, 0)), (sqrt(a)*x**4/4, True)) + c*f*h*Piecewise((8*a**3*sqrt(a + c*x**2)/(105*c**3) - 4*a**2*x**2*sqrt(a + c*x**2)/(105*c**2) + a*x**4*sqrt(a + c*x**2)/(35*c) + x**6*sqrt(a + c*x**2)/7, Ne(c, 0)), (sqrt(a)*x**6/6, True)) + c**2*d*g*x**5/(4*sqrt(a)*sqrt(1 + c*x**2/a)) + c**2*e*h*x**7/(6*sqrt(a)*sqrt(1 + c*x**2/a)) + c**2*f*g*x**7/(6*sqrt(a)*sqrt(1 + c*x**2/a))","A",0
91,1,348,0,17.012690," ","integrate((c*x**2+a)**(3/2)*(f*x**2+e*x+d),x)","\frac{a^{\frac{5}{2}} f x}{16 c \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{a^{\frac{3}{2}} d x \sqrt{1 + \frac{c x^{2}}{a}}}{2} + \frac{a^{\frac{3}{2}} d x}{8 \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{17 a^{\frac{3}{2}} f x^{3}}{48 \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{3 \sqrt{a} c d x^{3}}{8 \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{11 \sqrt{a} c f x^{5}}{24 \sqrt{1 + \frac{c x^{2}}{a}}} - \frac{a^{3} f \operatorname{asinh}{\left(\frac{\sqrt{c} x}{\sqrt{a}} \right)}}{16 c^{\frac{3}{2}}} + \frac{3 a^{2} d \operatorname{asinh}{\left(\frac{\sqrt{c} x}{\sqrt{a}} \right)}}{8 \sqrt{c}} + a e \left(\begin{cases} \frac{\sqrt{a} x^{2}}{2} & \text{for}\: c = 0 \\\frac{\left(a + c x^{2}\right)^{\frac{3}{2}}}{3 c} & \text{otherwise} \end{cases}\right) + c e \left(\begin{cases} - \frac{2 a^{2} \sqrt{a + c x^{2}}}{15 c^{2}} + \frac{a x^{2} \sqrt{a + c x^{2}}}{15 c} + \frac{x^{4} \sqrt{a + c x^{2}}}{5} & \text{for}\: c \neq 0 \\\frac{\sqrt{a} x^{4}}{4} & \text{otherwise} \end{cases}\right) + \frac{c^{2} d x^{5}}{4 \sqrt{a} \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{c^{2} f x^{7}}{6 \sqrt{a} \sqrt{1 + \frac{c x^{2}}{a}}}"," ",0,"a**(5/2)*f*x/(16*c*sqrt(1 + c*x**2/a)) + a**(3/2)*d*x*sqrt(1 + c*x**2/a)/2 + a**(3/2)*d*x/(8*sqrt(1 + c*x**2/a)) + 17*a**(3/2)*f*x**3/(48*sqrt(1 + c*x**2/a)) + 3*sqrt(a)*c*d*x**3/(8*sqrt(1 + c*x**2/a)) + 11*sqrt(a)*c*f*x**5/(24*sqrt(1 + c*x**2/a)) - a**3*f*asinh(sqrt(c)*x/sqrt(a))/(16*c**(3/2)) + 3*a**2*d*asinh(sqrt(c)*x/sqrt(a))/(8*sqrt(c)) + a*e*Piecewise((sqrt(a)*x**2/2, Eq(c, 0)), ((a + c*x**2)**(3/2)/(3*c), True)) + c*e*Piecewise((-2*a**2*sqrt(a + c*x**2)/(15*c**2) + a*x**2*sqrt(a + c*x**2)/(15*c) + x**4*sqrt(a + c*x**2)/5, Ne(c, 0)), (sqrt(a)*x**4/4, True)) + c**2*d*x**5/(4*sqrt(a)*sqrt(1 + c*x**2/a)) + c**2*f*x**7/(6*sqrt(a)*sqrt(1 + c*x**2/a))","A",0
92,0,0,0,0.000000," ","integrate((c*x**2+a)**(3/2)*(f*x**2+e*x+d)/(h*x+g),x)","\int \frac{\left(a + c x^{2}\right)^{\frac{3}{2}} \left(d + e x + f x^{2}\right)}{g + h x}\, dx"," ",0,"Integral((a + c*x**2)**(3/2)*(d + e*x + f*x**2)/(g + h*x), x)","F",0
93,0,0,0,0.000000," ","integrate((c*x**2+a)**(3/2)*(f*x**2+e*x+d)/(h*x+g)**2,x)","\int \frac{\left(a + c x^{2}\right)^{\frac{3}{2}} \left(d + e x + f x^{2}\right)}{\left(g + h x\right)^{2}}\, dx"," ",0,"Integral((a + c*x**2)**(3/2)*(d + e*x + f*x**2)/(g + h*x)**2, x)","F",0
94,0,0,0,0.000000," ","integrate((c*x**2+a)**(3/2)*(f*x**2+e*x+d)/(h*x+g)**3,x)","\int \frac{\left(a + c x^{2}\right)^{\frac{3}{2}} \left(d + e x + f x^{2}\right)}{\left(g + h x\right)^{3}}\, dx"," ",0,"Integral((a + c*x**2)**(3/2)*(d + e*x + f*x**2)/(g + h*x)**3, x)","F",0
95,0,0,0,0.000000," ","integrate((c*x**2+a)**(3/2)*(f*x**2+e*x+d)/(h*x+g)**4,x)","\int \frac{\left(a + c x^{2}\right)^{\frac{3}{2}} \left(d + e x + f x^{2}\right)}{\left(g + h x\right)^{4}}\, dx"," ",0,"Integral((a + c*x**2)**(3/2)*(d + e*x + f*x**2)/(g + h*x)**4, x)","F",0
96,0,0,0,0.000000," ","integrate((c*x**2+a)**(3/2)*(f*x**2+e*x+d)/(h*x+g)**5,x)","\int \frac{\left(a + c x^{2}\right)^{\frac{3}{2}} \left(d + e x + f x^{2}\right)}{\left(g + h x\right)^{5}}\, dx"," ",0,"Integral((a + c*x**2)**(3/2)*(d + e*x + f*x**2)/(g + h*x)**5, x)","F",0
97,-1,0,0,0.000000," ","integrate((c*x**2+a)**(3/2)*(f*x**2+e*x+d)/(h*x+g)**6,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
98,-1,0,0,0.000000," ","integrate((c*x**2+a)**(3/2)*(f*x**2+e*x+d)/(h*x+g)**7,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
99,-1,0,0,0.000000," ","integrate((c*x**2+a)**(3/2)*(f*x**2+e*x+d)/(h*x+g)**8,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
100,1,510,0,32.915512," ","integrate((c*x**2+a)**(5/2)*(C*x**2+B*x+A),x)","\frac{A a^{\frac{5}{2}} x \sqrt{1 + \frac{c x^{2}}{a}}}{2} + \frac{3 A a^{\frac{5}{2}} x}{16 \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{35 A a^{\frac{3}{2}} c x^{3}}{48 \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{17 A \sqrt{a} c^{2} x^{5}}{24 \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{5 A a^{3} \operatorname{asinh}{\left(\frac{\sqrt{c} x}{\sqrt{a}} \right)}}{16 \sqrt{c}} + \frac{A c^{3} x^{7}}{6 \sqrt{a} \sqrt{1 + \frac{c x^{2}}{a}}} + B a^{2} \left(\begin{cases} \frac{\sqrt{a} x^{2}}{2} & \text{for}\: c = 0 \\\frac{\left(a + c x^{2}\right)^{\frac{3}{2}}}{3 c} & \text{otherwise} \end{cases}\right) + 2 B a c \left(\begin{cases} - \frac{2 a^{2} \sqrt{a + c x^{2}}}{15 c^{2}} + \frac{a x^{2} \sqrt{a + c x^{2}}}{15 c} + \frac{x^{4} \sqrt{a + c x^{2}}}{5} & \text{for}\: c \neq 0 \\\frac{\sqrt{a} x^{4}}{4} & \text{otherwise} \end{cases}\right) + B c^{2} \left(\begin{cases} \frac{8 a^{3} \sqrt{a + c x^{2}}}{105 c^{3}} - \frac{4 a^{2} x^{2} \sqrt{a + c x^{2}}}{105 c^{2}} + \frac{a x^{4} \sqrt{a + c x^{2}}}{35 c} + \frac{x^{6} \sqrt{a + c x^{2}}}{7} & \text{for}\: c \neq 0 \\\frac{\sqrt{a} x^{6}}{6} & \text{otherwise} \end{cases}\right) + \frac{5 C a^{\frac{7}{2}} x}{128 c \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{133 C a^{\frac{5}{2}} x^{3}}{384 \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{127 C a^{\frac{3}{2}} c x^{5}}{192 \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{23 C \sqrt{a} c^{2} x^{7}}{48 \sqrt{1 + \frac{c x^{2}}{a}}} - \frac{5 C a^{4} \operatorname{asinh}{\left(\frac{\sqrt{c} x}{\sqrt{a}} \right)}}{128 c^{\frac{3}{2}}} + \frac{C c^{3} x^{9}}{8 \sqrt{a} \sqrt{1 + \frac{c x^{2}}{a}}}"," ",0,"A*a**(5/2)*x*sqrt(1 + c*x**2/a)/2 + 3*A*a**(5/2)*x/(16*sqrt(1 + c*x**2/a)) + 35*A*a**(3/2)*c*x**3/(48*sqrt(1 + c*x**2/a)) + 17*A*sqrt(a)*c**2*x**5/(24*sqrt(1 + c*x**2/a)) + 5*A*a**3*asinh(sqrt(c)*x/sqrt(a))/(16*sqrt(c)) + A*c**3*x**7/(6*sqrt(a)*sqrt(1 + c*x**2/a)) + B*a**2*Piecewise((sqrt(a)*x**2/2, Eq(c, 0)), ((a + c*x**2)**(3/2)/(3*c), True)) + 2*B*a*c*Piecewise((-2*a**2*sqrt(a + c*x**2)/(15*c**2) + a*x**2*sqrt(a + c*x**2)/(15*c) + x**4*sqrt(a + c*x**2)/5, Ne(c, 0)), (sqrt(a)*x**4/4, True)) + B*c**2*Piecewise((8*a**3*sqrt(a + c*x**2)/(105*c**3) - 4*a**2*x**2*sqrt(a + c*x**2)/(105*c**2) + a*x**4*sqrt(a + c*x**2)/(35*c) + x**6*sqrt(a + c*x**2)/7, Ne(c, 0)), (sqrt(a)*x**6/6, True)) + 5*C*a**(7/2)*x/(128*c*sqrt(1 + c*x**2/a)) + 133*C*a**(5/2)*x**3/(384*sqrt(1 + c*x**2/a)) + 127*C*a**(3/2)*c*x**5/(192*sqrt(1 + c*x**2/a)) + 23*C*sqrt(a)*c**2*x**7/(48*sqrt(1 + c*x**2/a)) - 5*C*a**4*asinh(sqrt(c)*x/sqrt(a))/(128*c**(3/2)) + C*c**3*x**9/(8*sqrt(a)*sqrt(1 + c*x**2/a))","A",0
101,1,796,0,22.204428," ","integrate((h*x+g)**3*(f*x**2+e*x+d)/(c*x**2+a)**(1/2),x)","- \frac{3 a^{\frac{3}{2}} e h^{3} x}{8 c^{2} \sqrt{1 + \frac{c x^{2}}{a}}} - \frac{9 a^{\frac{3}{2}} f g h^{2} x}{8 c^{2} \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{3 \sqrt{a} d g h^{2} x \sqrt{1 + \frac{c x^{2}}{a}}}{2 c} + \frac{3 \sqrt{a} e g^{2} h x \sqrt{1 + \frac{c x^{2}}{a}}}{2 c} - \frac{\sqrt{a} e h^{3} x^{3}}{8 c \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{\sqrt{a} f g^{3} x \sqrt{1 + \frac{c x^{2}}{a}}}{2 c} - \frac{3 \sqrt{a} f g h^{2} x^{3}}{8 c \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{3 a^{2} e h^{3} \operatorname{asinh}{\left(\frac{\sqrt{c} x}{\sqrt{a}} \right)}}{8 c^{\frac{5}{2}}} + \frac{9 a^{2} f g h^{2} \operatorname{asinh}{\left(\frac{\sqrt{c} x}{\sqrt{a}} \right)}}{8 c^{\frac{5}{2}}} - \frac{3 a d g h^{2} \operatorname{asinh}{\left(\frac{\sqrt{c} x}{\sqrt{a}} \right)}}{2 c^{\frac{3}{2}}} - \frac{3 a e g^{2} h \operatorname{asinh}{\left(\frac{\sqrt{c} x}{\sqrt{a}} \right)}}{2 c^{\frac{3}{2}}} - \frac{a f g^{3} \operatorname{asinh}{\left(\frac{\sqrt{c} x}{\sqrt{a}} \right)}}{2 c^{\frac{3}{2}}} + d g^{3} \left(\begin{cases} \frac{\sqrt{- \frac{a}{c}} \operatorname{asin}{\left(x \sqrt{- \frac{c}{a}} \right)}}{\sqrt{a}} & \text{for}\: a > 0 \wedge c < 0 \\\frac{\sqrt{\frac{a}{c}} \operatorname{asinh}{\left(x \sqrt{\frac{c}{a}} \right)}}{\sqrt{a}} & \text{for}\: a > 0 \wedge c > 0 \\\frac{\sqrt{- \frac{a}{c}} \operatorname{acosh}{\left(x \sqrt{- \frac{c}{a}} \right)}}{\sqrt{- a}} & \text{for}\: c > 0 \wedge a < 0 \end{cases}\right) + 3 d g^{2} h \left(\begin{cases} \frac{x^{2}}{2 \sqrt{a}} & \text{for}\: c = 0 \\\frac{\sqrt{a + c x^{2}}}{c} & \text{otherwise} \end{cases}\right) + d h^{3} \left(\begin{cases} - \frac{2 a \sqrt{a + c x^{2}}}{3 c^{2}} + \frac{x^{2} \sqrt{a + c x^{2}}}{3 c} & \text{for}\: c \neq 0 \\\frac{x^{4}}{4 \sqrt{a}} & \text{otherwise} \end{cases}\right) + e g^{3} \left(\begin{cases} \frac{x^{2}}{2 \sqrt{a}} & \text{for}\: c = 0 \\\frac{\sqrt{a + c x^{2}}}{c} & \text{otherwise} \end{cases}\right) + 3 e g h^{2} \left(\begin{cases} - \frac{2 a \sqrt{a + c x^{2}}}{3 c^{2}} + \frac{x^{2} \sqrt{a + c x^{2}}}{3 c} & \text{for}\: c \neq 0 \\\frac{x^{4}}{4 \sqrt{a}} & \text{otherwise} \end{cases}\right) + 3 f g^{2} h \left(\begin{cases} - \frac{2 a \sqrt{a + c x^{2}}}{3 c^{2}} + \frac{x^{2} \sqrt{a + c x^{2}}}{3 c} & \text{for}\: c \neq 0 \\\frac{x^{4}}{4 \sqrt{a}} & \text{otherwise} \end{cases}\right) + f h^{3} \left(\begin{cases} \frac{8 a^{2} \sqrt{a + c x^{2}}}{15 c^{3}} - \frac{4 a x^{2} \sqrt{a + c x^{2}}}{15 c^{2}} + \frac{x^{4} \sqrt{a + c x^{2}}}{5 c} & \text{for}\: c \neq 0 \\\frac{x^{6}}{6 \sqrt{a}} & \text{otherwise} \end{cases}\right) + \frac{e h^{3} x^{5}}{4 \sqrt{a} \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{3 f g h^{2} x^{5}}{4 \sqrt{a} \sqrt{1 + \frac{c x^{2}}{a}}}"," ",0,"-3*a**(3/2)*e*h**3*x/(8*c**2*sqrt(1 + c*x**2/a)) - 9*a**(3/2)*f*g*h**2*x/(8*c**2*sqrt(1 + c*x**2/a)) + 3*sqrt(a)*d*g*h**2*x*sqrt(1 + c*x**2/a)/(2*c) + 3*sqrt(a)*e*g**2*h*x*sqrt(1 + c*x**2/a)/(2*c) - sqrt(a)*e*h**3*x**3/(8*c*sqrt(1 + c*x**2/a)) + sqrt(a)*f*g**3*x*sqrt(1 + c*x**2/a)/(2*c) - 3*sqrt(a)*f*g*h**2*x**3/(8*c*sqrt(1 + c*x**2/a)) + 3*a**2*e*h**3*asinh(sqrt(c)*x/sqrt(a))/(8*c**(5/2)) + 9*a**2*f*g*h**2*asinh(sqrt(c)*x/sqrt(a))/(8*c**(5/2)) - 3*a*d*g*h**2*asinh(sqrt(c)*x/sqrt(a))/(2*c**(3/2)) - 3*a*e*g**2*h*asinh(sqrt(c)*x/sqrt(a))/(2*c**(3/2)) - a*f*g**3*asinh(sqrt(c)*x/sqrt(a))/(2*c**(3/2)) + d*g**3*Piecewise((sqrt(-a/c)*asin(x*sqrt(-c/a))/sqrt(a), (a > 0) & (c < 0)), (sqrt(a/c)*asinh(x*sqrt(c/a))/sqrt(a), (a > 0) & (c > 0)), (sqrt(-a/c)*acosh(x*sqrt(-c/a))/sqrt(-a), (c > 0) & (a < 0))) + 3*d*g**2*h*Piecewise((x**2/(2*sqrt(a)), Eq(c, 0)), (sqrt(a + c*x**2)/c, True)) + d*h**3*Piecewise((-2*a*sqrt(a + c*x**2)/(3*c**2) + x**2*sqrt(a + c*x**2)/(3*c), Ne(c, 0)), (x**4/(4*sqrt(a)), True)) + e*g**3*Piecewise((x**2/(2*sqrt(a)), Eq(c, 0)), (sqrt(a + c*x**2)/c, True)) + 3*e*g*h**2*Piecewise((-2*a*sqrt(a + c*x**2)/(3*c**2) + x**2*sqrt(a + c*x**2)/(3*c), Ne(c, 0)), (x**4/(4*sqrt(a)), True)) + 3*f*g**2*h*Piecewise((-2*a*sqrt(a + c*x**2)/(3*c**2) + x**2*sqrt(a + c*x**2)/(3*c), Ne(c, 0)), (x**4/(4*sqrt(a)), True)) + f*h**3*Piecewise((8*a**2*sqrt(a + c*x**2)/(15*c**3) - 4*a*x**2*sqrt(a + c*x**2)/(15*c**2) + x**4*sqrt(a + c*x**2)/(5*c), Ne(c, 0)), (x**6/(6*sqrt(a)), True)) + e*h**3*x**5/(4*sqrt(a)*sqrt(1 + c*x**2/a)) + 3*f*g*h**2*x**5/(4*sqrt(a)*sqrt(1 + c*x**2/a))","A",0
102,1,518,0,15.782403," ","integrate((h*x+g)**2*(f*x**2+e*x+d)/(c*x**2+a)**(1/2),x)","- \frac{3 a^{\frac{3}{2}} f h^{2} x}{8 c^{2} \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{\sqrt{a} d h^{2} x \sqrt{1 + \frac{c x^{2}}{a}}}{2 c} + \frac{\sqrt{a} e g h x \sqrt{1 + \frac{c x^{2}}{a}}}{c} + \frac{\sqrt{a} f g^{2} x \sqrt{1 + \frac{c x^{2}}{a}}}{2 c} - \frac{\sqrt{a} f h^{2} x^{3}}{8 c \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{3 a^{2} f h^{2} \operatorname{asinh}{\left(\frac{\sqrt{c} x}{\sqrt{a}} \right)}}{8 c^{\frac{5}{2}}} - \frac{a d h^{2} \operatorname{asinh}{\left(\frac{\sqrt{c} x}{\sqrt{a}} \right)}}{2 c^{\frac{3}{2}}} - \frac{a e g h \operatorname{asinh}{\left(\frac{\sqrt{c} x}{\sqrt{a}} \right)}}{c^{\frac{3}{2}}} - \frac{a f g^{2} \operatorname{asinh}{\left(\frac{\sqrt{c} x}{\sqrt{a}} \right)}}{2 c^{\frac{3}{2}}} + d g^{2} \left(\begin{cases} \frac{\sqrt{- \frac{a}{c}} \operatorname{asin}{\left(x \sqrt{- \frac{c}{a}} \right)}}{\sqrt{a}} & \text{for}\: a > 0 \wedge c < 0 \\\frac{\sqrt{\frac{a}{c}} \operatorname{asinh}{\left(x \sqrt{\frac{c}{a}} \right)}}{\sqrt{a}} & \text{for}\: a > 0 \wedge c > 0 \\\frac{\sqrt{- \frac{a}{c}} \operatorname{acosh}{\left(x \sqrt{- \frac{c}{a}} \right)}}{\sqrt{- a}} & \text{for}\: c > 0 \wedge a < 0 \end{cases}\right) + 2 d g h \left(\begin{cases} \frac{x^{2}}{2 \sqrt{a}} & \text{for}\: c = 0 \\\frac{\sqrt{a + c x^{2}}}{c} & \text{otherwise} \end{cases}\right) + e g^{2} \left(\begin{cases} \frac{x^{2}}{2 \sqrt{a}} & \text{for}\: c = 0 \\\frac{\sqrt{a + c x^{2}}}{c} & \text{otherwise} \end{cases}\right) + e h^{2} \left(\begin{cases} - \frac{2 a \sqrt{a + c x^{2}}}{3 c^{2}} + \frac{x^{2} \sqrt{a + c x^{2}}}{3 c} & \text{for}\: c \neq 0 \\\frac{x^{4}}{4 \sqrt{a}} & \text{otherwise} \end{cases}\right) + 2 f g h \left(\begin{cases} - \frac{2 a \sqrt{a + c x^{2}}}{3 c^{2}} + \frac{x^{2} \sqrt{a + c x^{2}}}{3 c} & \text{for}\: c \neq 0 \\\frac{x^{4}}{4 \sqrt{a}} & \text{otherwise} \end{cases}\right) + \frac{f h^{2} x^{5}}{4 \sqrt{a} \sqrt{1 + \frac{c x^{2}}{a}}}"," ",0,"-3*a**(3/2)*f*h**2*x/(8*c**2*sqrt(1 + c*x**2/a)) + sqrt(a)*d*h**2*x*sqrt(1 + c*x**2/a)/(2*c) + sqrt(a)*e*g*h*x*sqrt(1 + c*x**2/a)/c + sqrt(a)*f*g**2*x*sqrt(1 + c*x**2/a)/(2*c) - sqrt(a)*f*h**2*x**3/(8*c*sqrt(1 + c*x**2/a)) + 3*a**2*f*h**2*asinh(sqrt(c)*x/sqrt(a))/(8*c**(5/2)) - a*d*h**2*asinh(sqrt(c)*x/sqrt(a))/(2*c**(3/2)) - a*e*g*h*asinh(sqrt(c)*x/sqrt(a))/c**(3/2) - a*f*g**2*asinh(sqrt(c)*x/sqrt(a))/(2*c**(3/2)) + d*g**2*Piecewise((sqrt(-a/c)*asin(x*sqrt(-c/a))/sqrt(a), (a > 0) & (c < 0)), (sqrt(a/c)*asinh(x*sqrt(c/a))/sqrt(a), (a > 0) & (c > 0)), (sqrt(-a/c)*acosh(x*sqrt(-c/a))/sqrt(-a), (c > 0) & (a < 0))) + 2*d*g*h*Piecewise((x**2/(2*sqrt(a)), Eq(c, 0)), (sqrt(a + c*x**2)/c, True)) + e*g**2*Piecewise((x**2/(2*sqrt(a)), Eq(c, 0)), (sqrt(a + c*x**2)/c, True)) + e*h**2*Piecewise((-2*a*sqrt(a + c*x**2)/(3*c**2) + x**2*sqrt(a + c*x**2)/(3*c), Ne(c, 0)), (x**4/(4*sqrt(a)), True)) + 2*f*g*h*Piecewise((-2*a*sqrt(a + c*x**2)/(3*c**2) + x**2*sqrt(a + c*x**2)/(3*c), Ne(c, 0)), (x**4/(4*sqrt(a)), True)) + f*h**2*x**5/(4*sqrt(a)*sqrt(1 + c*x**2/a))","A",0
103,1,282,0,9.024171," ","integrate((h*x+g)*(f*x**2+e*x+d)/(c*x**2+a)**(1/2),x)","\frac{\sqrt{a} e h x \sqrt{1 + \frac{c x^{2}}{a}}}{2 c} + \frac{\sqrt{a} f g x \sqrt{1 + \frac{c x^{2}}{a}}}{2 c} - \frac{a e h \operatorname{asinh}{\left(\frac{\sqrt{c} x}{\sqrt{a}} \right)}}{2 c^{\frac{3}{2}}} - \frac{a f g \operatorname{asinh}{\left(\frac{\sqrt{c} x}{\sqrt{a}} \right)}}{2 c^{\frac{3}{2}}} + d g \left(\begin{cases} \frac{\sqrt{- \frac{a}{c}} \operatorname{asin}{\left(x \sqrt{- \frac{c}{a}} \right)}}{\sqrt{a}} & \text{for}\: a > 0 \wedge c < 0 \\\frac{\sqrt{\frac{a}{c}} \operatorname{asinh}{\left(x \sqrt{\frac{c}{a}} \right)}}{\sqrt{a}} & \text{for}\: a > 0 \wedge c > 0 \\\frac{\sqrt{- \frac{a}{c}} \operatorname{acosh}{\left(x \sqrt{- \frac{c}{a}} \right)}}{\sqrt{- a}} & \text{for}\: c > 0 \wedge a < 0 \end{cases}\right) + d h \left(\begin{cases} \frac{x^{2}}{2 \sqrt{a}} & \text{for}\: c = 0 \\\frac{\sqrt{a + c x^{2}}}{c} & \text{otherwise} \end{cases}\right) + e g \left(\begin{cases} \frac{x^{2}}{2 \sqrt{a}} & \text{for}\: c = 0 \\\frac{\sqrt{a + c x^{2}}}{c} & \text{otherwise} \end{cases}\right) + f h \left(\begin{cases} - \frac{2 a \sqrt{a + c x^{2}}}{3 c^{2}} + \frac{x^{2} \sqrt{a + c x^{2}}}{3 c} & \text{for}\: c \neq 0 \\\frac{x^{4}}{4 \sqrt{a}} & \text{otherwise} \end{cases}\right)"," ",0,"sqrt(a)*e*h*x*sqrt(1 + c*x**2/a)/(2*c) + sqrt(a)*f*g*x*sqrt(1 + c*x**2/a)/(2*c) - a*e*h*asinh(sqrt(c)*x/sqrt(a))/(2*c**(3/2)) - a*f*g*asinh(sqrt(c)*x/sqrt(a))/(2*c**(3/2)) + d*g*Piecewise((sqrt(-a/c)*asin(x*sqrt(-c/a))/sqrt(a), (a > 0) & (c < 0)), (sqrt(a/c)*asinh(x*sqrt(c/a))/sqrt(a), (a > 0) & (c > 0)), (sqrt(-a/c)*acosh(x*sqrt(-c/a))/sqrt(-a), (c > 0) & (a < 0))) + d*h*Piecewise((x**2/(2*sqrt(a)), Eq(c, 0)), (sqrt(a + c*x**2)/c, True)) + e*g*Piecewise((x**2/(2*sqrt(a)), Eq(c, 0)), (sqrt(a + c*x**2)/c, True)) + f*h*Piecewise((-2*a*sqrt(a + c*x**2)/(3*c**2) + x**2*sqrt(a + c*x**2)/(3*c), Ne(c, 0)), (x**4/(4*sqrt(a)), True))","A",0
104,1,150,0,3.496259," ","integrate((f*x**2+e*x+d)/(c*x**2+a)**(1/2),x)","\frac{\sqrt{a} f x \sqrt{1 + \frac{c x^{2}}{a}}}{2 c} - \frac{a f \operatorname{asinh}{\left(\frac{\sqrt{c} x}{\sqrt{a}} \right)}}{2 c^{\frac{3}{2}}} + d \left(\begin{cases} \frac{\sqrt{- \frac{a}{c}} \operatorname{asin}{\left(x \sqrt{- \frac{c}{a}} \right)}}{\sqrt{a}} & \text{for}\: a > 0 \wedge c < 0 \\\frac{\sqrt{\frac{a}{c}} \operatorname{asinh}{\left(x \sqrt{\frac{c}{a}} \right)}}{\sqrt{a}} & \text{for}\: a > 0 \wedge c > 0 \\\frac{\sqrt{- \frac{a}{c}} \operatorname{acosh}{\left(x \sqrt{- \frac{c}{a}} \right)}}{\sqrt{- a}} & \text{for}\: c > 0 \wedge a < 0 \end{cases}\right) + e \left(\begin{cases} \frac{x^{2}}{2 \sqrt{a}} & \text{for}\: c = 0 \\\frac{\sqrt{a + c x^{2}}}{c} & \text{otherwise} \end{cases}\right)"," ",0,"sqrt(a)*f*x*sqrt(1 + c*x**2/a)/(2*c) - a*f*asinh(sqrt(c)*x/sqrt(a))/(2*c**(3/2)) + d*Piecewise((sqrt(-a/c)*asin(x*sqrt(-c/a))/sqrt(a), (a > 0) & (c < 0)), (sqrt(a/c)*asinh(x*sqrt(c/a))/sqrt(a), (a > 0) & (c > 0)), (sqrt(-a/c)*acosh(x*sqrt(-c/a))/sqrt(-a), (c > 0) & (a < 0))) + e*Piecewise((x**2/(2*sqrt(a)), Eq(c, 0)), (sqrt(a + c*x**2)/c, True))","A",0
105,0,0,0,0.000000," ","integrate((f*x**2+e*x+d)/(h*x+g)/(c*x**2+a)**(1/2),x)","\int \frac{d + e x + f x^{2}}{\sqrt{a + c x^{2}} \left(g + h x\right)}\, dx"," ",0,"Integral((d + e*x + f*x**2)/(sqrt(a + c*x**2)*(g + h*x)), x)","F",0
106,0,0,0,0.000000," ","integrate((f*x**2+e*x+d)/(h*x+g)**2/(c*x**2+a)**(1/2),x)","\int \frac{d + e x + f x^{2}}{\sqrt{a + c x^{2}} \left(g + h x\right)^{2}}\, dx"," ",0,"Integral((d + e*x + f*x**2)/(sqrt(a + c*x**2)*(g + h*x)**2), x)","F",0
107,0,0,0,0.000000," ","integrate((f*x**2+e*x+d)/(h*x+g)**3/(c*x**2+a)**(1/2),x)","\int \frac{d + e x + f x^{2}}{\sqrt{a + c x^{2}} \left(g + h x\right)^{3}}\, dx"," ",0,"Integral((d + e*x + f*x**2)/(sqrt(a + c*x**2)*(g + h*x)**3), x)","F",0
108,0,0,0,0.000000," ","integrate((h*x+g)**3*(f*x**2+e*x+d)/(c*x**2+a)**(3/2),x)","\int \frac{\left(g + h x\right)^{3} \left(d + e x + f x^{2}\right)}{\left(a + c x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((g + h*x)**3*(d + e*x + f*x**2)/(a + c*x**2)**(3/2), x)","F",0
109,0,0,0,0.000000," ","integrate((h*x+g)**2*(f*x**2+e*x+d)/(c*x**2+a)**(3/2),x)","\int \frac{\left(g + h x\right)^{2} \left(d + e x + f x^{2}\right)}{\left(a + c x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((g + h*x)**2*(d + e*x + f*x**2)/(a + c*x**2)**(3/2), x)","F",0
110,1,209,0,18.839500," ","integrate((h*x+g)*(f*x**2+e*x+d)/(c*x**2+a)**(3/2),x)","d h \left(\begin{cases} - \frac{1}{c \sqrt{a + c x^{2}}} & \text{for}\: c \neq 0 \\\frac{x^{2}}{2 a^{\frac{3}{2}}} & \text{otherwise} \end{cases}\right) + e g \left(\begin{cases} - \frac{1}{c \sqrt{a + c x^{2}}} & \text{for}\: c \neq 0 \\\frac{x^{2}}{2 a^{\frac{3}{2}}} & \text{otherwise} \end{cases}\right) + e h \left(\frac{\operatorname{asinh}{\left(\frac{\sqrt{c} x}{\sqrt{a}} \right)}}{c^{\frac{3}{2}}} - \frac{x}{\sqrt{a} c \sqrt{1 + \frac{c x^{2}}{a}}}\right) + f g \left(\frac{\operatorname{asinh}{\left(\frac{\sqrt{c} x}{\sqrt{a}} \right)}}{c^{\frac{3}{2}}} - \frac{x}{\sqrt{a} c \sqrt{1 + \frac{c x^{2}}{a}}}\right) + f h \left(\begin{cases} \frac{2 a}{c^{2} \sqrt{a + c x^{2}}} + \frac{x^{2}}{c \sqrt{a + c x^{2}}} & \text{for}\: c \neq 0 \\\frac{x^{4}}{4 a^{\frac{3}{2}}} & \text{otherwise} \end{cases}\right) + \frac{d g x}{a^{\frac{3}{2}} \sqrt{1 + \frac{c x^{2}}{a}}}"," ",0,"d*h*Piecewise((-1/(c*sqrt(a + c*x**2)), Ne(c, 0)), (x**2/(2*a**(3/2)), True)) + e*g*Piecewise((-1/(c*sqrt(a + c*x**2)), Ne(c, 0)), (x**2/(2*a**(3/2)), True)) + e*h*(asinh(sqrt(c)*x/sqrt(a))/c**(3/2) - x/(sqrt(a)*c*sqrt(1 + c*x**2/a))) + f*g*(asinh(sqrt(c)*x/sqrt(a))/c**(3/2) - x/(sqrt(a)*c*sqrt(1 + c*x**2/a))) + f*h*Piecewise((2*a/(c**2*sqrt(a + c*x**2)) + x**2/(c*sqrt(a + c*x**2)), Ne(c, 0)), (x**4/(4*a**(3/2)), True)) + d*g*x/(a**(3/2)*sqrt(1 + c*x**2/a))","A",0
111,1,87,0,8.859372," ","integrate((f*x**2+e*x+d)/(c*x**2+a)**(3/2),x)","e \left(\begin{cases} - \frac{1}{c \sqrt{a + c x^{2}}} & \text{for}\: c \neq 0 \\\frac{x^{2}}{2 a^{\frac{3}{2}}} & \text{otherwise} \end{cases}\right) + f \left(\frac{\operatorname{asinh}{\left(\frac{\sqrt{c} x}{\sqrt{a}} \right)}}{c^{\frac{3}{2}}} - \frac{x}{\sqrt{a} c \sqrt{1 + \frac{c x^{2}}{a}}}\right) + \frac{d x}{a^{\frac{3}{2}} \sqrt{1 + \frac{c x^{2}}{a}}}"," ",0,"e*Piecewise((-1/(c*sqrt(a + c*x**2)), Ne(c, 0)), (x**2/(2*a**(3/2)), True)) + f*(asinh(sqrt(c)*x/sqrt(a))/c**(3/2) - x/(sqrt(a)*c*sqrt(1 + c*x**2/a))) + d*x/(a**(3/2)*sqrt(1 + c*x**2/a))","A",0
112,0,0,0,0.000000," ","integrate((f*x**2+e*x+d)/(h*x+g)/(c*x**2+a)**(3/2),x)","\int \frac{d + e x + f x^{2}}{\left(a + c x^{2}\right)^{\frac{3}{2}} \left(g + h x\right)}\, dx"," ",0,"Integral((d + e*x + f*x**2)/((a + c*x**2)**(3/2)*(g + h*x)), x)","F",0
113,-1,0,0,0.000000," ","integrate((f*x**2+e*x+d)/(h*x+g)**2/(c*x**2+a)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
114,-1,0,0,0.000000," ","integrate((f*x**2+e*x+d)/(h*x+g)**3/(c*x**2+a)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
115,1,194,0,17.130935," ","integrate((C*x**2+B*x+A)/(c*x**2+a)**(5/2),x)","A \left(\frac{3 a x}{3 a^{\frac{7}{2}} \sqrt{1 + \frac{c x^{2}}{a}} + 3 a^{\frac{5}{2}} c x^{2} \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{2 c x^{3}}{3 a^{\frac{7}{2}} \sqrt{1 + \frac{c x^{2}}{a}} + 3 a^{\frac{5}{2}} c x^{2} \sqrt{1 + \frac{c x^{2}}{a}}}\right) + B \left(\begin{cases} - \frac{1}{3 a c \sqrt{a + c x^{2}} + 3 c^{2} x^{2} \sqrt{a + c x^{2}}} & \text{for}\: c \neq 0 \\\frac{x^{2}}{2 a^{\frac{5}{2}}} & \text{otherwise} \end{cases}\right) + \frac{C x^{3}}{3 a^{\frac{5}{2}} \sqrt{1 + \frac{c x^{2}}{a}} + 3 a^{\frac{3}{2}} c x^{2} \sqrt{1 + \frac{c x^{2}}{a}}}"," ",0,"A*(3*a*x/(3*a**(7/2)*sqrt(1 + c*x**2/a) + 3*a**(5/2)*c*x**2*sqrt(1 + c*x**2/a)) + 2*c*x**3/(3*a**(7/2)*sqrt(1 + c*x**2/a) + 3*a**(5/2)*c*x**2*sqrt(1 + c*x**2/a))) + B*Piecewise((-1/(3*a*c*sqrt(a + c*x**2) + 3*c**2*x**2*sqrt(a + c*x**2)), Ne(c, 0)), (x**2/(2*a**(5/2)), True)) + C*x**3/(3*a**(5/2)*sqrt(1 + c*x**2/a) + 3*a**(3/2)*c*x**2*sqrt(1 + c*x**2/a))","A",0
116,1,638,0,37.218852," ","integrate((C*x**2+B*x+A)/(c*x**2+a)**(7/2),x)","A \left(\frac{15 a^{5} x}{15 a^{\frac{17}{2}} \sqrt{1 + \frac{c x^{2}}{a}} + 45 a^{\frac{15}{2}} c x^{2} \sqrt{1 + \frac{c x^{2}}{a}} + 45 a^{\frac{13}{2}} c^{2} x^{4} \sqrt{1 + \frac{c x^{2}}{a}} + 15 a^{\frac{11}{2}} c^{3} x^{6} \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{35 a^{4} c x^{3}}{15 a^{\frac{17}{2}} \sqrt{1 + \frac{c x^{2}}{a}} + 45 a^{\frac{15}{2}} c x^{2} \sqrt{1 + \frac{c x^{2}}{a}} + 45 a^{\frac{13}{2}} c^{2} x^{4} \sqrt{1 + \frac{c x^{2}}{a}} + 15 a^{\frac{11}{2}} c^{3} x^{6} \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{28 a^{3} c^{2} x^{5}}{15 a^{\frac{17}{2}} \sqrt{1 + \frac{c x^{2}}{a}} + 45 a^{\frac{15}{2}} c x^{2} \sqrt{1 + \frac{c x^{2}}{a}} + 45 a^{\frac{13}{2}} c^{2} x^{4} \sqrt{1 + \frac{c x^{2}}{a}} + 15 a^{\frac{11}{2}} c^{3} x^{6} \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{8 a^{2} c^{3} x^{7}}{15 a^{\frac{17}{2}} \sqrt{1 + \frac{c x^{2}}{a}} + 45 a^{\frac{15}{2}} c x^{2} \sqrt{1 + \frac{c x^{2}}{a}} + 45 a^{\frac{13}{2}} c^{2} x^{4} \sqrt{1 + \frac{c x^{2}}{a}} + 15 a^{\frac{11}{2}} c^{3} x^{6} \sqrt{1 + \frac{c x^{2}}{a}}}\right) + B \left(\begin{cases} - \frac{1}{5 a^{2} c \sqrt{a + c x^{2}} + 10 a c^{2} x^{2} \sqrt{a + c x^{2}} + 5 c^{3} x^{4} \sqrt{a + c x^{2}}} & \text{for}\: c \neq 0 \\\frac{x^{2}}{2 a^{\frac{7}{2}}} & \text{otherwise} \end{cases}\right) + C \left(\frac{5 a x^{3}}{15 a^{\frac{9}{2}} \sqrt{1 + \frac{c x^{2}}{a}} + 30 a^{\frac{7}{2}} c x^{2} \sqrt{1 + \frac{c x^{2}}{a}} + 15 a^{\frac{5}{2}} c^{2} x^{4} \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{2 c x^{5}}{15 a^{\frac{9}{2}} \sqrt{1 + \frac{c x^{2}}{a}} + 30 a^{\frac{7}{2}} c x^{2} \sqrt{1 + \frac{c x^{2}}{a}} + 15 a^{\frac{5}{2}} c^{2} x^{4} \sqrt{1 + \frac{c x^{2}}{a}}}\right)"," ",0,"A*(15*a**5*x/(15*a**(17/2)*sqrt(1 + c*x**2/a) + 45*a**(15/2)*c*x**2*sqrt(1 + c*x**2/a) + 45*a**(13/2)*c**2*x**4*sqrt(1 + c*x**2/a) + 15*a**(11/2)*c**3*x**6*sqrt(1 + c*x**2/a)) + 35*a**4*c*x**3/(15*a**(17/2)*sqrt(1 + c*x**2/a) + 45*a**(15/2)*c*x**2*sqrt(1 + c*x**2/a) + 45*a**(13/2)*c**2*x**4*sqrt(1 + c*x**2/a) + 15*a**(11/2)*c**3*x**6*sqrt(1 + c*x**2/a)) + 28*a**3*c**2*x**5/(15*a**(17/2)*sqrt(1 + c*x**2/a) + 45*a**(15/2)*c*x**2*sqrt(1 + c*x**2/a) + 45*a**(13/2)*c**2*x**4*sqrt(1 + c*x**2/a) + 15*a**(11/2)*c**3*x**6*sqrt(1 + c*x**2/a)) + 8*a**2*c**3*x**7/(15*a**(17/2)*sqrt(1 + c*x**2/a) + 45*a**(15/2)*c*x**2*sqrt(1 + c*x**2/a) + 45*a**(13/2)*c**2*x**4*sqrt(1 + c*x**2/a) + 15*a**(11/2)*c**3*x**6*sqrt(1 + c*x**2/a))) + B*Piecewise((-1/(5*a**2*c*sqrt(a + c*x**2) + 10*a*c**2*x**2*sqrt(a + c*x**2) + 5*c**3*x**4*sqrt(a + c*x**2)), Ne(c, 0)), (x**2/(2*a**(7/2)), True)) + C*(5*a*x**3/(15*a**(9/2)*sqrt(1 + c*x**2/a) + 30*a**(7/2)*c*x**2*sqrt(1 + c*x**2/a) + 15*a**(5/2)*c**2*x**4*sqrt(1 + c*x**2/a)) + 2*c*x**5/(15*a**(9/2)*sqrt(1 + c*x**2/a) + 30*a**(7/2)*c*x**2*sqrt(1 + c*x**2/a) + 15*a**(5/2)*c**2*x**4*sqrt(1 + c*x**2/a)))","B",0
117,1,1880,0,78.296576," ","integrate((C*x**2+B*x+A)/(c*x**2+a)**(9/2),x)","A \left(\frac{35 a^{14} x}{35 a^{\frac{37}{2}} \sqrt{1 + \frac{c x^{2}}{a}} + 210 a^{\frac{35}{2}} c x^{2} \sqrt{1 + \frac{c x^{2}}{a}} + 525 a^{\frac{33}{2}} c^{2} x^{4} \sqrt{1 + \frac{c x^{2}}{a}} + 700 a^{\frac{31}{2}} c^{3} x^{6} \sqrt{1 + \frac{c x^{2}}{a}} + 525 a^{\frac{29}{2}} c^{4} x^{8} \sqrt{1 + \frac{c x^{2}}{a}} + 210 a^{\frac{27}{2}} c^{5} x^{10} \sqrt{1 + \frac{c x^{2}}{a}} + 35 a^{\frac{25}{2}} c^{6} x^{12} \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{175 a^{13} c x^{3}}{35 a^{\frac{37}{2}} \sqrt{1 + \frac{c x^{2}}{a}} + 210 a^{\frac{35}{2}} c x^{2} \sqrt{1 + \frac{c x^{2}}{a}} + 525 a^{\frac{33}{2}} c^{2} x^{4} \sqrt{1 + \frac{c x^{2}}{a}} + 700 a^{\frac{31}{2}} c^{3} x^{6} \sqrt{1 + \frac{c x^{2}}{a}} + 525 a^{\frac{29}{2}} c^{4} x^{8} \sqrt{1 + \frac{c x^{2}}{a}} + 210 a^{\frac{27}{2}} c^{5} x^{10} \sqrt{1 + \frac{c x^{2}}{a}} + 35 a^{\frac{25}{2}} c^{6} x^{12} \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{371 a^{12} c^{2} x^{5}}{35 a^{\frac{37}{2}} \sqrt{1 + \frac{c x^{2}}{a}} + 210 a^{\frac{35}{2}} c x^{2} \sqrt{1 + \frac{c x^{2}}{a}} + 525 a^{\frac{33}{2}} c^{2} x^{4} \sqrt{1 + \frac{c x^{2}}{a}} + 700 a^{\frac{31}{2}} c^{3} x^{6} \sqrt{1 + \frac{c x^{2}}{a}} + 525 a^{\frac{29}{2}} c^{4} x^{8} \sqrt{1 + \frac{c x^{2}}{a}} + 210 a^{\frac{27}{2}} c^{5} x^{10} \sqrt{1 + \frac{c x^{2}}{a}} + 35 a^{\frac{25}{2}} c^{6} x^{12} \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{429 a^{11} c^{3} x^{7}}{35 a^{\frac{37}{2}} \sqrt{1 + \frac{c x^{2}}{a}} + 210 a^{\frac{35}{2}} c x^{2} \sqrt{1 + \frac{c x^{2}}{a}} + 525 a^{\frac{33}{2}} c^{2} x^{4} \sqrt{1 + \frac{c x^{2}}{a}} + 700 a^{\frac{31}{2}} c^{3} x^{6} \sqrt{1 + \frac{c x^{2}}{a}} + 525 a^{\frac{29}{2}} c^{4} x^{8} \sqrt{1 + \frac{c x^{2}}{a}} + 210 a^{\frac{27}{2}} c^{5} x^{10} \sqrt{1 + \frac{c x^{2}}{a}} + 35 a^{\frac{25}{2}} c^{6} x^{12} \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{286 a^{10} c^{4} x^{9}}{35 a^{\frac{37}{2}} \sqrt{1 + \frac{c x^{2}}{a}} + 210 a^{\frac{35}{2}} c x^{2} \sqrt{1 + \frac{c x^{2}}{a}} + 525 a^{\frac{33}{2}} c^{2} x^{4} \sqrt{1 + \frac{c x^{2}}{a}} + 700 a^{\frac{31}{2}} c^{3} x^{6} \sqrt{1 + \frac{c x^{2}}{a}} + 525 a^{\frac{29}{2}} c^{4} x^{8} \sqrt{1 + \frac{c x^{2}}{a}} + 210 a^{\frac{27}{2}} c^{5} x^{10} \sqrt{1 + \frac{c x^{2}}{a}} + 35 a^{\frac{25}{2}} c^{6} x^{12} \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{104 a^{9} c^{5} x^{11}}{35 a^{\frac{37}{2}} \sqrt{1 + \frac{c x^{2}}{a}} + 210 a^{\frac{35}{2}} c x^{2} \sqrt{1 + \frac{c x^{2}}{a}} + 525 a^{\frac{33}{2}} c^{2} x^{4} \sqrt{1 + \frac{c x^{2}}{a}} + 700 a^{\frac{31}{2}} c^{3} x^{6} \sqrt{1 + \frac{c x^{2}}{a}} + 525 a^{\frac{29}{2}} c^{4} x^{8} \sqrt{1 + \frac{c x^{2}}{a}} + 210 a^{\frac{27}{2}} c^{5} x^{10} \sqrt{1 + \frac{c x^{2}}{a}} + 35 a^{\frac{25}{2}} c^{6} x^{12} \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{16 a^{8} c^{6} x^{13}}{35 a^{\frac{37}{2}} \sqrt{1 + \frac{c x^{2}}{a}} + 210 a^{\frac{35}{2}} c x^{2} \sqrt{1 + \frac{c x^{2}}{a}} + 525 a^{\frac{33}{2}} c^{2} x^{4} \sqrt{1 + \frac{c x^{2}}{a}} + 700 a^{\frac{31}{2}} c^{3} x^{6} \sqrt{1 + \frac{c x^{2}}{a}} + 525 a^{\frac{29}{2}} c^{4} x^{8} \sqrt{1 + \frac{c x^{2}}{a}} + 210 a^{\frac{27}{2}} c^{5} x^{10} \sqrt{1 + \frac{c x^{2}}{a}} + 35 a^{\frac{25}{2}} c^{6} x^{12} \sqrt{1 + \frac{c x^{2}}{a}}}\right) + B \left(\begin{cases} - \frac{1}{7 a^{3} c \sqrt{a + c x^{2}} + 21 a^{2} c^{2} x^{2} \sqrt{a + c x^{2}} + 21 a c^{3} x^{4} \sqrt{a + c x^{2}} + 7 c^{4} x^{6} \sqrt{a + c x^{2}}} & \text{for}\: c \neq 0 \\\frac{x^{2}}{2 a^{\frac{9}{2}}} & \text{otherwise} \end{cases}\right) + C \left(\frac{35 a^{5} x^{3}}{105 a^{\frac{19}{2}} \sqrt{1 + \frac{c x^{2}}{a}} + 420 a^{\frac{17}{2}} c x^{2} \sqrt{1 + \frac{c x^{2}}{a}} + 630 a^{\frac{15}{2}} c^{2} x^{4} \sqrt{1 + \frac{c x^{2}}{a}} + 420 a^{\frac{13}{2}} c^{3} x^{6} \sqrt{1 + \frac{c x^{2}}{a}} + 105 a^{\frac{11}{2}} c^{4} x^{8} \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{63 a^{4} c x^{5}}{105 a^{\frac{19}{2}} \sqrt{1 + \frac{c x^{2}}{a}} + 420 a^{\frac{17}{2}} c x^{2} \sqrt{1 + \frac{c x^{2}}{a}} + 630 a^{\frac{15}{2}} c^{2} x^{4} \sqrt{1 + \frac{c x^{2}}{a}} + 420 a^{\frac{13}{2}} c^{3} x^{6} \sqrt{1 + \frac{c x^{2}}{a}} + 105 a^{\frac{11}{2}} c^{4} x^{8} \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{36 a^{3} c^{2} x^{7}}{105 a^{\frac{19}{2}} \sqrt{1 + \frac{c x^{2}}{a}} + 420 a^{\frac{17}{2}} c x^{2} \sqrt{1 + \frac{c x^{2}}{a}} + 630 a^{\frac{15}{2}} c^{2} x^{4} \sqrt{1 + \frac{c x^{2}}{a}} + 420 a^{\frac{13}{2}} c^{3} x^{6} \sqrt{1 + \frac{c x^{2}}{a}} + 105 a^{\frac{11}{2}} c^{4} x^{8} \sqrt{1 + \frac{c x^{2}}{a}}} + \frac{8 a^{2} c^{3} x^{9}}{105 a^{\frac{19}{2}} \sqrt{1 + \frac{c x^{2}}{a}} + 420 a^{\frac{17}{2}} c x^{2} \sqrt{1 + \frac{c x^{2}}{a}} + 630 a^{\frac{15}{2}} c^{2} x^{4} \sqrt{1 + \frac{c x^{2}}{a}} + 420 a^{\frac{13}{2}} c^{3} x^{6} \sqrt{1 + \frac{c x^{2}}{a}} + 105 a^{\frac{11}{2}} c^{4} x^{8} \sqrt{1 + \frac{c x^{2}}{a}}}\right)"," ",0,"A*(35*a**14*x/(35*a**(37/2)*sqrt(1 + c*x**2/a) + 210*a**(35/2)*c*x**2*sqrt(1 + c*x**2/a) + 525*a**(33/2)*c**2*x**4*sqrt(1 + c*x**2/a) + 700*a**(31/2)*c**3*x**6*sqrt(1 + c*x**2/a) + 525*a**(29/2)*c**4*x**8*sqrt(1 + c*x**2/a) + 210*a**(27/2)*c**5*x**10*sqrt(1 + c*x**2/a) + 35*a**(25/2)*c**6*x**12*sqrt(1 + c*x**2/a)) + 175*a**13*c*x**3/(35*a**(37/2)*sqrt(1 + c*x**2/a) + 210*a**(35/2)*c*x**2*sqrt(1 + c*x**2/a) + 525*a**(33/2)*c**2*x**4*sqrt(1 + c*x**2/a) + 700*a**(31/2)*c**3*x**6*sqrt(1 + c*x**2/a) + 525*a**(29/2)*c**4*x**8*sqrt(1 + c*x**2/a) + 210*a**(27/2)*c**5*x**10*sqrt(1 + c*x**2/a) + 35*a**(25/2)*c**6*x**12*sqrt(1 + c*x**2/a)) + 371*a**12*c**2*x**5/(35*a**(37/2)*sqrt(1 + c*x**2/a) + 210*a**(35/2)*c*x**2*sqrt(1 + c*x**2/a) + 525*a**(33/2)*c**2*x**4*sqrt(1 + c*x**2/a) + 700*a**(31/2)*c**3*x**6*sqrt(1 + c*x**2/a) + 525*a**(29/2)*c**4*x**8*sqrt(1 + c*x**2/a) + 210*a**(27/2)*c**5*x**10*sqrt(1 + c*x**2/a) + 35*a**(25/2)*c**6*x**12*sqrt(1 + c*x**2/a)) + 429*a**11*c**3*x**7/(35*a**(37/2)*sqrt(1 + c*x**2/a) + 210*a**(35/2)*c*x**2*sqrt(1 + c*x**2/a) + 525*a**(33/2)*c**2*x**4*sqrt(1 + c*x**2/a) + 700*a**(31/2)*c**3*x**6*sqrt(1 + c*x**2/a) + 525*a**(29/2)*c**4*x**8*sqrt(1 + c*x**2/a) + 210*a**(27/2)*c**5*x**10*sqrt(1 + c*x**2/a) + 35*a**(25/2)*c**6*x**12*sqrt(1 + c*x**2/a)) + 286*a**10*c**4*x**9/(35*a**(37/2)*sqrt(1 + c*x**2/a) + 210*a**(35/2)*c*x**2*sqrt(1 + c*x**2/a) + 525*a**(33/2)*c**2*x**4*sqrt(1 + c*x**2/a) + 700*a**(31/2)*c**3*x**6*sqrt(1 + c*x**2/a) + 525*a**(29/2)*c**4*x**8*sqrt(1 + c*x**2/a) + 210*a**(27/2)*c**5*x**10*sqrt(1 + c*x**2/a) + 35*a**(25/2)*c**6*x**12*sqrt(1 + c*x**2/a)) + 104*a**9*c**5*x**11/(35*a**(37/2)*sqrt(1 + c*x**2/a) + 210*a**(35/2)*c*x**2*sqrt(1 + c*x**2/a) + 525*a**(33/2)*c**2*x**4*sqrt(1 + c*x**2/a) + 700*a**(31/2)*c**3*x**6*sqrt(1 + c*x**2/a) + 525*a**(29/2)*c**4*x**8*sqrt(1 + c*x**2/a) + 210*a**(27/2)*c**5*x**10*sqrt(1 + c*x**2/a) + 35*a**(25/2)*c**6*x**12*sqrt(1 + c*x**2/a)) + 16*a**8*c**6*x**13/(35*a**(37/2)*sqrt(1 + c*x**2/a) + 210*a**(35/2)*c*x**2*sqrt(1 + c*x**2/a) + 525*a**(33/2)*c**2*x**4*sqrt(1 + c*x**2/a) + 700*a**(31/2)*c**3*x**6*sqrt(1 + c*x**2/a) + 525*a**(29/2)*c**4*x**8*sqrt(1 + c*x**2/a) + 210*a**(27/2)*c**5*x**10*sqrt(1 + c*x**2/a) + 35*a**(25/2)*c**6*x**12*sqrt(1 + c*x**2/a))) + B*Piecewise((-1/(7*a**3*c*sqrt(a + c*x**2) + 21*a**2*c**2*x**2*sqrt(a + c*x**2) + 21*a*c**3*x**4*sqrt(a + c*x**2) + 7*c**4*x**6*sqrt(a + c*x**2)), Ne(c, 0)), (x**2/(2*a**(9/2)), True)) + C*(35*a**5*x**3/(105*a**(19/2)*sqrt(1 + c*x**2/a) + 420*a**(17/2)*c*x**2*sqrt(1 + c*x**2/a) + 630*a**(15/2)*c**2*x**4*sqrt(1 + c*x**2/a) + 420*a**(13/2)*c**3*x**6*sqrt(1 + c*x**2/a) + 105*a**(11/2)*c**4*x**8*sqrt(1 + c*x**2/a)) + 63*a**4*c*x**5/(105*a**(19/2)*sqrt(1 + c*x**2/a) + 420*a**(17/2)*c*x**2*sqrt(1 + c*x**2/a) + 630*a**(15/2)*c**2*x**4*sqrt(1 + c*x**2/a) + 420*a**(13/2)*c**3*x**6*sqrt(1 + c*x**2/a) + 105*a**(11/2)*c**4*x**8*sqrt(1 + c*x**2/a)) + 36*a**3*c**2*x**7/(105*a**(19/2)*sqrt(1 + c*x**2/a) + 420*a**(17/2)*c*x**2*sqrt(1 + c*x**2/a) + 630*a**(15/2)*c**2*x**4*sqrt(1 + c*x**2/a) + 420*a**(13/2)*c**3*x**6*sqrt(1 + c*x**2/a) + 105*a**(11/2)*c**4*x**8*sqrt(1 + c*x**2/a)) + 8*a**2*c**3*x**9/(105*a**(19/2)*sqrt(1 + c*x**2/a) + 420*a**(17/2)*c*x**2*sqrt(1 + c*x**2/a) + 630*a**(15/2)*c**2*x**4*sqrt(1 + c*x**2/a) + 420*a**(13/2)*c**3*x**6*sqrt(1 + c*x**2/a) + 105*a**(11/2)*c**4*x**8*sqrt(1 + c*x**2/a)))","B",0
118,1,94,0,2.203000," ","integrate((1+2*x)**3*(4*x**2+3*x+1)/(3*x**2+2)**(1/2),x)","\frac{32 x^{4} \sqrt{3 x^{2} + 2}}{15} + 6 x^{3} \sqrt{3 x^{2} + 2} + \frac{764 x^{2} \sqrt{3 x^{2} + 2}}{135} - \frac{x \sqrt{3 x^{2} + 2}}{3} - \frac{1841 \sqrt{3 x^{2} + 2}}{405} + \frac{5 \sqrt{3} \operatorname{asinh}{\left(\frac{\sqrt{6} x}{2} \right)}}{9}"," ",0,"32*x**4*sqrt(3*x**2 + 2)/15 + 6*x**3*sqrt(3*x**2 + 2) + 764*x**2*sqrt(3*x**2 + 2)/135 - x*sqrt(3*x**2 + 2)/3 - 1841*sqrt(3*x**2 + 2)/405 + 5*sqrt(3)*asinh(sqrt(6)*x/2)/9","A",0
119,1,75,0,1.185044," ","integrate((1+2*x)**2*(4*x**2+3*x+1)/(3*x**2+2)**(1/2),x)","\frac{4 x^{3} \sqrt{3 x^{2} + 2}}{3} + \frac{28 x^{2} \sqrt{3 x^{2} + 2}}{9} + 2 x \sqrt{3 x^{2} + 2} - \frac{49 \sqrt{3 x^{2} + 2}}{27} - \sqrt{3} \operatorname{asinh}{\left(\frac{\sqrt{6} x}{2} \right)}"," ",0,"4*x**3*sqrt(3*x**2 + 2)/3 + 28*x**2*sqrt(3*x**2 + 2)/9 + 2*x*sqrt(3*x**2 + 2) - 49*sqrt(3*x**2 + 2)/27 - sqrt(3)*asinh(sqrt(6)*x/2)","A",0
120,1,63,0,0.551798," ","integrate((1+2*x)*(4*x**2+3*x+1)/(3*x**2+2)**(1/2),x)","\frac{8 x^{2} \sqrt{3 x^{2} + 2}}{9} + \frac{5 x \sqrt{3 x^{2} + 2}}{3} + \frac{13 \sqrt{3 x^{2} + 2}}{27} - \frac{7 \sqrt{3} \operatorname{asinh}{\left(\frac{\sqrt{6} x}{2} \right)}}{9}"," ",0,"8*x**2*sqrt(3*x**2 + 2)/9 + 5*x*sqrt(3*x**2 + 2)/3 + 13*sqrt(3*x**2 + 2)/27 - 7*sqrt(3)*asinh(sqrt(6)*x/2)/9","A",0
121,0,0,0,0.000000," ","integrate((4*x**2+3*x+1)/(1+2*x)/(3*x**2+2)**(1/2),x)","\int \frac{4 x^{2} + 3 x + 1}{\left(2 x + 1\right) \sqrt{3 x^{2} + 2}}\, dx"," ",0,"Integral((4*x**2 + 3*x + 1)/((2*x + 1)*sqrt(3*x**2 + 2)), x)","F",0
122,0,0,0,0.000000," ","integrate((4*x**2+3*x+1)/(1+2*x)**2/(3*x**2+2)**(1/2),x)","\int \frac{4 x^{2} + 3 x + 1}{\left(2 x + 1\right)^{2} \sqrt{3 x^{2} + 2}}\, dx"," ",0,"Integral((4*x**2 + 3*x + 1)/((2*x + 1)**2*sqrt(3*x**2 + 2)), x)","F",0
123,-1,0,0,0.000000," ","integrate((4*x**2+3*x+1)/(1+2*x)**3/(3*x**2+2)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
124,0,0,0,0.000000," ","integrate((1+2*x)**3*(4*x**2+3*x+1)/(3*x**2+2)**(3/2),x)","\int \frac{\left(2 x + 1\right)^{3} \left(4 x^{2} + 3 x + 1\right)}{\left(3 x^{2} + 2\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((2*x + 1)**3*(4*x**2 + 3*x + 1)/(3*x**2 + 2)**(3/2), x)","F",0
125,0,0,0,0.000000," ","integrate((1+2*x)**2*(4*x**2+3*x+1)/(3*x**2+2)**(3/2),x)","\int \frac{\left(2 x + 1\right)^{2} \left(4 x^{2} + 3 x + 1\right)}{\left(3 x^{2} + 2\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((2*x + 1)**2*(4*x**2 + 3*x + 1)/(3*x**2 + 2)**(3/2), x)","F",0
126,1,114,0,15.958645," ","integrate((1+2*x)*(4*x**2+3*x+1)/(3*x**2+2)**(3/2),x)","\frac{30 \sqrt{3} x^{2} \operatorname{asinh}{\left(\frac{\sqrt{6} x}{2} \right)}}{27 x^{2} + 18} + \frac{8 x^{2}}{3 \sqrt{3 x^{2} + 2}} - \frac{30 x \sqrt{3 x^{2} + 2}}{27 x^{2} + 18} + \frac{x}{2 \sqrt{3 x^{2} + 2}} + \frac{20 \sqrt{3} \operatorname{asinh}{\left(\frac{\sqrt{6} x}{2} \right)}}{27 x^{2} + 18} + \frac{17}{9 \sqrt{3 x^{2} + 2}}"," ",0,"30*sqrt(3)*x**2*asinh(sqrt(6)*x/2)/(27*x**2 + 18) + 8*x**2/(3*sqrt(3*x**2 + 2)) - 30*x*sqrt(3*x**2 + 2)/(27*x**2 + 18) + x/(2*sqrt(3*x**2 + 2)) + 20*sqrt(3)*asinh(sqrt(6)*x/2)/(27*x**2 + 18) + 17/(9*sqrt(3*x**2 + 2))","B",0
127,0,0,0,0.000000," ","integrate((4*x**2+3*x+1)/(1+2*x)/(3*x**2+2)**(3/2),x)","\int \frac{4 x^{2} + 3 x + 1}{\left(2 x + 1\right) \left(3 x^{2} + 2\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((4*x**2 + 3*x + 1)/((2*x + 1)*(3*x**2 + 2)**(3/2)), x)","F",0
128,-1,0,0,0.000000," ","integrate((4*x**2+3*x+1)/(1+2*x)**2/(3*x**2+2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
129,-1,0,0,0.000000," ","integrate((4*x**2+3*x+1)/(1+2*x)**3/(3*x**2+2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
130,0,0,0,0.000000," ","integrate((1+2*x)**3*(4*x**2+3*x+1)/(3*x**2+2)**(5/2),x)","\int \frac{\left(2 x + 1\right)^{3} \left(4 x^{2} + 3 x + 1\right)}{\left(3 x^{2} + 2\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((2*x + 1)**3*(4*x**2 + 3*x + 1)/(3*x**2 + 2)**(5/2), x)","F",0
131,0,0,0,0.000000," ","integrate((1+2*x)**2*(4*x**2+3*x+1)/(3*x**2+2)**(5/2),x)","\int \frac{\left(2 x + 1\right)^{2} \left(4 x^{2} + 3 x + 1\right)}{\left(3 x^{2} + 2\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((2*x + 1)**2*(4*x**2 + 3*x + 1)/(3*x**2 + 2)**(5/2), x)","F",0
132,1,180,0,77.502136," ","integrate((1+2*x)*(4*x**2+3*x+1)/(3*x**2+2)**(5/2),x)","\frac{10 x^{3}}{18 x^{2} \sqrt{3 x^{2} + 2} + 12 \sqrt{3 x^{2} + 2}} + \frac{x^{3}}{6 x^{2} \sqrt{3 x^{2} + 2} + 4 \sqrt{3 x^{2} + 2}} - \frac{72 x^{2}}{81 x^{2} \sqrt{3 x^{2} + 2} + 54 \sqrt{3 x^{2} + 2}} + \frac{x}{6 x^{2} \sqrt{3 x^{2} + 2} + 4 \sqrt{3 x^{2} + 2}} - \frac{32}{81 x^{2} \sqrt{3 x^{2} + 2} + 54 \sqrt{3 x^{2} + 2}} - \frac{5}{27 x^{2} \sqrt{3 x^{2} + 2} + 18 \sqrt{3 x^{2} + 2}}"," ",0,"10*x**3/(18*x**2*sqrt(3*x**2 + 2) + 12*sqrt(3*x**2 + 2)) + x**3/(6*x**2*sqrt(3*x**2 + 2) + 4*sqrt(3*x**2 + 2)) - 72*x**2/(81*x**2*sqrt(3*x**2 + 2) + 54*sqrt(3*x**2 + 2)) + x/(6*x**2*sqrt(3*x**2 + 2) + 4*sqrt(3*x**2 + 2)) - 32/(81*x**2*sqrt(3*x**2 + 2) + 54*sqrt(3*x**2 + 2)) - 5/(27*x**2*sqrt(3*x**2 + 2) + 18*sqrt(3*x**2 + 2))","B",0
133,-1,0,0,0.000000," ","integrate((4*x**2+3*x+1)/(1+2*x)/(3*x**2+2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
134,-1,0,0,0.000000," ","integrate((4*x**2+3*x+1)/(1+2*x)**2/(3*x**2+2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
135,-1,0,0,0.000000," ","integrate((4*x**2+3*x+1)/(1+2*x)**3/(3*x**2+2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
136,-1,0,0,0.000000," ","integrate((h*x+g)**m*(c*x**2+a)**p*(f*x**2+e*x+d),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
137,0,0,0,0.000000," ","integrate((h*x+g)**m*(f*x**2+e*x+d)*(c*x**2+a)**(1/2),x)","\int \sqrt{a + c x^{2}} \left(g + h x\right)^{m} \left(d + e x + f x^{2}\right)\, dx"," ",0,"Integral(sqrt(a + c*x**2)*(g + h*x)**m*(d + e*x + f*x**2), x)","F",0
138,-1,0,0,0.000000," ","integrate((h*x+g)**(-3-2*p)*(c*x**2+a)**p*(f*x**2+e*x+d),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
139,-2,0,0,0.000000," ","integrate((e*x+d)**m*(c*e**2*x**2+b*e**2*x+b*d*e-c*d**2)**p*(-(-b*e+c*d)*f+(b*e*g-c*d*g+c*e*f)*x+c*e*g*x**2),x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
140,1,320,0,0.136319," ","integrate((c*x**2+b*x+a)**4*(C*x**2+A),x)","A a^{4} x + 2 A a^{3} b x^{2} + \frac{2 C b c^{3} x^{10}}{5} + \frac{C c^{4} x^{11}}{11} + x^{9} \left(\frac{A c^{4}}{9} + \frac{4 C a c^{3}}{9} + \frac{2 C b^{2} c^{2}}{3}\right) + x^{8} \left(\frac{A b c^{3}}{2} + \frac{3 C a b c^{2}}{2} + \frac{C b^{3} c}{2}\right) + x^{7} \left(\frac{4 A a c^{3}}{7} + \frac{6 A b^{2} c^{2}}{7} + \frac{6 C a^{2} c^{2}}{7} + \frac{12 C a b^{2} c}{7} + \frac{C b^{4}}{7}\right) + x^{6} \left(2 A a b c^{2} + \frac{2 A b^{3} c}{3} + 2 C a^{2} b c + \frac{2 C a b^{3}}{3}\right) + x^{5} \left(\frac{6 A a^{2} c^{2}}{5} + \frac{12 A a b^{2} c}{5} + \frac{A b^{4}}{5} + \frac{4 C a^{3} c}{5} + \frac{6 C a^{2} b^{2}}{5}\right) + x^{4} \left(3 A a^{2} b c + A a b^{3} + C a^{3} b\right) + x^{3} \left(\frac{4 A a^{3} c}{3} + 2 A a^{2} b^{2} + \frac{C a^{4}}{3}\right)"," ",0,"A*a**4*x + 2*A*a**3*b*x**2 + 2*C*b*c**3*x**10/5 + C*c**4*x**11/11 + x**9*(A*c**4/9 + 4*C*a*c**3/9 + 2*C*b**2*c**2/3) + x**8*(A*b*c**3/2 + 3*C*a*b*c**2/2 + C*b**3*c/2) + x**7*(4*A*a*c**3/7 + 6*A*b**2*c**2/7 + 6*C*a**2*c**2/7 + 12*C*a*b**2*c/7 + C*b**4/7) + x**6*(2*A*a*b*c**2 + 2*A*b**3*c/3 + 2*C*a**2*b*c + 2*C*a*b**3/3) + x**5*(6*A*a**2*c**2/5 + 12*A*a*b**2*c/5 + A*b**4/5 + 4*C*a**3*c/5 + 6*C*a**2*b**2/5) + x**4*(3*A*a**2*b*c + A*a*b**3 + C*a**3*b) + x**3*(4*A*a**3*c/3 + 2*A*a**2*b**2 + C*a**4/3)","A",0
141,1,197,0,0.108071," ","integrate((c*x**2+b*x+a)**3*(C*x**2+A),x)","A a^{3} x + \frac{3 A a^{2} b x^{2}}{2} + \frac{3 C b c^{2} x^{8}}{8} + \frac{C c^{3} x^{9}}{9} + x^{7} \left(\frac{A c^{3}}{7} + \frac{3 C a c^{2}}{7} + \frac{3 C b^{2} c}{7}\right) + x^{6} \left(\frac{A b c^{2}}{2} + C a b c + \frac{C b^{3}}{6}\right) + x^{5} \left(\frac{3 A a c^{2}}{5} + \frac{3 A b^{2} c}{5} + \frac{3 C a^{2} c}{5} + \frac{3 C a b^{2}}{5}\right) + x^{4} \left(\frac{3 A a b c}{2} + \frac{A b^{3}}{4} + \frac{3 C a^{2} b}{4}\right) + x^{3} \left(A a^{2} c + A a b^{2} + \frac{C a^{3}}{3}\right)"," ",0,"A*a**3*x + 3*A*a**2*b*x**2/2 + 3*C*b*c**2*x**8/8 + C*c**3*x**9/9 + x**7*(A*c**3/7 + 3*C*a*c**2/7 + 3*C*b**2*c/7) + x**6*(A*b*c**2/2 + C*a*b*c + C*b**3/6) + x**5*(3*A*a*c**2/5 + 3*A*b**2*c/5 + 3*C*a**2*c/5 + 3*C*a*b**2/5) + x**4*(3*A*a*b*c/2 + A*b**3/4 + 3*C*a**2*b/4) + x**3*(A*a**2*c + A*a*b**2 + C*a**3/3)","A",0
142,1,102,0,0.089244," ","integrate((c*x**2+b*x+a)**2*(C*x**2+A),x)","A a^{2} x + A a b x^{2} + \frac{C b c x^{6}}{3} + \frac{C c^{2} x^{7}}{7} + x^{5} \left(\frac{A c^{2}}{5} + \frac{2 C a c}{5} + \frac{C b^{2}}{5}\right) + x^{4} \left(\frac{A b c}{2} + \frac{C a b}{2}\right) + x^{3} \left(\frac{2 A a c}{3} + \frac{A b^{2}}{3} + \frac{C a^{2}}{3}\right)"," ",0,"A*a**2*x + A*a*b*x**2 + C*b*c*x**6/3 + C*c**2*x**7/7 + x**5*(A*c**2/5 + 2*C*a*c/5 + C*b**2/5) + x**4*(A*b*c/2 + C*a*b/2) + x**3*(2*A*a*c/3 + A*b**2/3 + C*a**2/3)","A",0
143,1,42,0,0.068502," ","integrate((c*x**2+b*x+a)*(C*x**2+A),x)","A a x + \frac{A b x^{2}}{2} + \frac{C b x^{4}}{4} + \frac{C c x^{5}}{5} + x^{3} \left(\frac{A c}{3} + \frac{C a}{3}\right)"," ",0,"A*a*x + A*b*x**2/2 + C*b*x**4/4 + C*c*x**5/5 + x**3*(A*c/3 + C*a/3)","A",0
144,1,413,0,1.212570," ","integrate((C*x**2+A)/(c*x**2+b*x+a),x)","\frac{C x}{c} + \left(- \frac{C b}{2 c^{2}} - \frac{\sqrt{- 4 a c + b^{2}} \left(- 2 A c^{2} + 2 C a c - C b^{2}\right)}{2 c^{2} \left(4 a c - b^{2}\right)}\right) \log{\left(x + \frac{- A b c - C a b - 4 a c^{2} \left(- \frac{C b}{2 c^{2}} - \frac{\sqrt{- 4 a c + b^{2}} \left(- 2 A c^{2} + 2 C a c - C b^{2}\right)}{2 c^{2} \left(4 a c - b^{2}\right)}\right) + b^{2} c \left(- \frac{C b}{2 c^{2}} - \frac{\sqrt{- 4 a c + b^{2}} \left(- 2 A c^{2} + 2 C a c - C b^{2}\right)}{2 c^{2} \left(4 a c - b^{2}\right)}\right)}{- 2 A c^{2} + 2 C a c - C b^{2}} \right)} + \left(- \frac{C b}{2 c^{2}} + \frac{\sqrt{- 4 a c + b^{2}} \left(- 2 A c^{2} + 2 C a c - C b^{2}\right)}{2 c^{2} \left(4 a c - b^{2}\right)}\right) \log{\left(x + \frac{- A b c - C a b - 4 a c^{2} \left(- \frac{C b}{2 c^{2}} + \frac{\sqrt{- 4 a c + b^{2}} \left(- 2 A c^{2} + 2 C a c - C b^{2}\right)}{2 c^{2} \left(4 a c - b^{2}\right)}\right) + b^{2} c \left(- \frac{C b}{2 c^{2}} + \frac{\sqrt{- 4 a c + b^{2}} \left(- 2 A c^{2} + 2 C a c - C b^{2}\right)}{2 c^{2} \left(4 a c - b^{2}\right)}\right)}{- 2 A c^{2} + 2 C a c - C b^{2}} \right)}"," ",0,"C*x/c + (-C*b/(2*c**2) - sqrt(-4*a*c + b**2)*(-2*A*c**2 + 2*C*a*c - C*b**2)/(2*c**2*(4*a*c - b**2)))*log(x + (-A*b*c - C*a*b - 4*a*c**2*(-C*b/(2*c**2) - sqrt(-4*a*c + b**2)*(-2*A*c**2 + 2*C*a*c - C*b**2)/(2*c**2*(4*a*c - b**2))) + b**2*c*(-C*b/(2*c**2) - sqrt(-4*a*c + b**2)*(-2*A*c**2 + 2*C*a*c - C*b**2)/(2*c**2*(4*a*c - b**2))))/(-2*A*c**2 + 2*C*a*c - C*b**2)) + (-C*b/(2*c**2) + sqrt(-4*a*c + b**2)*(-2*A*c**2 + 2*C*a*c - C*b**2)/(2*c**2*(4*a*c - b**2)))*log(x + (-A*b*c - C*a*b - 4*a*c**2*(-C*b/(2*c**2) + sqrt(-4*a*c + b**2)*(-2*A*c**2 + 2*C*a*c - C*b**2)/(2*c**2*(4*a*c - b**2))) + b**2*c*(-C*b/(2*c**2) + sqrt(-4*a*c + b**2)*(-2*A*c**2 + 2*C*a*c - C*b**2)/(2*c**2*(4*a*c - b**2))))/(-2*A*c**2 + 2*C*a*c - C*b**2))","B",0
145,1,376,0,1.211576," ","integrate((C*x**2+A)/(c*x**2+b*x+a)**2,x)","- 2 \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} \left(A c + C a\right) \log{\left(x + \frac{2 A b c + 2 C a b - 32 a^{2} c^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} \left(A c + C a\right) + 16 a b^{2} c \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} \left(A c + C a\right) - 2 b^{4} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} \left(A c + C a\right)}{4 A c^{2} + 4 C a c} \right)} + 2 \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} \left(A c + C a\right) \log{\left(x + \frac{2 A b c + 2 C a b + 32 a^{2} c^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} \left(A c + C a\right) - 16 a b^{2} c \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} \left(A c + C a\right) + 2 b^{4} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} \left(A c + C a\right)}{4 A c^{2} + 4 C a c} \right)} + \frac{A b c + C a b + x \left(2 A c^{2} - 2 C a c + C b^{2}\right)}{4 a^{2} c^{2} - a b^{2} c + x^{2} \left(4 a c^{3} - b^{2} c^{2}\right) + x \left(4 a b c^{2} - b^{3} c\right)}"," ",0,"-2*sqrt(-1/(4*a*c - b**2)**3)*(A*c + C*a)*log(x + (2*A*b*c + 2*C*a*b - 32*a**2*c**2*sqrt(-1/(4*a*c - b**2)**3)*(A*c + C*a) + 16*a*b**2*c*sqrt(-1/(4*a*c - b**2)**3)*(A*c + C*a) - 2*b**4*sqrt(-1/(4*a*c - b**2)**3)*(A*c + C*a))/(4*A*c**2 + 4*C*a*c)) + 2*sqrt(-1/(4*a*c - b**2)**3)*(A*c + C*a)*log(x + (2*A*b*c + 2*C*a*b + 32*a**2*c**2*sqrt(-1/(4*a*c - b**2)**3)*(A*c + C*a) - 16*a*b**2*c*sqrt(-1/(4*a*c - b**2)**3)*(A*c + C*a) + 2*b**4*sqrt(-1/(4*a*c - b**2)**3)*(A*c + C*a))/(4*A*c**2 + 4*C*a*c)) + (A*b*c + C*a*b + x*(2*A*c**2 - 2*C*a*c + C*b**2))/(4*a**2*c**2 - a*b**2*c + x**2*(4*a*c**3 - b**2*c**2) + x*(4*a*b*c**2 - b**3*c))","B",0
146,1,774,0,2.362330," ","integrate((C*x**2+A)/(c*x**2+b*x+a)**3,x)","- \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \left(6 A c^{2} + 2 C a c + C b^{2}\right) \log{\left(x + \frac{6 A b c^{2} + 2 C a b c + C b^{3} - 64 a^{3} c^{3} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \left(6 A c^{2} + 2 C a c + C b^{2}\right) + 48 a^{2} b^{2} c^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \left(6 A c^{2} + 2 C a c + C b^{2}\right) - 12 a b^{4} c \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \left(6 A c^{2} + 2 C a c + C b^{2}\right) + b^{6} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \left(6 A c^{2} + 2 C a c + C b^{2}\right)}{12 A c^{3} + 4 C a c^{2} + 2 C b^{2} c} \right)} + \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \left(6 A c^{2} + 2 C a c + C b^{2}\right) \log{\left(x + \frac{6 A b c^{2} + 2 C a b c + C b^{3} + 64 a^{3} c^{3} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \left(6 A c^{2} + 2 C a c + C b^{2}\right) - 48 a^{2} b^{2} c^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \left(6 A c^{2} + 2 C a c + C b^{2}\right) + 12 a b^{4} c \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \left(6 A c^{2} + 2 C a c + C b^{2}\right) - b^{6} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{5}}} \left(6 A c^{2} + 2 C a c + C b^{2}\right)}{12 A c^{3} + 4 C a c^{2} + 2 C b^{2} c} \right)} + \frac{10 A a b c - A b^{3} + 6 C a^{2} b + x^{3} \left(12 A c^{3} + 4 C a c^{2} + 2 C b^{2} c\right) + x^{2} \left(18 A b c^{2} + 6 C a b c + 3 C b^{3}\right) + x \left(20 A a c^{2} + 4 A b^{2} c - 4 C a^{2} c + 10 C a b^{2}\right)}{32 a^{4} c^{2} - 16 a^{3} b^{2} c + 2 a^{2} b^{4} + x^{4} \left(32 a^{2} c^{4} - 16 a b^{2} c^{3} + 2 b^{4} c^{2}\right) + x^{3} \left(64 a^{2} b c^{3} - 32 a b^{3} c^{2} + 4 b^{5} c\right) + x^{2} \left(64 a^{3} c^{3} - 12 a b^{4} c + 2 b^{6}\right) + x \left(64 a^{3} b c^{2} - 32 a^{2} b^{3} c + 4 a b^{5}\right)}"," ",0,"-sqrt(-1/(4*a*c - b**2)**5)*(6*A*c**2 + 2*C*a*c + C*b**2)*log(x + (6*A*b*c**2 + 2*C*a*b*c + C*b**3 - 64*a**3*c**3*sqrt(-1/(4*a*c - b**2)**5)*(6*A*c**2 + 2*C*a*c + C*b**2) + 48*a**2*b**2*c**2*sqrt(-1/(4*a*c - b**2)**5)*(6*A*c**2 + 2*C*a*c + C*b**2) - 12*a*b**4*c*sqrt(-1/(4*a*c - b**2)**5)*(6*A*c**2 + 2*C*a*c + C*b**2) + b**6*sqrt(-1/(4*a*c - b**2)**5)*(6*A*c**2 + 2*C*a*c + C*b**2))/(12*A*c**3 + 4*C*a*c**2 + 2*C*b**2*c)) + sqrt(-1/(4*a*c - b**2)**5)*(6*A*c**2 + 2*C*a*c + C*b**2)*log(x + (6*A*b*c**2 + 2*C*a*b*c + C*b**3 + 64*a**3*c**3*sqrt(-1/(4*a*c - b**2)**5)*(6*A*c**2 + 2*C*a*c + C*b**2) - 48*a**2*b**2*c**2*sqrt(-1/(4*a*c - b**2)**5)*(6*A*c**2 + 2*C*a*c + C*b**2) + 12*a*b**4*c*sqrt(-1/(4*a*c - b**2)**5)*(6*A*c**2 + 2*C*a*c + C*b**2) - b**6*sqrt(-1/(4*a*c - b**2)**5)*(6*A*c**2 + 2*C*a*c + C*b**2))/(12*A*c**3 + 4*C*a*c**2 + 2*C*b**2*c)) + (10*A*a*b*c - A*b**3 + 6*C*a**2*b + x**3*(12*A*c**3 + 4*C*a*c**2 + 2*C*b**2*c) + x**2*(18*A*b*c**2 + 6*C*a*b*c + 3*C*b**3) + x*(20*A*a*c**2 + 4*A*b**2*c - 4*C*a**2*c + 10*C*a*b**2))/(32*a**4*c**2 - 16*a**3*b**2*c + 2*a**2*b**4 + x**4*(32*a**2*c**4 - 16*a*b**2*c**3 + 2*b**4*c**2) + x**3*(64*a**2*b*c**3 - 32*a*b**3*c**2 + 4*b**5*c) + x**2*(64*a**3*c**3 - 12*a*b**4*c + 2*b**6) + x*(64*a**3*b*c**2 - 32*a**2*b**3*c + 4*a*b**5))","B",0
147,1,1224,0,4.220240," ","integrate((C*x**2+A)/(c*x**2+b*x+a)**4,x)","- 4 c \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{7}}} \left(5 A c^{2} + C a c + C b^{2}\right) \log{\left(x + \frac{20 A b c^{3} + 4 C a b c^{2} + 4 C b^{3} c - 1024 a^{4} c^{5} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{7}}} \left(5 A c^{2} + C a c + C b^{2}\right) + 1024 a^{3} b^{2} c^{4} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{7}}} \left(5 A c^{2} + C a c + C b^{2}\right) - 384 a^{2} b^{4} c^{3} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{7}}} \left(5 A c^{2} + C a c + C b^{2}\right) + 64 a b^{6} c^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{7}}} \left(5 A c^{2} + C a c + C b^{2}\right) - 4 b^{8} c \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{7}}} \left(5 A c^{2} + C a c + C b^{2}\right)}{40 A c^{4} + 8 C a c^{3} + 8 C b^{2} c^{2}} \right)} + 4 c \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{7}}} \left(5 A c^{2} + C a c + C b^{2}\right) \log{\left(x + \frac{20 A b c^{3} + 4 C a b c^{2} + 4 C b^{3} c + 1024 a^{4} c^{5} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{7}}} \left(5 A c^{2} + C a c + C b^{2}\right) - 1024 a^{3} b^{2} c^{4} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{7}}} \left(5 A c^{2} + C a c + C b^{2}\right) + 384 a^{2} b^{4} c^{3} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{7}}} \left(5 A c^{2} + C a c + C b^{2}\right) - 64 a b^{6} c^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{7}}} \left(5 A c^{2} + C a c + C b^{2}\right) + 4 b^{8} c \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{7}}} \left(5 A c^{2} + C a c + C b^{2}\right)}{40 A c^{4} + 8 C a c^{3} + 8 C b^{2} c^{2}} \right)} + \frac{66 A a^{2} b c^{2} - 13 A a b^{3} c + A b^{5} + 26 C a^{3} b c + C a^{2} b^{3} + x^{5} \left(60 A c^{5} + 12 C a c^{4} + 12 C b^{2} c^{3}\right) + x^{4} \left(150 A b c^{4} + 30 C a b c^{3} + 30 C b^{3} c^{2}\right) + x^{3} \left(160 A a c^{4} + 110 A b^{2} c^{3} + 32 C a^{2} c^{3} + 54 C a b^{2} c^{2} + 22 C b^{4} c\right) + x^{2} \left(240 A a b c^{3} + 15 A b^{3} c^{2} + 48 C a^{2} b c^{2} + 51 C a b^{3} c + 3 C b^{5}\right) + x \left(132 A a^{2} c^{3} + 54 A a b^{2} c^{2} - 3 A b^{4} c - 12 C a^{3} c^{2} + 66 C a^{2} b^{2} c + 3 C a b^{4}\right)}{192 a^{6} c^{3} - 144 a^{5} b^{2} c^{2} + 36 a^{4} b^{4} c - 3 a^{3} b^{6} + x^{6} \left(192 a^{3} c^{6} - 144 a^{2} b^{2} c^{5} + 36 a b^{4} c^{4} - 3 b^{6} c^{3}\right) + x^{5} \left(576 a^{3} b c^{5} - 432 a^{2} b^{3} c^{4} + 108 a b^{5} c^{3} - 9 b^{7} c^{2}\right) + x^{4} \left(576 a^{4} c^{5} + 144 a^{3} b^{2} c^{4} - 324 a^{2} b^{4} c^{3} + 99 a b^{6} c^{2} - 9 b^{8} c\right) + x^{3} \left(1152 a^{4} b c^{4} - 672 a^{3} b^{3} c^{3} + 72 a^{2} b^{5} c^{2} + 18 a b^{7} c - 3 b^{9}\right) + x^{2} \left(576 a^{5} c^{4} + 144 a^{4} b^{2} c^{3} - 324 a^{3} b^{4} c^{2} + 99 a^{2} b^{6} c - 9 a b^{8}\right) + x \left(576 a^{5} b c^{3} - 432 a^{4} b^{3} c^{2} + 108 a^{3} b^{5} c - 9 a^{2} b^{7}\right)}"," ",0,"-4*c*sqrt(-1/(4*a*c - b**2)**7)*(5*A*c**2 + C*a*c + C*b**2)*log(x + (20*A*b*c**3 + 4*C*a*b*c**2 + 4*C*b**3*c - 1024*a**4*c**5*sqrt(-1/(4*a*c - b**2)**7)*(5*A*c**2 + C*a*c + C*b**2) + 1024*a**3*b**2*c**4*sqrt(-1/(4*a*c - b**2)**7)*(5*A*c**2 + C*a*c + C*b**2) - 384*a**2*b**4*c**3*sqrt(-1/(4*a*c - b**2)**7)*(5*A*c**2 + C*a*c + C*b**2) + 64*a*b**6*c**2*sqrt(-1/(4*a*c - b**2)**7)*(5*A*c**2 + C*a*c + C*b**2) - 4*b**8*c*sqrt(-1/(4*a*c - b**2)**7)*(5*A*c**2 + C*a*c + C*b**2))/(40*A*c**4 + 8*C*a*c**3 + 8*C*b**2*c**2)) + 4*c*sqrt(-1/(4*a*c - b**2)**7)*(5*A*c**2 + C*a*c + C*b**2)*log(x + (20*A*b*c**3 + 4*C*a*b*c**2 + 4*C*b**3*c + 1024*a**4*c**5*sqrt(-1/(4*a*c - b**2)**7)*(5*A*c**2 + C*a*c + C*b**2) - 1024*a**3*b**2*c**4*sqrt(-1/(4*a*c - b**2)**7)*(5*A*c**2 + C*a*c + C*b**2) + 384*a**2*b**4*c**3*sqrt(-1/(4*a*c - b**2)**7)*(5*A*c**2 + C*a*c + C*b**2) - 64*a*b**6*c**2*sqrt(-1/(4*a*c - b**2)**7)*(5*A*c**2 + C*a*c + C*b**2) + 4*b**8*c*sqrt(-1/(4*a*c - b**2)**7)*(5*A*c**2 + C*a*c + C*b**2))/(40*A*c**4 + 8*C*a*c**3 + 8*C*b**2*c**2)) + (66*A*a**2*b*c**2 - 13*A*a*b**3*c + A*b**5 + 26*C*a**3*b*c + C*a**2*b**3 + x**5*(60*A*c**5 + 12*C*a*c**4 + 12*C*b**2*c**3) + x**4*(150*A*b*c**4 + 30*C*a*b*c**3 + 30*C*b**3*c**2) + x**3*(160*A*a*c**4 + 110*A*b**2*c**3 + 32*C*a**2*c**3 + 54*C*a*b**2*c**2 + 22*C*b**4*c) + x**2*(240*A*a*b*c**3 + 15*A*b**3*c**2 + 48*C*a**2*b*c**2 + 51*C*a*b**3*c + 3*C*b**5) + x*(132*A*a**2*c**3 + 54*A*a*b**2*c**2 - 3*A*b**4*c - 12*C*a**3*c**2 + 66*C*a**2*b**2*c + 3*C*a*b**4))/(192*a**6*c**3 - 144*a**5*b**2*c**2 + 36*a**4*b**4*c - 3*a**3*b**6 + x**6*(192*a**3*c**6 - 144*a**2*b**2*c**5 + 36*a*b**4*c**4 - 3*b**6*c**3) + x**5*(576*a**3*b*c**5 - 432*a**2*b**3*c**4 + 108*a*b**5*c**3 - 9*b**7*c**2) + x**4*(576*a**4*c**5 + 144*a**3*b**2*c**4 - 324*a**2*b**4*c**3 + 99*a*b**6*c**2 - 9*b**8*c) + x**3*(1152*a**4*b*c**4 - 672*a**3*b**3*c**3 + 72*a**2*b**5*c**2 + 18*a*b**7*c - 3*b**9) + x**2*(576*a**5*c**4 + 144*a**4*b**2*c**3 - 324*a**3*b**4*c**2 + 99*a**2*b**6*c - 9*a*b**8) + x*(576*a**5*b*c**3 - 432*a**4*b**3*c**2 + 108*a**3*b**5*c - 9*a**2*b**7))","B",0
148,1,4972,0,118.420172," ","integrate((e*x+d)**3*(h*x**2+g*x+f)/(c*x**2+b*x+a),x)","x^{3} \left(- \frac{b e^{3} h}{3 c^{2}} + \frac{d e^{2} h}{c} + \frac{e^{3} g}{3 c}\right) + x^{2} \left(- \frac{a e^{3} h}{2 c^{2}} + \frac{b^{2} e^{3} h}{2 c^{3}} - \frac{3 b d e^{2} h}{2 c^{2}} - \frac{b e^{3} g}{2 c^{2}} + \frac{3 d^{2} e h}{2 c} + \frac{3 d e^{2} g}{2 c} + \frac{e^{3} f}{2 c}\right) + x \left(\frac{2 a b e^{3} h}{c^{3}} - \frac{3 a d e^{2} h}{c^{2}} - \frac{a e^{3} g}{c^{2}} - \frac{b^{3} e^{3} h}{c^{4}} + \frac{3 b^{2} d e^{2} h}{c^{3}} + \frac{b^{2} e^{3} g}{c^{3}} - \frac{3 b d^{2} e h}{c^{2}} - \frac{3 b d e^{2} g}{c^{2}} - \frac{b e^{3} f}{c^{2}} + \frac{d^{3} h}{c} + \frac{3 d^{2} e g}{c} + \frac{3 d e^{2} f}{c}\right) + \left(- \frac{\sqrt{- 4 a c + b^{2}} \left(5 a^{2} b c^{2} e^{3} h - 6 a^{2} c^{3} d e^{2} h - 2 a^{2} c^{3} e^{3} g - 5 a b^{3} c e^{3} h + 12 a b^{2} c^{2} d e^{2} h + 4 a b^{2} c^{2} e^{3} g - 9 a b c^{3} d^{2} e h - 9 a b c^{3} d e^{2} g - 3 a b c^{3} e^{3} f + 2 a c^{4} d^{3} h + 6 a c^{4} d^{2} e g + 6 a c^{4} d e^{2} f + b^{5} e^{3} h - 3 b^{4} c d e^{2} h - b^{4} c e^{3} g + 3 b^{3} c^{2} d^{2} e h + 3 b^{3} c^{2} d e^{2} g + b^{3} c^{2} e^{3} f - b^{2} c^{3} d^{3} h - 3 b^{2} c^{3} d^{2} e g - 3 b^{2} c^{3} d e^{2} f + b c^{4} d^{3} g + 3 b c^{4} d^{2} e f - 2 c^{5} d^{3} f\right)}{2 c^{5} \left(4 a c - b^{2}\right)} + \frac{a^{2} c^{2} e^{3} h - 3 a b^{2} c e^{3} h + 6 a b c^{2} d e^{2} h + 2 a b c^{2} e^{3} g - 3 a c^{3} d^{2} e h - 3 a c^{3} d e^{2} g - a c^{3} e^{3} f + b^{4} e^{3} h - 3 b^{3} c d e^{2} h - b^{3} c e^{3} g + 3 b^{2} c^{2} d^{2} e h + 3 b^{2} c^{2} d e^{2} g + b^{2} c^{2} e^{3} f - b c^{3} d^{3} h - 3 b c^{3} d^{2} e g - 3 b c^{3} d e^{2} f + c^{4} d^{3} g + 3 c^{4} d^{2} e f}{2 c^{5}}\right) \log{\left(x + \frac{2 a^{3} c^{2} e^{3} h - 4 a^{2} b^{2} c e^{3} h + 9 a^{2} b c^{2} d e^{2} h + 3 a^{2} b c^{2} e^{3} g - 6 a^{2} c^{3} d^{2} e h - 6 a^{2} c^{3} d e^{2} g - 2 a^{2} c^{3} e^{3} f + a b^{4} e^{3} h - 3 a b^{3} c d e^{2} h - a b^{3} c e^{3} g + 3 a b^{2} c^{2} d^{2} e h + 3 a b^{2} c^{2} d e^{2} g + a b^{2} c^{2} e^{3} f - a b c^{3} d^{3} h - 3 a b c^{3} d^{2} e g - 3 a b c^{3} d e^{2} f - 4 a c^{5} \left(- \frac{\sqrt{- 4 a c + b^{2}} \left(5 a^{2} b c^{2} e^{3} h - 6 a^{2} c^{3} d e^{2} h - 2 a^{2} c^{3} e^{3} g - 5 a b^{3} c e^{3} h + 12 a b^{2} c^{2} d e^{2} h + 4 a b^{2} c^{2} e^{3} g - 9 a b c^{3} d^{2} e h - 9 a b c^{3} d e^{2} g - 3 a b c^{3} e^{3} f + 2 a c^{4} d^{3} h + 6 a c^{4} d^{2} e g + 6 a c^{4} d e^{2} f + b^{5} e^{3} h - 3 b^{4} c d e^{2} h - b^{4} c e^{3} g + 3 b^{3} c^{2} d^{2} e h + 3 b^{3} c^{2} d e^{2} g + b^{3} c^{2} e^{3} f - b^{2} c^{3} d^{3} h - 3 b^{2} c^{3} d^{2} e g - 3 b^{2} c^{3} d e^{2} f + b c^{4} d^{3} g + 3 b c^{4} d^{2} e f - 2 c^{5} d^{3} f\right)}{2 c^{5} \left(4 a c - b^{2}\right)} + \frac{a^{2} c^{2} e^{3} h - 3 a b^{2} c e^{3} h + 6 a b c^{2} d e^{2} h + 2 a b c^{2} e^{3} g - 3 a c^{3} d^{2} e h - 3 a c^{3} d e^{2} g - a c^{3} e^{3} f + b^{4} e^{3} h - 3 b^{3} c d e^{2} h - b^{3} c e^{3} g + 3 b^{2} c^{2} d^{2} e h + 3 b^{2} c^{2} d e^{2} g + b^{2} c^{2} e^{3} f - b c^{3} d^{3} h - 3 b c^{3} d^{2} e g - 3 b c^{3} d e^{2} f + c^{4} d^{3} g + 3 c^{4} d^{2} e f}{2 c^{5}}\right) + 2 a c^{4} d^{3} g + 6 a c^{4} d^{2} e f + b^{2} c^{4} \left(- \frac{\sqrt{- 4 a c + b^{2}} \left(5 a^{2} b c^{2} e^{3} h - 6 a^{2} c^{3} d e^{2} h - 2 a^{2} c^{3} e^{3} g - 5 a b^{3} c e^{3} h + 12 a b^{2} c^{2} d e^{2} h + 4 a b^{2} c^{2} e^{3} g - 9 a b c^{3} d^{2} e h - 9 a b c^{3} d e^{2} g - 3 a b c^{3} e^{3} f + 2 a c^{4} d^{3} h + 6 a c^{4} d^{2} e g + 6 a c^{4} d e^{2} f + b^{5} e^{3} h - 3 b^{4} c d e^{2} h - b^{4} c e^{3} g + 3 b^{3} c^{2} d^{2} e h + 3 b^{3} c^{2} d e^{2} g + b^{3} c^{2} e^{3} f - b^{2} c^{3} d^{3} h - 3 b^{2} c^{3} d^{2} e g - 3 b^{2} c^{3} d e^{2} f + b c^{4} d^{3} g + 3 b c^{4} d^{2} e f - 2 c^{5} d^{3} f\right)}{2 c^{5} \left(4 a c - b^{2}\right)} + \frac{a^{2} c^{2} e^{3} h - 3 a b^{2} c e^{3} h + 6 a b c^{2} d e^{2} h + 2 a b c^{2} e^{3} g - 3 a c^{3} d^{2} e h - 3 a c^{3} d e^{2} g - a c^{3} e^{3} f + b^{4} e^{3} h - 3 b^{3} c d e^{2} h - b^{3} c e^{3} g + 3 b^{2} c^{2} d^{2} e h + 3 b^{2} c^{2} d e^{2} g + b^{2} c^{2} e^{3} f - b c^{3} d^{3} h - 3 b c^{3} d^{2} e g - 3 b c^{3} d e^{2} f + c^{4} d^{3} g + 3 c^{4} d^{2} e f}{2 c^{5}}\right) - b c^{4} d^{3} f}{5 a^{2} b c^{2} e^{3} h - 6 a^{2} c^{3} d e^{2} h - 2 a^{2} c^{3} e^{3} g - 5 a b^{3} c e^{3} h + 12 a b^{2} c^{2} d e^{2} h + 4 a b^{2} c^{2} e^{3} g - 9 a b c^{3} d^{2} e h - 9 a b c^{3} d e^{2} g - 3 a b c^{3} e^{3} f + 2 a c^{4} d^{3} h + 6 a c^{4} d^{2} e g + 6 a c^{4} d e^{2} f + b^{5} e^{3} h - 3 b^{4} c d e^{2} h - b^{4} c e^{3} g + 3 b^{3} c^{2} d^{2} e h + 3 b^{3} c^{2} d e^{2} g + b^{3} c^{2} e^{3} f - b^{2} c^{3} d^{3} h - 3 b^{2} c^{3} d^{2} e g - 3 b^{2} c^{3} d e^{2} f + b c^{4} d^{3} g + 3 b c^{4} d^{2} e f - 2 c^{5} d^{3} f} \right)} + \left(\frac{\sqrt{- 4 a c + b^{2}} \left(5 a^{2} b c^{2} e^{3} h - 6 a^{2} c^{3} d e^{2} h - 2 a^{2} c^{3} e^{3} g - 5 a b^{3} c e^{3} h + 12 a b^{2} c^{2} d e^{2} h + 4 a b^{2} c^{2} e^{3} g - 9 a b c^{3} d^{2} e h - 9 a b c^{3} d e^{2} g - 3 a b c^{3} e^{3} f + 2 a c^{4} d^{3} h + 6 a c^{4} d^{2} e g + 6 a c^{4} d e^{2} f + b^{5} e^{3} h - 3 b^{4} c d e^{2} h - b^{4} c e^{3} g + 3 b^{3} c^{2} d^{2} e h + 3 b^{3} c^{2} d e^{2} g + b^{3} c^{2} e^{3} f - b^{2} c^{3} d^{3} h - 3 b^{2} c^{3} d^{2} e g - 3 b^{2} c^{3} d e^{2} f + b c^{4} d^{3} g + 3 b c^{4} d^{2} e f - 2 c^{5} d^{3} f\right)}{2 c^{5} \left(4 a c - b^{2}\right)} + \frac{a^{2} c^{2} e^{3} h - 3 a b^{2} c e^{3} h + 6 a b c^{2} d e^{2} h + 2 a b c^{2} e^{3} g - 3 a c^{3} d^{2} e h - 3 a c^{3} d e^{2} g - a c^{3} e^{3} f + b^{4} e^{3} h - 3 b^{3} c d e^{2} h - b^{3} c e^{3} g + 3 b^{2} c^{2} d^{2} e h + 3 b^{2} c^{2} d e^{2} g + b^{2} c^{2} e^{3} f - b c^{3} d^{3} h - 3 b c^{3} d^{2} e g - 3 b c^{3} d e^{2} f + c^{4} d^{3} g + 3 c^{4} d^{2} e f}{2 c^{5}}\right) \log{\left(x + \frac{2 a^{3} c^{2} e^{3} h - 4 a^{2} b^{2} c e^{3} h + 9 a^{2} b c^{2} d e^{2} h + 3 a^{2} b c^{2} e^{3} g - 6 a^{2} c^{3} d^{2} e h - 6 a^{2} c^{3} d e^{2} g - 2 a^{2} c^{3} e^{3} f + a b^{4} e^{3} h - 3 a b^{3} c d e^{2} h - a b^{3} c e^{3} g + 3 a b^{2} c^{2} d^{2} e h + 3 a b^{2} c^{2} d e^{2} g + a b^{2} c^{2} e^{3} f - a b c^{3} d^{3} h - 3 a b c^{3} d^{2} e g - 3 a b c^{3} d e^{2} f - 4 a c^{5} \left(\frac{\sqrt{- 4 a c + b^{2}} \left(5 a^{2} b c^{2} e^{3} h - 6 a^{2} c^{3} d e^{2} h - 2 a^{2} c^{3} e^{3} g - 5 a b^{3} c e^{3} h + 12 a b^{2} c^{2} d e^{2} h + 4 a b^{2} c^{2} e^{3} g - 9 a b c^{3} d^{2} e h - 9 a b c^{3} d e^{2} g - 3 a b c^{3} e^{3} f + 2 a c^{4} d^{3} h + 6 a c^{4} d^{2} e g + 6 a c^{4} d e^{2} f + b^{5} e^{3} h - 3 b^{4} c d e^{2} h - b^{4} c e^{3} g + 3 b^{3} c^{2} d^{2} e h + 3 b^{3} c^{2} d e^{2} g + b^{3} c^{2} e^{3} f - b^{2} c^{3} d^{3} h - 3 b^{2} c^{3} d^{2} e g - 3 b^{2} c^{3} d e^{2} f + b c^{4} d^{3} g + 3 b c^{4} d^{2} e f - 2 c^{5} d^{3} f\right)}{2 c^{5} \left(4 a c - b^{2}\right)} + \frac{a^{2} c^{2} e^{3} h - 3 a b^{2} c e^{3} h + 6 a b c^{2} d e^{2} h + 2 a b c^{2} e^{3} g - 3 a c^{3} d^{2} e h - 3 a c^{3} d e^{2} g - a c^{3} e^{3} f + b^{4} e^{3} h - 3 b^{3} c d e^{2} h - b^{3} c e^{3} g + 3 b^{2} c^{2} d^{2} e h + 3 b^{2} c^{2} d e^{2} g + b^{2} c^{2} e^{3} f - b c^{3} d^{3} h - 3 b c^{3} d^{2} e g - 3 b c^{3} d e^{2} f + c^{4} d^{3} g + 3 c^{4} d^{2} e f}{2 c^{5}}\right) + 2 a c^{4} d^{3} g + 6 a c^{4} d^{2} e f + b^{2} c^{4} \left(\frac{\sqrt{- 4 a c + b^{2}} \left(5 a^{2} b c^{2} e^{3} h - 6 a^{2} c^{3} d e^{2} h - 2 a^{2} c^{3} e^{3} g - 5 a b^{3} c e^{3} h + 12 a b^{2} c^{2} d e^{2} h + 4 a b^{2} c^{2} e^{3} g - 9 a b c^{3} d^{2} e h - 9 a b c^{3} d e^{2} g - 3 a b c^{3} e^{3} f + 2 a c^{4} d^{3} h + 6 a c^{4} d^{2} e g + 6 a c^{4} d e^{2} f + b^{5} e^{3} h - 3 b^{4} c d e^{2} h - b^{4} c e^{3} g + 3 b^{3} c^{2} d^{2} e h + 3 b^{3} c^{2} d e^{2} g + b^{3} c^{2} e^{3} f - b^{2} c^{3} d^{3} h - 3 b^{2} c^{3} d^{2} e g - 3 b^{2} c^{3} d e^{2} f + b c^{4} d^{3} g + 3 b c^{4} d^{2} e f - 2 c^{5} d^{3} f\right)}{2 c^{5} \left(4 a c - b^{2}\right)} + \frac{a^{2} c^{2} e^{3} h - 3 a b^{2} c e^{3} h + 6 a b c^{2} d e^{2} h + 2 a b c^{2} e^{3} g - 3 a c^{3} d^{2} e h - 3 a c^{3} d e^{2} g - a c^{3} e^{3} f + b^{4} e^{3} h - 3 b^{3} c d e^{2} h - b^{3} c e^{3} g + 3 b^{2} c^{2} d^{2} e h + 3 b^{2} c^{2} d e^{2} g + b^{2} c^{2} e^{3} f - b c^{3} d^{3} h - 3 b c^{3} d^{2} e g - 3 b c^{3} d e^{2} f + c^{4} d^{3} g + 3 c^{4} d^{2} e f}{2 c^{5}}\right) - b c^{4} d^{3} f}{5 a^{2} b c^{2} e^{3} h - 6 a^{2} c^{3} d e^{2} h - 2 a^{2} c^{3} e^{3} g - 5 a b^{3} c e^{3} h + 12 a b^{2} c^{2} d e^{2} h + 4 a b^{2} c^{2} e^{3} g - 9 a b c^{3} d^{2} e h - 9 a b c^{3} d e^{2} g - 3 a b c^{3} e^{3} f + 2 a c^{4} d^{3} h + 6 a c^{4} d^{2} e g + 6 a c^{4} d e^{2} f + b^{5} e^{3} h - 3 b^{4} c d e^{2} h - b^{4} c e^{3} g + 3 b^{3} c^{2} d^{2} e h + 3 b^{3} c^{2} d e^{2} g + b^{3} c^{2} e^{3} f - b^{2} c^{3} d^{3} h - 3 b^{2} c^{3} d^{2} e g - 3 b^{2} c^{3} d e^{2} f + b c^{4} d^{3} g + 3 b c^{4} d^{2} e f - 2 c^{5} d^{3} f} \right)} + \frac{e^{3} h x^{4}}{4 c}"," ",0,"x**3*(-b*e**3*h/(3*c**2) + d*e**2*h/c + e**3*g/(3*c)) + x**2*(-a*e**3*h/(2*c**2) + b**2*e**3*h/(2*c**3) - 3*b*d*e**2*h/(2*c**2) - b*e**3*g/(2*c**2) + 3*d**2*e*h/(2*c) + 3*d*e**2*g/(2*c) + e**3*f/(2*c)) + x*(2*a*b*e**3*h/c**3 - 3*a*d*e**2*h/c**2 - a*e**3*g/c**2 - b**3*e**3*h/c**4 + 3*b**2*d*e**2*h/c**3 + b**2*e**3*g/c**3 - 3*b*d**2*e*h/c**2 - 3*b*d*e**2*g/c**2 - b*e**3*f/c**2 + d**3*h/c + 3*d**2*e*g/c + 3*d*e**2*f/c) + (-sqrt(-4*a*c + b**2)*(5*a**2*b*c**2*e**3*h - 6*a**2*c**3*d*e**2*h - 2*a**2*c**3*e**3*g - 5*a*b**3*c*e**3*h + 12*a*b**2*c**2*d*e**2*h + 4*a*b**2*c**2*e**3*g - 9*a*b*c**3*d**2*e*h - 9*a*b*c**3*d*e**2*g - 3*a*b*c**3*e**3*f + 2*a*c**4*d**3*h + 6*a*c**4*d**2*e*g + 6*a*c**4*d*e**2*f + b**5*e**3*h - 3*b**4*c*d*e**2*h - b**4*c*e**3*g + 3*b**3*c**2*d**2*e*h + 3*b**3*c**2*d*e**2*g + b**3*c**2*e**3*f - b**2*c**3*d**3*h - 3*b**2*c**3*d**2*e*g - 3*b**2*c**3*d*e**2*f + b*c**4*d**3*g + 3*b*c**4*d**2*e*f - 2*c**5*d**3*f)/(2*c**5*(4*a*c - b**2)) + (a**2*c**2*e**3*h - 3*a*b**2*c*e**3*h + 6*a*b*c**2*d*e**2*h + 2*a*b*c**2*e**3*g - 3*a*c**3*d**2*e*h - 3*a*c**3*d*e**2*g - a*c**3*e**3*f + b**4*e**3*h - 3*b**3*c*d*e**2*h - b**3*c*e**3*g + 3*b**2*c**2*d**2*e*h + 3*b**2*c**2*d*e**2*g + b**2*c**2*e**3*f - b*c**3*d**3*h - 3*b*c**3*d**2*e*g - 3*b*c**3*d*e**2*f + c**4*d**3*g + 3*c**4*d**2*e*f)/(2*c**5))*log(x + (2*a**3*c**2*e**3*h - 4*a**2*b**2*c*e**3*h + 9*a**2*b*c**2*d*e**2*h + 3*a**2*b*c**2*e**3*g - 6*a**2*c**3*d**2*e*h - 6*a**2*c**3*d*e**2*g - 2*a**2*c**3*e**3*f + a*b**4*e**3*h - 3*a*b**3*c*d*e**2*h - a*b**3*c*e**3*g + 3*a*b**2*c**2*d**2*e*h + 3*a*b**2*c**2*d*e**2*g + a*b**2*c**2*e**3*f - a*b*c**3*d**3*h - 3*a*b*c**3*d**2*e*g - 3*a*b*c**3*d*e**2*f - 4*a*c**5*(-sqrt(-4*a*c + b**2)*(5*a**2*b*c**2*e**3*h - 6*a**2*c**3*d*e**2*h - 2*a**2*c**3*e**3*g - 5*a*b**3*c*e**3*h + 12*a*b**2*c**2*d*e**2*h + 4*a*b**2*c**2*e**3*g - 9*a*b*c**3*d**2*e*h - 9*a*b*c**3*d*e**2*g - 3*a*b*c**3*e**3*f + 2*a*c**4*d**3*h + 6*a*c**4*d**2*e*g + 6*a*c**4*d*e**2*f + b**5*e**3*h - 3*b**4*c*d*e**2*h - b**4*c*e**3*g + 3*b**3*c**2*d**2*e*h + 3*b**3*c**2*d*e**2*g + b**3*c**2*e**3*f - b**2*c**3*d**3*h - 3*b**2*c**3*d**2*e*g - 3*b**2*c**3*d*e**2*f + b*c**4*d**3*g + 3*b*c**4*d**2*e*f - 2*c**5*d**3*f)/(2*c**5*(4*a*c - b**2)) + (a**2*c**2*e**3*h - 3*a*b**2*c*e**3*h + 6*a*b*c**2*d*e**2*h + 2*a*b*c**2*e**3*g - 3*a*c**3*d**2*e*h - 3*a*c**3*d*e**2*g - a*c**3*e**3*f + b**4*e**3*h - 3*b**3*c*d*e**2*h - b**3*c*e**3*g + 3*b**2*c**2*d**2*e*h + 3*b**2*c**2*d*e**2*g + b**2*c**2*e**3*f - b*c**3*d**3*h - 3*b*c**3*d**2*e*g - 3*b*c**3*d*e**2*f + c**4*d**3*g + 3*c**4*d**2*e*f)/(2*c**5)) + 2*a*c**4*d**3*g + 6*a*c**4*d**2*e*f + b**2*c**4*(-sqrt(-4*a*c + b**2)*(5*a**2*b*c**2*e**3*h - 6*a**2*c**3*d*e**2*h - 2*a**2*c**3*e**3*g - 5*a*b**3*c*e**3*h + 12*a*b**2*c**2*d*e**2*h + 4*a*b**2*c**2*e**3*g - 9*a*b*c**3*d**2*e*h - 9*a*b*c**3*d*e**2*g - 3*a*b*c**3*e**3*f + 2*a*c**4*d**3*h + 6*a*c**4*d**2*e*g + 6*a*c**4*d*e**2*f + b**5*e**3*h - 3*b**4*c*d*e**2*h - b**4*c*e**3*g + 3*b**3*c**2*d**2*e*h + 3*b**3*c**2*d*e**2*g + b**3*c**2*e**3*f - b**2*c**3*d**3*h - 3*b**2*c**3*d**2*e*g - 3*b**2*c**3*d*e**2*f + b*c**4*d**3*g + 3*b*c**4*d**2*e*f - 2*c**5*d**3*f)/(2*c**5*(4*a*c - b**2)) + (a**2*c**2*e**3*h - 3*a*b**2*c*e**3*h + 6*a*b*c**2*d*e**2*h + 2*a*b*c**2*e**3*g - 3*a*c**3*d**2*e*h - 3*a*c**3*d*e**2*g - a*c**3*e**3*f + b**4*e**3*h - 3*b**3*c*d*e**2*h - b**3*c*e**3*g + 3*b**2*c**2*d**2*e*h + 3*b**2*c**2*d*e**2*g + b**2*c**2*e**3*f - b*c**3*d**3*h - 3*b*c**3*d**2*e*g - 3*b*c**3*d*e**2*f + c**4*d**3*g + 3*c**4*d**2*e*f)/(2*c**5)) - b*c**4*d**3*f)/(5*a**2*b*c**2*e**3*h - 6*a**2*c**3*d*e**2*h - 2*a**2*c**3*e**3*g - 5*a*b**3*c*e**3*h + 12*a*b**2*c**2*d*e**2*h + 4*a*b**2*c**2*e**3*g - 9*a*b*c**3*d**2*e*h - 9*a*b*c**3*d*e**2*g - 3*a*b*c**3*e**3*f + 2*a*c**4*d**3*h + 6*a*c**4*d**2*e*g + 6*a*c**4*d*e**2*f + b**5*e**3*h - 3*b**4*c*d*e**2*h - b**4*c*e**3*g + 3*b**3*c**2*d**2*e*h + 3*b**3*c**2*d*e**2*g + b**3*c**2*e**3*f - b**2*c**3*d**3*h - 3*b**2*c**3*d**2*e*g - 3*b**2*c**3*d*e**2*f + b*c**4*d**3*g + 3*b*c**4*d**2*e*f - 2*c**5*d**3*f)) + (sqrt(-4*a*c + b**2)*(5*a**2*b*c**2*e**3*h - 6*a**2*c**3*d*e**2*h - 2*a**2*c**3*e**3*g - 5*a*b**3*c*e**3*h + 12*a*b**2*c**2*d*e**2*h + 4*a*b**2*c**2*e**3*g - 9*a*b*c**3*d**2*e*h - 9*a*b*c**3*d*e**2*g - 3*a*b*c**3*e**3*f + 2*a*c**4*d**3*h + 6*a*c**4*d**2*e*g + 6*a*c**4*d*e**2*f + b**5*e**3*h - 3*b**4*c*d*e**2*h - b**4*c*e**3*g + 3*b**3*c**2*d**2*e*h + 3*b**3*c**2*d*e**2*g + b**3*c**2*e**3*f - b**2*c**3*d**3*h - 3*b**2*c**3*d**2*e*g - 3*b**2*c**3*d*e**2*f + b*c**4*d**3*g + 3*b*c**4*d**2*e*f - 2*c**5*d**3*f)/(2*c**5*(4*a*c - b**2)) + (a**2*c**2*e**3*h - 3*a*b**2*c*e**3*h + 6*a*b*c**2*d*e**2*h + 2*a*b*c**2*e**3*g - 3*a*c**3*d**2*e*h - 3*a*c**3*d*e**2*g - a*c**3*e**3*f + b**4*e**3*h - 3*b**3*c*d*e**2*h - b**3*c*e**3*g + 3*b**2*c**2*d**2*e*h + 3*b**2*c**2*d*e**2*g + b**2*c**2*e**3*f - b*c**3*d**3*h - 3*b*c**3*d**2*e*g - 3*b*c**3*d*e**2*f + c**4*d**3*g + 3*c**4*d**2*e*f)/(2*c**5))*log(x + (2*a**3*c**2*e**3*h - 4*a**2*b**2*c*e**3*h + 9*a**2*b*c**2*d*e**2*h + 3*a**2*b*c**2*e**3*g - 6*a**2*c**3*d**2*e*h - 6*a**2*c**3*d*e**2*g - 2*a**2*c**3*e**3*f + a*b**4*e**3*h - 3*a*b**3*c*d*e**2*h - a*b**3*c*e**3*g + 3*a*b**2*c**2*d**2*e*h + 3*a*b**2*c**2*d*e**2*g + a*b**2*c**2*e**3*f - a*b*c**3*d**3*h - 3*a*b*c**3*d**2*e*g - 3*a*b*c**3*d*e**2*f - 4*a*c**5*(sqrt(-4*a*c + b**2)*(5*a**2*b*c**2*e**3*h - 6*a**2*c**3*d*e**2*h - 2*a**2*c**3*e**3*g - 5*a*b**3*c*e**3*h + 12*a*b**2*c**2*d*e**2*h + 4*a*b**2*c**2*e**3*g - 9*a*b*c**3*d**2*e*h - 9*a*b*c**3*d*e**2*g - 3*a*b*c**3*e**3*f + 2*a*c**4*d**3*h + 6*a*c**4*d**2*e*g + 6*a*c**4*d*e**2*f + b**5*e**3*h - 3*b**4*c*d*e**2*h - b**4*c*e**3*g + 3*b**3*c**2*d**2*e*h + 3*b**3*c**2*d*e**2*g + b**3*c**2*e**3*f - b**2*c**3*d**3*h - 3*b**2*c**3*d**2*e*g - 3*b**2*c**3*d*e**2*f + b*c**4*d**3*g + 3*b*c**4*d**2*e*f - 2*c**5*d**3*f)/(2*c**5*(4*a*c - b**2)) + (a**2*c**2*e**3*h - 3*a*b**2*c*e**3*h + 6*a*b*c**2*d*e**2*h + 2*a*b*c**2*e**3*g - 3*a*c**3*d**2*e*h - 3*a*c**3*d*e**2*g - a*c**3*e**3*f + b**4*e**3*h - 3*b**3*c*d*e**2*h - b**3*c*e**3*g + 3*b**2*c**2*d**2*e*h + 3*b**2*c**2*d*e**2*g + b**2*c**2*e**3*f - b*c**3*d**3*h - 3*b*c**3*d**2*e*g - 3*b*c**3*d*e**2*f + c**4*d**3*g + 3*c**4*d**2*e*f)/(2*c**5)) + 2*a*c**4*d**3*g + 6*a*c**4*d**2*e*f + b**2*c**4*(sqrt(-4*a*c + b**2)*(5*a**2*b*c**2*e**3*h - 6*a**2*c**3*d*e**2*h - 2*a**2*c**3*e**3*g - 5*a*b**3*c*e**3*h + 12*a*b**2*c**2*d*e**2*h + 4*a*b**2*c**2*e**3*g - 9*a*b*c**3*d**2*e*h - 9*a*b*c**3*d*e**2*g - 3*a*b*c**3*e**3*f + 2*a*c**4*d**3*h + 6*a*c**4*d**2*e*g + 6*a*c**4*d*e**2*f + b**5*e**3*h - 3*b**4*c*d*e**2*h - b**4*c*e**3*g + 3*b**3*c**2*d**2*e*h + 3*b**3*c**2*d*e**2*g + b**3*c**2*e**3*f - b**2*c**3*d**3*h - 3*b**2*c**3*d**2*e*g - 3*b**2*c**3*d*e**2*f + b*c**4*d**3*g + 3*b*c**4*d**2*e*f - 2*c**5*d**3*f)/(2*c**5*(4*a*c - b**2)) + (a**2*c**2*e**3*h - 3*a*b**2*c*e**3*h + 6*a*b*c**2*d*e**2*h + 2*a*b*c**2*e**3*g - 3*a*c**3*d**2*e*h - 3*a*c**3*d*e**2*g - a*c**3*e**3*f + b**4*e**3*h - 3*b**3*c*d*e**2*h - b**3*c*e**3*g + 3*b**2*c**2*d**2*e*h + 3*b**2*c**2*d*e**2*g + b**2*c**2*e**3*f - b*c**3*d**3*h - 3*b*c**3*d**2*e*g - 3*b*c**3*d*e**2*f + c**4*d**3*g + 3*c**4*d**2*e*f)/(2*c**5)) - b*c**4*d**3*f)/(5*a**2*b*c**2*e**3*h - 6*a**2*c**3*d*e**2*h - 2*a**2*c**3*e**3*g - 5*a*b**3*c*e**3*h + 12*a*b**2*c**2*d*e**2*h + 4*a*b**2*c**2*e**3*g - 9*a*b*c**3*d**2*e*h - 9*a*b*c**3*d*e**2*g - 3*a*b*c**3*e**3*f + 2*a*c**4*d**3*h + 6*a*c**4*d**2*e*g + 6*a*c**4*d*e**2*f + b**5*e**3*h - 3*b**4*c*d*e**2*h - b**4*c*e**3*g + 3*b**3*c**2*d**2*e*h + 3*b**3*c**2*d*e**2*g + b**3*c**2*e**3*f - b**2*c**3*d**3*h - 3*b**2*c**3*d**2*e*g - 3*b**2*c**3*d*e**2*f + b*c**4*d**3*g + 3*b*c**4*d**2*e*f - 2*c**5*d**3*f)) + e**3*h*x**4/(4*c)","B",0
149,1,2839,0,47.192591," ","integrate((e*x+d)**2*(h*x**2+g*x+f)/(c*x**2+b*x+a),x)","x^{2} \left(- \frac{b e^{2} h}{2 c^{2}} + \frac{d e h}{c} + \frac{e^{2} g}{2 c}\right) + x \left(- \frac{a e^{2} h}{c^{2}} + \frac{b^{2} e^{2} h}{c^{3}} - \frac{2 b d e h}{c^{2}} - \frac{b e^{2} g}{c^{2}} + \frac{d^{2} h}{c} + \frac{2 d e g}{c} + \frac{e^{2} f}{c}\right) + \left(- \frac{\sqrt{- 4 a c + b^{2}} \left(2 a^{2} c^{2} e^{2} h - 4 a b^{2} c e^{2} h + 6 a b c^{2} d e h + 3 a b c^{2} e^{2} g - 2 a c^{3} d^{2} h - 4 a c^{3} d e g - 2 a c^{3} e^{2} f + b^{4} e^{2} h - 2 b^{3} c d e h - b^{3} c e^{2} g + b^{2} c^{2} d^{2} h + 2 b^{2} c^{2} d e g + b^{2} c^{2} e^{2} f - b c^{3} d^{2} g - 2 b c^{3} d e f + 2 c^{4} d^{2} f\right)}{2 c^{4} \left(4 a c - b^{2}\right)} + \frac{2 a b c e^{2} h - 2 a c^{2} d e h - a c^{2} e^{2} g - b^{3} e^{2} h + 2 b^{2} c d e h + b^{2} c e^{2} g - b c^{2} d^{2} h - 2 b c^{2} d e g - b c^{2} e^{2} f + c^{3} d^{2} g + 2 c^{3} d e f}{2 c^{4}}\right) \log{\left(x + \frac{- 3 a^{2} b c e^{2} h + 4 a^{2} c^{2} d e h + 2 a^{2} c^{2} e^{2} g + a b^{3} e^{2} h - 2 a b^{2} c d e h - a b^{2} c e^{2} g + a b c^{2} d^{2} h + 2 a b c^{2} d e g + a b c^{2} e^{2} f + 4 a c^{4} \left(- \frac{\sqrt{- 4 a c + b^{2}} \left(2 a^{2} c^{2} e^{2} h - 4 a b^{2} c e^{2} h + 6 a b c^{2} d e h + 3 a b c^{2} e^{2} g - 2 a c^{3} d^{2} h - 4 a c^{3} d e g - 2 a c^{3} e^{2} f + b^{4} e^{2} h - 2 b^{3} c d e h - b^{3} c e^{2} g + b^{2} c^{2} d^{2} h + 2 b^{2} c^{2} d e g + b^{2} c^{2} e^{2} f - b c^{3} d^{2} g - 2 b c^{3} d e f + 2 c^{4} d^{2} f\right)}{2 c^{4} \left(4 a c - b^{2}\right)} + \frac{2 a b c e^{2} h - 2 a c^{2} d e h - a c^{2} e^{2} g - b^{3} e^{2} h + 2 b^{2} c d e h + b^{2} c e^{2} g - b c^{2} d^{2} h - 2 b c^{2} d e g - b c^{2} e^{2} f + c^{3} d^{2} g + 2 c^{3} d e f}{2 c^{4}}\right) - 2 a c^{3} d^{2} g - 4 a c^{3} d e f - b^{2} c^{3} \left(- \frac{\sqrt{- 4 a c + b^{2}} \left(2 a^{2} c^{2} e^{2} h - 4 a b^{2} c e^{2} h + 6 a b c^{2} d e h + 3 a b c^{2} e^{2} g - 2 a c^{3} d^{2} h - 4 a c^{3} d e g - 2 a c^{3} e^{2} f + b^{4} e^{2} h - 2 b^{3} c d e h - b^{3} c e^{2} g + b^{2} c^{2} d^{2} h + 2 b^{2} c^{2} d e g + b^{2} c^{2} e^{2} f - b c^{3} d^{2} g - 2 b c^{3} d e f + 2 c^{4} d^{2} f\right)}{2 c^{4} \left(4 a c - b^{2}\right)} + \frac{2 a b c e^{2} h - 2 a c^{2} d e h - a c^{2} e^{2} g - b^{3} e^{2} h + 2 b^{2} c d e h + b^{2} c e^{2} g - b c^{2} d^{2} h - 2 b c^{2} d e g - b c^{2} e^{2} f + c^{3} d^{2} g + 2 c^{3} d e f}{2 c^{4}}\right) + b c^{3} d^{2} f}{2 a^{2} c^{2} e^{2} h - 4 a b^{2} c e^{2} h + 6 a b c^{2} d e h + 3 a b c^{2} e^{2} g - 2 a c^{3} d^{2} h - 4 a c^{3} d e g - 2 a c^{3} e^{2} f + b^{4} e^{2} h - 2 b^{3} c d e h - b^{3} c e^{2} g + b^{2} c^{2} d^{2} h + 2 b^{2} c^{2} d e g + b^{2} c^{2} e^{2} f - b c^{3} d^{2} g - 2 b c^{3} d e f + 2 c^{4} d^{2} f} \right)} + \left(\frac{\sqrt{- 4 a c + b^{2}} \left(2 a^{2} c^{2} e^{2} h - 4 a b^{2} c e^{2} h + 6 a b c^{2} d e h + 3 a b c^{2} e^{2} g - 2 a c^{3} d^{2} h - 4 a c^{3} d e g - 2 a c^{3} e^{2} f + b^{4} e^{2} h - 2 b^{3} c d e h - b^{3} c e^{2} g + b^{2} c^{2} d^{2} h + 2 b^{2} c^{2} d e g + b^{2} c^{2} e^{2} f - b c^{3} d^{2} g - 2 b c^{3} d e f + 2 c^{4} d^{2} f\right)}{2 c^{4} \left(4 a c - b^{2}\right)} + \frac{2 a b c e^{2} h - 2 a c^{2} d e h - a c^{2} e^{2} g - b^{3} e^{2} h + 2 b^{2} c d e h + b^{2} c e^{2} g - b c^{2} d^{2} h - 2 b c^{2} d e g - b c^{2} e^{2} f + c^{3} d^{2} g + 2 c^{3} d e f}{2 c^{4}}\right) \log{\left(x + \frac{- 3 a^{2} b c e^{2} h + 4 a^{2} c^{2} d e h + 2 a^{2} c^{2} e^{2} g + a b^{3} e^{2} h - 2 a b^{2} c d e h - a b^{2} c e^{2} g + a b c^{2} d^{2} h + 2 a b c^{2} d e g + a b c^{2} e^{2} f + 4 a c^{4} \left(\frac{\sqrt{- 4 a c + b^{2}} \left(2 a^{2} c^{2} e^{2} h - 4 a b^{2} c e^{2} h + 6 a b c^{2} d e h + 3 a b c^{2} e^{2} g - 2 a c^{3} d^{2} h - 4 a c^{3} d e g - 2 a c^{3} e^{2} f + b^{4} e^{2} h - 2 b^{3} c d e h - b^{3} c e^{2} g + b^{2} c^{2} d^{2} h + 2 b^{2} c^{2} d e g + b^{2} c^{2} e^{2} f - b c^{3} d^{2} g - 2 b c^{3} d e f + 2 c^{4} d^{2} f\right)}{2 c^{4} \left(4 a c - b^{2}\right)} + \frac{2 a b c e^{2} h - 2 a c^{2} d e h - a c^{2} e^{2} g - b^{3} e^{2} h + 2 b^{2} c d e h + b^{2} c e^{2} g - b c^{2} d^{2} h - 2 b c^{2} d e g - b c^{2} e^{2} f + c^{3} d^{2} g + 2 c^{3} d e f}{2 c^{4}}\right) - 2 a c^{3} d^{2} g - 4 a c^{3} d e f - b^{2} c^{3} \left(\frac{\sqrt{- 4 a c + b^{2}} \left(2 a^{2} c^{2} e^{2} h - 4 a b^{2} c e^{2} h + 6 a b c^{2} d e h + 3 a b c^{2} e^{2} g - 2 a c^{3} d^{2} h - 4 a c^{3} d e g - 2 a c^{3} e^{2} f + b^{4} e^{2} h - 2 b^{3} c d e h - b^{3} c e^{2} g + b^{2} c^{2} d^{2} h + 2 b^{2} c^{2} d e g + b^{2} c^{2} e^{2} f - b c^{3} d^{2} g - 2 b c^{3} d e f + 2 c^{4} d^{2} f\right)}{2 c^{4} \left(4 a c - b^{2}\right)} + \frac{2 a b c e^{2} h - 2 a c^{2} d e h - a c^{2} e^{2} g - b^{3} e^{2} h + 2 b^{2} c d e h + b^{2} c e^{2} g - b c^{2} d^{2} h - 2 b c^{2} d e g - b c^{2} e^{2} f + c^{3} d^{2} g + 2 c^{3} d e f}{2 c^{4}}\right) + b c^{3} d^{2} f}{2 a^{2} c^{2} e^{2} h - 4 a b^{2} c e^{2} h + 6 a b c^{2} d e h + 3 a b c^{2} e^{2} g - 2 a c^{3} d^{2} h - 4 a c^{3} d e g - 2 a c^{3} e^{2} f + b^{4} e^{2} h - 2 b^{3} c d e h - b^{3} c e^{2} g + b^{2} c^{2} d^{2} h + 2 b^{2} c^{2} d e g + b^{2} c^{2} e^{2} f - b c^{3} d^{2} g - 2 b c^{3} d e f + 2 c^{4} d^{2} f} \right)} + \frac{e^{2} h x^{3}}{3 c}"," ",0,"x**2*(-b*e**2*h/(2*c**2) + d*e*h/c + e**2*g/(2*c)) + x*(-a*e**2*h/c**2 + b**2*e**2*h/c**3 - 2*b*d*e*h/c**2 - b*e**2*g/c**2 + d**2*h/c + 2*d*e*g/c + e**2*f/c) + (-sqrt(-4*a*c + b**2)*(2*a**2*c**2*e**2*h - 4*a*b**2*c*e**2*h + 6*a*b*c**2*d*e*h + 3*a*b*c**2*e**2*g - 2*a*c**3*d**2*h - 4*a*c**3*d*e*g - 2*a*c**3*e**2*f + b**4*e**2*h - 2*b**3*c*d*e*h - b**3*c*e**2*g + b**2*c**2*d**2*h + 2*b**2*c**2*d*e*g + b**2*c**2*e**2*f - b*c**3*d**2*g - 2*b*c**3*d*e*f + 2*c**4*d**2*f)/(2*c**4*(4*a*c - b**2)) + (2*a*b*c*e**2*h - 2*a*c**2*d*e*h - a*c**2*e**2*g - b**3*e**2*h + 2*b**2*c*d*e*h + b**2*c*e**2*g - b*c**2*d**2*h - 2*b*c**2*d*e*g - b*c**2*e**2*f + c**3*d**2*g + 2*c**3*d*e*f)/(2*c**4))*log(x + (-3*a**2*b*c*e**2*h + 4*a**2*c**2*d*e*h + 2*a**2*c**2*e**2*g + a*b**3*e**2*h - 2*a*b**2*c*d*e*h - a*b**2*c*e**2*g + a*b*c**2*d**2*h + 2*a*b*c**2*d*e*g + a*b*c**2*e**2*f + 4*a*c**4*(-sqrt(-4*a*c + b**2)*(2*a**2*c**2*e**2*h - 4*a*b**2*c*e**2*h + 6*a*b*c**2*d*e*h + 3*a*b*c**2*e**2*g - 2*a*c**3*d**2*h - 4*a*c**3*d*e*g - 2*a*c**3*e**2*f + b**4*e**2*h - 2*b**3*c*d*e*h - b**3*c*e**2*g + b**2*c**2*d**2*h + 2*b**2*c**2*d*e*g + b**2*c**2*e**2*f - b*c**3*d**2*g - 2*b*c**3*d*e*f + 2*c**4*d**2*f)/(2*c**4*(4*a*c - b**2)) + (2*a*b*c*e**2*h - 2*a*c**2*d*e*h - a*c**2*e**2*g - b**3*e**2*h + 2*b**2*c*d*e*h + b**2*c*e**2*g - b*c**2*d**2*h - 2*b*c**2*d*e*g - b*c**2*e**2*f + c**3*d**2*g + 2*c**3*d*e*f)/(2*c**4)) - 2*a*c**3*d**2*g - 4*a*c**3*d*e*f - b**2*c**3*(-sqrt(-4*a*c + b**2)*(2*a**2*c**2*e**2*h - 4*a*b**2*c*e**2*h + 6*a*b*c**2*d*e*h + 3*a*b*c**2*e**2*g - 2*a*c**3*d**2*h - 4*a*c**3*d*e*g - 2*a*c**3*e**2*f + b**4*e**2*h - 2*b**3*c*d*e*h - b**3*c*e**2*g + b**2*c**2*d**2*h + 2*b**2*c**2*d*e*g + b**2*c**2*e**2*f - b*c**3*d**2*g - 2*b*c**3*d*e*f + 2*c**4*d**2*f)/(2*c**4*(4*a*c - b**2)) + (2*a*b*c*e**2*h - 2*a*c**2*d*e*h - a*c**2*e**2*g - b**3*e**2*h + 2*b**2*c*d*e*h + b**2*c*e**2*g - b*c**2*d**2*h - 2*b*c**2*d*e*g - b*c**2*e**2*f + c**3*d**2*g + 2*c**3*d*e*f)/(2*c**4)) + b*c**3*d**2*f)/(2*a**2*c**2*e**2*h - 4*a*b**2*c*e**2*h + 6*a*b*c**2*d*e*h + 3*a*b*c**2*e**2*g - 2*a*c**3*d**2*h - 4*a*c**3*d*e*g - 2*a*c**3*e**2*f + b**4*e**2*h - 2*b**3*c*d*e*h - b**3*c*e**2*g + b**2*c**2*d**2*h + 2*b**2*c**2*d*e*g + b**2*c**2*e**2*f - b*c**3*d**2*g - 2*b*c**3*d*e*f + 2*c**4*d**2*f)) + (sqrt(-4*a*c + b**2)*(2*a**2*c**2*e**2*h - 4*a*b**2*c*e**2*h + 6*a*b*c**2*d*e*h + 3*a*b*c**2*e**2*g - 2*a*c**3*d**2*h - 4*a*c**3*d*e*g - 2*a*c**3*e**2*f + b**4*e**2*h - 2*b**3*c*d*e*h - b**3*c*e**2*g + b**2*c**2*d**2*h + 2*b**2*c**2*d*e*g + b**2*c**2*e**2*f - b*c**3*d**2*g - 2*b*c**3*d*e*f + 2*c**4*d**2*f)/(2*c**4*(4*a*c - b**2)) + (2*a*b*c*e**2*h - 2*a*c**2*d*e*h - a*c**2*e**2*g - b**3*e**2*h + 2*b**2*c*d*e*h + b**2*c*e**2*g - b*c**2*d**2*h - 2*b*c**2*d*e*g - b*c**2*e**2*f + c**3*d**2*g + 2*c**3*d*e*f)/(2*c**4))*log(x + (-3*a**2*b*c*e**2*h + 4*a**2*c**2*d*e*h + 2*a**2*c**2*e**2*g + a*b**3*e**2*h - 2*a*b**2*c*d*e*h - a*b**2*c*e**2*g + a*b*c**2*d**2*h + 2*a*b*c**2*d*e*g + a*b*c**2*e**2*f + 4*a*c**4*(sqrt(-4*a*c + b**2)*(2*a**2*c**2*e**2*h - 4*a*b**2*c*e**2*h + 6*a*b*c**2*d*e*h + 3*a*b*c**2*e**2*g - 2*a*c**3*d**2*h - 4*a*c**3*d*e*g - 2*a*c**3*e**2*f + b**4*e**2*h - 2*b**3*c*d*e*h - b**3*c*e**2*g + b**2*c**2*d**2*h + 2*b**2*c**2*d*e*g + b**2*c**2*e**2*f - b*c**3*d**2*g - 2*b*c**3*d*e*f + 2*c**4*d**2*f)/(2*c**4*(4*a*c - b**2)) + (2*a*b*c*e**2*h - 2*a*c**2*d*e*h - a*c**2*e**2*g - b**3*e**2*h + 2*b**2*c*d*e*h + b**2*c*e**2*g - b*c**2*d**2*h - 2*b*c**2*d*e*g - b*c**2*e**2*f + c**3*d**2*g + 2*c**3*d*e*f)/(2*c**4)) - 2*a*c**3*d**2*g - 4*a*c**3*d*e*f - b**2*c**3*(sqrt(-4*a*c + b**2)*(2*a**2*c**2*e**2*h - 4*a*b**2*c*e**2*h + 6*a*b*c**2*d*e*h + 3*a*b*c**2*e**2*g - 2*a*c**3*d**2*h - 4*a*c**3*d*e*g - 2*a*c**3*e**2*f + b**4*e**2*h - 2*b**3*c*d*e*h - b**3*c*e**2*g + b**2*c**2*d**2*h + 2*b**2*c**2*d*e*g + b**2*c**2*e**2*f - b*c**3*d**2*g - 2*b*c**3*d*e*f + 2*c**4*d**2*f)/(2*c**4*(4*a*c - b**2)) + (2*a*b*c*e**2*h - 2*a*c**2*d*e*h - a*c**2*e**2*g - b**3*e**2*h + 2*b**2*c*d*e*h + b**2*c*e**2*g - b*c**2*d**2*h - 2*b*c**2*d*e*g - b*c**2*e**2*f + c**3*d**2*g + 2*c**3*d*e*f)/(2*c**4)) + b*c**3*d**2*f)/(2*a**2*c**2*e**2*h - 4*a*b**2*c*e**2*h + 6*a*b*c**2*d*e*h + 3*a*b*c**2*e**2*g - 2*a*c**3*d**2*h - 4*a*c**3*d*e*g - 2*a*c**3*e**2*f + b**4*e**2*h - 2*b**3*c*d*e*h - b**3*c*e**2*g + b**2*c**2*d**2*h + 2*b**2*c**2*d*e*g + b**2*c**2*e**2*f - b*c**3*d**2*g - 2*b*c**3*d*e*f + 2*c**4*d**2*f)) + e**2*h*x**3/(3*c)","B",0
150,1,1265,0,14.461890," ","integrate((e*x+d)*(h*x**2+g*x+f)/(c*x**2+b*x+a),x)","x \left(- \frac{b e h}{c^{2}} + \frac{d h}{c} + \frac{e g}{c}\right) + \left(- \frac{\sqrt{- 4 a c + b^{2}} \left(3 a b c e h - 2 a c^{2} d h - 2 a c^{2} e g - b^{3} e h + b^{2} c d h + b^{2} c e g - b c^{2} d g - b c^{2} e f + 2 c^{3} d f\right)}{2 c^{3} \left(4 a c - b^{2}\right)} - \frac{a c e h - b^{2} e h + b c d h + b c e g - c^{2} d g - c^{2} e f}{2 c^{3}}\right) \log{\left(x + \frac{2 a^{2} c e h - a b^{2} e h + a b c d h + a b c e g + 4 a c^{3} \left(- \frac{\sqrt{- 4 a c + b^{2}} \left(3 a b c e h - 2 a c^{2} d h - 2 a c^{2} e g - b^{3} e h + b^{2} c d h + b^{2} c e g - b c^{2} d g - b c^{2} e f + 2 c^{3} d f\right)}{2 c^{3} \left(4 a c - b^{2}\right)} - \frac{a c e h - b^{2} e h + b c d h + b c e g - c^{2} d g - c^{2} e f}{2 c^{3}}\right) - 2 a c^{2} d g - 2 a c^{2} e f - b^{2} c^{2} \left(- \frac{\sqrt{- 4 a c + b^{2}} \left(3 a b c e h - 2 a c^{2} d h - 2 a c^{2} e g - b^{3} e h + b^{2} c d h + b^{2} c e g - b c^{2} d g - b c^{2} e f + 2 c^{3} d f\right)}{2 c^{3} \left(4 a c - b^{2}\right)} - \frac{a c e h - b^{2} e h + b c d h + b c e g - c^{2} d g - c^{2} e f}{2 c^{3}}\right) + b c^{2} d f}{3 a b c e h - 2 a c^{2} d h - 2 a c^{2} e g - b^{3} e h + b^{2} c d h + b^{2} c e g - b c^{2} d g - b c^{2} e f + 2 c^{3} d f} \right)} + \left(\frac{\sqrt{- 4 a c + b^{2}} \left(3 a b c e h - 2 a c^{2} d h - 2 a c^{2} e g - b^{3} e h + b^{2} c d h + b^{2} c e g - b c^{2} d g - b c^{2} e f + 2 c^{3} d f\right)}{2 c^{3} \left(4 a c - b^{2}\right)} - \frac{a c e h - b^{2} e h + b c d h + b c e g - c^{2} d g - c^{2} e f}{2 c^{3}}\right) \log{\left(x + \frac{2 a^{2} c e h - a b^{2} e h + a b c d h + a b c e g + 4 a c^{3} \left(\frac{\sqrt{- 4 a c + b^{2}} \left(3 a b c e h - 2 a c^{2} d h - 2 a c^{2} e g - b^{3} e h + b^{2} c d h + b^{2} c e g - b c^{2} d g - b c^{2} e f + 2 c^{3} d f\right)}{2 c^{3} \left(4 a c - b^{2}\right)} - \frac{a c e h - b^{2} e h + b c d h + b c e g - c^{2} d g - c^{2} e f}{2 c^{3}}\right) - 2 a c^{2} d g - 2 a c^{2} e f - b^{2} c^{2} \left(\frac{\sqrt{- 4 a c + b^{2}} \left(3 a b c e h - 2 a c^{2} d h - 2 a c^{2} e g - b^{3} e h + b^{2} c d h + b^{2} c e g - b c^{2} d g - b c^{2} e f + 2 c^{3} d f\right)}{2 c^{3} \left(4 a c - b^{2}\right)} - \frac{a c e h - b^{2} e h + b c d h + b c e g - c^{2} d g - c^{2} e f}{2 c^{3}}\right) + b c^{2} d f}{3 a b c e h - 2 a c^{2} d h - 2 a c^{2} e g - b^{3} e h + b^{2} c d h + b^{2} c e g - b c^{2} d g - b c^{2} e f + 2 c^{3} d f} \right)} + \frac{e h x^{2}}{2 c}"," ",0,"x*(-b*e*h/c**2 + d*h/c + e*g/c) + (-sqrt(-4*a*c + b**2)*(3*a*b*c*e*h - 2*a*c**2*d*h - 2*a*c**2*e*g - b**3*e*h + b**2*c*d*h + b**2*c*e*g - b*c**2*d*g - b*c**2*e*f + 2*c**3*d*f)/(2*c**3*(4*a*c - b**2)) - (a*c*e*h - b**2*e*h + b*c*d*h + b*c*e*g - c**2*d*g - c**2*e*f)/(2*c**3))*log(x + (2*a**2*c*e*h - a*b**2*e*h + a*b*c*d*h + a*b*c*e*g + 4*a*c**3*(-sqrt(-4*a*c + b**2)*(3*a*b*c*e*h - 2*a*c**2*d*h - 2*a*c**2*e*g - b**3*e*h + b**2*c*d*h + b**2*c*e*g - b*c**2*d*g - b*c**2*e*f + 2*c**3*d*f)/(2*c**3*(4*a*c - b**2)) - (a*c*e*h - b**2*e*h + b*c*d*h + b*c*e*g - c**2*d*g - c**2*e*f)/(2*c**3)) - 2*a*c**2*d*g - 2*a*c**2*e*f - b**2*c**2*(-sqrt(-4*a*c + b**2)*(3*a*b*c*e*h - 2*a*c**2*d*h - 2*a*c**2*e*g - b**3*e*h + b**2*c*d*h + b**2*c*e*g - b*c**2*d*g - b*c**2*e*f + 2*c**3*d*f)/(2*c**3*(4*a*c - b**2)) - (a*c*e*h - b**2*e*h + b*c*d*h + b*c*e*g - c**2*d*g - c**2*e*f)/(2*c**3)) + b*c**2*d*f)/(3*a*b*c*e*h - 2*a*c**2*d*h - 2*a*c**2*e*g - b**3*e*h + b**2*c*d*h + b**2*c*e*g - b*c**2*d*g - b*c**2*e*f + 2*c**3*d*f)) + (sqrt(-4*a*c + b**2)*(3*a*b*c*e*h - 2*a*c**2*d*h - 2*a*c**2*e*g - b**3*e*h + b**2*c*d*h + b**2*c*e*g - b*c**2*d*g - b*c**2*e*f + 2*c**3*d*f)/(2*c**3*(4*a*c - b**2)) - (a*c*e*h - b**2*e*h + b*c*d*h + b*c*e*g - c**2*d*g - c**2*e*f)/(2*c**3))*log(x + (2*a**2*c*e*h - a*b**2*e*h + a*b*c*d*h + a*b*c*e*g + 4*a*c**3*(sqrt(-4*a*c + b**2)*(3*a*b*c*e*h - 2*a*c**2*d*h - 2*a*c**2*e*g - b**3*e*h + b**2*c*d*h + b**2*c*e*g - b*c**2*d*g - b*c**2*e*f + 2*c**3*d*f)/(2*c**3*(4*a*c - b**2)) - (a*c*e*h - b**2*e*h + b*c*d*h + b*c*e*g - c**2*d*g - c**2*e*f)/(2*c**3)) - 2*a*c**2*d*g - 2*a*c**2*e*f - b**2*c**2*(sqrt(-4*a*c + b**2)*(3*a*b*c*e*h - 2*a*c**2*d*h - 2*a*c**2*e*g - b**3*e*h + b**2*c*d*h + b**2*c*e*g - b*c**2*d*g - b*c**2*e*f + 2*c**3*d*f)/(2*c**3*(4*a*c - b**2)) - (a*c*e*h - b**2*e*h + b*c*d*h + b*c*e*g - c**2*d*g - c**2*e*f)/(2*c**3)) + b*c**2*d*f)/(3*a*b*c*e*h - 2*a*c**2*d*h - 2*a*c**2*e*g - b**3*e*h + b**2*c*d*h + b**2*c*e*g - b*c**2*d*g - b*c**2*e*f + 2*c**3*d*f)) + e*h*x**2/(2*c)","B",0
151,1,488,0,2.139364," ","integrate((h*x**2+g*x+f)/(c*x**2+b*x+a),x)","\left(- \frac{\sqrt{- 4 a c + b^{2}} \left(2 a c h - b^{2} h + b c g - 2 c^{2} f\right)}{2 c^{2} \left(4 a c - b^{2}\right)} - \frac{b h - c g}{2 c^{2}}\right) \log{\left(x + \frac{- a b h - 4 a c^{2} \left(- \frac{\sqrt{- 4 a c + b^{2}} \left(2 a c h - b^{2} h + b c g - 2 c^{2} f\right)}{2 c^{2} \left(4 a c - b^{2}\right)} - \frac{b h - c g}{2 c^{2}}\right) + 2 a c g + b^{2} c \left(- \frac{\sqrt{- 4 a c + b^{2}} \left(2 a c h - b^{2} h + b c g - 2 c^{2} f\right)}{2 c^{2} \left(4 a c - b^{2}\right)} - \frac{b h - c g}{2 c^{2}}\right) - b c f}{2 a c h - b^{2} h + b c g - 2 c^{2} f} \right)} + \left(\frac{\sqrt{- 4 a c + b^{2}} \left(2 a c h - b^{2} h + b c g - 2 c^{2} f\right)}{2 c^{2} \left(4 a c - b^{2}\right)} - \frac{b h - c g}{2 c^{2}}\right) \log{\left(x + \frac{- a b h - 4 a c^{2} \left(\frac{\sqrt{- 4 a c + b^{2}} \left(2 a c h - b^{2} h + b c g - 2 c^{2} f\right)}{2 c^{2} \left(4 a c - b^{2}\right)} - \frac{b h - c g}{2 c^{2}}\right) + 2 a c g + b^{2} c \left(\frac{\sqrt{- 4 a c + b^{2}} \left(2 a c h - b^{2} h + b c g - 2 c^{2} f\right)}{2 c^{2} \left(4 a c - b^{2}\right)} - \frac{b h - c g}{2 c^{2}}\right) - b c f}{2 a c h - b^{2} h + b c g - 2 c^{2} f} \right)} + \frac{h x}{c}"," ",0,"(-sqrt(-4*a*c + b**2)*(2*a*c*h - b**2*h + b*c*g - 2*c**2*f)/(2*c**2*(4*a*c - b**2)) - (b*h - c*g)/(2*c**2))*log(x + (-a*b*h - 4*a*c**2*(-sqrt(-4*a*c + b**2)*(2*a*c*h - b**2*h + b*c*g - 2*c**2*f)/(2*c**2*(4*a*c - b**2)) - (b*h - c*g)/(2*c**2)) + 2*a*c*g + b**2*c*(-sqrt(-4*a*c + b**2)*(2*a*c*h - b**2*h + b*c*g - 2*c**2*f)/(2*c**2*(4*a*c - b**2)) - (b*h - c*g)/(2*c**2)) - b*c*f)/(2*a*c*h - b**2*h + b*c*g - 2*c**2*f)) + (sqrt(-4*a*c + b**2)*(2*a*c*h - b**2*h + b*c*g - 2*c**2*f)/(2*c**2*(4*a*c - b**2)) - (b*h - c*g)/(2*c**2))*log(x + (-a*b*h - 4*a*c**2*(sqrt(-4*a*c + b**2)*(2*a*c*h - b**2*h + b*c*g - 2*c**2*f)/(2*c**2*(4*a*c - b**2)) - (b*h - c*g)/(2*c**2)) + 2*a*c*g + b**2*c*(sqrt(-4*a*c + b**2)*(2*a*c*h - b**2*h + b*c*g - 2*c**2*f)/(2*c**2*(4*a*c - b**2)) - (b*h - c*g)/(2*c**2)) - b*c*f)/(2*a*c*h - b**2*h + b*c*g - 2*c**2*f)) + h*x/c","B",0
152,-1,0,0,0.000000," ","integrate((h*x**2+g*x+f)/(e*x+d)/(c*x**2+b*x+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
153,-1,0,0,0.000000," ","integrate((h*x**2+g*x+f)/(e*x+d)**2/(c*x**2+b*x+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
154,-1,0,0,0.000000," ","integrate((h*x**2+g*x+f)/(e*x+d)**3/(c*x**2+b*x+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
155,-1,0,0,0.000000," ","integrate((e*x+d)**2*(h*x**2+g*x+f)/(c*x**2+b*x+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
156,1,1535,0,60.261993," ","integrate((e*x+d)*(h*x**2+g*x+f)/(c*x**2+b*x+a)**2,x)","\left(\frac{e h}{2 c^{2}} - \frac{\sqrt{- \left(4 a c - b^{2}\right)^{3}} \left(6 a b c e h - 4 a c^{2} d h - 4 a c^{2} e g - b^{3} e h + 2 b c^{2} d g + 2 b c^{2} e f - 4 c^{3} d f\right)}{2 c^{2} \left(64 a^{3} c^{3} - 48 a^{2} b^{2} c^{2} + 12 a b^{4} c - b^{6}\right)}\right) \log{\left(x + \frac{- 16 a^{2} c^{3} \left(\frac{e h}{2 c^{2}} - \frac{\sqrt{- \left(4 a c - b^{2}\right)^{3}} \left(6 a b c e h - 4 a c^{2} d h - 4 a c^{2} e g - b^{3} e h + 2 b c^{2} d g + 2 b c^{2} e f - 4 c^{3} d f\right)}{2 c^{2} \left(64 a^{3} c^{3} - 48 a^{2} b^{2} c^{2} + 12 a b^{4} c - b^{6}\right)}\right) + 8 a^{2} c e h + 8 a b^{2} c^{2} \left(\frac{e h}{2 c^{2}} - \frac{\sqrt{- \left(4 a c - b^{2}\right)^{3}} \left(6 a b c e h - 4 a c^{2} d h - 4 a c^{2} e g - b^{3} e h + 2 b c^{2} d g + 2 b c^{2} e f - 4 c^{3} d f\right)}{2 c^{2} \left(64 a^{3} c^{3} - 48 a^{2} b^{2} c^{2} + 12 a b^{4} c - b^{6}\right)}\right) - a b^{2} e h - 2 a b c d h - 2 a b c e g - b^{4} c \left(\frac{e h}{2 c^{2}} - \frac{\sqrt{- \left(4 a c - b^{2}\right)^{3}} \left(6 a b c e h - 4 a c^{2} d h - 4 a c^{2} e g - b^{3} e h + 2 b c^{2} d g + 2 b c^{2} e f - 4 c^{3} d f\right)}{2 c^{2} \left(64 a^{3} c^{3} - 48 a^{2} b^{2} c^{2} + 12 a b^{4} c - b^{6}\right)}\right) + b^{2} c d g + b^{2} c e f - 2 b c^{2} d f}{6 a b c e h - 4 a c^{2} d h - 4 a c^{2} e g - b^{3} e h + 2 b c^{2} d g + 2 b c^{2} e f - 4 c^{3} d f} \right)} + \left(\frac{e h}{2 c^{2}} + \frac{\sqrt{- \left(4 a c - b^{2}\right)^{3}} \left(6 a b c e h - 4 a c^{2} d h - 4 a c^{2} e g - b^{3} e h + 2 b c^{2} d g + 2 b c^{2} e f - 4 c^{3} d f\right)}{2 c^{2} \left(64 a^{3} c^{3} - 48 a^{2} b^{2} c^{2} + 12 a b^{4} c - b^{6}\right)}\right) \log{\left(x + \frac{- 16 a^{2} c^{3} \left(\frac{e h}{2 c^{2}} + \frac{\sqrt{- \left(4 a c - b^{2}\right)^{3}} \left(6 a b c e h - 4 a c^{2} d h - 4 a c^{2} e g - b^{3} e h + 2 b c^{2} d g + 2 b c^{2} e f - 4 c^{3} d f\right)}{2 c^{2} \left(64 a^{3} c^{3} - 48 a^{2} b^{2} c^{2} + 12 a b^{4} c - b^{6}\right)}\right) + 8 a^{2} c e h + 8 a b^{2} c^{2} \left(\frac{e h}{2 c^{2}} + \frac{\sqrt{- \left(4 a c - b^{2}\right)^{3}} \left(6 a b c e h - 4 a c^{2} d h - 4 a c^{2} e g - b^{3} e h + 2 b c^{2} d g + 2 b c^{2} e f - 4 c^{3} d f\right)}{2 c^{2} \left(64 a^{3} c^{3} - 48 a^{2} b^{2} c^{2} + 12 a b^{4} c - b^{6}\right)}\right) - a b^{2} e h - 2 a b c d h - 2 a b c e g - b^{4} c \left(\frac{e h}{2 c^{2}} + \frac{\sqrt{- \left(4 a c - b^{2}\right)^{3}} \left(6 a b c e h - 4 a c^{2} d h - 4 a c^{2} e g - b^{3} e h + 2 b c^{2} d g + 2 b c^{2} e f - 4 c^{3} d f\right)}{2 c^{2} \left(64 a^{3} c^{3} - 48 a^{2} b^{2} c^{2} + 12 a b^{4} c - b^{6}\right)}\right) + b^{2} c d g + b^{2} c e f - 2 b c^{2} d f}{6 a b c e h - 4 a c^{2} d h - 4 a c^{2} e g - b^{3} e h + 2 b c^{2} d g + 2 b c^{2} e f - 4 c^{3} d f} \right)} + \frac{2 a^{2} c e h - a b^{2} e h + a b c d h + a b c e g - 2 a c^{2} d g - 2 a c^{2} e f + b c^{2} d f + x \left(3 a b c e h - 2 a c^{2} d h - 2 a c^{2} e g - b^{3} e h + b^{2} c d h + b^{2} c e g - b c^{2} d g - b c^{2} e f + 2 c^{3} d f\right)}{4 a^{2} c^{3} - a b^{2} c^{2} + x^{2} \left(4 a c^{4} - b^{2} c^{3}\right) + x \left(4 a b c^{3} - b^{3} c^{2}\right)}"," ",0,"(e*h/(2*c**2) - sqrt(-(4*a*c - b**2)**3)*(6*a*b*c*e*h - 4*a*c**2*d*h - 4*a*c**2*e*g - b**3*e*h + 2*b*c**2*d*g + 2*b*c**2*e*f - 4*c**3*d*f)/(2*c**2*(64*a**3*c**3 - 48*a**2*b**2*c**2 + 12*a*b**4*c - b**6)))*log(x + (-16*a**2*c**3*(e*h/(2*c**2) - sqrt(-(4*a*c - b**2)**3)*(6*a*b*c*e*h - 4*a*c**2*d*h - 4*a*c**2*e*g - b**3*e*h + 2*b*c**2*d*g + 2*b*c**2*e*f - 4*c**3*d*f)/(2*c**2*(64*a**3*c**3 - 48*a**2*b**2*c**2 + 12*a*b**4*c - b**6))) + 8*a**2*c*e*h + 8*a*b**2*c**2*(e*h/(2*c**2) - sqrt(-(4*a*c - b**2)**3)*(6*a*b*c*e*h - 4*a*c**2*d*h - 4*a*c**2*e*g - b**3*e*h + 2*b*c**2*d*g + 2*b*c**2*e*f - 4*c**3*d*f)/(2*c**2*(64*a**3*c**3 - 48*a**2*b**2*c**2 + 12*a*b**4*c - b**6))) - a*b**2*e*h - 2*a*b*c*d*h - 2*a*b*c*e*g - b**4*c*(e*h/(2*c**2) - sqrt(-(4*a*c - b**2)**3)*(6*a*b*c*e*h - 4*a*c**2*d*h - 4*a*c**2*e*g - b**3*e*h + 2*b*c**2*d*g + 2*b*c**2*e*f - 4*c**3*d*f)/(2*c**2*(64*a**3*c**3 - 48*a**2*b**2*c**2 + 12*a*b**4*c - b**6))) + b**2*c*d*g + b**2*c*e*f - 2*b*c**2*d*f)/(6*a*b*c*e*h - 4*a*c**2*d*h - 4*a*c**2*e*g - b**3*e*h + 2*b*c**2*d*g + 2*b*c**2*e*f - 4*c**3*d*f)) + (e*h/(2*c**2) + sqrt(-(4*a*c - b**2)**3)*(6*a*b*c*e*h - 4*a*c**2*d*h - 4*a*c**2*e*g - b**3*e*h + 2*b*c**2*d*g + 2*b*c**2*e*f - 4*c**3*d*f)/(2*c**2*(64*a**3*c**3 - 48*a**2*b**2*c**2 + 12*a*b**4*c - b**6)))*log(x + (-16*a**2*c**3*(e*h/(2*c**2) + sqrt(-(4*a*c - b**2)**3)*(6*a*b*c*e*h - 4*a*c**2*d*h - 4*a*c**2*e*g - b**3*e*h + 2*b*c**2*d*g + 2*b*c**2*e*f - 4*c**3*d*f)/(2*c**2*(64*a**3*c**3 - 48*a**2*b**2*c**2 + 12*a*b**4*c - b**6))) + 8*a**2*c*e*h + 8*a*b**2*c**2*(e*h/(2*c**2) + sqrt(-(4*a*c - b**2)**3)*(6*a*b*c*e*h - 4*a*c**2*d*h - 4*a*c**2*e*g - b**3*e*h + 2*b*c**2*d*g + 2*b*c**2*e*f - 4*c**3*d*f)/(2*c**2*(64*a**3*c**3 - 48*a**2*b**2*c**2 + 12*a*b**4*c - b**6))) - a*b**2*e*h - 2*a*b*c*d*h - 2*a*b*c*e*g - b**4*c*(e*h/(2*c**2) + sqrt(-(4*a*c - b**2)**3)*(6*a*b*c*e*h - 4*a*c**2*d*h - 4*a*c**2*e*g - b**3*e*h + 2*b*c**2*d*g + 2*b*c**2*e*f - 4*c**3*d*f)/(2*c**2*(64*a**3*c**3 - 48*a**2*b**2*c**2 + 12*a*b**4*c - b**6))) + b**2*c*d*g + b**2*c*e*f - 2*b*c**2*d*f)/(6*a*b*c*e*h - 4*a*c**2*d*h - 4*a*c**2*e*g - b**3*e*h + 2*b*c**2*d*g + 2*b*c**2*e*f - 4*c**3*d*f)) + (2*a**2*c*e*h - a*b**2*e*h + a*b*c*d*h + a*b*c*e*g - 2*a*c**2*d*g - 2*a*c**2*e*f + b*c**2*d*f + x*(3*a*b*c*e*h - 2*a*c**2*d*h - 2*a*c**2*e*g - b**3*e*h + b**2*c*d*h + b**2*c*e*g - b*c**2*d*g - b*c**2*e*f + 2*c**3*d*f))/(4*a**2*c**3 - a*b**2*c**2 + x**2*(4*a*c**4 - b**2*c**3) + x*(4*a*b*c**3 - b**3*c**2))","B",0
157,1,459,0,2.235651," ","integrate((h*x**2+g*x+f)/(c*x**2+b*x+a)**2,x)","- \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} \left(2 a h - b g + 2 c f\right) \log{\left(x + \frac{- 16 a^{2} c^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} \left(2 a h - b g + 2 c f\right) + 8 a b^{2} c \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} \left(2 a h - b g + 2 c f\right) + 2 a b h - b^{4} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} \left(2 a h - b g + 2 c f\right) - b^{2} g + 2 b c f}{4 a c h - 2 b c g + 4 c^{2} f} \right)} + \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} \left(2 a h - b g + 2 c f\right) \log{\left(x + \frac{16 a^{2} c^{2} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} \left(2 a h - b g + 2 c f\right) - 8 a b^{2} c \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} \left(2 a h - b g + 2 c f\right) + 2 a b h + b^{4} \sqrt{- \frac{1}{\left(4 a c - b^{2}\right)^{3}}} \left(2 a h - b g + 2 c f\right) - b^{2} g + 2 b c f}{4 a c h - 2 b c g + 4 c^{2} f} \right)} + \frac{a b h - 2 a c g + b c f + x \left(- 2 a c h + b^{2} h - b c g + 2 c^{2} f\right)}{4 a^{2} c^{2} - a b^{2} c + x^{2} \left(4 a c^{3} - b^{2} c^{2}\right) + x \left(4 a b c^{2} - b^{3} c\right)}"," ",0,"-sqrt(-1/(4*a*c - b**2)**3)*(2*a*h - b*g + 2*c*f)*log(x + (-16*a**2*c**2*sqrt(-1/(4*a*c - b**2)**3)*(2*a*h - b*g + 2*c*f) + 8*a*b**2*c*sqrt(-1/(4*a*c - b**2)**3)*(2*a*h - b*g + 2*c*f) + 2*a*b*h - b**4*sqrt(-1/(4*a*c - b**2)**3)*(2*a*h - b*g + 2*c*f) - b**2*g + 2*b*c*f)/(4*a*c*h - 2*b*c*g + 4*c**2*f)) + sqrt(-1/(4*a*c - b**2)**3)*(2*a*h - b*g + 2*c*f)*log(x + (16*a**2*c**2*sqrt(-1/(4*a*c - b**2)**3)*(2*a*h - b*g + 2*c*f) - 8*a*b**2*c*sqrt(-1/(4*a*c - b**2)**3)*(2*a*h - b*g + 2*c*f) + 2*a*b*h + b**4*sqrt(-1/(4*a*c - b**2)**3)*(2*a*h - b*g + 2*c*f) - b**2*g + 2*b*c*f)/(4*a*c*h - 2*b*c*g + 4*c**2*f)) + (a*b*h - 2*a*c*g + b*c*f + x*(-2*a*c*h + b**2*h - b*c*g + 2*c**2*f))/(4*a**2*c**2 - a*b**2*c + x**2*(4*a*c**3 - b**2*c**2) + x*(4*a*b*c**2 - b**3*c))","B",0
158,-1,0,0,0.000000," ","integrate((h*x**2+g*x+f)/(e*x+d)/(c*x**2+b*x+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
159,-1,0,0,0.000000," ","integrate((h*x**2+g*x+f)/(e*x+d)**2/(c*x**2+b*x+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
160,1,60,0,0.157860," ","integrate(x**3*(x**2+x+1)/(x**2-x+1)**2,x)","\frac{x^{2}}{2} + 3 x + \frac{4 - 2 x}{3 x^{2} - 3 x + 3} + 2 \log{\left(x^{2} - x + 1 \right)} - \frac{10 \sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} x}{3} - \frac{\sqrt{3}}{3} \right)}}{9}"," ",0,"x**2/2 + 3*x + (4 - 2*x)/(3*x**2 - 3*x + 3) + 2*log(x**2 - x + 1) - 10*sqrt(3)*atan(2*sqrt(3)*x/3 - sqrt(3)/3)/9","A",0
161,1,54,0,0.151070," ","integrate(x**2*(x**2+x+1)/(x**2-x+1)**2,x)","x + \frac{2 - 4 x}{3 x^{2} - 3 x + 3} + \frac{3 \log{\left(x^{2} - x + 1 \right)}}{2} + \frac{7 \sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} x}{3} - \frac{\sqrt{3}}{3} \right)}}{9}"," ",0,"x + (2 - 4*x)/(3*x**2 - 3*x + 3) + 3*log(x**2 - x + 1)/2 + 7*sqrt(3)*atan(2*sqrt(3)*x/3 - sqrt(3)/3)/9","A",0
162,1,53,0,0.148030," ","integrate(x*(x**2+x+1)/(x**2-x+1)**2,x)","\frac{- 2 x - 2}{3 x^{2} - 3 x + 3} + \frac{\log{\left(x^{2} - x + 1 \right)}}{2} + \frac{11 \sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} x}{3} - \frac{\sqrt{3}}{3} \right)}}{9}"," ",0,"(-2*x - 2)/(3*x**2 - 3*x + 3) + log(x**2 - x + 1)/2 + 11*sqrt(3)*atan(2*sqrt(3)*x/3 - sqrt(3)/3)/9","A",0
163,1,41,0,0.137177," ","integrate((x**2+x+1)/(x**2-x+1)**2,x)","\frac{2 x - 4}{3 x^{2} - 3 x + 3} + \frac{10 \sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} x}{3} - \frac{\sqrt{3}}{3} \right)}}{9}"," ",0,"(2*x - 4)/(3*x**2 - 3*x + 3) + 10*sqrt(3)*atan(2*sqrt(3)*x/3 - sqrt(3)/3)/9","A",0
164,1,54,0,0.183502," ","integrate((x**2+x+1)/x/(x**2-x+1)**2,x)","\frac{4 x - 2}{3 x^{2} - 3 x + 3} + \log{\left(x \right)} - \frac{\log{\left(x^{2} - x + 1 \right)}}{2} + \frac{11 \sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} x}{3} - \frac{\sqrt{3}}{3} \right)}}{9}"," ",0,"(4*x - 2)/(3*x**2 - 3*x + 3) + log(x) - log(x**2 - x + 1)/2 + 11*sqrt(3)*atan(2*sqrt(3)*x/3 - sqrt(3)/3)/9","A",0
165,1,65,0,0.197758," ","integrate((x**2+x+1)/x**2/(x**2-x+1)**2,x)","\frac{- x^{2} + 5 x - 3}{3 x^{3} - 3 x^{2} + 3 x} + 3 \log{\left(x \right)} - \frac{3 \log{\left(x^{2} - x + 1 \right)}}{2} + \frac{7 \sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} x}{3} - \frac{\sqrt{3}}{3} \right)}}{9}"," ",0,"(-x**2 + 5*x - 3)/(3*x**3 - 3*x**2 + 3*x) + 3*log(x) - 3*log(x**2 - x + 1)/2 + 7*sqrt(3)*atan(2*sqrt(3)*x/3 - sqrt(3)/3)/9","A",0
166,1,71,0,0.217293," ","integrate((x**2+x+1)/x**3/(x**2-x+1)**2,x)","4 \log{\left(x \right)} - 2 \log{\left(x^{2} - x + 1 \right)} - \frac{10 \sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} x}{3} - \frac{\sqrt{3}}{3} \right)}}{9} + \frac{- 22 x^{3} + 23 x^{2} - 15 x - 3}{6 x^{4} - 6 x^{3} + 6 x^{2}}"," ",0,"4*log(x) - 2*log(x**2 - x + 1) - 10*sqrt(3)*atan(2*sqrt(3)*x/3 - sqrt(3)/3)/9 + (-22*x**3 + 23*x**2 - 15*x - 3)/(6*x**4 - 6*x**3 + 6*x**2)","A",0
167,1,7,0,0.095245," ","integrate((-x**2+1)/(x**2+x+1)**2,x)","\frac{x}{x^{2} + x + 1}"," ",0,"x/(x**2 + x + 1)","A",0
168,1,36,0,0.116786," ","integrate((x**2+1)/(x**2+x+1),x)","x - \frac{\log{\left(x^{2} + x + 1 \right)}}{2} + \frac{\sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} x}{3} + \frac{\sqrt{3}}{3} \right)}}{3}"," ",0,"x - log(x**2 + x + 1)/2 + sqrt(3)*atan(2*sqrt(3)*x/3 + sqrt(3)/3)/3","A",0
169,1,22,0,0.110248," ","integrate((x**2-1)/(x**2-6*x+25),x)","x + 3 \log{\left(x^{2} - 6 x + 25 \right)} - 2 \operatorname{atan}{\left(\frac{x}{4} - \frac{3}{4} \right)}"," ",0,"x + 3*log(x**2 - 6*x + 25) - 2*atan(x/4 - 3/4)","A",0
170,1,14,0,0.087369," ","integrate((3*x**2-10)/(x**2-4*x+4),x)","3 x + 12 \log{\left(x - 2 \right)} - \frac{2}{x - 2}"," ",0,"3*x + 12*log(x - 2) - 2/(x - 2)","A",0
171,1,14,0,0.111371," ","integrate((x**2+8)/(x**2-5*x+6),x)","x + 17 \log{\left(x - 3 \right)} - 12 \log{\left(x - 2 \right)}"," ",0,"x + 17*log(x - 3) - 12*log(x - 2)","A",0
172,1,12,0,0.114285," ","integrate((x**2+3*x-4)/(x**2-2*x-8),x)","x + 4 \log{\left(x - 4 \right)} + \log{\left(x + 2 \right)}"," ",0,"x + 4*log(x - 4) + log(x + 2)","A",0
173,1,22,0,0.122894," ","integrate((4*x**2+5*x+7)/(4*x**2+4*x+5),x)","x + \frac{\log{\left(x^{2} + x + \frac{5}{4} \right)}}{8} + \frac{3 \operatorname{atan}{\left(x + \frac{1}{2} \right)}}{8}"," ",0,"x + log(x**2 + x + 5/4)/8 + 3*atan(x + 1/2)/8","A",0
174,1,46,0,0.122925," ","integrate((x**2-x+2)/(x**2+2*x-5),x)","x + \left(- \frac{5 \sqrt{6}}{6} - \frac{3}{2}\right) \log{\left(x + 1 + \sqrt{6} \right)} + \left(- \frac{3}{2} + \frac{5 \sqrt{6}}{6}\right) \log{\left(x - \sqrt{6} + 1 \right)}"," ",0,"x + (-5*sqrt(6)/6 - 3/2)*log(x + 1 + sqrt(6)) + (-3/2 + 5*sqrt(6)/6)*log(x - sqrt(6) + 1)","A",0
175,1,15,0,0.119152," ","integrate((3*x**2+4*x+1)/(2*x**2+7*x+4)**2,x)","\frac{- 3 x - 2}{4 x^{2} + 14 x + 8}"," ",0,"(-3*x - 2)/(4*x**2 + 14*x + 8)","A",0
176,1,37,0,0.136272," ","integrate((x**2+x+1)/(x**2+2*x+3)**2,x)","\frac{1 - x}{4 x^{2} + 8 x + 12} + \frac{3 \sqrt{2} \operatorname{atan}{\left(\frac{\sqrt{2} x}{2} + \frac{\sqrt{2}}{2} \right)}}{8}"," ",0,"(1 - x)/(4*x**2 + 8*x + 12) + 3*sqrt(2)*atan(sqrt(2)*x/2 + sqrt(2)/2)/8","A",0
177,1,31,0,0.132032," ","integrate((5*x**2+2*x-1)/(x**2+x+1)**4,x)","- \frac{x}{x^{6} + 3 x^{5} + 6 x^{4} + 7 x^{3} + 6 x^{2} + 3 x + 1}"," ",0,"-x/(x**6 + 3*x**5 + 6*x**4 + 7*x**3 + 6*x**2 + 3*x + 1)","B",0
178,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(5/2)*(C*x**2+A),x)","\int \left(A + C x^{2}\right) \left(a + b x + c x^{2}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral((A + C*x**2)*(a + b*x + c*x**2)**(5/2), x)","F",0
179,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(3/2)*(C*x**2+A),x)","\int \left(A + C x^{2}\right) \left(a + b x + c x^{2}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((A + C*x**2)*(a + b*x + c*x**2)**(3/2), x)","F",0
180,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(1/2)*(C*x**2+A),x)","\int \left(A + C x^{2}\right) \sqrt{a + b x + c x^{2}}\, dx"," ",0,"Integral((A + C*x**2)*sqrt(a + b*x + c*x**2), x)","F",0
181,0,0,0,0.000000," ","integrate((C*x**2+A)/(c*x**2+b*x+a)**(1/2),x)","\int \frac{A + C x^{2}}{\sqrt{a + b x + c x^{2}}}\, dx"," ",0,"Integral((A + C*x**2)/sqrt(a + b*x + c*x**2), x)","F",0
182,0,0,0,0.000000," ","integrate((C*x**2+A)/(c*x**2+b*x+a)**(3/2),x)","\int \frac{A + C x^{2}}{\left(a + b x + c x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((A + C*x**2)/(a + b*x + c*x**2)**(3/2), x)","F",0
183,-1,0,0,0.000000," ","integrate((C*x**2+A)/(c*x**2+b*x+a)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
184,-1,0,0,0.000000," ","integrate((C*x**2+A)/(c*x**2+b*x+a)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
185,-1,0,0,0.000000," ","integrate((C*x**2+A)/(c*x**2+b*x+a)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
186,0,0,0,0.000000," ","integrate((h*x+g)**3*(f*x**2+e*x+d)*(c*x**2+b*x+a)**(1/2),x)","\int \left(g + h x\right)^{3} \sqrt{a + b x + c x^{2}} \left(d + e x + f x^{2}\right)\, dx"," ",0,"Integral((g + h*x)**3*sqrt(a + b*x + c*x**2)*(d + e*x + f*x**2), x)","F",0
187,0,0,0,0.000000," ","integrate((h*x+g)**2*(f*x**2+e*x+d)*(c*x**2+b*x+a)**(1/2),x)","\int \left(g + h x\right)^{2} \sqrt{a + b x + c x^{2}} \left(d + e x + f x^{2}\right)\, dx"," ",0,"Integral((g + h*x)**2*sqrt(a + b*x + c*x**2)*(d + e*x + f*x**2), x)","F",0
188,0,0,0,0.000000," ","integrate((h*x+g)*(f*x**2+e*x+d)*(c*x**2+b*x+a)**(1/2),x)","\int \left(g + h x\right) \sqrt{a + b x + c x^{2}} \left(d + e x + f x^{2}\right)\, dx"," ",0,"Integral((g + h*x)*sqrt(a + b*x + c*x**2)*(d + e*x + f*x**2), x)","F",0
189,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(1/2)*(f*x**2+e*x+d),x)","\int \sqrt{a + b x + c x^{2}} \left(d + e x + f x^{2}\right)\, dx"," ",0,"Integral(sqrt(a + b*x + c*x**2)*(d + e*x + f*x**2), x)","F",0
190,0,0,0,0.000000," ","integrate((f*x**2+e*x+d)*(c*x**2+b*x+a)**(1/2)/(h*x+g),x)","\int \frac{\sqrt{a + b x + c x^{2}} \left(d + e x + f x^{2}\right)}{g + h x}\, dx"," ",0,"Integral(sqrt(a + b*x + c*x**2)*(d + e*x + f*x**2)/(g + h*x), x)","F",0
191,0,0,0,0.000000," ","integrate((f*x**2+e*x+d)*(c*x**2+b*x+a)**(1/2)/(h*x+g)**2,x)","\int \frac{\sqrt{a + b x + c x^{2}} \left(d + e x + f x^{2}\right)}{\left(g + h x\right)^{2}}\, dx"," ",0,"Integral(sqrt(a + b*x + c*x**2)*(d + e*x + f*x**2)/(g + h*x)**2, x)","F",0
192,0,0,0,0.000000," ","integrate((f*x**2+e*x+d)*(c*x**2+b*x+a)**(1/2)/(h*x+g)**3,x)","\int \frac{\sqrt{a + b x + c x^{2}} \left(d + e x + f x^{2}\right)}{\left(g + h x\right)^{3}}\, dx"," ",0,"Integral(sqrt(a + b*x + c*x**2)*(d + e*x + f*x**2)/(g + h*x)**3, x)","F",0
193,0,0,0,0.000000," ","integrate((f*x**2+e*x+d)*(c*x**2+b*x+a)**(1/2)/(h*x+g)**4,x)","\int \frac{\sqrt{a + b x + c x^{2}} \left(d + e x + f x^{2}\right)}{\left(g + h x\right)^{4}}\, dx"," ",0,"Integral(sqrt(a + b*x + c*x**2)*(d + e*x + f*x**2)/(g + h*x)**4, x)","F",0
194,0,0,0,0.000000," ","integrate((f*x**2+e*x+d)*(c*x**2+b*x+a)**(1/2)/(h*x+g)**5,x)","\int \frac{\sqrt{a + b x + c x^{2}} \left(d + e x + f x^{2}\right)}{\left(g + h x\right)^{5}}\, dx"," ",0,"Integral(sqrt(a + b*x + c*x**2)*(d + e*x + f*x**2)/(g + h*x)**5, x)","F",0
195,0,0,0,0.000000," ","integrate((f*x**2+e*x+d)*(c*x**2+b*x+a)**(1/2)/(h*x+g)**6,x)","\int \frac{\sqrt{a + b x + c x^{2}} \left(d + e x + f x^{2}\right)}{\left(g + h x\right)^{6}}\, dx"," ",0,"Integral(sqrt(a + b*x + c*x**2)*(d + e*x + f*x**2)/(g + h*x)**6, x)","F",0
196,0,0,0,0.000000," ","integrate((h*x+g)**3*(c*x**2+b*x+a)**(3/2)*(f*x**2+e*x+d),x)","\int \left(g + h x\right)^{3} \left(a + b x + c x^{2}\right)^{\frac{3}{2}} \left(d + e x + f x^{2}\right)\, dx"," ",0,"Integral((g + h*x)**3*(a + b*x + c*x**2)**(3/2)*(d + e*x + f*x**2), x)","F",0
197,0,0,0,0.000000," ","integrate((h*x+g)**2*(c*x**2+b*x+a)**(3/2)*(f*x**2+e*x+d),x)","\int \left(g + h x\right)^{2} \left(a + b x + c x^{2}\right)^{\frac{3}{2}} \left(d + e x + f x^{2}\right)\, dx"," ",0,"Integral((g + h*x)**2*(a + b*x + c*x**2)**(3/2)*(d + e*x + f*x**2), x)","F",0
198,0,0,0,0.000000," ","integrate((h*x+g)*(c*x**2+b*x+a)**(3/2)*(f*x**2+e*x+d),x)","\int \left(g + h x\right) \left(a + b x + c x^{2}\right)^{\frac{3}{2}} \left(d + e x + f x^{2}\right)\, dx"," ",0,"Integral((g + h*x)*(a + b*x + c*x**2)**(3/2)*(d + e*x + f*x**2), x)","F",0
199,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(3/2)*(f*x**2+e*x+d),x)","\int \left(a + b x + c x^{2}\right)^{\frac{3}{2}} \left(d + e x + f x^{2}\right)\, dx"," ",0,"Integral((a + b*x + c*x**2)**(3/2)*(d + e*x + f*x**2), x)","F",0
200,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(3/2)*(f*x**2+e*x+d)/(h*x+g),x)","\int \frac{\left(a + b x + c x^{2}\right)^{\frac{3}{2}} \left(d + e x + f x^{2}\right)}{g + h x}\, dx"," ",0,"Integral((a + b*x + c*x**2)**(3/2)*(d + e*x + f*x**2)/(g + h*x), x)","F",0
201,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(3/2)*(f*x**2+e*x+d)/(h*x+g)**2,x)","\int \frac{\left(a + b x + c x^{2}\right)^{\frac{3}{2}} \left(d + e x + f x^{2}\right)}{\left(g + h x\right)^{2}}\, dx"," ",0,"Integral((a + b*x + c*x**2)**(3/2)*(d + e*x + f*x**2)/(g + h*x)**2, x)","F",0
202,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(3/2)*(f*x**2+e*x+d)/(h*x+g)**3,x)","\int \frac{\left(a + b x + c x^{2}\right)^{\frac{3}{2}} \left(d + e x + f x^{2}\right)}{\left(g + h x\right)^{3}}\, dx"," ",0,"Integral((a + b*x + c*x**2)**(3/2)*(d + e*x + f*x**2)/(g + h*x)**3, x)","F",0
203,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(3/2)*(f*x**2+e*x+d)/(h*x+g)**4,x)","\int \frac{\left(a + b x + c x^{2}\right)^{\frac{3}{2}} \left(d + e x + f x^{2}\right)}{\left(g + h x\right)^{4}}\, dx"," ",0,"Integral((a + b*x + c*x**2)**(3/2)*(d + e*x + f*x**2)/(g + h*x)**4, x)","F",0
204,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(3/2)*(f*x**2+e*x+d)/(h*x+g)**5,x)","\int \frac{\left(a + b x + c x^{2}\right)^{\frac{3}{2}} \left(d + e x + f x^{2}\right)}{\left(g + h x\right)^{5}}\, dx"," ",0,"Integral((a + b*x + c*x**2)**(3/2)*(d + e*x + f*x**2)/(g + h*x)**5, x)","F",0
205,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(3/2)*(f*x**2+e*x+d)/(h*x+g)**6,x)","\int \frac{\left(a + b x + c x^{2}\right)^{\frac{3}{2}} \left(d + e x + f x^{2}\right)}{\left(g + h x\right)^{6}}\, dx"," ",0,"Integral((a + b*x + c*x**2)**(3/2)*(d + e*x + f*x**2)/(g + h*x)**6, x)","F",0
206,0,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(3/2)*(f*x**2+e*x+d)/(h*x+g)**7,x)","\int \frac{\left(a + b x + c x^{2}\right)^{\frac{3}{2}} \left(d + e x + f x^{2}\right)}{\left(g + h x\right)^{7}}\, dx"," ",0,"Integral((a + b*x + c*x**2)**(3/2)*(d + e*x + f*x**2)/(g + h*x)**7, x)","F",0
207,-1,0,0,0.000000," ","integrate((c*x**2+b*x+a)**(3/2)*(f*x**2+e*x+d)/(h*x+g)**8,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
208,0,0,0,0.000000," ","integrate((1+2*x)**3*(4*x**2+3*x+1)*(3*x**2-x+2)**(1/2),x)","\int \left(2 x + 1\right)^{3} \sqrt{3 x^{2} - x + 2} \left(4 x^{2} + 3 x + 1\right)\, dx"," ",0,"Integral((2*x + 1)**3*sqrt(3*x**2 - x + 2)*(4*x**2 + 3*x + 1), x)","F",0
209,0,0,0,0.000000," ","integrate((1+2*x)**2*(4*x**2+3*x+1)*(3*x**2-x+2)**(1/2),x)","\int \left(2 x + 1\right)^{2} \sqrt{3 x^{2} - x + 2} \left(4 x^{2} + 3 x + 1\right)\, dx"," ",0,"Integral((2*x + 1)**2*sqrt(3*x**2 - x + 2)*(4*x**2 + 3*x + 1), x)","F",0
210,0,0,0,0.000000," ","integrate((1+2*x)*(4*x**2+3*x+1)*(3*x**2-x+2)**(1/2),x)","\int \left(2 x + 1\right) \sqrt{3 x^{2} - x + 2} \left(4 x^{2} + 3 x + 1\right)\, dx"," ",0,"Integral((2*x + 1)*sqrt(3*x**2 - x + 2)*(4*x**2 + 3*x + 1), x)","F",0
211,0,0,0,0.000000," ","integrate((4*x**2+3*x+1)*(3*x**2-x+2)**(1/2)/(1+2*x),x)","\int \frac{\sqrt{3 x^{2} - x + 2} \left(4 x^{2} + 3 x + 1\right)}{2 x + 1}\, dx"," ",0,"Integral(sqrt(3*x**2 - x + 2)*(4*x**2 + 3*x + 1)/(2*x + 1), x)","F",0
212,0,0,0,0.000000," ","integrate((4*x**2+3*x+1)*(3*x**2-x+2)**(1/2)/(1+2*x)**2,x)","\int \frac{\sqrt{3 x^{2} - x + 2} \left(4 x^{2} + 3 x + 1\right)}{\left(2 x + 1\right)^{2}}\, dx"," ",0,"Integral(sqrt(3*x**2 - x + 2)*(4*x**2 + 3*x + 1)/(2*x + 1)**2, x)","F",0
213,0,0,0,0.000000," ","integrate((4*x**2+3*x+1)*(3*x**2-x+2)**(1/2)/(1+2*x)**3,x)","\int \frac{\sqrt{3 x^{2} - x + 2} \left(4 x^{2} + 3 x + 1\right)}{\left(2 x + 1\right)^{3}}\, dx"," ",0,"Integral(sqrt(3*x**2 - x + 2)*(4*x**2 + 3*x + 1)/(2*x + 1)**3, x)","F",0
214,0,0,0,0.000000," ","integrate((1+2*x)**3*(3*x**2-x+2)**(3/2)*(4*x**2+3*x+1),x)","\int \left(2 x + 1\right)^{3} \left(3 x^{2} - x + 2\right)^{\frac{3}{2}} \left(4 x^{2} + 3 x + 1\right)\, dx"," ",0,"Integral((2*x + 1)**3*(3*x**2 - x + 2)**(3/2)*(4*x**2 + 3*x + 1), x)","F",0
215,0,0,0,0.000000," ","integrate((1+2*x)**2*(3*x**2-x+2)**(3/2)*(4*x**2+3*x+1),x)","\int \left(2 x + 1\right)^{2} \left(3 x^{2} - x + 2\right)^{\frac{3}{2}} \left(4 x^{2} + 3 x + 1\right)\, dx"," ",0,"Integral((2*x + 1)**2*(3*x**2 - x + 2)**(3/2)*(4*x**2 + 3*x + 1), x)","F",0
216,0,0,0,0.000000," ","integrate((1+2*x)*(3*x**2-x+2)**(3/2)*(4*x**2+3*x+1),x)","\int \left(2 x + 1\right) \left(3 x^{2} - x + 2\right)^{\frac{3}{2}} \left(4 x^{2} + 3 x + 1\right)\, dx"," ",0,"Integral((2*x + 1)*(3*x**2 - x + 2)**(3/2)*(4*x**2 + 3*x + 1), x)","F",0
217,0,0,0,0.000000," ","integrate((3*x**2-x+2)**(3/2)*(4*x**2+3*x+1)/(1+2*x),x)","\int \frac{\left(3 x^{2} - x + 2\right)^{\frac{3}{2}} \left(4 x^{2} + 3 x + 1\right)}{2 x + 1}\, dx"," ",0,"Integral((3*x**2 - x + 2)**(3/2)*(4*x**2 + 3*x + 1)/(2*x + 1), x)","F",0
218,0,0,0,0.000000," ","integrate((3*x**2-x+2)**(3/2)*(4*x**2+3*x+1)/(1+2*x)**2,x)","\int \frac{\left(3 x^{2} - x + 2\right)^{\frac{3}{2}} \left(4 x^{2} + 3 x + 1\right)}{\left(2 x + 1\right)^{2}}\, dx"," ",0,"Integral((3*x**2 - x + 2)**(3/2)*(4*x**2 + 3*x + 1)/(2*x + 1)**2, x)","F",0
219,0,0,0,0.000000," ","integrate((3*x**2-x+2)**(3/2)*(4*x**2+3*x+1)/(1+2*x)**3,x)","\int \frac{\left(3 x^{2} - x + 2\right)^{\frac{3}{2}} \left(4 x^{2} + 3 x + 1\right)}{\left(2 x + 1\right)^{3}}\, dx"," ",0,"Integral((3*x**2 - x + 2)**(3/2)*(4*x**2 + 3*x + 1)/(2*x + 1)**3, x)","F",0
220,0,0,0,0.000000," ","integrate((1+2*x)**3*(3*x**2-x+2)**(5/2)*(4*x**2+3*x+1),x)","\int \left(2 x + 1\right)^{3} \left(3 x^{2} - x + 2\right)^{\frac{5}{2}} \left(4 x^{2} + 3 x + 1\right)\, dx"," ",0,"Integral((2*x + 1)**3*(3*x**2 - x + 2)**(5/2)*(4*x**2 + 3*x + 1), x)","F",0
221,0,0,0,0.000000," ","integrate((1+2*x)**2*(3*x**2-x+2)**(5/2)*(4*x**2+3*x+1),x)","\int \left(2 x + 1\right)^{2} \left(3 x^{2} - x + 2\right)^{\frac{5}{2}} \left(4 x^{2} + 3 x + 1\right)\, dx"," ",0,"Integral((2*x + 1)**2*(3*x**2 - x + 2)**(5/2)*(4*x**2 + 3*x + 1), x)","F",0
222,0,0,0,0.000000," ","integrate((1+2*x)*(3*x**2-x+2)**(5/2)*(4*x**2+3*x+1),x)","\int \left(2 x + 1\right) \left(3 x^{2} - x + 2\right)^{\frac{5}{2}} \left(4 x^{2} + 3 x + 1\right)\, dx"," ",0,"Integral((2*x + 1)*(3*x**2 - x + 2)**(5/2)*(4*x**2 + 3*x + 1), x)","F",0
223,0,0,0,0.000000," ","integrate((3*x**2-x+2)**(5/2)*(4*x**2+3*x+1)/(1+2*x),x)","\int \frac{\left(3 x^{2} - x + 2\right)^{\frac{5}{2}} \left(4 x^{2} + 3 x + 1\right)}{2 x + 1}\, dx"," ",0,"Integral((3*x**2 - x + 2)**(5/2)*(4*x**2 + 3*x + 1)/(2*x + 1), x)","F",0
224,0,0,0,0.000000," ","integrate((3*x**2-x+2)**(5/2)*(4*x**2+3*x+1)/(1+2*x)**2,x)","\int \frac{\left(3 x^{2} - x + 2\right)^{\frac{5}{2}} \left(4 x^{2} + 3 x + 1\right)}{\left(2 x + 1\right)^{2}}\, dx"," ",0,"Integral((3*x**2 - x + 2)**(5/2)*(4*x**2 + 3*x + 1)/(2*x + 1)**2, x)","F",0
225,0,0,0,0.000000," ","integrate((3*x**2-x+2)**(5/2)*(4*x**2+3*x+1)/(1+2*x)**3,x)","\int \frac{\left(3 x^{2} - x + 2\right)^{\frac{5}{2}} \left(4 x^{2} + 3 x + 1\right)}{\left(2 x + 1\right)^{3}}\, dx"," ",0,"Integral((3*x**2 - x + 2)**(5/2)*(4*x**2 + 3*x + 1)/(2*x + 1)**3, x)","F",0
226,0,0,0,0.000000," ","integrate((h*x+g)**3*(f*x**2+e*x+d)/(c*x**2+b*x+a)**(1/2),x)","\int \frac{\left(g + h x\right)^{3} \left(d + e x + f x^{2}\right)}{\sqrt{a + b x + c x^{2}}}\, dx"," ",0,"Integral((g + h*x)**3*(d + e*x + f*x**2)/sqrt(a + b*x + c*x**2), x)","F",0
227,0,0,0,0.000000," ","integrate((h*x+g)**2*(f*x**2+e*x+d)/(c*x**2+b*x+a)**(1/2),x)","\int \frac{\left(g + h x\right)^{2} \left(d + e x + f x^{2}\right)}{\sqrt{a + b x + c x^{2}}}\, dx"," ",0,"Integral((g + h*x)**2*(d + e*x + f*x**2)/sqrt(a + b*x + c*x**2), x)","F",0
228,0,0,0,0.000000," ","integrate((h*x+g)*(f*x**2+e*x+d)/(c*x**2+b*x+a)**(1/2),x)","\int \frac{\left(g + h x\right) \left(d + e x + f x^{2}\right)}{\sqrt{a + b x + c x^{2}}}\, dx"," ",0,"Integral((g + h*x)*(d + e*x + f*x**2)/sqrt(a + b*x + c*x**2), x)","F",0
229,0,0,0,0.000000," ","integrate((f*x**2+e*x+d)/(c*x**2+b*x+a)**(1/2),x)","\int \frac{d + e x + f x^{2}}{\sqrt{a + b x + c x^{2}}}\, dx"," ",0,"Integral((d + e*x + f*x**2)/sqrt(a + b*x + c*x**2), x)","F",0
230,0,0,0,0.000000," ","integrate((f*x**2+e*x+d)/(h*x+g)/(c*x**2+b*x+a)**(1/2),x)","\int \frac{d + e x + f x^{2}}{\left(g + h x\right) \sqrt{a + b x + c x^{2}}}\, dx"," ",0,"Integral((d + e*x + f*x**2)/((g + h*x)*sqrt(a + b*x + c*x**2)), x)","F",0
231,0,0,0,0.000000," ","integrate((f*x**2+e*x+d)/(h*x+g)**2/(c*x**2+b*x+a)**(1/2),x)","\int \frac{d + e x + f x^{2}}{\left(g + h x\right)^{2} \sqrt{a + b x + c x^{2}}}\, dx"," ",0,"Integral((d + e*x + f*x**2)/((g + h*x)**2*sqrt(a + b*x + c*x**2)), x)","F",0
232,0,0,0,0.000000," ","integrate((f*x**2+e*x+d)/(h*x+g)**3/(c*x**2+b*x+a)**(1/2),x)","\int \frac{d + e x + f x^{2}}{\left(g + h x\right)^{3} \sqrt{a + b x + c x^{2}}}\, dx"," ",0,"Integral((d + e*x + f*x**2)/((g + h*x)**3*sqrt(a + b*x + c*x**2)), x)","F",0
233,0,0,0,0.000000," ","integrate((h*x+g)**3*(f*x**2+e*x+d)/(c*x**2+b*x+a)**(3/2),x)","\int \frac{\left(g + h x\right)^{3} \left(d + e x + f x^{2}\right)}{\left(a + b x + c x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((g + h*x)**3*(d + e*x + f*x**2)/(a + b*x + c*x**2)**(3/2), x)","F",0
234,0,0,0,0.000000," ","integrate((h*x+g)**2*(f*x**2+e*x+d)/(c*x**2+b*x+a)**(3/2),x)","\int \frac{\left(g + h x\right)^{2} \left(d + e x + f x^{2}\right)}{\left(a + b x + c x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((g + h*x)**2*(d + e*x + f*x**2)/(a + b*x + c*x**2)**(3/2), x)","F",0
235,0,0,0,0.000000," ","integrate((h*x+g)*(f*x**2+e*x+d)/(c*x**2+b*x+a)**(3/2),x)","\int \frac{\left(g + h x\right) \left(d + e x + f x^{2}\right)}{\left(a + b x + c x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((g + h*x)*(d + e*x + f*x**2)/(a + b*x + c*x**2)**(3/2), x)","F",0
236,0,0,0,0.000000," ","integrate((f*x**2+e*x+d)/(c*x**2+b*x+a)**(3/2),x)","\int \frac{d + e x + f x^{2}}{\left(a + b x + c x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((d + e*x + f*x**2)/(a + b*x + c*x**2)**(3/2), x)","F",0
237,0,0,0,0.000000," ","integrate((f*x**2+e*x+d)/(h*x+g)/(c*x**2+b*x+a)**(3/2),x)","\int \frac{d + e x + f x^{2}}{\left(g + h x\right) \left(a + b x + c x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((d + e*x + f*x**2)/((g + h*x)*(a + b*x + c*x**2)**(3/2)), x)","F",0
238,-1,0,0,0.000000," ","integrate((f*x**2+e*x+d)/(h*x+g)**2/(c*x**2+b*x+a)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
239,-1,0,0,0.000000," ","integrate((f*x**2+e*x+d)/(h*x+g)**3/(c*x**2+b*x+a)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
240,0,0,0,0.000000," ","integrate((1+2*x)**3*(4*x**2+3*x+1)/(3*x**2-x+2)**(1/2),x)","\int \frac{\left(2 x + 1\right)^{3} \left(4 x^{2} + 3 x + 1\right)}{\sqrt{3 x^{2} - x + 2}}\, dx"," ",0,"Integral((2*x + 1)**3*(4*x**2 + 3*x + 1)/sqrt(3*x**2 - x + 2), x)","F",0
241,0,0,0,0.000000," ","integrate((1+2*x)**2*(4*x**2+3*x+1)/(3*x**2-x+2)**(1/2),x)","\int \frac{\left(2 x + 1\right)^{2} \left(4 x^{2} + 3 x + 1\right)}{\sqrt{3 x^{2} - x + 2}}\, dx"," ",0,"Integral((2*x + 1)**2*(4*x**2 + 3*x + 1)/sqrt(3*x**2 - x + 2), x)","F",0
242,0,0,0,0.000000," ","integrate((1+2*x)*(4*x**2+3*x+1)/(3*x**2-x+2)**(1/2),x)","\int \frac{\left(2 x + 1\right) \left(4 x^{2} + 3 x + 1\right)}{\sqrt{3 x^{2} - x + 2}}\, dx"," ",0,"Integral((2*x + 1)*(4*x**2 + 3*x + 1)/sqrt(3*x**2 - x + 2), x)","F",0
243,0,0,0,0.000000," ","integrate((4*x**2+3*x+1)/(1+2*x)/(3*x**2-x+2)**(1/2),x)","\int \frac{4 x^{2} + 3 x + 1}{\left(2 x + 1\right) \sqrt{3 x^{2} - x + 2}}\, dx"," ",0,"Integral((4*x**2 + 3*x + 1)/((2*x + 1)*sqrt(3*x**2 - x + 2)), x)","F",0
244,0,0,0,0.000000," ","integrate((4*x**2+3*x+1)/(1+2*x)**2/(3*x**2-x+2)**(1/2),x)","\int \frac{4 x^{2} + 3 x + 1}{\left(2 x + 1\right)^{2} \sqrt{3 x^{2} - x + 2}}\, dx"," ",0,"Integral((4*x**2 + 3*x + 1)/((2*x + 1)**2*sqrt(3*x**2 - x + 2)), x)","F",0
245,0,0,0,0.000000," ","integrate((4*x**2+3*x+1)/(1+2*x)**3/(3*x**2-x+2)**(1/2),x)","\int \frac{4 x^{2} + 3 x + 1}{\left(2 x + 1\right)^{3} \sqrt{3 x^{2} - x + 2}}\, dx"," ",0,"Integral((4*x**2 + 3*x + 1)/((2*x + 1)**3*sqrt(3*x**2 - x + 2)), x)","F",0
246,0,0,0,0.000000," ","integrate((1+2*x)**3*(4*x**2+3*x+1)/(3*x**2-x+2)**(3/2),x)","\int \frac{\left(2 x + 1\right)^{3} \left(4 x^{2} + 3 x + 1\right)}{\left(3 x^{2} - x + 2\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((2*x + 1)**3*(4*x**2 + 3*x + 1)/(3*x**2 - x + 2)**(3/2), x)","F",0
247,0,0,0,0.000000," ","integrate((1+2*x)**2*(4*x**2+3*x+1)/(3*x**2-x+2)**(3/2),x)","\int \frac{\left(2 x + 1\right)^{2} \left(4 x^{2} + 3 x + 1\right)}{\left(3 x^{2} - x + 2\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((2*x + 1)**2*(4*x**2 + 3*x + 1)/(3*x**2 - x + 2)**(3/2), x)","F",0
248,0,0,0,0.000000," ","integrate((1+2*x)*(4*x**2+3*x+1)/(3*x**2-x+2)**(3/2),x)","\int \frac{\left(2 x + 1\right) \left(4 x^{2} + 3 x + 1\right)}{\left(3 x^{2} - x + 2\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((2*x + 1)*(4*x**2 + 3*x + 1)/(3*x**2 - x + 2)**(3/2), x)","F",0
249,0,0,0,0.000000," ","integrate((4*x**2+3*x+1)/(1+2*x)/(3*x**2-x+2)**(3/2),x)","\int \frac{4 x^{2} + 3 x + 1}{\left(2 x + 1\right) \left(3 x^{2} - x + 2\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((4*x**2 + 3*x + 1)/((2*x + 1)*(3*x**2 - x + 2)**(3/2)), x)","F",0
250,0,0,0,0.000000," ","integrate((4*x**2+3*x+1)/(1+2*x)**2/(3*x**2-x+2)**(3/2),x)","\int \frac{4 x^{2} + 3 x + 1}{\left(2 x + 1\right)^{2} \left(3 x^{2} - x + 2\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((4*x**2 + 3*x + 1)/((2*x + 1)**2*(3*x**2 - x + 2)**(3/2)), x)","F",0
251,0,0,0,0.000000," ","integrate((4*x**2+3*x+1)/(1+2*x)**3/(3*x**2-x+2)**(3/2),x)","\int \frac{4 x^{2} + 3 x + 1}{\left(2 x + 1\right)^{3} \left(3 x^{2} - x + 2\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((4*x**2 + 3*x + 1)/((2*x + 1)**3*(3*x**2 - x + 2)**(3/2)), x)","F",0
252,0,0,0,0.000000," ","integrate((1+2*x)**3*(4*x**2+3*x+1)/(3*x**2-x+2)**(5/2),x)","\int \frac{\left(2 x + 1\right)^{3} \left(4 x^{2} + 3 x + 1\right)}{\left(3 x^{2} - x + 2\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((2*x + 1)**3*(4*x**2 + 3*x + 1)/(3*x**2 - x + 2)**(5/2), x)","F",0
253,0,0,0,0.000000," ","integrate((1+2*x)**2*(4*x**2+3*x+1)/(3*x**2-x+2)**(5/2),x)","\int \frac{\left(2 x + 1\right)^{2} \left(4 x^{2} + 3 x + 1\right)}{\left(3 x^{2} - x + 2\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((2*x + 1)**2*(4*x**2 + 3*x + 1)/(3*x**2 - x + 2)**(5/2), x)","F",0
254,0,0,0,0.000000," ","integrate((1+2*x)*(4*x**2+3*x+1)/(3*x**2-x+2)**(5/2),x)","\int \frac{\left(2 x + 1\right) \left(4 x^{2} + 3 x + 1\right)}{\left(3 x^{2} - x + 2\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((2*x + 1)*(4*x**2 + 3*x + 1)/(3*x**2 - x + 2)**(5/2), x)","F",0
255,0,0,0,0.000000," ","integrate((4*x**2+3*x+1)/(1+2*x)/(3*x**2-x+2)**(5/2),x)","\int \frac{4 x^{2} + 3 x + 1}{\left(2 x + 1\right) \left(3 x^{2} - x + 2\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((4*x**2 + 3*x + 1)/((2*x + 1)*(3*x**2 - x + 2)**(5/2)), x)","F",0
256,0,0,0,0.000000," ","integrate((4*x**2+3*x+1)/(1+2*x)**2/(3*x**2-x+2)**(5/2),x)","\int \frac{4 x^{2} + 3 x + 1}{\left(2 x + 1\right)^{2} \left(3 x^{2} - x + 2\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((4*x**2 + 3*x + 1)/((2*x + 1)**2*(3*x**2 - x + 2)**(5/2)), x)","F",0
257,0,0,0,0.000000," ","integrate((4*x**2+3*x+1)/(1+2*x)**3/(3*x**2-x+2)**(5/2),x)","\int \frac{4 x^{2} + 3 x + 1}{\left(2 x + 1\right)^{3} \left(3 x^{2} - x + 2\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((4*x**2 + 3*x + 1)/((2*x + 1)**3*(3*x**2 - x + 2)**(5/2)), x)","F",0
258,0,0,0,0.000000," ","integrate((f*x**2+e*x+d)/(h*x+g)/(c*h**2*x**2+b*h**2*x+b*g*h-c*g**2)**(3/2),x)","\int \frac{d + e x + f x^{2}}{\left(\left(g + h x\right) \left(b h - c g + c h x\right)\right)^{\frac{3}{2}} \left(g + h x\right)}\, dx"," ",0,"Integral((d + e*x + f*x**2)/(((g + h*x)*(b*h - c*g + c*h*x))**(3/2)*(g + h*x)), x)","F",0
259,0,0,0,0.000000," ","integrate((e*x+d)**(1/2)*(C*x**2+B*x+A)*(c*x**2+b*x+a)**(1/2),x)","\int \sqrt{d + e x} \left(A + B x + C x^{2}\right) \sqrt{a + b x + c x^{2}}\, dx"," ",0,"Integral(sqrt(d + e*x)*(A + B*x + C*x**2)*sqrt(a + b*x + c*x**2), x)","F",0
260,-1,0,0,0.000000," ","integrate((C*x**2+B*x+A)*(c*x**2+b*x+a)**(1/2)/(e*x+d)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
261,0,0,0,0.000000," ","integrate((C*x**2+B*x+A)*(c*x**2+b*x+a)**(1/2)/(e*x+d)**(3/2),x)","\int \frac{\left(A + B x + C x^{2}\right) \sqrt{a + b x + c x^{2}}}{\left(d + e x\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((A + B*x + C*x**2)*sqrt(a + b*x + c*x**2)/(d + e*x)**(3/2), x)","F",0
262,0,0,0,0.000000," ","integrate((C*x**2+B*x+A)*(c*x**2+b*x+a)**(1/2)/(e*x+d)**(5/2),x)","\int \frac{\left(A + B x + C x^{2}\right) \sqrt{a + b x + c x^{2}}}{\left(d + e x\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((A + B*x + C*x**2)*sqrt(a + b*x + c*x**2)/(d + e*x)**(5/2), x)","F",0
263,0,0,0,0.000000," ","integrate((C*x**2+B*x+A)*(c*x**2+b*x+a)**(1/2)/(e*x+d)**(7/2),x)","\int \frac{\left(A + B x + C x^{2}\right) \sqrt{a + b x + c x^{2}}}{\left(d + e x\right)^{\frac{7}{2}}}\, dx"," ",0,"Integral((A + B*x + C*x**2)*sqrt(a + b*x + c*x**2)/(d + e*x)**(7/2), x)","F",0
264,0,0,0,0.000000," ","integrate((C*x**2+B*x+A)*(c*x**2+b*x+a)**(1/2)/(e*x+d)**(9/2),x)","\int \frac{\left(A + B x + C x^{2}\right) \sqrt{a + b x + c x^{2}}}{\left(d + e x\right)^{\frac{9}{2}}}\, dx"," ",0,"Integral((A + B*x + C*x**2)*sqrt(a + b*x + c*x**2)/(d + e*x)**(9/2), x)","F",0
265,-1,0,0,0.000000," ","integrate((C*x**2+B*x+A)*(c*x**2+b*x+a)**(1/2)/(e*x+d)**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
266,0,0,0,0.000000," ","integrate((e*x+d)**(3/2)*(C*x**2+B*x+A)/(c*x**2+b*x+a)**(1/2),x)","\int \frac{\left(d + e x\right)^{\frac{3}{2}} \left(A + B x + C x^{2}\right)}{\sqrt{a + b x + c x^{2}}}\, dx"," ",0,"Integral((d + e*x)**(3/2)*(A + B*x + C*x**2)/sqrt(a + b*x + c*x**2), x)","F",0
267,0,0,0,0.000000," ","integrate((e*x+d)**(1/2)*(C*x**2+B*x+A)/(c*x**2+b*x+a)**(1/2),x)","\int \frac{\sqrt{d + e x} \left(A + B x + C x^{2}\right)}{\sqrt{a + b x + c x^{2}}}\, dx"," ",0,"Integral(sqrt(d + e*x)*(A + B*x + C*x**2)/sqrt(a + b*x + c*x**2), x)","F",0
268,0,0,0,0.000000," ","integrate((C*x**2+B*x+A)/(e*x+d)**(1/2)/(c*x**2+b*x+a)**(1/2),x)","\int \frac{A + B x + C x^{2}}{\sqrt{d + e x} \sqrt{a + b x + c x^{2}}}\, dx"," ",0,"Integral((A + B*x + C*x**2)/(sqrt(d + e*x)*sqrt(a + b*x + c*x**2)), x)","F",0
269,0,0,0,0.000000," ","integrate((C*x**2+B*x+A)/(e*x+d)**(3/2)/(c*x**2+b*x+a)**(1/2),x)","\int \frac{A + B x + C x^{2}}{\left(d + e x\right)^{\frac{3}{2}} \sqrt{a + b x + c x^{2}}}\, dx"," ",0,"Integral((A + B*x + C*x**2)/((d + e*x)**(3/2)*sqrt(a + b*x + c*x**2)), x)","F",0
270,0,0,0,0.000000," ","integrate((C*x**2+B*x+A)/(e*x+d)**(5/2)/(c*x**2+b*x+a)**(1/2),x)","\int \frac{A + B x + C x^{2}}{\left(d + e x\right)^{\frac{5}{2}} \sqrt{a + b x + c x^{2}}}\, dx"," ",0,"Integral((A + B*x + C*x**2)/((d + e*x)**(5/2)*sqrt(a + b*x + c*x**2)), x)","F",0
271,0,0,0,0.000000," ","integrate((C*x**2+B*x+A)/(e*x+d)**(7/2)/(c*x**2+b*x+a)**(1/2),x)","\int \frac{A + B x + C x^{2}}{\left(d + e x\right)^{\frac{7}{2}} \sqrt{a + b x + c x^{2}}}\, dx"," ",0,"Integral((A + B*x + C*x**2)/((d + e*x)**(7/2)*sqrt(a + b*x + c*x**2)), x)","F",0
272,-1,0,0,0.000000," ","integrate((h*x+g)**m*(c*x**2+b*x+a)**p*(f*x**2+e*x+d),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
273,0,0,0,0.000000," ","integrate((h*x+g)**m*(f*x**2+e*x+d)*(c*x**2+b*x+a)**(1/2),x)","\int \left(g + h x\right)^{m} \sqrt{a + b x + c x^{2}} \left(d + e x + f x^{2}\right)\, dx"," ",0,"Integral((g + h*x)**m*sqrt(a + b*x + c*x**2)*(d + e*x + f*x**2), x)","F",0
274,-1,0,0,0.000000," ","integrate((h*x+g)**(-3-2*p)*(c*x**2+b*x+a)**p*(f*x**2+e*x+d),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
275,1,221,0,13.247684," ","integrate((f*x**2+d)**p*(2*c*d*f+2*b*f**2*(3+2*p)*x+2*c*f**2*(3+2*p)*x**2),x)","\begin{cases} \frac{2 b d f p \left(d + f x^{2}\right)^{p}}{p + 1} + \frac{3 b d f \left(d + f x^{2}\right)^{p}}{p + 1} + \frac{2 b f^{2} p x^{2} \left(d + f x^{2}\right)^{p}}{p + 1} + \frac{3 b f^{2} x^{2} \left(d + f x^{2}\right)^{p}}{p + 1} + \frac{2 c d f p x \left(d + f x^{2}\right)^{p}}{p + 1} + \frac{2 c d f x \left(d + f x^{2}\right)^{p}}{p + 1} + \frac{2 c f^{2} p x^{3} \left(d + f x^{2}\right)^{p}}{p + 1} + \frac{2 c f^{2} x^{3} \left(d + f x^{2}\right)^{p}}{p + 1} & \text{for}\: p \neq -1 \\b f \log{\left(- i \sqrt{d} \sqrt{\frac{1}{f}} + x \right)} + b f \log{\left(i \sqrt{d} \sqrt{\frac{1}{f}} + x \right)} + 2 c f x & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*b*d*f*p*(d + f*x**2)**p/(p + 1) + 3*b*d*f*(d + f*x**2)**p/(p + 1) + 2*b*f**2*p*x**2*(d + f*x**2)**p/(p + 1) + 3*b*f**2*x**2*(d + f*x**2)**p/(p + 1) + 2*c*d*f*p*x*(d + f*x**2)**p/(p + 1) + 2*c*d*f*x*(d + f*x**2)**p/(p + 1) + 2*c*f**2*p*x**3*(d + f*x**2)**p/(p + 1) + 2*c*f**2*x**3*(d + f*x**2)**p/(p + 1), Ne(p, -1)), (b*f*log(-I*sqrt(d)*sqrt(1/f) + x) + b*f*log(I*sqrt(d)*sqrt(1/f) + x) + 2*c*f*x, True))","B",0
276,1,280,0,173.946604," ","integrate((f*x**2+e*x+d)**p*(-2*c*e**2+2*c*d*f-c*e**2*p+2*c*f**2*(3+2*p)*x**2),x)","\begin{cases} - \frac{c d e p \left(d + e x + f x^{2}\right)^{p}}{p + 1} - \frac{2 c d e \left(d + e x + f x^{2}\right)^{p}}{p + 1} + \frac{2 c d f p x \left(d + e x + f x^{2}\right)^{p}}{p + 1} + \frac{2 c d f x \left(d + e x + f x^{2}\right)^{p}}{p + 1} - \frac{c e^{2} p x \left(d + e x + f x^{2}\right)^{p}}{p + 1} - \frac{2 c e^{2} x \left(d + e x + f x^{2}\right)^{p}}{p + 1} + \frac{c e f p x^{2} \left(d + e x + f x^{2}\right)^{p}}{p + 1} + \frac{2 c f^{2} p x^{3} \left(d + e x + f x^{2}\right)^{p}}{p + 1} + \frac{2 c f^{2} x^{3} \left(d + e x + f x^{2}\right)^{p}}{p + 1} & \text{for}\: p \neq -1 \\- c e \log{\left(\frac{e}{2 f} + x - \frac{\sqrt{- 4 d f + e^{2}}}{2 f} \right)} - c e \log{\left(\frac{e}{2 f} + x + \frac{\sqrt{- 4 d f + e^{2}}}{2 f} \right)} + 2 c f x & \text{otherwise} \end{cases}"," ",0,"Piecewise((-c*d*e*p*(d + e*x + f*x**2)**p/(p + 1) - 2*c*d*e*(d + e*x + f*x**2)**p/(p + 1) + 2*c*d*f*p*x*(d + e*x + f*x**2)**p/(p + 1) + 2*c*d*f*x*(d + e*x + f*x**2)**p/(p + 1) - c*e**2*p*x*(d + e*x + f*x**2)**p/(p + 1) - 2*c*e**2*x*(d + e*x + f*x**2)**p/(p + 1) + c*e*f*p*x**2*(d + e*x + f*x**2)**p/(p + 1) + 2*c*f**2*p*x**3*(d + e*x + f*x**2)**p/(p + 1) + 2*c*f**2*x**3*(d + e*x + f*x**2)**p/(p + 1), Ne(p, -1)), (-c*e*log(e/(2*f) + x - sqrt(-4*d*f + e**2)/(2*f)) - c*e*log(e/(2*f) + x + sqrt(-4*d*f + e**2)/(2*f)) + 2*c*f*x, True))","A",0
277,1,483,0,171.168240," ","integrate((f*x**2+e*x+d)**p*(-2*c*e**2+2*c*d*f+3*b*e*f-c*e**2*p+2*b*e*f*p+2*b*f**2*(3+2*p)*x+2*c*f**2*(3+2*p)*x**2),x)","\begin{cases} \frac{2 b d f p \left(d + e x + f x^{2}\right)^{p}}{p + 1} + \frac{3 b d f \left(d + e x + f x^{2}\right)^{p}}{p + 1} + \frac{2 b e f p x \left(d + e x + f x^{2}\right)^{p}}{p + 1} + \frac{3 b e f x \left(d + e x + f x^{2}\right)^{p}}{p + 1} + \frac{2 b f^{2} p x^{2} \left(d + e x + f x^{2}\right)^{p}}{p + 1} + \frac{3 b f^{2} x^{2} \left(d + e x + f x^{2}\right)^{p}}{p + 1} - \frac{c d e p \left(d + e x + f x^{2}\right)^{p}}{p + 1} - \frac{2 c d e \left(d + e x + f x^{2}\right)^{p}}{p + 1} + \frac{2 c d f p x \left(d + e x + f x^{2}\right)^{p}}{p + 1} + \frac{2 c d f x \left(d + e x + f x^{2}\right)^{p}}{p + 1} - \frac{c e^{2} p x \left(d + e x + f x^{2}\right)^{p}}{p + 1} - \frac{2 c e^{2} x \left(d + e x + f x^{2}\right)^{p}}{p + 1} + \frac{c e f p x^{2} \left(d + e x + f x^{2}\right)^{p}}{p + 1} + \frac{2 c f^{2} p x^{3} \left(d + e x + f x^{2}\right)^{p}}{p + 1} + \frac{2 c f^{2} x^{3} \left(d + e x + f x^{2}\right)^{p}}{p + 1} & \text{for}\: p \neq -1 \\b f \log{\left(\frac{e}{2 f} + x - \frac{\sqrt{- 4 d f + e^{2}}}{2 f} \right)} + b f \log{\left(\frac{e}{2 f} + x + \frac{\sqrt{- 4 d f + e^{2}}}{2 f} \right)} - c e \log{\left(\frac{e}{2 f} + x - \frac{\sqrt{- 4 d f + e^{2}}}{2 f} \right)} - c e \log{\left(\frac{e}{2 f} + x + \frac{\sqrt{- 4 d f + e^{2}}}{2 f} \right)} + 2 c f x & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*b*d*f*p*(d + e*x + f*x**2)**p/(p + 1) + 3*b*d*f*(d + e*x + f*x**2)**p/(p + 1) + 2*b*e*f*p*x*(d + e*x + f*x**2)**p/(p + 1) + 3*b*e*f*x*(d + e*x + f*x**2)**p/(p + 1) + 2*b*f**2*p*x**2*(d + e*x + f*x**2)**p/(p + 1) + 3*b*f**2*x**2*(d + e*x + f*x**2)**p/(p + 1) - c*d*e*p*(d + e*x + f*x**2)**p/(p + 1) - 2*c*d*e*(d + e*x + f*x**2)**p/(p + 1) + 2*c*d*f*p*x*(d + e*x + f*x**2)**p/(p + 1) + 2*c*d*f*x*(d + e*x + f*x**2)**p/(p + 1) - c*e**2*p*x*(d + e*x + f*x**2)**p/(p + 1) - 2*c*e**2*x*(d + e*x + f*x**2)**p/(p + 1) + c*e*f*p*x**2*(d + e*x + f*x**2)**p/(p + 1) + 2*c*f**2*p*x**3*(d + e*x + f*x**2)**p/(p + 1) + 2*c*f**2*x**3*(d + e*x + f*x**2)**p/(p + 1), Ne(p, -1)), (b*f*log(e/(2*f) + x - sqrt(-4*d*f + e**2)/(2*f)) + b*f*log(e/(2*f) + x + sqrt(-4*d*f + e**2)/(2*f)) - c*e*log(e/(2*f) + x - sqrt(-4*d*f + e**2)/(2*f)) - c*e*log(e/(2*f) + x + sqrt(-4*d*f + e**2)/(2*f)) + 2*c*f*x, True))","B",0
278,1,2281,0,1.526962," ","integrate((e*x+d)**3*(c*x**2+b*x+a)**5*(d*(5*a*e+6*b*d)+(5*a*e**2+17*b*d*e+12*c*d**2)*x+e*(11*b*e+29*c*d)*x**2+17*c*e**2*x**3),x)","c^{6} e^{5} x^{17} + x^{16} \left(6 b c^{5} e^{5} + 5 c^{6} d e^{4}\right) + x^{15} \left(6 a c^{5} e^{5} + 15 b^{2} c^{4} e^{5} + 30 b c^{5} d e^{4} + 10 c^{6} d^{2} e^{3}\right) + x^{14} \left(30 a b c^{4} e^{5} + 30 a c^{5} d e^{4} + 20 b^{3} c^{3} e^{5} + 75 b^{2} c^{4} d e^{4} + 60 b c^{5} d^{2} e^{3} + 10 c^{6} d^{3} e^{2}\right) + x^{13} \left(15 a^{2} c^{4} e^{5} + 60 a b^{2} c^{3} e^{5} + 150 a b c^{4} d e^{4} + 60 a c^{5} d^{2} e^{3} + 15 b^{4} c^{2} e^{5} + 100 b^{3} c^{3} d e^{4} + 150 b^{2} c^{4} d^{2} e^{3} + 60 b c^{5} d^{3} e^{2} + 5 c^{6} d^{4} e\right) + x^{12} \left(60 a^{2} b c^{3} e^{5} + 75 a^{2} c^{4} d e^{4} + 60 a b^{3} c^{2} e^{5} + 300 a b^{2} c^{3} d e^{4} + 300 a b c^{4} d^{2} e^{3} + 60 a c^{5} d^{3} e^{2} + 6 b^{5} c e^{5} + 75 b^{4} c^{2} d e^{4} + 200 b^{3} c^{3} d^{2} e^{3} + 150 b^{2} c^{4} d^{3} e^{2} + 30 b c^{5} d^{4} e + c^{6} d^{5}\right) + x^{11} \left(20 a^{3} c^{3} e^{5} + 90 a^{2} b^{2} c^{2} e^{5} + 300 a^{2} b c^{3} d e^{4} + 150 a^{2} c^{4} d^{2} e^{3} + 30 a b^{4} c e^{5} + 300 a b^{3} c^{2} d e^{4} + 600 a b^{2} c^{3} d^{2} e^{3} + 300 a b c^{4} d^{3} e^{2} + 30 a c^{5} d^{4} e + b^{6} e^{5} + 30 b^{5} c d e^{4} + 150 b^{4} c^{2} d^{2} e^{3} + 200 b^{3} c^{3} d^{3} e^{2} + 75 b^{2} c^{4} d^{4} e + 6 b c^{5} d^{5}\right) + x^{10} \left(60 a^{3} b c^{2} e^{5} + 100 a^{3} c^{3} d e^{4} + 60 a^{2} b^{3} c e^{5} + 450 a^{2} b^{2} c^{2} d e^{4} + 600 a^{2} b c^{3} d^{2} e^{3} + 150 a^{2} c^{4} d^{3} e^{2} + 6 a b^{5} e^{5} + 150 a b^{4} c d e^{4} + 600 a b^{3} c^{2} d^{2} e^{3} + 600 a b^{2} c^{3} d^{3} e^{2} + 150 a b c^{4} d^{4} e + 6 a c^{5} d^{5} + 5 b^{6} d e^{4} + 60 b^{5} c d^{2} e^{3} + 150 b^{4} c^{2} d^{3} e^{2} + 100 b^{3} c^{3} d^{4} e + 15 b^{2} c^{4} d^{5}\right) + x^{9} \left(15 a^{4} c^{2} e^{5} + 60 a^{3} b^{2} c e^{5} + 300 a^{3} b c^{2} d e^{4} + 200 a^{3} c^{3} d^{2} e^{3} + 15 a^{2} b^{4} e^{5} + 300 a^{2} b^{3} c d e^{4} + 900 a^{2} b^{2} c^{2} d^{2} e^{3} + 600 a^{2} b c^{3} d^{3} e^{2} + 75 a^{2} c^{4} d^{4} e + 30 a b^{5} d e^{4} + 300 a b^{4} c d^{2} e^{3} + 600 a b^{3} c^{2} d^{3} e^{2} + 300 a b^{2} c^{3} d^{4} e + 30 a b c^{4} d^{5} + 10 b^{6} d^{2} e^{3} + 60 b^{5} c d^{3} e^{2} + 75 b^{4} c^{2} d^{4} e + 20 b^{3} c^{3} d^{5}\right) + x^{8} \left(30 a^{4} b c e^{5} + 75 a^{4} c^{2} d e^{4} + 20 a^{3} b^{3} e^{5} + 300 a^{3} b^{2} c d e^{4} + 600 a^{3} b c^{2} d^{2} e^{3} + 200 a^{3} c^{3} d^{3} e^{2} + 75 a^{2} b^{4} d e^{4} + 600 a^{2} b^{3} c d^{2} e^{3} + 900 a^{2} b^{2} c^{2} d^{3} e^{2} + 300 a^{2} b c^{3} d^{4} e + 15 a^{2} c^{4} d^{5} + 60 a b^{5} d^{2} e^{3} + 300 a b^{4} c d^{3} e^{2} + 300 a b^{3} c^{2} d^{4} e + 60 a b^{2} c^{3} d^{5} + 10 b^{6} d^{3} e^{2} + 30 b^{5} c d^{4} e + 15 b^{4} c^{2} d^{5}\right) + x^{7} \left(6 a^{5} c e^{5} + 15 a^{4} b^{2} e^{5} + 150 a^{4} b c d e^{4} + 150 a^{4} c^{2} d^{2} e^{3} + 100 a^{3} b^{3} d e^{4} + 600 a^{3} b^{2} c d^{2} e^{3} + 600 a^{3} b c^{2} d^{3} e^{2} + 100 a^{3} c^{3} d^{4} e + 150 a^{2} b^{4} d^{2} e^{3} + 600 a^{2} b^{3} c d^{3} e^{2} + 450 a^{2} b^{2} c^{2} d^{4} e + 60 a^{2} b c^{3} d^{5} + 60 a b^{5} d^{3} e^{2} + 150 a b^{4} c d^{4} e + 60 a b^{3} c^{2} d^{5} + 5 b^{6} d^{4} e + 6 b^{5} c d^{5}\right) + x^{6} \left(6 a^{5} b e^{5} + 30 a^{5} c d e^{4} + 75 a^{4} b^{2} d e^{4} + 300 a^{4} b c d^{2} e^{3} + 150 a^{4} c^{2} d^{3} e^{2} + 200 a^{3} b^{3} d^{2} e^{3} + 600 a^{3} b^{2} c d^{3} e^{2} + 300 a^{3} b c^{2} d^{4} e + 20 a^{3} c^{3} d^{5} + 150 a^{2} b^{4} d^{3} e^{2} + 300 a^{2} b^{3} c d^{4} e + 90 a^{2} b^{2} c^{2} d^{5} + 30 a b^{5} d^{4} e + 30 a b^{4} c d^{5} + b^{6} d^{5}\right) + x^{5} \left(a^{6} e^{5} + 30 a^{5} b d e^{4} + 60 a^{5} c d^{2} e^{3} + 150 a^{4} b^{2} d^{2} e^{3} + 300 a^{4} b c d^{3} e^{2} + 75 a^{4} c^{2} d^{4} e + 200 a^{3} b^{3} d^{3} e^{2} + 300 a^{3} b^{2} c d^{4} e + 60 a^{3} b c^{2} d^{5} + 75 a^{2} b^{4} d^{4} e + 60 a^{2} b^{3} c d^{5} + 6 a b^{5} d^{5}\right) + x^{4} \left(5 a^{6} d e^{4} + 60 a^{5} b d^{2} e^{3} + 60 a^{5} c d^{3} e^{2} + 150 a^{4} b^{2} d^{3} e^{2} + 150 a^{4} b c d^{4} e + 15 a^{4} c^{2} d^{5} + 100 a^{3} b^{3} d^{4} e + 60 a^{3} b^{2} c d^{5} + 15 a^{2} b^{4} d^{5}\right) + x^{3} \left(10 a^{6} d^{2} e^{3} + 60 a^{5} b d^{3} e^{2} + 30 a^{5} c d^{4} e + 75 a^{4} b^{2} d^{4} e + 30 a^{4} b c d^{5} + 20 a^{3} b^{3} d^{5}\right) + x^{2} \left(10 a^{6} d^{3} e^{2} + 30 a^{5} b d^{4} e + 6 a^{5} c d^{5} + 15 a^{4} b^{2} d^{5}\right) + x \left(5 a^{6} d^{4} e + 6 a^{5} b d^{5}\right)"," ",0,"c**6*e**5*x**17 + x**16*(6*b*c**5*e**5 + 5*c**6*d*e**4) + x**15*(6*a*c**5*e**5 + 15*b**2*c**4*e**5 + 30*b*c**5*d*e**4 + 10*c**6*d**2*e**3) + x**14*(30*a*b*c**4*e**5 + 30*a*c**5*d*e**4 + 20*b**3*c**3*e**5 + 75*b**2*c**4*d*e**4 + 60*b*c**5*d**2*e**3 + 10*c**6*d**3*e**2) + x**13*(15*a**2*c**4*e**5 + 60*a*b**2*c**3*e**5 + 150*a*b*c**4*d*e**4 + 60*a*c**5*d**2*e**3 + 15*b**4*c**2*e**5 + 100*b**3*c**3*d*e**4 + 150*b**2*c**4*d**2*e**3 + 60*b*c**5*d**3*e**2 + 5*c**6*d**4*e) + x**12*(60*a**2*b*c**3*e**5 + 75*a**2*c**4*d*e**4 + 60*a*b**3*c**2*e**5 + 300*a*b**2*c**3*d*e**4 + 300*a*b*c**4*d**2*e**3 + 60*a*c**5*d**3*e**2 + 6*b**5*c*e**5 + 75*b**4*c**2*d*e**4 + 200*b**3*c**3*d**2*e**3 + 150*b**2*c**4*d**3*e**2 + 30*b*c**5*d**4*e + c**6*d**5) + x**11*(20*a**3*c**3*e**5 + 90*a**2*b**2*c**2*e**5 + 300*a**2*b*c**3*d*e**4 + 150*a**2*c**4*d**2*e**3 + 30*a*b**4*c*e**5 + 300*a*b**3*c**2*d*e**4 + 600*a*b**2*c**3*d**2*e**3 + 300*a*b*c**4*d**3*e**2 + 30*a*c**5*d**4*e + b**6*e**5 + 30*b**5*c*d*e**4 + 150*b**4*c**2*d**2*e**3 + 200*b**3*c**3*d**3*e**2 + 75*b**2*c**4*d**4*e + 6*b*c**5*d**5) + x**10*(60*a**3*b*c**2*e**5 + 100*a**3*c**3*d*e**4 + 60*a**2*b**3*c*e**5 + 450*a**2*b**2*c**2*d*e**4 + 600*a**2*b*c**3*d**2*e**3 + 150*a**2*c**4*d**3*e**2 + 6*a*b**5*e**5 + 150*a*b**4*c*d*e**4 + 600*a*b**3*c**2*d**2*e**3 + 600*a*b**2*c**3*d**3*e**2 + 150*a*b*c**4*d**4*e + 6*a*c**5*d**5 + 5*b**6*d*e**4 + 60*b**5*c*d**2*e**3 + 150*b**4*c**2*d**3*e**2 + 100*b**3*c**3*d**4*e + 15*b**2*c**4*d**5) + x**9*(15*a**4*c**2*e**5 + 60*a**3*b**2*c*e**5 + 300*a**3*b*c**2*d*e**4 + 200*a**3*c**3*d**2*e**3 + 15*a**2*b**4*e**5 + 300*a**2*b**3*c*d*e**4 + 900*a**2*b**2*c**2*d**2*e**3 + 600*a**2*b*c**3*d**3*e**2 + 75*a**2*c**4*d**4*e + 30*a*b**5*d*e**4 + 300*a*b**4*c*d**2*e**3 + 600*a*b**3*c**2*d**3*e**2 + 300*a*b**2*c**3*d**4*e + 30*a*b*c**4*d**5 + 10*b**6*d**2*e**3 + 60*b**5*c*d**3*e**2 + 75*b**4*c**2*d**4*e + 20*b**3*c**3*d**5) + x**8*(30*a**4*b*c*e**5 + 75*a**4*c**2*d*e**4 + 20*a**3*b**3*e**5 + 300*a**3*b**2*c*d*e**4 + 600*a**3*b*c**2*d**2*e**3 + 200*a**3*c**3*d**3*e**2 + 75*a**2*b**4*d*e**4 + 600*a**2*b**3*c*d**2*e**3 + 900*a**2*b**2*c**2*d**3*e**2 + 300*a**2*b*c**3*d**4*e + 15*a**2*c**4*d**5 + 60*a*b**5*d**2*e**3 + 300*a*b**4*c*d**3*e**2 + 300*a*b**3*c**2*d**4*e + 60*a*b**2*c**3*d**5 + 10*b**6*d**3*e**2 + 30*b**5*c*d**4*e + 15*b**4*c**2*d**5) + x**7*(6*a**5*c*e**5 + 15*a**4*b**2*e**5 + 150*a**4*b*c*d*e**4 + 150*a**4*c**2*d**2*e**3 + 100*a**3*b**3*d*e**4 + 600*a**3*b**2*c*d**2*e**3 + 600*a**3*b*c**2*d**3*e**2 + 100*a**3*c**3*d**4*e + 150*a**2*b**4*d**2*e**3 + 600*a**2*b**3*c*d**3*e**2 + 450*a**2*b**2*c**2*d**4*e + 60*a**2*b*c**3*d**5 + 60*a*b**5*d**3*e**2 + 150*a*b**4*c*d**4*e + 60*a*b**3*c**2*d**5 + 5*b**6*d**4*e + 6*b**5*c*d**5) + x**6*(6*a**5*b*e**5 + 30*a**5*c*d*e**4 + 75*a**4*b**2*d*e**4 + 300*a**4*b*c*d**2*e**3 + 150*a**4*c**2*d**3*e**2 + 200*a**3*b**3*d**2*e**3 + 600*a**3*b**2*c*d**3*e**2 + 300*a**3*b*c**2*d**4*e + 20*a**3*c**3*d**5 + 150*a**2*b**4*d**3*e**2 + 300*a**2*b**3*c*d**4*e + 90*a**2*b**2*c**2*d**5 + 30*a*b**5*d**4*e + 30*a*b**4*c*d**5 + b**6*d**5) + x**5*(a**6*e**5 + 30*a**5*b*d*e**4 + 60*a**5*c*d**2*e**3 + 150*a**4*b**2*d**2*e**3 + 300*a**4*b*c*d**3*e**2 + 75*a**4*c**2*d**4*e + 200*a**3*b**3*d**3*e**2 + 300*a**3*b**2*c*d**4*e + 60*a**3*b*c**2*d**5 + 75*a**2*b**4*d**4*e + 60*a**2*b**3*c*d**5 + 6*a*b**5*d**5) + x**4*(5*a**6*d*e**4 + 60*a**5*b*d**2*e**3 + 60*a**5*c*d**3*e**2 + 150*a**4*b**2*d**3*e**2 + 150*a**4*b*c*d**4*e + 15*a**4*c**2*d**5 + 100*a**3*b**3*d**4*e + 60*a**3*b**2*c*d**5 + 15*a**2*b**4*d**5) + x**3*(10*a**6*d**2*e**3 + 60*a**5*b*d**3*e**2 + 30*a**5*c*d**4*e + 75*a**4*b**2*d**4*e + 30*a**4*b*c*d**5 + 20*a**3*b**3*d**5) + x**2*(10*a**6*d**3*e**2 + 30*a**5*b*d**4*e + 6*a**5*c*d**5 + 15*a**4*b**2*d**5) + x*(5*a**6*d**4*e + 6*a**5*b*d**5)","B",0
279,1,20,0,0.243664," ","integrate((x**3+x**2)/(x**2+x-2),x)","\frac{x^{2}}{2} + \frac{2 \log{\left(x - 1 \right)}}{3} + \frac{4 \log{\left(x + 2 \right)}}{3}"," ",0,"x**2/2 + 2*log(x - 1)/3 + 4*log(x + 2)/3","A",0
280,0,0,0,0.000000," ","integrate(x**2*(g*x**3+f*x**2+e*x+d)/(c*x**2+b*x+a)**(1/2),x)","\int \frac{x^{2} \left(d + e x + f x^{2} + g x^{3}\right)}{\sqrt{a + b x + c x^{2}}}\, dx"," ",0,"Integral(x**2*(d + e*x + f*x**2 + g*x**3)/sqrt(a + b*x + c*x**2), x)","F",0
281,0,0,0,0.000000," ","integrate(x*(g*x**3+f*x**2+e*x+d)/(c*x**2+b*x+a)**(1/2),x)","\int \frac{x \left(d + e x + f x^{2} + g x^{3}\right)}{\sqrt{a + b x + c x^{2}}}\, dx"," ",0,"Integral(x*(d + e*x + f*x**2 + g*x**3)/sqrt(a + b*x + c*x**2), x)","F",0
282,0,0,0,0.000000," ","integrate((g*x**3+f*x**2+e*x+d)/(c*x**2+b*x+a)**(1/2),x)","\int \frac{d + e x + f x^{2} + g x^{3}}{\sqrt{a + b x + c x^{2}}}\, dx"," ",0,"Integral((d + e*x + f*x**2 + g*x**3)/sqrt(a + b*x + c*x**2), x)","F",0
283,0,0,0,0.000000," ","integrate((g*x**3+f*x**2+e*x+d)/x/(c*x**2+b*x+a)**(1/2),x)","\int \frac{d + e x + f x^{2} + g x^{3}}{x \sqrt{a + b x + c x^{2}}}\, dx"," ",0,"Integral((d + e*x + f*x**2 + g*x**3)/(x*sqrt(a + b*x + c*x**2)), x)","F",0
284,0,0,0,0.000000," ","integrate((g*x**3+f*x**2+e*x+d)/x**2/(c*x**2+b*x+a)**(1/2),x)","\int \frac{d + e x + f x^{2} + g x^{3}}{x^{2} \sqrt{a + b x + c x^{2}}}\, dx"," ",0,"Integral((d + e*x + f*x**2 + g*x**3)/(x**2*sqrt(a + b*x + c*x**2)), x)","F",0
285,0,0,0,0.000000," ","integrate((g*x**3+f*x**2+e*x+d)/x**3/(c*x**2+b*x+a)**(1/2),x)","\int \frac{d + e x + f x^{2} + g x^{3}}{x^{3} \sqrt{a + b x + c x^{2}}}\, dx"," ",0,"Integral((d + e*x + f*x**2 + g*x**3)/(x**3*sqrt(a + b*x + c*x**2)), x)","F",0
286,0,0,0,0.000000," ","integrate((g*x**3+f*x**2+e*x+d)/x**4/(c*x**2+b*x+a)**(1/2),x)","\int \frac{d + e x + f x^{2} + g x^{3}}{x^{4} \sqrt{a + b x + c x^{2}}}\, dx"," ",0,"Integral((d + e*x + f*x**2 + g*x**3)/(x**4*sqrt(a + b*x + c*x**2)), x)","F",0
287,0,0,0,0.000000," ","integrate((g*x**3+f*x**2+e*x+d)/x**5/(c*x**2+b*x+a)**(1/2),x)","\int \frac{d + e x + f x^{2} + g x^{3}}{x^{5} \sqrt{a + b x + c x^{2}}}\, dx"," ",0,"Integral((d + e*x + f*x**2 + g*x**3)/(x**5*sqrt(a + b*x + c*x**2)), x)","F",0
288,0,0,0,0.000000," ","integrate((g*x**3+f*x**2+e*x+d)/x**6/(c*x**2+b*x+a)**(1/2),x)","\int \frac{d + e x + f x^{2} + g x^{3}}{x^{6} \sqrt{a + b x + c x^{2}}}\, dx"," ",0,"Integral((d + e*x + f*x**2 + g*x**3)/(x**6*sqrt(a + b*x + c*x**2)), x)","F",0
289,1,230,0,0.518401," ","integrate((e*x+d)**3*(5*x**2+2*x+3)*(4*x**4-5*x**3+3*x**2+x+2),x)","6 d^{3} x + 2 e^{3} x^{10} + x^{9} \left(\frac{20 d e^{2}}{3} - \frac{17 e^{3}}{9}\right) + x^{8} \left(\frac{15 d^{2} e}{2} - \frac{51 d e^{2}}{8} + \frac{17 e^{3}}{8}\right) + x^{7} \left(\frac{20 d^{3}}{7} - \frac{51 d^{2} e}{7} + \frac{51 d e^{2}}{7} - \frac{4 e^{3}}{7}\right) + x^{6} \left(- \frac{17 d^{3}}{6} + \frac{17 d^{2} e}{2} - 2 d e^{2} + \frac{7 e^{3}}{2}\right) + x^{5} \left(\frac{17 d^{3}}{5} - \frac{12 d^{2} e}{5} + \frac{63 d e^{2}}{5} + \frac{7 e^{3}}{5}\right) + x^{4} \left(- d^{3} + \frac{63 d^{2} e}{4} + \frac{21 d e^{2}}{4} + \frac{3 e^{3}}{2}\right) + x^{3} \left(7 d^{3} + 7 d^{2} e + 6 d e^{2}\right) + x^{2} \left(\frac{7 d^{3}}{2} + 9 d^{2} e\right)"," ",0,"6*d**3*x + 2*e**3*x**10 + x**9*(20*d*e**2/3 - 17*e**3/9) + x**8*(15*d**2*e/2 - 51*d*e**2/8 + 17*e**3/8) + x**7*(20*d**3/7 - 51*d**2*e/7 + 51*d*e**2/7 - 4*e**3/7) + x**6*(-17*d**3/6 + 17*d**2*e/2 - 2*d*e**2 + 7*e**3/2) + x**5*(17*d**3/5 - 12*d**2*e/5 + 63*d*e**2/5 + 7*e**3/5) + x**4*(-d**3 + 63*d**2*e/4 + 21*d*e**2/4 + 3*e**3/2) + x**3*(7*d**3 + 7*d**2*e + 6*d*e**2) + x**2*(7*d**3/2 + 9*d**2*e)","A",0
290,1,158,0,0.152620," ","integrate((e*x+d)**2*(5*x**2+2*x+3)*(4*x**4-5*x**3+3*x**2+x+2),x)","6 d^{2} x + \frac{20 e^{2} x^{9}}{9} + x^{8} \left(5 d e - \frac{17 e^{2}}{8}\right) + x^{7} \left(\frac{20 d^{2}}{7} - \frac{34 d e}{7} + \frac{17 e^{2}}{7}\right) + x^{6} \left(- \frac{17 d^{2}}{6} + \frac{17 d e}{3} - \frac{2 e^{2}}{3}\right) + x^{5} \left(\frac{17 d^{2}}{5} - \frac{8 d e}{5} + \frac{21 e^{2}}{5}\right) + x^{4} \left(- d^{2} + \frac{21 d e}{2} + \frac{7 e^{2}}{4}\right) + x^{3} \left(7 d^{2} + \frac{14 d e}{3} + 2 e^{2}\right) + x^{2} \left(\frac{7 d^{2}}{2} + 6 d e\right)"," ",0,"6*d**2*x + 20*e**2*x**9/9 + x**8*(5*d*e - 17*e**2/8) + x**7*(20*d**2/7 - 34*d*e/7 + 17*e**2/7) + x**6*(-17*d**2/6 + 17*d*e/3 - 2*e**2/3) + x**5*(17*d**2/5 - 8*d*e/5 + 21*e**2/5) + x**4*(-d**2 + 21*d*e/2 + 7*e**2/4) + x**3*(7*d**2 + 14*d*e/3 + 2*e**2) + x**2*(7*d**2/2 + 6*d*e)","A",0
291,1,87,0,1.910999," ","integrate((e*x+d)*(5*x**2+2*x+3)*(4*x**4-5*x**3+3*x**2+x+2),x)","6 d x + \frac{5 e x^{8}}{2} + x^{7} \left(\frac{20 d}{7} - \frac{17 e}{7}\right) + x^{6} \left(- \frac{17 d}{6} + \frac{17 e}{6}\right) + x^{5} \left(\frac{17 d}{5} - \frac{4 e}{5}\right) + x^{4} \left(- d + \frac{21 e}{4}\right) + x^{3} \left(7 d + \frac{7 e}{3}\right) + x^{2} \left(\frac{7 d}{2} + 3 e\right)"," ",0,"6*d*x + 5*e*x**8/2 + x**7*(20*d/7 - 17*e/7) + x**6*(-17*d/6 + 17*e/6) + x**5*(17*d/5 - 4*e/5) + x**4*(-d + 21*e/4) + x**3*(7*d + 7*e/3) + x**2*(7*d/2 + 3*e)","A",0
292,1,37,0,0.288115," ","integrate((5*x**2+2*x+3)*(4*x**4-5*x**3+3*x**2+x+2),x)","\frac{20 x^{7}}{7} - \frac{17 x^{6}}{6} + \frac{17 x^{5}}{5} - x^{4} + 7 x^{3} + \frac{7 x^{2}}{2} + 6 x"," ",0,"20*x**7/7 - 17*x**6/6 + 17*x**5/5 - x**4 + 7*x**3 + 7*x**2/2 + 6*x","A",0
293,1,235,0,1.174471," ","integrate((5*x**2+2*x+3)*(4*x**4-5*x**3+3*x**2+x+2)/(e*x+d),x)","x^{5} \left(- \frac{4 d}{e^{2}} - \frac{17}{5 e}\right) + x^{4} \left(\frac{5 d^{2}}{e^{3}} + \frac{17 d}{4 e^{2}} + \frac{17}{4 e}\right) + x^{3} \left(- \frac{20 d^{3}}{3 e^{4}} - \frac{17 d^{2}}{3 e^{3}} - \frac{17 d}{3 e^{2}} - \frac{4}{3 e}\right) + x^{2} \left(\frac{10 d^{4}}{e^{5}} + \frac{17 d^{3}}{2 e^{4}} + \frac{17 d^{2}}{2 e^{3}} + \frac{2 d}{e^{2}} + \frac{21}{2 e}\right) + x \left(- \frac{20 d^{5}}{e^{6}} - \frac{17 d^{4}}{e^{5}} - \frac{17 d^{3}}{e^{4}} - \frac{4 d^{2}}{e^{3}} - \frac{21 d}{e^{2}} + \frac{7}{e}\right) + \frac{10 x^{6}}{3 e} + \frac{\left(5 d^{2} - 2 d e + 3 e^{2}\right) \left(4 d^{4} + 5 d^{3} e + 3 d^{2} e^{2} - d e^{3} + 2 e^{4}\right) \log{\left(d + e x \right)}}{e^{7}}"," ",0,"x**5*(-4*d/e**2 - 17/(5*e)) + x**4*(5*d**2/e**3 + 17*d/(4*e**2) + 17/(4*e)) + x**3*(-20*d**3/(3*e**4) - 17*d**2/(3*e**3) - 17*d/(3*e**2) - 4/(3*e)) + x**2*(10*d**4/e**5 + 17*d**3/(2*e**4) + 17*d**2/(2*e**3) + 2*d/e**2 + 21/(2*e)) + x*(-20*d**5/e**6 - 17*d**4/e**5 - 17*d**3/e**4 - 4*d**2/e**3 - 21*d/e**2 + 7/e) + 10*x**6/(3*e) + (5*d**2 - 2*d*e + 3*e**2)*(4*d**4 + 5*d**3*e + 3*d**2*e**2 - d*e**3 + 2*e**4)*log(d + e*x)/e**7","A",0
294,1,238,0,1.133780," ","integrate((5*x**2+2*x+3)*(4*x**4-5*x**3+3*x**2+x+2)/(e*x+d)**2,x)","x^{4} \left(- \frac{10 d}{e^{3}} - \frac{17}{4 e^{2}}\right) + x^{3} \left(\frac{20 d^{2}}{e^{4}} + \frac{34 d}{3 e^{3}} + \frac{17}{3 e^{2}}\right) + x^{2} \left(- \frac{40 d^{3}}{e^{5}} - \frac{51 d^{2}}{2 e^{4}} - \frac{17 d}{e^{3}} - \frac{2}{e^{2}}\right) + x \left(\frac{100 d^{4}}{e^{6}} + \frac{68 d^{3}}{e^{5}} + \frac{51 d^{2}}{e^{4}} + \frac{8 d}{e^{3}} + \frac{21}{e^{2}}\right) + \frac{- 20 d^{6} - 17 d^{5} e - 17 d^{4} e^{2} - 4 d^{3} e^{3} - 21 d^{2} e^{4} + 7 d e^{5} - 6 e^{6}}{d e^{7} + e^{8} x} + \frac{4 x^{5}}{e^{2}} - \frac{\left(120 d^{5} + 85 d^{4} e + 68 d^{3} e^{2} + 12 d^{2} e^{3} + 42 d e^{4} - 7 e^{5}\right) \log{\left(d + e x \right)}}{e^{7}}"," ",0,"x**4*(-10*d/e**3 - 17/(4*e**2)) + x**3*(20*d**2/e**4 + 34*d/(3*e**3) + 17/(3*e**2)) + x**2*(-40*d**3/e**5 - 51*d**2/(2*e**4) - 17*d/e**3 - 2/e**2) + x*(100*d**4/e**6 + 68*d**3/e**5 + 51*d**2/e**4 + 8*d/e**3 + 21/e**2) + (-20*d**6 - 17*d**5*e - 17*d**4*e**2 - 4*d**3*e**3 - 21*d**2*e**4 + 7*d*e**5 - 6*e**6)/(d*e**7 + e**8*x) + 4*x**5/e**2 - (120*d**5 + 85*d**4*e + 68*d**3*e**2 + 12*d**2*e**3 + 42*d*e**4 - 7*e**5)*log(d + e*x)/e**7","A",0
295,1,248,0,2.627017," ","integrate((5*x**2+2*x+3)*(4*x**4-5*x**3+3*x**2+x+2)/(e*x+d)**3,x)","x^{3} \left(- \frac{20 d}{e^{4}} - \frac{17}{3 e^{3}}\right) + x^{2} \left(\frac{60 d^{2}}{e^{5}} + \frac{51 d}{2 e^{4}} + \frac{17}{2 e^{3}}\right) + x \left(- \frac{200 d^{3}}{e^{6}} - \frac{102 d^{2}}{e^{5}} - \frac{51 d}{e^{4}} - \frac{4}{e^{3}}\right) + \frac{220 d^{6} + 153 d^{5} e + 119 d^{4} e^{2} + 20 d^{3} e^{3} + 63 d^{2} e^{4} - 7 d e^{5} - 6 e^{6} + x \left(240 d^{5} e + 170 d^{4} e^{2} + 136 d^{3} e^{3} + 24 d^{2} e^{4} + 84 d e^{5} - 14 e^{6}\right)}{2 d^{2} e^{7} + 4 d e^{8} x + 2 e^{9} x^{2}} + \frac{5 x^{4}}{e^{3}} + \frac{\left(300 d^{4} + 170 d^{3} e + 102 d^{2} e^{2} + 12 d e^{3} + 21 e^{4}\right) \log{\left(d + e x \right)}}{e^{7}}"," ",0,"x**3*(-20*d/e**4 - 17/(3*e**3)) + x**2*(60*d**2/e**5 + 51*d/(2*e**4) + 17/(2*e**3)) + x*(-200*d**3/e**6 - 102*d**2/e**5 - 51*d/e**4 - 4/e**3) + (220*d**6 + 153*d**5*e + 119*d**4*e**2 + 20*d**3*e**3 + 63*d**2*e**4 - 7*d*e**5 - 6*e**6 + x*(240*d**5*e + 170*d**4*e**2 + 136*d**3*e**3 + 24*d**2*e**4 + 84*d*e**5 - 14*e**6))/(2*d**2*e**7 + 4*d*e**8*x + 2*e**9*x**2) + 5*x**4/e**3 + (300*d**4 + 170*d**3*e + 102*d**2*e**2 + 12*d*e**3 + 21*e**4)*log(d + e*x)/e**7","A",0
296,1,298,0,0.203421," ","integrate((e*x+d)**3*(5*x**2+2*x+3)**2*(4*x**4-5*x**3+3*x**2+x+2),x)","18 d^{3} x + \frac{25 e^{3} x^{12}}{3} + x^{11} \left(\frac{300 d e^{2}}{11} - \frac{45 e^{3}}{11}\right) + x^{10} \left(30 d^{2} e - \frac{27 d e^{2}}{2} + \frac{111 e^{3}}{10}\right) + x^{9} \left(\frac{100 d^{3}}{9} - 15 d^{2} e + 37 d e^{2} - \frac{37 e^{3}}{9}\right) + x^{8} \left(- \frac{45 d^{3}}{8} + \frac{333 d^{2} e}{8} - \frac{111 d e^{2}}{8} + \frac{37 e^{3}}{2}\right) + x^{7} \left(\frac{111 d^{3}}{7} - \frac{111 d^{2} e}{7} + \frac{444 d e^{2}}{7} + \frac{65 e^{3}}{7}\right) + x^{6} \left(- \frac{37 d^{3}}{6} + 74 d^{2} e + \frac{65 d e^{2}}{2} + \frac{107 e^{3}}{6}\right) + x^{5} \left(\frac{148 d^{3}}{5} + 39 d^{2} e + \frac{321 d e^{2}}{5} + \frac{33 e^{3}}{5}\right) + x^{4} \left(\frac{65 d^{3}}{4} + \frac{321 d^{2} e}{4} + \frac{99 d e^{2}}{4} + \frac{9 e^{3}}{2}\right) + x^{3} \left(\frac{107 d^{3}}{3} + 33 d^{2} e + 18 d e^{2}\right) + x^{2} \left(\frac{33 d^{3}}{2} + 27 d^{2} e\right)"," ",0,"18*d**3*x + 25*e**3*x**12/3 + x**11*(300*d*e**2/11 - 45*e**3/11) + x**10*(30*d**2*e - 27*d*e**2/2 + 111*e**3/10) + x**9*(100*d**3/9 - 15*d**2*e + 37*d*e**2 - 37*e**3/9) + x**8*(-45*d**3/8 + 333*d**2*e/8 - 111*d*e**2/8 + 37*e**3/2) + x**7*(111*d**3/7 - 111*d**2*e/7 + 444*d*e**2/7 + 65*e**3/7) + x**6*(-37*d**3/6 + 74*d**2*e + 65*d*e**2/2 + 107*e**3/6) + x**5*(148*d**3/5 + 39*d**2*e + 321*d*e**2/5 + 33*e**3/5) + x**4*(65*d**3/4 + 321*d**2*e/4 + 99*d*e**2/4 + 9*e**3/2) + x**3*(107*d**3/3 + 33*d**2*e + 18*d*e**2) + x**2*(33*d**3/2 + 27*d**2*e)","A",0
297,1,206,0,0.145806," ","integrate((e*x+d)**2*(5*x**2+2*x+3)**2*(4*x**4-5*x**3+3*x**2+x+2),x)","18 d^{2} x + \frac{100 e^{2} x^{11}}{11} + x^{10} \left(20 d e - \frac{9 e^{2}}{2}\right) + x^{9} \left(\frac{100 d^{2}}{9} - 10 d e + \frac{37 e^{2}}{3}\right) + x^{8} \left(- \frac{45 d^{2}}{8} + \frac{111 d e}{4} - \frac{37 e^{2}}{8}\right) + x^{7} \left(\frac{111 d^{2}}{7} - \frac{74 d e}{7} + \frac{148 e^{2}}{7}\right) + x^{6} \left(- \frac{37 d^{2}}{6} + \frac{148 d e}{3} + \frac{65 e^{2}}{6}\right) + x^{5} \left(\frac{148 d^{2}}{5} + 26 d e + \frac{107 e^{2}}{5}\right) + x^{4} \left(\frac{65 d^{2}}{4} + \frac{107 d e}{2} + \frac{33 e^{2}}{4}\right) + x^{3} \left(\frac{107 d^{2}}{3} + 22 d e + 6 e^{2}\right) + x^{2} \left(\frac{33 d^{2}}{2} + 18 d e\right)"," ",0,"18*d**2*x + 100*e**2*x**11/11 + x**10*(20*d*e - 9*e**2/2) + x**9*(100*d**2/9 - 10*d*e + 37*e**2/3) + x**8*(-45*d**2/8 + 111*d*e/4 - 37*e**2/8) + x**7*(111*d**2/7 - 74*d*e/7 + 148*e**2/7) + x**6*(-37*d**2/6 + 148*d*e/3 + 65*e**2/6) + x**5*(148*d**2/5 + 26*d*e + 107*e**2/5) + x**4*(65*d**2/4 + 107*d*e/2 + 33*e**2/4) + x**3*(107*d**2/3 + 22*d*e + 6*e**2) + x**2*(33*d**2/2 + 18*d*e)","A",0
298,1,112,0,0.136354," ","integrate((e*x+d)*(5*x**2+2*x+3)**2*(4*x**4-5*x**3+3*x**2+x+2),x)","18 d x + 10 e x^{10} + x^{9} \left(\frac{100 d}{9} - 5 e\right) + x^{8} \left(- \frac{45 d}{8} + \frac{111 e}{8}\right) + x^{7} \left(\frac{111 d}{7} - \frac{37 e}{7}\right) + x^{6} \left(- \frac{37 d}{6} + \frac{74 e}{3}\right) + x^{5} \left(\frac{148 d}{5} + 13 e\right) + x^{4} \left(\frac{65 d}{4} + \frac{107 e}{4}\right) + x^{3} \left(\frac{107 d}{3} + 11 e\right) + x^{2} \left(\frac{33 d}{2} + 9 e\right)"," ",0,"18*d*x + 10*e*x**10 + x**9*(100*d/9 - 5*e) + x**8*(-45*d/8 + 111*e/8) + x**7*(111*d/7 - 37*e/7) + x**6*(-37*d/6 + 74*e/3) + x**5*(148*d/5 + 13*e) + x**4*(65*d/4 + 107*e/4) + x**3*(107*d/3 + 11*e) + x**2*(33*d/2 + 9*e)","A",0
299,1,56,0,0.154733," ","integrate((5*x**2+2*x+3)**2*(4*x**4-5*x**3+3*x**2+x+2),x)","\frac{100 x^{9}}{9} - \frac{45 x^{8}}{8} + \frac{111 x^{7}}{7} - \frac{37 x^{6}}{6} + \frac{148 x^{5}}{5} + \frac{65 x^{4}}{4} + \frac{107 x^{3}}{3} + \frac{33 x^{2}}{2} + 18 x"," ",0,"100*x**9/9 - 45*x**8/8 + 111*x**7/7 - 37*x**6/6 + 148*x**5/5 + 65*x**4/4 + 107*x**3/3 + 33*x**2/2 + 18*x","A",0
300,1,372,0,0.996997," ","integrate((5*x**2+2*x+3)**2*(4*x**4-5*x**3+3*x**2+x+2)/(e*x+d),x)","x^{7} \left(- \frac{100 d}{7 e^{2}} - \frac{45}{7 e}\right) + x^{6} \left(\frac{50 d^{2}}{3 e^{3}} + \frac{15 d}{2 e^{2}} + \frac{37}{2 e}\right) + x^{5} \left(- \frac{20 d^{3}}{e^{4}} - \frac{9 d^{2}}{e^{3}} - \frac{111 d}{5 e^{2}} - \frac{37}{5 e}\right) + x^{4} \left(\frac{25 d^{4}}{e^{5}} + \frac{45 d^{3}}{4 e^{4}} + \frac{111 d^{2}}{4 e^{3}} + \frac{37 d}{4 e^{2}} + \frac{37}{e}\right) + x^{3} \left(- \frac{100 d^{5}}{3 e^{6}} - \frac{15 d^{4}}{e^{5}} - \frac{37 d^{3}}{e^{4}} - \frac{37 d^{2}}{3 e^{3}} - \frac{148 d}{3 e^{2}} + \frac{65}{3 e}\right) + x^{2} \left(\frac{50 d^{6}}{e^{7}} + \frac{45 d^{5}}{2 e^{6}} + \frac{111 d^{4}}{2 e^{5}} + \frac{37 d^{3}}{2 e^{4}} + \frac{74 d^{2}}{e^{3}} - \frac{65 d}{2 e^{2}} + \frac{107}{2 e}\right) + x \left(- \frac{100 d^{7}}{e^{8}} - \frac{45 d^{6}}{e^{7}} - \frac{111 d^{5}}{e^{6}} - \frac{37 d^{4}}{e^{5}} - \frac{148 d^{3}}{e^{4}} + \frac{65 d^{2}}{e^{3}} - \frac{107 d}{e^{2}} + \frac{33}{e}\right) + \frac{25 x^{8}}{2 e} + \frac{\left(5 d^{2} - 2 d e + 3 e^{2}\right)^{2} \left(4 d^{4} + 5 d^{3} e + 3 d^{2} e^{2} - d e^{3} + 2 e^{4}\right) \log{\left(d + e x \right)}}{e^{9}}"," ",0,"x**7*(-100*d/(7*e**2) - 45/(7*e)) + x**6*(50*d**2/(3*e**3) + 15*d/(2*e**2) + 37/(2*e)) + x**5*(-20*d**3/e**4 - 9*d**2/e**3 - 111*d/(5*e**2) - 37/(5*e)) + x**4*(25*d**4/e**5 + 45*d**3/(4*e**4) + 111*d**2/(4*e**3) + 37*d/(4*e**2) + 37/e) + x**3*(-100*d**5/(3*e**6) - 15*d**4/e**5 - 37*d**3/e**4 - 37*d**2/(3*e**3) - 148*d/(3*e**2) + 65/(3*e)) + x**2*(50*d**6/e**7 + 45*d**5/(2*e**6) + 111*d**4/(2*e**5) + 37*d**3/(2*e**4) + 74*d**2/e**3 - 65*d/(2*e**2) + 107/(2*e)) + x*(-100*d**7/e**8 - 45*d**6/e**7 - 111*d**5/e**6 - 37*d**4/e**5 - 148*d**3/e**4 + 65*d**2/e**3 - 107*d/e**2 + 33/e) + 25*x**8/(2*e) + (5*d**2 - 2*d*e + 3*e**2)**2*(4*d**4 + 5*d**3*e + 3*d**2*e**2 - d*e**3 + 2*e**4)*log(d + e*x)/e**9","A",0
301,1,393,0,2.311312," ","integrate((5*x**2+2*x+3)**2*(4*x**4-5*x**3+3*x**2+x+2)/(e*x+d)**2,x)","x^{6} \left(- \frac{100 d}{3 e^{3}} - \frac{15}{2 e^{2}}\right) + x^{5} \left(\frac{60 d^{2}}{e^{4}} + \frac{18 d}{e^{3}} + \frac{111}{5 e^{2}}\right) + x^{4} \left(- \frac{100 d^{3}}{e^{5}} - \frac{135 d^{2}}{4 e^{4}} - \frac{111 d}{2 e^{3}} - \frac{37}{4 e^{2}}\right) + x^{3} \left(\frac{500 d^{4}}{3 e^{6}} + \frac{60 d^{3}}{e^{5}} + \frac{111 d^{2}}{e^{4}} + \frac{74 d}{3 e^{3}} + \frac{148}{3 e^{2}}\right) + x^{2} \left(- \frac{300 d^{5}}{e^{7}} - \frac{225 d^{4}}{2 e^{6}} - \frac{222 d^{3}}{e^{5}} - \frac{111 d^{2}}{2 e^{4}} - \frac{148 d}{e^{3}} + \frac{65}{2 e^{2}}\right) + x \left(\frac{700 d^{6}}{e^{8}} + \frac{270 d^{5}}{e^{7}} + \frac{555 d^{4}}{e^{6}} + \frac{148 d^{3}}{e^{5}} + \frac{444 d^{2}}{e^{4}} - \frac{130 d}{e^{3}} + \frac{107}{e^{2}}\right) + \frac{- 100 d^{8} - 45 d^{7} e - 111 d^{6} e^{2} - 37 d^{5} e^{3} - 148 d^{4} e^{4} + 65 d^{3} e^{5} - 107 d^{2} e^{6} + 33 d e^{7} - 18 e^{8}}{d e^{9} + e^{10} x} + \frac{100 x^{7}}{7 e^{2}} - \frac{\left(5 d^{2} - 2 d e + 3 e^{2}\right) \left(160 d^{5} + 127 d^{4} e + 88 d^{3} e^{2} - 4 d^{2} e^{3} + 64 d e^{4} - 11 e^{5}\right) \log{\left(d + e x \right)}}{e^{9}}"," ",0,"x**6*(-100*d/(3*e**3) - 15/(2*e**2)) + x**5*(60*d**2/e**4 + 18*d/e**3 + 111/(5*e**2)) + x**4*(-100*d**3/e**5 - 135*d**2/(4*e**4) - 111*d/(2*e**3) - 37/(4*e**2)) + x**3*(500*d**4/(3*e**6) + 60*d**3/e**5 + 111*d**2/e**4 + 74*d/(3*e**3) + 148/(3*e**2)) + x**2*(-300*d**5/e**7 - 225*d**4/(2*e**6) - 222*d**3/e**5 - 111*d**2/(2*e**4) - 148*d/e**3 + 65/(2*e**2)) + x*(700*d**6/e**8 + 270*d**5/e**7 + 555*d**4/e**6 + 148*d**3/e**5 + 444*d**2/e**4 - 130*d/e**3 + 107/e**2) + (-100*d**8 - 45*d**7*e - 111*d**6*e**2 - 37*d**5*e**3 - 148*d**4*e**4 + 65*d**3*e**5 - 107*d**2*e**6 + 33*d*e**7 - 18*e**8)/(d*e**9 + e**10*x) + 100*x**7/(7*e**2) - (5*d**2 - 2*d*e + 3*e**2)*(160*d**5 + 127*d**4*e + 88*d**3*e**2 - 4*d**2*e**3 + 64*d*e**4 - 11*e**5)*log(d + e*x)/e**9","A",0
302,1,394,0,4.871930," ","integrate((5*x**2+2*x+3)**2*(4*x**4-5*x**3+3*x**2+x+2)/(e*x+d)**3,x)","x^{5} \left(- \frac{60 d}{e^{4}} - \frac{9}{e^{3}}\right) + x^{4} \left(\frac{150 d^{2}}{e^{5}} + \frac{135 d}{4 e^{4}} + \frac{111}{4 e^{3}}\right) + x^{3} \left(- \frac{1000 d^{3}}{3 e^{6}} - \frac{90 d^{2}}{e^{5}} - \frac{111 d}{e^{4}} - \frac{37}{3 e^{3}}\right) + x^{2} \left(\frac{750 d^{4}}{e^{7}} + \frac{225 d^{3}}{e^{6}} + \frac{333 d^{2}}{e^{5}} + \frac{111 d}{2 e^{4}} + \frac{74}{e^{3}}\right) + x \left(- \frac{2100 d^{5}}{e^{8}} - \frac{675 d^{4}}{e^{7}} - \frac{1110 d^{3}}{e^{6}} - \frac{222 d^{2}}{e^{5}} - \frac{444 d}{e^{4}} + \frac{65}{e^{3}}\right) + \frac{1500 d^{8} + 585 d^{7} e + 1221 d^{6} e^{2} + 333 d^{5} e^{3} + 1036 d^{4} e^{4} - 325 d^{3} e^{5} + 321 d^{2} e^{6} - 33 d e^{7} - 18 e^{8} + x \left(1600 d^{7} e + 630 d^{6} e^{2} + 1332 d^{5} e^{3} + 370 d^{4} e^{4} + 1184 d^{3} e^{5} - 390 d^{2} e^{6} + 428 d e^{7} - 66 e^{8}\right)}{2 d^{2} e^{9} + 4 d e^{10} x + 2 e^{11} x^{2}} + \frac{50 x^{6}}{3 e^{3}} + \frac{\left(2800 d^{6} + 945 d^{5} e + 1665 d^{4} e^{2} + 370 d^{3} e^{3} + 888 d^{2} e^{4} - 195 d e^{5} + 107 e^{6}\right) \log{\left(d + e x \right)}}{e^{9}}"," ",0,"x**5*(-60*d/e**4 - 9/e**3) + x**4*(150*d**2/e**5 + 135*d/(4*e**4) + 111/(4*e**3)) + x**3*(-1000*d**3/(3*e**6) - 90*d**2/e**5 - 111*d/e**4 - 37/(3*e**3)) + x**2*(750*d**4/e**7 + 225*d**3/e**6 + 333*d**2/e**5 + 111*d/(2*e**4) + 74/e**3) + x*(-2100*d**5/e**8 - 675*d**4/e**7 - 1110*d**3/e**6 - 222*d**2/e**5 - 444*d/e**4 + 65/e**3) + (1500*d**8 + 585*d**7*e + 1221*d**6*e**2 + 333*d**5*e**3 + 1036*d**4*e**4 - 325*d**3*e**5 + 321*d**2*e**6 - 33*d*e**7 - 18*e**8 + x*(1600*d**7*e + 630*d**6*e**2 + 1332*d**5*e**3 + 370*d**4*e**4 + 1184*d**3*e**5 - 390*d**2*e**6 + 428*d*e**7 - 66*e**8))/(2*d**2*e**9 + 4*d*e**10*x + 2*e**11*x**2) + 50*x**6/(3*e**3) + (2800*d**6 + 945*d**5*e + 1665*d**4*e**2 + 370*d**3*e**3 + 888*d**2*e**4 - 195*d*e**5 + 107*e**6)*log(d + e*x)/e**9","A",0
303,1,401,0,8.089211," ","integrate((5*x**2+2*x+3)**2*(4*x**4-5*x**3+3*x**2+x+2)/(e*x+d)**4,x)","x^{4} \left(- \frac{100 d}{e^{5}} - \frac{45}{4 e^{4}}\right) + x^{3} \left(\frac{1000 d^{2}}{3 e^{6}} + \frac{60 d}{e^{5}} + \frac{37}{e^{4}}\right) + x^{2} \left(- \frac{1000 d^{3}}{e^{7}} - \frac{225 d^{2}}{e^{6}} - \frac{222 d}{e^{5}} - \frac{37}{2 e^{4}}\right) + x \left(\frac{3500 d^{4}}{e^{8}} + \frac{900 d^{3}}{e^{7}} + \frac{1110 d^{2}}{e^{6}} + \frac{148 d}{e^{5}} + \frac{148}{e^{4}}\right) + \frac{- 14600 d^{8} - 4815 d^{7} e - 8214 d^{6} e^{2} - 1739 d^{5} e^{3} - 3848 d^{4} e^{4} + 715 d^{3} e^{5} - 214 d^{2} e^{6} - 33 d e^{7} - 36 e^{8} + x^{2} \left(- 16800 d^{6} e^{2} - 5670 d^{5} e^{3} - 9990 d^{4} e^{4} - 2220 d^{3} e^{5} - 5328 d^{2} e^{6} + 1170 d e^{7} - 642 e^{8}\right) + x \left(- 31200 d^{7} e - 10395 d^{6} e^{2} - 17982 d^{5} e^{3} - 3885 d^{4} e^{4} - 8880 d^{3} e^{5} + 1755 d^{2} e^{6} - 642 d e^{7} - 99 e^{8}\right)}{6 d^{3} e^{9} + 18 d^{2} e^{10} x + 18 d e^{11} x^{2} + 6 e^{12} x^{3}} + \frac{20 x^{5}}{e^{4}} - \frac{\left(5600 d^{5} + 1575 d^{4} e + 2220 d^{3} e^{2} + 370 d^{2} e^{3} + 592 d e^{4} - 65 e^{5}\right) \log{\left(d + e x \right)}}{e^{9}}"," ",0,"x**4*(-100*d/e**5 - 45/(4*e**4)) + x**3*(1000*d**2/(3*e**6) + 60*d/e**5 + 37/e**4) + x**2*(-1000*d**3/e**7 - 225*d**2/e**6 - 222*d/e**5 - 37/(2*e**4)) + x*(3500*d**4/e**8 + 900*d**3/e**7 + 1110*d**2/e**6 + 148*d/e**5 + 148/e**4) + (-14600*d**8 - 4815*d**7*e - 8214*d**6*e**2 - 1739*d**5*e**3 - 3848*d**4*e**4 + 715*d**3*e**5 - 214*d**2*e**6 - 33*d*e**7 - 36*e**8 + x**2*(-16800*d**6*e**2 - 5670*d**5*e**3 - 9990*d**4*e**4 - 2220*d**3*e**5 - 5328*d**2*e**6 + 1170*d*e**7 - 642*e**8) + x*(-31200*d**7*e - 10395*d**6*e**2 - 17982*d**5*e**3 - 3885*d**4*e**4 - 8880*d**3*e**5 + 1755*d**2*e**6 - 642*d*e**7 - 99*e**8))/(6*d**3*e**9 + 18*d**2*e**10*x + 18*d*e**11*x**2 + 6*e**12*x**3) + 20*x**5/e**4 - (5600*d**5 + 1575*d**4*e + 2220*d**3*e**2 + 370*d**2*e**3 + 592*d*e**4 - 65*e**5)*log(d + e*x)/e**9","A",0
304,1,450,0,2.578796," ","integrate((e*x+d)**3*(4*x**4-5*x**3+3*x**2+x+2)/(5*x**2+2*x+3),x)","\frac{2 e^{3} x^{6}}{15} + x^{5} \left(\frac{12 d e^{2}}{25} - \frac{33 e^{3}}{125}\right) + x^{4} \left(\frac{3 d^{2} e}{5} - \frac{99 d e^{2}}{100} + \frac{81 e^{3}}{500}\right) + x^{3} \left(\frac{4 d^{3}}{15} - \frac{33 d^{2} e}{25} + \frac{81 d e^{2}}{125} + \frac{458 e^{3}}{1875}\right) + x^{2} \left(- \frac{33 d^{3}}{50} + \frac{243 d^{2} e}{250} + \frac{687 d e^{2}}{625} - \frac{881 e^{3}}{6250}\right) + x \left(\frac{81 d^{3}}{125} + \frac{1374 d^{2} e}{625} - \frac{2643 d e^{2}}{3125} - \frac{5108 e^{3}}{15625}\right) + \left(\frac{229 d^{3}}{625} - \frac{2643 d^{2} e}{6250} - \frac{7662 d e^{2}}{15625} + \frac{23431 e^{3}}{156250} - \frac{\sqrt{14} i \left(52875 d^{3} + 449175 d^{2} e - 274845 d e^{2} - 53189 e^{3}\right)}{2187500}\right) \log{\left(x + \frac{10575 d^{3} + 89835 d^{2} e - 54969 d e^{2} - \frac{53189 e^{3}}{5} + \frac{\sqrt{14} i \left(52875 d^{3} + 449175 d^{2} e - 274845 d e^{2} - 53189 e^{3}\right)}{5}}{52875 d^{3} + 449175 d^{2} e - 274845 d e^{2} - 53189 e^{3}} \right)} + \left(\frac{229 d^{3}}{625} - \frac{2643 d^{2} e}{6250} - \frac{7662 d e^{2}}{15625} + \frac{23431 e^{3}}{156250} + \frac{\sqrt{14} i \left(52875 d^{3} + 449175 d^{2} e - 274845 d e^{2} - 53189 e^{3}\right)}{2187500}\right) \log{\left(x + \frac{10575 d^{3} + 89835 d^{2} e - 54969 d e^{2} - \frac{53189 e^{3}}{5} - \frac{\sqrt{14} i \left(52875 d^{3} + 449175 d^{2} e - 274845 d e^{2} - 53189 e^{3}\right)}{5}}{52875 d^{3} + 449175 d^{2} e - 274845 d e^{2} - 53189 e^{3}} \right)}"," ",0,"2*e**3*x**6/15 + x**5*(12*d*e**2/25 - 33*e**3/125) + x**4*(3*d**2*e/5 - 99*d*e**2/100 + 81*e**3/500) + x**3*(4*d**3/15 - 33*d**2*e/25 + 81*d*e**2/125 + 458*e**3/1875) + x**2*(-33*d**3/50 + 243*d**2*e/250 + 687*d*e**2/625 - 881*e**3/6250) + x*(81*d**3/125 + 1374*d**2*e/625 - 2643*d*e**2/3125 - 5108*e**3/15625) + (229*d**3/625 - 2643*d**2*e/6250 - 7662*d*e**2/15625 + 23431*e**3/156250 - sqrt(14)*I*(52875*d**3 + 449175*d**2*e - 274845*d*e**2 - 53189*e**3)/2187500)*log(x + (10575*d**3 + 89835*d**2*e - 54969*d*e**2 - 53189*e**3/5 + sqrt(14)*I*(52875*d**3 + 449175*d**2*e - 274845*d*e**2 - 53189*e**3)/5)/(52875*d**3 + 449175*d**2*e - 274845*d*e**2 - 53189*e**3)) + (229*d**3/625 - 2643*d**2*e/6250 - 7662*d*e**2/15625 + 23431*e**3/156250 + sqrt(14)*I*(52875*d**3 + 449175*d**2*e - 274845*d*e**2 - 53189*e**3)/2187500)*log(x + (10575*d**3 + 89835*d**2*e - 54969*d*e**2 - 53189*e**3/5 - sqrt(14)*I*(52875*d**3 + 449175*d**2*e - 274845*d*e**2 - 53189*e**3)/5)/(52875*d**3 + 449175*d**2*e - 274845*d*e**2 - 53189*e**3))","C",0
305,1,303,0,1.719013," ","integrate((e*x+d)**2*(4*x**4-5*x**3+3*x**2+x+2)/(5*x**2+2*x+3),x)","\frac{4 e^{2} x^{5}}{25} + x^{4} \left(\frac{2 d e}{5} - \frac{33 e^{2}}{100}\right) + x^{3} \left(\frac{4 d^{2}}{15} - \frac{22 d e}{25} + \frac{27 e^{2}}{125}\right) + x^{2} \left(- \frac{33 d^{2}}{50} + \frac{81 d e}{125} + \frac{229 e^{2}}{625}\right) + x \left(\frac{81 d^{2}}{125} + \frac{916 d e}{625} - \frac{881 e^{2}}{3125}\right) + \left(\frac{229 d^{2}}{625} - \frac{881 d e}{3125} - \frac{2554 e^{2}}{15625} - \frac{\sqrt{14} i \left(10575 d^{2} + 59890 d e - 18323 e^{2}\right)}{437500}\right) \log{\left(x + \frac{2115 d^{2} + 11978 d e - \frac{18323 e^{2}}{5} + \frac{\sqrt{14} i \left(10575 d^{2} + 59890 d e - 18323 e^{2}\right)}{5}}{10575 d^{2} + 59890 d e - 18323 e^{2}} \right)} + \left(\frac{229 d^{2}}{625} - \frac{881 d e}{3125} - \frac{2554 e^{2}}{15625} + \frac{\sqrt{14} i \left(10575 d^{2} + 59890 d e - 18323 e^{2}\right)}{437500}\right) \log{\left(x + \frac{2115 d^{2} + 11978 d e - \frac{18323 e^{2}}{5} - \frac{\sqrt{14} i \left(10575 d^{2} + 59890 d e - 18323 e^{2}\right)}{5}}{10575 d^{2} + 59890 d e - 18323 e^{2}} \right)}"," ",0,"4*e**2*x**5/25 + x**4*(2*d*e/5 - 33*e**2/100) + x**3*(4*d**2/15 - 22*d*e/25 + 27*e**2/125) + x**2*(-33*d**2/50 + 81*d*e/125 + 229*e**2/625) + x*(81*d**2/125 + 916*d*e/625 - 881*e**2/3125) + (229*d**2/625 - 881*d*e/3125 - 2554*e**2/15625 - sqrt(14)*I*(10575*d**2 + 59890*d*e - 18323*e**2)/437500)*log(x + (2115*d**2 + 11978*d*e - 18323*e**2/5 + sqrt(14)*I*(10575*d**2 + 59890*d*e - 18323*e**2)/5)/(10575*d**2 + 59890*d*e - 18323*e**2)) + (229*d**2/625 - 881*d*e/3125 - 2554*e**2/15625 + sqrt(14)*I*(10575*d**2 + 59890*d*e - 18323*e**2)/437500)*log(x + (2115*d**2 + 11978*d*e - 18323*e**2/5 - sqrt(14)*I*(10575*d**2 + 59890*d*e - 18323*e**2)/5)/(10575*d**2 + 59890*d*e - 18323*e**2))","C",0
306,1,163,0,0.848808," ","integrate((e*x+d)*(4*x**4-5*x**3+3*x**2+x+2)/(5*x**2+2*x+3),x)","\frac{e x^{4}}{5} + x^{3} \left(\frac{4 d}{15} - \frac{11 e}{25}\right) + x^{2} \left(- \frac{33 d}{50} + \frac{81 e}{250}\right) + x \left(\frac{81 d}{125} + \frac{458 e}{625}\right) + \left(\frac{229 d}{625} - \frac{881 e}{6250} - \frac{\sqrt{14} i \left(2115 d + 5989 e\right)}{87500}\right) \log{\left(x + \frac{423 d + \frac{5989 e}{5} + \frac{\sqrt{14} i \left(2115 d + 5989 e\right)}{5}}{2115 d + 5989 e} \right)} + \left(\frac{229 d}{625} - \frac{881 e}{6250} + \frac{\sqrt{14} i \left(2115 d + 5989 e\right)}{87500}\right) \log{\left(x + \frac{423 d + \frac{5989 e}{5} - \frac{\sqrt{14} i \left(2115 d + 5989 e\right)}{5}}{2115 d + 5989 e} \right)}"," ",0,"e*x**4/5 + x**3*(4*d/15 - 11*e/25) + x**2*(-33*d/50 + 81*e/250) + x*(81*d/125 + 458*e/625) + (229*d/625 - 881*e/6250 - sqrt(14)*I*(2115*d + 5989*e)/87500)*log(x + (423*d + 5989*e/5 + sqrt(14)*I*(2115*d + 5989*e)/5)/(2115*d + 5989*e)) + (229*d/625 - 881*e/6250 + sqrt(14)*I*(2115*d + 5989*e)/87500)*log(x + (423*d + 5989*e/5 - sqrt(14)*I*(2115*d + 5989*e)/5)/(2115*d + 5989*e))","C",0
307,1,61,0,0.232205," ","integrate((4*x**4-5*x**3+3*x**2+x+2)/(5*x**2+2*x+3),x)","\frac{4 x^{3}}{15} - \frac{33 x^{2}}{50} + \frac{81 x}{125} + \frac{229 \log{\left(x^{2} + \frac{2 x}{5} + \frac{3}{5} \right)}}{625} - \frac{423 \sqrt{14} \operatorname{atan}{\left(\frac{5 \sqrt{14} x}{14} + \frac{\sqrt{14}}{14} \right)}}{8750}"," ",0,"4*x**3/15 - 33*x**2/50 + 81*x/125 + 229*log(x**2 + 2*x/5 + 3/5)/625 - 423*sqrt(14)*atan(5*sqrt(14)*x/14 + sqrt(14)/14)/8750","A",0
308,-1,0,0,0.000000," ","integrate((4*x**4-5*x**3+3*x**2+x+2)/(e*x+d)/(5*x**2+2*x+3),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
309,-1,0,0,0.000000," ","integrate((4*x**4-5*x**3+3*x**2+x+2)/(e*x+d)**2/(5*x**2+2*x+3),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
310,-1,0,0,0.000000," ","integrate((4*x**4-5*x**3+3*x**2+x+2)/(e*x+d)**3/(5*x**2+2*x+3),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
311,1,444,0,2.772471," ","integrate((e*x+d)**3*(4*x**4-5*x**3+3*x**2+x+2)/(5*x**2+2*x+3)**2,x)","\frac{e^{3} x^{4}}{25} + x^{3} \left(\frac{4 d e^{2}}{25} - \frac{41 e^{3}}{375}\right) + x^{2} \left(\frac{6 d^{2} e}{25} - \frac{123 d e^{2}}{250} + \frac{103 e^{3}}{1250}\right) + x \left(\frac{4 d^{3}}{25} - \frac{123 d^{2} e}{125} + \frac{309 d e^{2}}{625} + \frac{867 e^{3}}{3125}\right) + \left(- \frac{41 d^{3}}{250} + \frac{309 d^{2} e}{1250} + \frac{2601 d e^{2}}{6250} - \frac{416 e^{3}}{3125} - \frac{\sqrt{14} i \left(32825 d^{3} + 317565 d^{2} e - 221643 d e^{2} - 67499 e^{3}\right)}{2450000}\right) \log{\left(x + \frac{6565 d^{3} + 63513 d^{2} e - \frac{221643 d e^{2}}{5} - \frac{67499 e^{3}}{5} - \frac{\sqrt{14} i \left(32825 d^{3} + 317565 d^{2} e - 221643 d e^{2} - 67499 e^{3}\right)}{5}}{32825 d^{3} + 317565 d^{2} e - 221643 d e^{2} - 67499 e^{3}} \right)} + \left(- \frac{41 d^{3}}{250} + \frac{309 d^{2} e}{1250} + \frac{2601 d e^{2}}{6250} - \frac{416 e^{3}}{3125} + \frac{\sqrt{14} i \left(32825 d^{3} + 317565 d^{2} e - 221643 d e^{2} - 67499 e^{3}\right)}{2450000}\right) \log{\left(x + \frac{6565 d^{3} + 63513 d^{2} e - \frac{221643 d e^{2}}{5} - \frac{67499 e^{3}}{5} + \frac{\sqrt{14} i \left(32825 d^{3} + 317565 d^{2} e - 221643 d e^{2} - 67499 e^{3}\right)}{5}}{32825 d^{3} + 317565 d^{2} e - 221643 d e^{2} - 67499 e^{3}} \right)} + \frac{- 170875 d^{3} + 95175 d^{2} e + 269505 d e^{2} - 54969 e^{3} + x \left(- 52875 d^{3} - 449175 d^{2} e + 274845 d e^{2} + 53189 e^{3}\right)}{2187500 x^{2} + 875000 x + 1312500}"," ",0,"e**3*x**4/25 + x**3*(4*d*e**2/25 - 41*e**3/375) + x**2*(6*d**2*e/25 - 123*d*e**2/250 + 103*e**3/1250) + x*(4*d**3/25 - 123*d**2*e/125 + 309*d*e**2/625 + 867*e**3/3125) + (-41*d**3/250 + 309*d**2*e/1250 + 2601*d*e**2/6250 - 416*e**3/3125 - sqrt(14)*I*(32825*d**3 + 317565*d**2*e - 221643*d*e**2 - 67499*e**3)/2450000)*log(x + (6565*d**3 + 63513*d**2*e - 221643*d*e**2/5 - 67499*e**3/5 - sqrt(14)*I*(32825*d**3 + 317565*d**2*e - 221643*d*e**2 - 67499*e**3)/5)/(32825*d**3 + 317565*d**2*e - 221643*d*e**2 - 67499*e**3)) + (-41*d**3/250 + 309*d**2*e/1250 + 2601*d*e**2/6250 - 416*e**3/3125 + sqrt(14)*I*(32825*d**3 + 317565*d**2*e - 221643*d*e**2 - 67499*e**3)/2450000)*log(x + (6565*d**3 + 63513*d**2*e - 221643*d*e**2/5 - 67499*e**3/5 + sqrt(14)*I*(32825*d**3 + 317565*d**2*e - 221643*d*e**2 - 67499*e**3)/5)/(32825*d**3 + 317565*d**2*e - 221643*d*e**2 - 67499*e**3)) + (-170875*d**3 + 95175*d**2*e + 269505*d*e**2 - 54969*e**3 + x*(-52875*d**3 - 449175*d**2*e + 274845*d*e**2 + 53189*e**3))/(2187500*x**2 + 875000*x + 1312500)","C",0
312,1,298,0,1.960972," ","integrate((e*x+d)**2*(4*x**4-5*x**3+3*x**2+x+2)/(5*x**2+2*x+3)**2,x)","\frac{4 e^{2} x^{3}}{75} + x^{2} \left(\frac{4 d e}{25} - \frac{41 e^{2}}{250}\right) + x \left(\frac{4 d^{2}}{25} - \frac{82 d e}{125} + \frac{103 e^{2}}{625}\right) + \left(- \frac{41 d^{2}}{250} + \frac{103 d e}{625} + \frac{867 e^{2}}{6250} - \frac{\sqrt{14} i \left(32825 d^{2} + 211710 d e - 73881 e^{2}\right)}{2450000}\right) \log{\left(x + \frac{6565 d^{2} + 42342 d e - \frac{73881 e^{2}}{5} - \frac{\sqrt{14} i \left(32825 d^{2} + 211710 d e - 73881 e^{2}\right)}{5}}{32825 d^{2} + 211710 d e - 73881 e^{2}} \right)} + \left(- \frac{41 d^{2}}{250} + \frac{103 d e}{625} + \frac{867 e^{2}}{6250} + \frac{\sqrt{14} i \left(32825 d^{2} + 211710 d e - 73881 e^{2}\right)}{2450000}\right) \log{\left(x + \frac{6565 d^{2} + 42342 d e - \frac{73881 e^{2}}{5} + \frac{\sqrt{14} i \left(32825 d^{2} + 211710 d e - 73881 e^{2}\right)}{5}}{32825 d^{2} + 211710 d e - 73881 e^{2}} \right)} + \frac{- 34175 d^{2} + 12690 d e + 17967 e^{2} + x \left(- 10575 d^{2} - 59890 d e + 18323 e^{2}\right)}{437500 x^{2} + 175000 x + 262500}"," ",0,"4*e**2*x**3/75 + x**2*(4*d*e/25 - 41*e**2/250) + x*(4*d**2/25 - 82*d*e/125 + 103*e**2/625) + (-41*d**2/250 + 103*d*e/625 + 867*e**2/6250 - sqrt(14)*I*(32825*d**2 + 211710*d*e - 73881*e**2)/2450000)*log(x + (6565*d**2 + 42342*d*e - 73881*e**2/5 - sqrt(14)*I*(32825*d**2 + 211710*d*e - 73881*e**2)/5)/(32825*d**2 + 211710*d*e - 73881*e**2)) + (-41*d**2/250 + 103*d*e/625 + 867*e**2/6250 + sqrt(14)*I*(32825*d**2 + 211710*d*e - 73881*e**2)/2450000)*log(x + (6565*d**2 + 42342*d*e - 73881*e**2/5 + sqrt(14)*I*(32825*d**2 + 211710*d*e - 73881*e**2)/5)/(32825*d**2 + 211710*d*e - 73881*e**2)) + (-34175*d**2 + 12690*d*e + 17967*e**2 + x*(-10575*d**2 - 59890*d*e + 18323*e**2))/(437500*x**2 + 175000*x + 262500)","C",0
313,1,165,0,1.022711," ","integrate((e*x+d)*(4*x**4-5*x**3+3*x**2+x+2)/(5*x**2+2*x+3)**2,x)","\frac{2 e x^{2}}{25} + x \left(\frac{4 d}{25} - \frac{41 e}{125}\right) + \frac{- 6835 d + 1269 e + x \left(- 2115 d - 5989 e\right)}{87500 x^{2} + 35000 x + 52500} + \left(- \frac{41 d}{250} + \frac{103 e}{1250} - \frac{\sqrt{14} i \left(6565 d + 21171 e\right)}{490000}\right) \log{\left(x + \frac{1313 d + \frac{21171 e}{5} - \frac{\sqrt{14} i \left(6565 d + 21171 e\right)}{5}}{6565 d + 21171 e} \right)} + \left(- \frac{41 d}{250} + \frac{103 e}{1250} + \frac{\sqrt{14} i \left(6565 d + 21171 e\right)}{490000}\right) \log{\left(x + \frac{1313 d + \frac{21171 e}{5} + \frac{\sqrt{14} i \left(6565 d + 21171 e\right)}{5}}{6565 d + 21171 e} \right)}"," ",0,"2*e*x**2/25 + x*(4*d/25 - 41*e/125) + (-6835*d + 1269*e + x*(-2115*d - 5989*e))/(87500*x**2 + 35000*x + 52500) + (-41*d/250 + 103*e/1250 - sqrt(14)*I*(6565*d + 21171*e)/490000)*log(x + (1313*d + 21171*e/5 - sqrt(14)*I*(6565*d + 21171*e)/5)/(6565*d + 21171*e)) + (-41*d/250 + 103*e/1250 + sqrt(14)*I*(6565*d + 21171*e)/490000)*log(x + (1313*d + 21171*e/5 + sqrt(14)*I*(6565*d + 21171*e)/5)/(6565*d + 21171*e))","C",0
314,1,65,0,0.191606," ","integrate((4*x**4-5*x**3+3*x**2+x+2)/(5*x**2+2*x+3)**2,x)","\frac{4 x}{25} + \frac{- 423 x - 1367}{17500 x^{2} + 7000 x + 10500} - \frac{41 \log{\left(x^{2} + \frac{2 x}{5} + \frac{3}{5} \right)}}{250} + \frac{1313 \sqrt{14} \operatorname{atan}{\left(\frac{5 \sqrt{14} x}{14} + \frac{\sqrt{14}}{14} \right)}}{49000}"," ",0,"4*x/25 + (-423*x - 1367)/(17500*x**2 + 7000*x + 10500) - 41*log(x**2 + 2*x/5 + 3/5)/250 + 1313*sqrt(14)*atan(5*sqrt(14)*x/14 + sqrt(14)/14)/49000","A",0
315,-1,0,0,0.000000," ","integrate((4*x**4-5*x**3+3*x**2+x+2)/(e*x+d)/(5*x**2+2*x+3)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
316,-1,0,0,0.000000," ","integrate((4*x**4-5*x**3+3*x**2+x+2)/(e*x+d)**2/(5*x**2+2*x+3)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
317,-1,0,0,0.000000," ","integrate((4*x**4-5*x**3+3*x**2+x+2)/(e*x+d)**3/(5*x**2+2*x+3)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
318,1,469,0,8.078353," ","integrate((e*x+d)**3*(4*x**4-5*x**3+3*x**2+x+2)/(5*x**2+2*x+3)**3,x)","\frac{2 e^{3} x^{2}}{125} + x \left(\frac{12 d e^{2}}{125} - \frac{49 e^{3}}{625}\right) + \left(\frac{3 e \left(100 d^{2} - 245 d e + 47 e^{2}\right)}{6250} - \frac{3 \sqrt{14} i \left(353125 d^{3} - 855175 d^{2} e + 74085 d e^{2} + 556349 e^{3}\right)}{137200000}\right) \log{\left(x + \frac{211875 d^{3} - 1830225 d^{2} e + 3271395 d e^{2} - 285237 e^{3} + \frac{65856 e \left(100 d^{2} - 245 d e + 47 e^{2}\right)}{5} - \frac{3 \sqrt{14} i \left(353125 d^{3} - 855175 d^{2} e + 74085 d e^{2} + 556349 e^{3}\right)}{5}}{1059375 d^{3} - 2565525 d^{2} e + 222255 d e^{2} + 1669047 e^{3}} \right)} + \left(\frac{3 e \left(100 d^{2} - 245 d e + 47 e^{2}\right)}{6250} + \frac{3 \sqrt{14} i \left(353125 d^{3} - 855175 d^{2} e + 74085 d e^{2} + 556349 e^{3}\right)}{137200000}\right) \log{\left(x + \frac{211875 d^{3} - 1830225 d^{2} e + 3271395 d e^{2} - 285237 e^{3} + \frac{65856 e \left(100 d^{2} - 245 d e + 47 e^{2}\right)}{5} + \frac{3 \sqrt{14} i \left(353125 d^{3} - 855175 d^{2} e + 74085 d e^{2} + 556349 e^{3}\right)}{5}}{1059375 d^{3} - 2565525 d^{2} e + 222255 d e^{2} + 1669047 e^{3}} \right)} + \frac{1619125 d^{3} - 1464975 d^{2} e - 5773275 d e^{2} + 1275957 e^{3} + x^{3} \left(1376875 d^{3} + 13632375 d^{2} e - 9707925 d e^{2} - 3109005 e^{3}\right) + x^{2} \left(4844125 d^{3} + 2123025 d^{2} e - 16020675 d e^{2} + 1396037 e^{3}\right) + x \left(2247375 d^{3} + 4332075 d^{2} e - 9140625 d e^{2} - 511689 e^{3}\right)}{122500000 x^{4} + 98000000 x^{3} + 166600000 x^{2} + 58800000 x + 44100000}"," ",0,"2*e**3*x**2/125 + x*(12*d*e**2/125 - 49*e**3/625) + (3*e*(100*d**2 - 245*d*e + 47*e**2)/6250 - 3*sqrt(14)*I*(353125*d**3 - 855175*d**2*e + 74085*d*e**2 + 556349*e**3)/137200000)*log(x + (211875*d**3 - 1830225*d**2*e + 3271395*d*e**2 - 285237*e**3 + 65856*e*(100*d**2 - 245*d*e + 47*e**2)/5 - 3*sqrt(14)*I*(353125*d**3 - 855175*d**2*e + 74085*d*e**2 + 556349*e**3)/5)/(1059375*d**3 - 2565525*d**2*e + 222255*d*e**2 + 1669047*e**3)) + (3*e*(100*d**2 - 245*d*e + 47*e**2)/6250 + 3*sqrt(14)*I*(353125*d**3 - 855175*d**2*e + 74085*d*e**2 + 556349*e**3)/137200000)*log(x + (211875*d**3 - 1830225*d**2*e + 3271395*d*e**2 - 285237*e**3 + 65856*e*(100*d**2 - 245*d*e + 47*e**2)/5 + 3*sqrt(14)*I*(353125*d**3 - 855175*d**2*e + 74085*d*e**2 + 556349*e**3)/5)/(1059375*d**3 - 2565525*d**2*e + 222255*d*e**2 + 1669047*e**3)) + (1619125*d**3 - 1464975*d**2*e - 5773275*d*e**2 + 1275957*e**3 + x**3*(1376875*d**3 + 13632375*d**2*e - 9707925*d*e**2 - 3109005*e**3) + x**2*(4844125*d**3 + 2123025*d**2*e - 16020675*d*e**2 + 1396037*e**3) + x*(2247375*d**3 + 4332075*d**2*e - 9140625*d*e**2 - 511689*e**3))/(122500000*x**4 + 98000000*x**3 + 166600000*x**2 + 58800000*x + 44100000)","C",0
319,1,304,0,3.963131," ","integrate((e*x+d)**2*(4*x**4-5*x**3+3*x**2+x+2)/(5*x**2+2*x+3)**3,x)","\frac{4 e^{2} x}{125} + \left(\frac{e \left(40 d - 49 e\right)}{1250} - \frac{\sqrt{14} i \left(211875 d^{2} - 342070 d e + 14817 e^{2}\right)}{27440000}\right) \log{\left(x + \frac{42375 d^{2} - 244030 d e + 218093 e^{2} + \frac{21952 e \left(40 d - 49 e\right)}{5} - \frac{\sqrt{14} i \left(211875 d^{2} - 342070 d e + 14817 e^{2}\right)}{5}}{211875 d^{2} - 342070 d e + 14817 e^{2}} \right)} + \left(\frac{e \left(40 d - 49 e\right)}{1250} + \frac{\sqrt{14} i \left(211875 d^{2} - 342070 d e + 14817 e^{2}\right)}{27440000}\right) \log{\left(x + \frac{42375 d^{2} - 244030 d e + 218093 e^{2} + \frac{21952 e \left(40 d - 49 e\right)}{5} + \frac{\sqrt{14} i \left(211875 d^{2} - 342070 d e + 14817 e^{2}\right)}{5}}{211875 d^{2} - 342070 d e + 14817 e^{2}} \right)} + \frac{64765 d^{2} - 39066 d e - 76977 e^{2} + x^{3} \left(55075 d^{2} + 363530 d e - 129439 e^{2}\right) + x^{2} \left(193765 d^{2} + 56614 d e - 213609 e^{2}\right) + x \left(89895 d^{2} + 115522 d e - 121875 e^{2}\right)}{4900000 x^{4} + 3920000 x^{3} + 6664000 x^{2} + 2352000 x + 1764000}"," ",0,"4*e**2*x/125 + (e*(40*d - 49*e)/1250 - sqrt(14)*I*(211875*d**2 - 342070*d*e + 14817*e**2)/27440000)*log(x + (42375*d**2 - 244030*d*e + 218093*e**2 + 21952*e*(40*d - 49*e)/5 - sqrt(14)*I*(211875*d**2 - 342070*d*e + 14817*e**2)/5)/(211875*d**2 - 342070*d*e + 14817*e**2)) + (e*(40*d - 49*e)/1250 + sqrt(14)*I*(211875*d**2 - 342070*d*e + 14817*e**2)/27440000)*log(x + (42375*d**2 - 244030*d*e + 218093*e**2 + 21952*e*(40*d - 49*e)/5 + sqrt(14)*I*(211875*d**2 - 342070*d*e + 14817*e**2)/5)/(211875*d**2 - 342070*d*e + 14817*e**2)) + (64765*d**2 - 39066*d*e - 76977*e**2 + x**3*(55075*d**2 + 363530*d*e - 129439*e**2) + x**2*(193765*d**2 + 56614*d*e - 213609*e**2) + x*(89895*d**2 + 115522*d*e - 121875*e**2))/(4900000*x**4 + 3920000*x**3 + 6664000*x**2 + 2352000*x + 1764000)","C",0
320,1,163,0,2.310704," ","integrate((e*x+d)*(4*x**4-5*x**3+3*x**2+x+2)/(5*x**2+2*x+3)**3,x)","\left(\frac{2 e}{125} - \frac{\sqrt{14} i \left(42375 d - 34207 e\right)}{5488000}\right) \log{\left(x + \frac{8475 d - \frac{34207 e}{5} - \frac{\sqrt{14} i \left(42375 d - 34207 e\right)}{5}}{42375 d - 34207 e} \right)} + \left(\frac{2 e}{125} + \frac{\sqrt{14} i \left(42375 d - 34207 e\right)}{5488000}\right) \log{\left(x + \frac{8475 d - \frac{34207 e}{5} + \frac{\sqrt{14} i \left(42375 d - 34207 e\right)}{5}}{42375 d - 34207 e} \right)} + \frac{64765 d - 19533 e + x^{3} \left(55075 d + 181765 e\right) + x^{2} \left(193765 d + 28307 e\right) + x \left(89895 d + 57761 e\right)}{4900000 x^{4} + 3920000 x^{3} + 6664000 x^{2} + 2352000 x + 1764000}"," ",0,"(2*e/125 - sqrt(14)*I*(42375*d - 34207*e)/5488000)*log(x + (8475*d - 34207*e/5 - sqrt(14)*I*(42375*d - 34207*e)/5)/(42375*d - 34207*e)) + (2*e/125 + sqrt(14)*I*(42375*d - 34207*e)/5488000)*log(x + (8475*d - 34207*e/5 + sqrt(14)*I*(42375*d - 34207*e)/5)/(42375*d - 34207*e)) + (64765*d - 19533*e + x**3*(55075*d + 181765*e) + x**2*(193765*d + 28307*e) + x*(89895*d + 57761*e))/(4900000*x**4 + 3920000*x**3 + 6664000*x**2 + 2352000*x + 1764000)","C",0
321,1,61,0,0.200866," ","integrate((4*x**4-5*x**3+3*x**2+x+2)/(5*x**2+2*x+3)**3,x)","\frac{11015 x^{3} + 38753 x^{2} + 17979 x + 12953}{980000 x^{4} + 784000 x^{3} + 1332800 x^{2} + 470400 x + 352800} + \frac{339 \sqrt{14} \operatorname{atan}{\left(\frac{5 \sqrt{14} x}{14} + \frac{\sqrt{14}}{14} \right)}}{21952}"," ",0,"(11015*x**3 + 38753*x**2 + 17979*x + 12953)/(980000*x**4 + 784000*x**3 + 1332800*x**2 + 470400*x + 352800) + 339*sqrt(14)*atan(5*sqrt(14)*x/14 + sqrt(14)/14)/21952","A",0
322,-1,0,0,0.000000," ","integrate((4*x**4-5*x**3+3*x**2+x+2)/(e*x+d)/(5*x**2+2*x+3)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
323,-1,0,0,0.000000," ","integrate((4*x**4-5*x**3+3*x**2+x+2)/(e*x+d)**2/(5*x**2+2*x+3)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
324,0,0,0,0.000000," ","integrate((5+2*x)*(5*x**4-x**3+3*x**2+x+2)*(2*x**2-x+3)**(1/2),x)","\int \left(2 x + 5\right) \sqrt{2 x^{2} - x + 3} \left(5 x^{4} - x^{3} + 3 x^{2} + x + 2\right)\, dx"," ",0,"Integral((2*x + 5)*sqrt(2*x**2 - x + 3)*(5*x**4 - x**3 + 3*x**2 + x + 2), x)","F",0
325,0,0,0,0.000000," ","integrate((5*x**4-x**3+3*x**2+x+2)*(2*x**2-x+3)**(1/2),x)","\int \sqrt{2 x^{2} - x + 3} \left(5 x^{4} - x^{3} + 3 x^{2} + x + 2\right)\, dx"," ",0,"Integral(sqrt(2*x**2 - x + 3)*(5*x**4 - x**3 + 3*x**2 + x + 2), x)","F",0
326,0,0,0,0.000000," ","integrate((5*x**4-x**3+3*x**2+x+2)*(2*x**2-x+3)**(1/2)/(5+2*x),x)","\int \frac{\sqrt{2 x^{2} - x + 3} \left(5 x^{4} - x^{3} + 3 x^{2} + x + 2\right)}{2 x + 5}\, dx"," ",0,"Integral(sqrt(2*x**2 - x + 3)*(5*x**4 - x**3 + 3*x**2 + x + 2)/(2*x + 5), x)","F",0
327,0,0,0,0.000000," ","integrate((5*x**4-x**3+3*x**2+x+2)*(2*x**2-x+3)**(1/2)/(5+2*x)**2,x)","\int \frac{\sqrt{2 x^{2} - x + 3} \left(5 x^{4} - x^{3} + 3 x^{2} + x + 2\right)}{\left(2 x + 5\right)^{2}}\, dx"," ",0,"Integral(sqrt(2*x**2 - x + 3)*(5*x**4 - x**3 + 3*x**2 + x + 2)/(2*x + 5)**2, x)","F",0
328,0,0,0,0.000000," ","integrate((5*x**4-x**3+3*x**2+x+2)*(2*x**2-x+3)**(1/2)/(5+2*x)**3,x)","\int \frac{\sqrt{2 x^{2} - x + 3} \left(5 x^{4} - x^{3} + 3 x^{2} + x + 2\right)}{\left(2 x + 5\right)^{3}}\, dx"," ",0,"Integral(sqrt(2*x**2 - x + 3)*(5*x**4 - x**3 + 3*x**2 + x + 2)/(2*x + 5)**3, x)","F",0
329,0,0,0,0.000000," ","integrate((5*x**4-x**3+3*x**2+x+2)*(2*x**2-x+3)**(1/2)/(5+2*x)**4,x)","\int \frac{\sqrt{2 x^{2} - x + 3} \left(5 x^{4} - x^{3} + 3 x^{2} + x + 2\right)}{\left(2 x + 5\right)^{4}}\, dx"," ",0,"Integral(sqrt(2*x**2 - x + 3)*(5*x**4 - x**3 + 3*x**2 + x + 2)/(2*x + 5)**4, x)","F",0
330,0,0,0,0.000000," ","integrate((5*x**4-x**3+3*x**2+x+2)*(2*x**2-x+3)**(1/2)/(5+2*x)**5,x)","\int \frac{\sqrt{2 x^{2} - x + 3} \left(5 x^{4} - x^{3} + 3 x^{2} + x + 2\right)}{\left(2 x + 5\right)^{5}}\, dx"," ",0,"Integral(sqrt(2*x**2 - x + 3)*(5*x**4 - x**3 + 3*x**2 + x + 2)/(2*x + 5)**5, x)","F",0
331,0,0,0,0.000000," ","integrate((5*x**4-x**3+3*x**2+x+2)*(2*x**2-x+3)**(1/2)/(5+2*x)**6,x)","\int \frac{\sqrt{2 x^{2} - x + 3} \left(5 x^{4} - x^{3} + 3 x^{2} + x + 2\right)}{\left(2 x + 5\right)^{6}}\, dx"," ",0,"Integral(sqrt(2*x**2 - x + 3)*(5*x**4 - x**3 + 3*x**2 + x + 2)/(2*x + 5)**6, x)","F",0
332,0,0,0,0.000000," ","integrate((5*x**4-x**3+3*x**2+x+2)*(2*x**2-x+3)**(1/2)/(5+2*x)**7,x)","\int \frac{\sqrt{2 x^{2} - x + 3} \left(5 x^{4} - x^{3} + 3 x^{2} + x + 2\right)}{\left(2 x + 5\right)^{7}}\, dx"," ",0,"Integral(sqrt(2*x**2 - x + 3)*(5*x**4 - x**3 + 3*x**2 + x + 2)/(2*x + 5)**7, x)","F",0
333,0,0,0,0.000000," ","integrate((5*x**4-x**3+3*x**2+x+2)*(2*x**2-x+3)**(1/2)/(5+2*x)**8,x)","\int \frac{\sqrt{2 x^{2} - x + 3} \left(5 x^{4} - x^{3} + 3 x^{2} + x + 2\right)}{\left(2 x + 5\right)^{8}}\, dx"," ",0,"Integral(sqrt(2*x**2 - x + 3)*(5*x**4 - x**3 + 3*x**2 + x + 2)/(2*x + 5)**8, x)","F",0
334,0,0,0,0.000000," ","integrate((5+2*x)*(2*x**2-x+3)**(3/2)*(5*x**4-x**3+3*x**2+x+2),x)","\int \left(2 x + 5\right) \left(2 x^{2} - x + 3\right)^{\frac{3}{2}} \left(5 x^{4} - x^{3} + 3 x^{2} + x + 2\right)\, dx"," ",0,"Integral((2*x + 5)*(2*x**2 - x + 3)**(3/2)*(5*x**4 - x**3 + 3*x**2 + x + 2), x)","F",0
335,0,0,0,0.000000," ","integrate((2*x**2-x+3)**(3/2)*(5*x**4-x**3+3*x**2+x+2),x)","\int \left(2 x^{2} - x + 3\right)^{\frac{3}{2}} \left(5 x^{4} - x^{3} + 3 x^{2} + x + 2\right)\, dx"," ",0,"Integral((2*x**2 - x + 3)**(3/2)*(5*x**4 - x**3 + 3*x**2 + x + 2), x)","F",0
336,0,0,0,0.000000," ","integrate((2*x**2-x+3)**(3/2)*(5*x**4-x**3+3*x**2+x+2)/(5+2*x),x)","\int \frac{\left(2 x^{2} - x + 3\right)^{\frac{3}{2}} \left(5 x^{4} - x^{3} + 3 x^{2} + x + 2\right)}{2 x + 5}\, dx"," ",0,"Integral((2*x**2 - x + 3)**(3/2)*(5*x**4 - x**3 + 3*x**2 + x + 2)/(2*x + 5), x)","F",0
337,0,0,0,0.000000," ","integrate((2*x**2-x+3)**(3/2)*(5*x**4-x**3+3*x**2+x+2)/(5+2*x)**2,x)","\int \frac{\left(2 x^{2} - x + 3\right)^{\frac{3}{2}} \left(5 x^{4} - x^{3} + 3 x^{2} + x + 2\right)}{\left(2 x + 5\right)^{2}}\, dx"," ",0,"Integral((2*x**2 - x + 3)**(3/2)*(5*x**4 - x**3 + 3*x**2 + x + 2)/(2*x + 5)**2, x)","F",0
338,0,0,0,0.000000," ","integrate((2*x**2-x+3)**(3/2)*(5*x**4-x**3+3*x**2+x+2)/(5+2*x)**3,x)","\int \frac{\left(2 x^{2} - x + 3\right)^{\frac{3}{2}} \left(5 x^{4} - x^{3} + 3 x^{2} + x + 2\right)}{\left(2 x + 5\right)^{3}}\, dx"," ",0,"Integral((2*x**2 - x + 3)**(3/2)*(5*x**4 - x**3 + 3*x**2 + x + 2)/(2*x + 5)**3, x)","F",0
339,0,0,0,0.000000," ","integrate((2*x**2-x+3)**(3/2)*(5*x**4-x**3+3*x**2+x+2)/(5+2*x)**4,x)","\int \frac{\left(2 x^{2} - x + 3\right)^{\frac{3}{2}} \left(5 x^{4} - x^{3} + 3 x^{2} + x + 2\right)}{\left(2 x + 5\right)^{4}}\, dx"," ",0,"Integral((2*x**2 - x + 3)**(3/2)*(5*x**4 - x**3 + 3*x**2 + x + 2)/(2*x + 5)**4, x)","F",0
340,0,0,0,0.000000," ","integrate((2*x**2-x+3)**(3/2)*(5*x**4-x**3+3*x**2+x+2)/(5+2*x)**5,x)","\int \frac{\left(2 x^{2} - x + 3\right)^{\frac{3}{2}} \left(5 x^{4} - x^{3} + 3 x^{2} + x + 2\right)}{\left(2 x + 5\right)^{5}}\, dx"," ",0,"Integral((2*x**2 - x + 3)**(3/2)*(5*x**4 - x**3 + 3*x**2 + x + 2)/(2*x + 5)**5, x)","F",0
341,0,0,0,0.000000," ","integrate((2*x**2-x+3)**(3/2)*(5*x**4-x**3+3*x**2+x+2)/(5+2*x)**6,x)","\int \frac{\left(2 x^{2} - x + 3\right)^{\frac{3}{2}} \left(5 x^{4} - x^{3} + 3 x^{2} + x + 2\right)}{\left(2 x + 5\right)^{6}}\, dx"," ",0,"Integral((2*x**2 - x + 3)**(3/2)*(5*x**4 - x**3 + 3*x**2 + x + 2)/(2*x + 5)**6, x)","F",0
342,0,0,0,0.000000," ","integrate((2*x**2-x+3)**(3/2)*(5*x**4-x**3+3*x**2+x+2)/(5+2*x)**7,x)","\int \frac{\left(2 x^{2} - x + 3\right)^{\frac{3}{2}} \left(5 x^{4} - x^{3} + 3 x^{2} + x + 2\right)}{\left(2 x + 5\right)^{7}}\, dx"," ",0,"Integral((2*x**2 - x + 3)**(3/2)*(5*x**4 - x**3 + 3*x**2 + x + 2)/(2*x + 5)**7, x)","F",0
343,0,0,0,0.000000," ","integrate((2*x**2-x+3)**(3/2)*(5*x**4-x**3+3*x**2+x+2)/(5+2*x)**8,x)","\int \frac{\left(2 x^{2} - x + 3\right)^{\frac{3}{2}} \left(5 x^{4} - x^{3} + 3 x^{2} + x + 2\right)}{\left(2 x + 5\right)^{8}}\, dx"," ",0,"Integral((2*x**2 - x + 3)**(3/2)*(5*x**4 - x**3 + 3*x**2 + x + 2)/(2*x + 5)**8, x)","F",0
344,0,0,0,0.000000," ","integrate((5+2*x)*(5*x**4-x**3+3*x**2+x+2)/(2*x**2-x+3)**(1/2),x)","\int \frac{\left(2 x + 5\right) \left(5 x^{4} - x^{3} + 3 x^{2} + x + 2\right)}{\sqrt{2 x^{2} - x + 3}}\, dx"," ",0,"Integral((2*x + 5)*(5*x**4 - x**3 + 3*x**2 + x + 2)/sqrt(2*x**2 - x + 3), x)","F",0
345,0,0,0,0.000000," ","integrate((5*x**4-x**3+3*x**2+x+2)/(2*x**2-x+3)**(1/2),x)","\int \frac{5 x^{4} - x^{3} + 3 x^{2} + x + 2}{\sqrt{2 x^{2} - x + 3}}\, dx"," ",0,"Integral((5*x**4 - x**3 + 3*x**2 + x + 2)/sqrt(2*x**2 - x + 3), x)","F",0
346,0,0,0,0.000000," ","integrate((5*x**4-x**3+3*x**2+x+2)/(5+2*x)/(2*x**2-x+3)**(1/2),x)","\int \frac{5 x^{4} - x^{3} + 3 x^{2} + x + 2}{\left(2 x + 5\right) \sqrt{2 x^{2} - x + 3}}\, dx"," ",0,"Integral((5*x**4 - x**3 + 3*x**2 + x + 2)/((2*x + 5)*sqrt(2*x**2 - x + 3)), x)","F",0
347,0,0,0,0.000000," ","integrate((5*x**4-x**3+3*x**2+x+2)/(5+2*x)**2/(2*x**2-x+3)**(1/2),x)","\int \frac{5 x^{4} - x^{3} + 3 x^{2} + x + 2}{\left(2 x + 5\right)^{2} \sqrt{2 x^{2} - x + 3}}\, dx"," ",0,"Integral((5*x**4 - x**3 + 3*x**2 + x + 2)/((2*x + 5)**2*sqrt(2*x**2 - x + 3)), x)","F",0
348,0,0,0,0.000000," ","integrate((5*x**4-x**3+3*x**2+x+2)/(5+2*x)**3/(2*x**2-x+3)**(1/2),x)","\int \frac{5 x^{4} - x^{3} + 3 x^{2} + x + 2}{\left(2 x + 5\right)^{3} \sqrt{2 x^{2} - x + 3}}\, dx"," ",0,"Integral((5*x**4 - x**3 + 3*x**2 + x + 2)/((2*x + 5)**3*sqrt(2*x**2 - x + 3)), x)","F",0
349,0,0,0,0.000000," ","integrate((5*x**4-x**3+3*x**2+x+2)/(5+2*x)**4/(2*x**2-x+3)**(1/2),x)","\int \frac{5 x^{4} - x^{3} + 3 x^{2} + x + 2}{\left(2 x + 5\right)^{4} \sqrt{2 x^{2} - x + 3}}\, dx"," ",0,"Integral((5*x**4 - x**3 + 3*x**2 + x + 2)/((2*x + 5)**4*sqrt(2*x**2 - x + 3)), x)","F",0
350,0,0,0,0.000000," ","integrate((5*x**4-x**3+3*x**2+x+2)/(5+2*x)**5/(2*x**2-x+3)**(1/2),x)","\int \frac{5 x^{4} - x^{3} + 3 x^{2} + x + 2}{\left(2 x + 5\right)^{5} \sqrt{2 x^{2} - x + 3}}\, dx"," ",0,"Integral((5*x**4 - x**3 + 3*x**2 + x + 2)/((2*x + 5)**5*sqrt(2*x**2 - x + 3)), x)","F",0
351,0,0,0,0.000000," ","integrate((5+2*x)**2*(5*x**4-x**3+3*x**2+x+2)/(2*x**2-x+3)**(3/2),x)","\int \frac{\left(2 x + 5\right)^{2} \left(5 x^{4} - x^{3} + 3 x^{2} + x + 2\right)}{\left(2 x^{2} - x + 3\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((2*x + 5)**2*(5*x**4 - x**3 + 3*x**2 + x + 2)/(2*x**2 - x + 3)**(3/2), x)","F",0
352,0,0,0,0.000000," ","integrate((5+2*x)*(5*x**4-x**3+3*x**2+x+2)/(2*x**2-x+3)**(3/2),x)","\int \frac{\left(2 x + 5\right) \left(5 x^{4} - x^{3} + 3 x^{2} + x + 2\right)}{\left(2 x^{2} - x + 3\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((2*x + 5)*(5*x**4 - x**3 + 3*x**2 + x + 2)/(2*x**2 - x + 3)**(3/2), x)","F",0
353,0,0,0,0.000000," ","integrate((5*x**4-x**3+3*x**2+x+2)/(2*x**2-x+3)**(3/2),x)","\int \frac{5 x^{4} - x^{3} + 3 x^{2} + x + 2}{\left(2 x^{2} - x + 3\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((5*x**4 - x**3 + 3*x**2 + x + 2)/(2*x**2 - x + 3)**(3/2), x)","F",0
354,0,0,0,0.000000," ","integrate((5*x**4-x**3+3*x**2+x+2)/(5+2*x)/(2*x**2-x+3)**(3/2),x)","\int \frac{5 x^{4} - x^{3} + 3 x^{2} + x + 2}{\left(2 x + 5\right) \left(2 x^{2} - x + 3\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((5*x**4 - x**3 + 3*x**2 + x + 2)/((2*x + 5)*(2*x**2 - x + 3)**(3/2)), x)","F",0
355,0,0,0,0.000000," ","integrate((5*x**4-x**3+3*x**2+x+2)/(5+2*x)**2/(2*x**2-x+3)**(3/2),x)","\int \frac{5 x^{4} - x^{3} + 3 x^{2} + x + 2}{\left(2 x + 5\right)^{2} \left(2 x^{2} - x + 3\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((5*x**4 - x**3 + 3*x**2 + x + 2)/((2*x + 5)**2*(2*x**2 - x + 3)**(3/2)), x)","F",0
356,0,0,0,0.000000," ","integrate((5*x**4-x**3+3*x**2+x+2)/(5+2*x)**3/(2*x**2-x+3)**(3/2),x)","\int \frac{5 x^{4} - x^{3} + 3 x^{2} + x + 2}{\left(2 x + 5\right)^{3} \left(2 x^{2} - x + 3\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((5*x**4 - x**3 + 3*x**2 + x + 2)/((2*x + 5)**3*(2*x**2 - x + 3)**(3/2)), x)","F",0
357,0,0,0,0.000000," ","integrate((5*x**4-x**3+3*x**2+x+2)/(5+2*x)**4/(2*x**2-x+3)**(3/2),x)","\int \frac{5 x^{4} - x^{3} + 3 x^{2} + x + 2}{\left(2 x + 5\right)^{4} \left(2 x^{2} - x + 3\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((5*x**4 - x**3 + 3*x**2 + x + 2)/((2*x + 5)**4*(2*x**2 - x + 3)**(3/2)), x)","F",0
358,0,0,0,0.000000," ","integrate((5+2*x)**2*(5*x**4-x**3+3*x**2+x+2)/(2*x**2-x+3)**(5/2),x)","\int \frac{\left(2 x + 5\right)^{2} \left(5 x^{4} - x^{3} + 3 x^{2} + x + 2\right)}{\left(2 x^{2} - x + 3\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((2*x + 5)**2*(5*x**4 - x**3 + 3*x**2 + x + 2)/(2*x**2 - x + 3)**(5/2), x)","F",0
359,0,0,0,0.000000," ","integrate((5+2*x)*(5*x**4-x**3+3*x**2+x+2)/(2*x**2-x+3)**(5/2),x)","\int \frac{\left(2 x + 5\right) \left(5 x^{4} - x^{3} + 3 x^{2} + x + 2\right)}{\left(2 x^{2} - x + 3\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((2*x + 5)*(5*x**4 - x**3 + 3*x**2 + x + 2)/(2*x**2 - x + 3)**(5/2), x)","F",0
360,0,0,0,0.000000," ","integrate((5*x**4-x**3+3*x**2+x+2)/(2*x**2-x+3)**(5/2),x)","\int \frac{5 x^{4} - x^{3} + 3 x^{2} + x + 2}{\left(2 x^{2} - x + 3\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((5*x**4 - x**3 + 3*x**2 + x + 2)/(2*x**2 - x + 3)**(5/2), x)","F",0
361,0,0,0,0.000000," ","integrate((5*x**4-x**3+3*x**2+x+2)/(5+2*x)/(2*x**2-x+3)**(5/2),x)","\int \frac{5 x^{4} - x^{3} + 3 x^{2} + x + 2}{\left(2 x + 5\right) \left(2 x^{2} - x + 3\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((5*x**4 - x**3 + 3*x**2 + x + 2)/((2*x + 5)*(2*x**2 - x + 3)**(5/2)), x)","F",0
362,0,0,0,0.000000," ","integrate((5*x**4-x**3+3*x**2+x+2)/(5+2*x)**2/(2*x**2-x+3)**(5/2),x)","\int \frac{5 x^{4} - x^{3} + 3 x^{2} + x + 2}{\left(2 x + 5\right)^{2} \left(2 x^{2} - x + 3\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((5*x**4 - x**3 + 3*x**2 + x + 2)/((2*x + 5)**2*(2*x**2 - x + 3)**(5/2)), x)","F",0
363,0,0,0,0.000000," ","integrate((5*x**4-x**3+3*x**2+x+2)/(5+2*x)**3/(2*x**2-x+3)**(5/2),x)","\int \frac{5 x^{4} - x^{3} + 3 x^{2} + x + 2}{\left(2 x + 5\right)^{3} \left(2 x^{2} - x + 3\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((5*x**4 - x**3 + 3*x**2 + x + 2)/((2*x + 5)**3*(2*x**2 - x + 3)**(5/2)), x)","F",0
364,0,0,0,0.000000," ","integrate((5*x**4-x**3+3*x**2+x+2)/(5+2*x)**4/(2*x**2-x+3)**(5/2),x)","\int \frac{5 x^{4} - x^{3} + 3 x^{2} + x + 2}{\left(2 x + 5\right)^{4} \left(2 x^{2} - x + 3\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((5*x**4 - x**3 + 3*x**2 + x + 2)/((2*x + 5)**4*(2*x**2 - x + 3)**(5/2)), x)","F",0
365,-1,0,0,0.000000," ","integrate((j*x**4+i*x**3+h*x**2+g*x+f)/(c*x**2+b*x+a)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
366,-1,0,0,0.000000," ","integrate((j*x**4+i*x**3+h*x**2+g*x+f)/(-c*x**2+b*x+a)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
367,-1,0,0,0.000000," ","integrate((e*x+d)**m*(5*x**2+2*x+3)**3*(4*x**4-5*x**3+3*x**2+x+2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
368,-1,0,0,0.000000," ","integrate((e*x+d)**m*(5*x**2+2*x+3)**2*(4*x**4-5*x**3+3*x**2+x+2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
369,-1,0,0,0.000000," ","integrate((e*x+d)**m*(5*x**2+2*x+3)*(4*x**4-5*x**3+3*x**2+x+2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
370,-1,0,0,0.000000," ","integrate((e*x+d)**m*(4*x**4-5*x**3+3*x**2+x+2)/(5*x**2+2*x+3),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
371,-1,0,0,0.000000," ","integrate((e*x+d)**m*(4*x**4-5*x**3+3*x**2+x+2)/(5*x**2+2*x+3)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
372,-1,0,0,0.000000," ","integrate((i*x**5+h*x**4+g*x**3+f*x**2+e*x+d)/(c*x**2+b*x+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
373,-1,0,0,0.000000," ","integrate((m*x**8+l*x**7+k*x**6+j*x**5+h*x**4+g*x**3+f*x**2+e*x+d)/(c*x**2+b*x+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
374,0,0,0,0.000000," ","integrate((-7*x**2+4*x+1)**3*(x**2+5*x+2)*(5*x**2+2*x+3)**(1/2),x)","- \int \left(- 29 x \sqrt{5 x^{2} + 2 x + 3}\right)\, dx - \int \left(- 115 x^{2} \sqrt{5 x^{2} + 2 x + 3}\right)\, dx - \int 61 x^{3} \sqrt{5 x^{2} + 2 x + 3}\, dx - \int 871 x^{4} \sqrt{5 x^{2} + 2 x + 3}\, dx - \int \left(- 127 x^{5} \sqrt{5 x^{2} + 2 x + 3}\right)\, dx - \int \left(- 2065 x^{6} \sqrt{5 x^{2} + 2 x + 3}\right)\, dx - \int 1127 x^{7} \sqrt{5 x^{2} + 2 x + 3}\, dx - \int 343 x^{8} \sqrt{5 x^{2} + 2 x + 3}\, dx - \int \left(- 2 \sqrt{5 x^{2} + 2 x + 3}\right)\, dx"," ",0,"-Integral(-29*x*sqrt(5*x**2 + 2*x + 3), x) - Integral(-115*x**2*sqrt(5*x**2 + 2*x + 3), x) - Integral(61*x**3*sqrt(5*x**2 + 2*x + 3), x) - Integral(871*x**4*sqrt(5*x**2 + 2*x + 3), x) - Integral(-127*x**5*sqrt(5*x**2 + 2*x + 3), x) - Integral(-2065*x**6*sqrt(5*x**2 + 2*x + 3), x) - Integral(1127*x**7*sqrt(5*x**2 + 2*x + 3), x) - Integral(343*x**8*sqrt(5*x**2 + 2*x + 3), x) - Integral(-2*sqrt(5*x**2 + 2*x + 3), x)","F",0
375,0,0,0,0.000000," ","integrate((-7*x**2+4*x+1)**2*(x**2+5*x+2)*(5*x**2+2*x+3)**(1/2),x)","\int \left(x^{2} + 5 x + 2\right) \sqrt{5 x^{2} + 2 x + 3} \left(7 x^{2} - 4 x - 1\right)^{2}\, dx"," ",0,"Integral((x**2 + 5*x + 2)*sqrt(5*x**2 + 2*x + 3)*(7*x**2 - 4*x - 1)**2, x)","F",0
376,0,0,0,0.000000," ","integrate((-7*x**2+4*x+1)*(x**2+5*x+2)*(5*x**2+2*x+3)**(1/2),x)","- \int \left(- 13 x \sqrt{5 x^{2} + 2 x + 3}\right)\, dx - \int \left(- 7 x^{2} \sqrt{5 x^{2} + 2 x + 3}\right)\, dx - \int 31 x^{3} \sqrt{5 x^{2} + 2 x + 3}\, dx - \int 7 x^{4} \sqrt{5 x^{2} + 2 x + 3}\, dx - \int \left(- 2 \sqrt{5 x^{2} + 2 x + 3}\right)\, dx"," ",0,"-Integral(-13*x*sqrt(5*x**2 + 2*x + 3), x) - Integral(-7*x**2*sqrt(5*x**2 + 2*x + 3), x) - Integral(31*x**3*sqrt(5*x**2 + 2*x + 3), x) - Integral(7*x**4*sqrt(5*x**2 + 2*x + 3), x) - Integral(-2*sqrt(5*x**2 + 2*x + 3), x)","F",0
377,0,0,0,0.000000," ","integrate((x**2+5*x+2)*(5*x**2+2*x+3)**(1/2)/(-7*x**2+4*x+1),x)","- \int \frac{2 \sqrt{5 x^{2} + 2 x + 3}}{7 x^{2} - 4 x - 1}\, dx - \int \frac{5 x \sqrt{5 x^{2} + 2 x + 3}}{7 x^{2} - 4 x - 1}\, dx - \int \frac{x^{2} \sqrt{5 x^{2} + 2 x + 3}}{7 x^{2} - 4 x - 1}\, dx"," ",0,"-Integral(2*sqrt(5*x**2 + 2*x + 3)/(7*x**2 - 4*x - 1), x) - Integral(5*x*sqrt(5*x**2 + 2*x + 3)/(7*x**2 - 4*x - 1), x) - Integral(x**2*sqrt(5*x**2 + 2*x + 3)/(7*x**2 - 4*x - 1), x)","F",0
378,0,0,0,0.000000," ","integrate((x**2+5*x+2)*(5*x**2+2*x+3)**(1/2)/(-7*x**2+4*x+1)**2,x)","\int \frac{\left(x^{2} + 5 x + 2\right) \sqrt{5 x^{2} + 2 x + 3}}{\left(7 x^{2} - 4 x - 1\right)^{2}}\, dx"," ",0,"Integral((x**2 + 5*x + 2)*sqrt(5*x**2 + 2*x + 3)/(7*x**2 - 4*x - 1)**2, x)","F",0
379,0,0,0,0.000000," ","integrate((x**2+5*x+2)*(5*x**2+2*x+3)**(1/2)/(-7*x**2+4*x+1)**3,x)","- \int \frac{2 \sqrt{5 x^{2} + 2 x + 3}}{343 x^{6} - 588 x^{5} + 189 x^{4} + 104 x^{3} - 27 x^{2} - 12 x - 1}\, dx - \int \frac{5 x \sqrt{5 x^{2} + 2 x + 3}}{343 x^{6} - 588 x^{5} + 189 x^{4} + 104 x^{3} - 27 x^{2} - 12 x - 1}\, dx - \int \frac{x^{2} \sqrt{5 x^{2} + 2 x + 3}}{343 x^{6} - 588 x^{5} + 189 x^{4} + 104 x^{3} - 27 x^{2} - 12 x - 1}\, dx"," ",0,"-Integral(2*sqrt(5*x**2 + 2*x + 3)/(343*x**6 - 588*x**5 + 189*x**4 + 104*x**3 - 27*x**2 - 12*x - 1), x) - Integral(5*x*sqrt(5*x**2 + 2*x + 3)/(343*x**6 - 588*x**5 + 189*x**4 + 104*x**3 - 27*x**2 - 12*x - 1), x) - Integral(x**2*sqrt(5*x**2 + 2*x + 3)/(343*x**6 - 588*x**5 + 189*x**4 + 104*x**3 - 27*x**2 - 12*x - 1), x)","F",0
380,0,0,0,0.000000," ","integrate((-7*x**2+4*x+1)**3*(x**2+5*x+2)*(5*x**2+2*x+3)**(3/2),x)","- \int \left(- 91 x \sqrt{5 x^{2} + 2 x + 3}\right)\, dx - \int \left(- 413 x^{2} \sqrt{5 x^{2} + 2 x + 3}\right)\, dx - \int \left(- 192 x^{3} \sqrt{5 x^{2} + 2 x + 3}\right)\, dx - \int 2160 x^{4} \sqrt{5 x^{2} + 2 x + 3}\, dx - \int 1666 x^{5} \sqrt{5 x^{2} + 2 x + 3}\, dx - \int \left(- 2094 x^{6} \sqrt{5 x^{2} + 2 x + 3}\right)\, dx - \int \left(- 1384 x^{7} \sqrt{5 x^{2} + 2 x + 3}\right)\, dx - \int \left(- 7042 x^{8} \sqrt{5 x^{2} + 2 x + 3}\right)\, dx - \int 6321 x^{9} \sqrt{5 x^{2} + 2 x + 3}\, dx - \int 1715 x^{10} \sqrt{5 x^{2} + 2 x + 3}\, dx - \int \left(- 6 \sqrt{5 x^{2} + 2 x + 3}\right)\, dx"," ",0,"-Integral(-91*x*sqrt(5*x**2 + 2*x + 3), x) - Integral(-413*x**2*sqrt(5*x**2 + 2*x + 3), x) - Integral(-192*x**3*sqrt(5*x**2 + 2*x + 3), x) - Integral(2160*x**4*sqrt(5*x**2 + 2*x + 3), x) - Integral(1666*x**5*sqrt(5*x**2 + 2*x + 3), x) - Integral(-2094*x**6*sqrt(5*x**2 + 2*x + 3), x) - Integral(-1384*x**7*sqrt(5*x**2 + 2*x + 3), x) - Integral(-7042*x**8*sqrt(5*x**2 + 2*x + 3), x) - Integral(6321*x**9*sqrt(5*x**2 + 2*x + 3), x) - Integral(1715*x**10*sqrt(5*x**2 + 2*x + 3), x) - Integral(-6*sqrt(5*x**2 + 2*x + 3), x)","F",0
381,0,0,0,0.000000," ","integrate((-7*x**2+4*x+1)**2*(x**2+5*x+2)*(5*x**2+2*x+3)**(3/2),x)","\int \left(x^{2} + 5 x + 2\right) \left(5 x^{2} + 2 x + 3\right)^{\frac{3}{2}} \left(7 x^{2} - 4 x - 1\right)^{2}\, dx"," ",0,"Integral((x**2 + 5*x + 2)*(5*x**2 + 2*x + 3)**(3/2)*(7*x**2 - 4*x - 1)**2, x)","F",0
382,0,0,0,0.000000," ","integrate((-7*x**2+4*x+1)*(x**2+5*x+2)*(5*x**2+2*x+3)**(3/2),x)","- \int \left(- 43 x \sqrt{5 x^{2} + 2 x + 3}\right)\, dx - \int \left(- 57 x^{2} \sqrt{5 x^{2} + 2 x + 3}\right)\, dx - \int 14 x^{3} \sqrt{5 x^{2} + 2 x + 3}\, dx - \int 48 x^{4} \sqrt{5 x^{2} + 2 x + 3}\, dx - \int 169 x^{5} \sqrt{5 x^{2} + 2 x + 3}\, dx - \int 35 x^{6} \sqrt{5 x^{2} + 2 x + 3}\, dx - \int \left(- 6 \sqrt{5 x^{2} + 2 x + 3}\right)\, dx"," ",0,"-Integral(-43*x*sqrt(5*x**2 + 2*x + 3), x) - Integral(-57*x**2*sqrt(5*x**2 + 2*x + 3), x) - Integral(14*x**3*sqrt(5*x**2 + 2*x + 3), x) - Integral(48*x**4*sqrt(5*x**2 + 2*x + 3), x) - Integral(169*x**5*sqrt(5*x**2 + 2*x + 3), x) - Integral(35*x**6*sqrt(5*x**2 + 2*x + 3), x) - Integral(-6*sqrt(5*x**2 + 2*x + 3), x)","F",0
383,0,0,0,0.000000," ","integrate((x**2+5*x+2)*(5*x**2+2*x+3)**(3/2)/(-7*x**2+4*x+1),x)","- \int \frac{6 \sqrt{5 x^{2} + 2 x + 3}}{7 x^{2} - 4 x - 1}\, dx - \int \frac{19 x \sqrt{5 x^{2} + 2 x + 3}}{7 x^{2} - 4 x - 1}\, dx - \int \frac{23 x^{2} \sqrt{5 x^{2} + 2 x + 3}}{7 x^{2} - 4 x - 1}\, dx - \int \frac{27 x^{3} \sqrt{5 x^{2} + 2 x + 3}}{7 x^{2} - 4 x - 1}\, dx - \int \frac{5 x^{4} \sqrt{5 x^{2} + 2 x + 3}}{7 x^{2} - 4 x - 1}\, dx"," ",0,"-Integral(6*sqrt(5*x**2 + 2*x + 3)/(7*x**2 - 4*x - 1), x) - Integral(19*x*sqrt(5*x**2 + 2*x + 3)/(7*x**2 - 4*x - 1), x) - Integral(23*x**2*sqrt(5*x**2 + 2*x + 3)/(7*x**2 - 4*x - 1), x) - Integral(27*x**3*sqrt(5*x**2 + 2*x + 3)/(7*x**2 - 4*x - 1), x) - Integral(5*x**4*sqrt(5*x**2 + 2*x + 3)/(7*x**2 - 4*x - 1), x)","F",0
384,0,0,0,0.000000," ","integrate((x**2+5*x+2)*(5*x**2+2*x+3)**(3/2)/(-7*x**2+4*x+1)**2,x)","\int \frac{\left(x^{2} + 5 x + 2\right) \left(5 x^{2} + 2 x + 3\right)^{\frac{3}{2}}}{\left(7 x^{2} - 4 x - 1\right)^{2}}\, dx"," ",0,"Integral((x**2 + 5*x + 2)*(5*x**2 + 2*x + 3)**(3/2)/(7*x**2 - 4*x - 1)**2, x)","F",0
385,0,0,0,0.000000," ","integrate((x**2+5*x+2)*(5*x**2+2*x+3)**(3/2)/(-7*x**2+4*x+1)**3,x)","- \int \frac{6 \sqrt{5 x^{2} + 2 x + 3}}{343 x^{6} - 588 x^{5} + 189 x^{4} + 104 x^{3} - 27 x^{2} - 12 x - 1}\, dx - \int \frac{19 x \sqrt{5 x^{2} + 2 x + 3}}{343 x^{6} - 588 x^{5} + 189 x^{4} + 104 x^{3} - 27 x^{2} - 12 x - 1}\, dx - \int \frac{23 x^{2} \sqrt{5 x^{2} + 2 x + 3}}{343 x^{6} - 588 x^{5} + 189 x^{4} + 104 x^{3} - 27 x^{2} - 12 x - 1}\, dx - \int \frac{27 x^{3} \sqrt{5 x^{2} + 2 x + 3}}{343 x^{6} - 588 x^{5} + 189 x^{4} + 104 x^{3} - 27 x^{2} - 12 x - 1}\, dx - \int \frac{5 x^{4} \sqrt{5 x^{2} + 2 x + 3}}{343 x^{6} - 588 x^{5} + 189 x^{4} + 104 x^{3} - 27 x^{2} - 12 x - 1}\, dx"," ",0,"-Integral(6*sqrt(5*x**2 + 2*x + 3)/(343*x**6 - 588*x**5 + 189*x**4 + 104*x**3 - 27*x**2 - 12*x - 1), x) - Integral(19*x*sqrt(5*x**2 + 2*x + 3)/(343*x**6 - 588*x**5 + 189*x**4 + 104*x**3 - 27*x**2 - 12*x - 1), x) - Integral(23*x**2*sqrt(5*x**2 + 2*x + 3)/(343*x**6 - 588*x**5 + 189*x**4 + 104*x**3 - 27*x**2 - 12*x - 1), x) - Integral(27*x**3*sqrt(5*x**2 + 2*x + 3)/(343*x**6 - 588*x**5 + 189*x**4 + 104*x**3 - 27*x**2 - 12*x - 1), x) - Integral(5*x**4*sqrt(5*x**2 + 2*x + 3)/(343*x**6 - 588*x**5 + 189*x**4 + 104*x**3 - 27*x**2 - 12*x - 1), x)","F",0
386,0,0,0,0.000000," ","integrate((-7*x**2+4*x+1)**3*(x**2+5*x+2)/(5*x**2+2*x+3)**(1/2),x)","- \int \left(- \frac{29 x}{\sqrt{5 x^{2} + 2 x + 3}}\right)\, dx - \int \left(- \frac{115 x^{2}}{\sqrt{5 x^{2} + 2 x + 3}}\right)\, dx - \int \frac{61 x^{3}}{\sqrt{5 x^{2} + 2 x + 3}}\, dx - \int \frac{871 x^{4}}{\sqrt{5 x^{2} + 2 x + 3}}\, dx - \int \left(- \frac{127 x^{5}}{\sqrt{5 x^{2} + 2 x + 3}}\right)\, dx - \int \left(- \frac{2065 x^{6}}{\sqrt{5 x^{2} + 2 x + 3}}\right)\, dx - \int \frac{1127 x^{7}}{\sqrt{5 x^{2} + 2 x + 3}}\, dx - \int \frac{343 x^{8}}{\sqrt{5 x^{2} + 2 x + 3}}\, dx - \int \left(- \frac{2}{\sqrt{5 x^{2} + 2 x + 3}}\right)\, dx"," ",0,"-Integral(-29*x/sqrt(5*x**2 + 2*x + 3), x) - Integral(-115*x**2/sqrt(5*x**2 + 2*x + 3), x) - Integral(61*x**3/sqrt(5*x**2 + 2*x + 3), x) - Integral(871*x**4/sqrt(5*x**2 + 2*x + 3), x) - Integral(-127*x**5/sqrt(5*x**2 + 2*x + 3), x) - Integral(-2065*x**6/sqrt(5*x**2 + 2*x + 3), x) - Integral(1127*x**7/sqrt(5*x**2 + 2*x + 3), x) - Integral(343*x**8/sqrt(5*x**2 + 2*x + 3), x) - Integral(-2/sqrt(5*x**2 + 2*x + 3), x)","F",0
387,0,0,0,0.000000," ","integrate((-7*x**2+4*x+1)**2*(x**2+5*x+2)/(5*x**2+2*x+3)**(1/2),x)","\int \frac{\left(x^{2} + 5 x + 2\right) \left(7 x^{2} - 4 x - 1\right)^{2}}{\sqrt{5 x^{2} + 2 x + 3}}\, dx"," ",0,"Integral((x**2 + 5*x + 2)*(7*x**2 - 4*x - 1)**2/sqrt(5*x**2 + 2*x + 3), x)","F",0
388,0,0,0,0.000000," ","integrate((-7*x**2+4*x+1)*(x**2+5*x+2)/(5*x**2+2*x+3)**(1/2),x)","- \int \left(- \frac{13 x}{\sqrt{5 x^{2} + 2 x + 3}}\right)\, dx - \int \left(- \frac{7 x^{2}}{\sqrt{5 x^{2} + 2 x + 3}}\right)\, dx - \int \frac{31 x^{3}}{\sqrt{5 x^{2} + 2 x + 3}}\, dx - \int \frac{7 x^{4}}{\sqrt{5 x^{2} + 2 x + 3}}\, dx - \int \left(- \frac{2}{\sqrt{5 x^{2} + 2 x + 3}}\right)\, dx"," ",0,"-Integral(-13*x/sqrt(5*x**2 + 2*x + 3), x) - Integral(-7*x**2/sqrt(5*x**2 + 2*x + 3), x) - Integral(31*x**3/sqrt(5*x**2 + 2*x + 3), x) - Integral(7*x**4/sqrt(5*x**2 + 2*x + 3), x) - Integral(-2/sqrt(5*x**2 + 2*x + 3), x)","F",0
389,0,0,0,0.000000," ","integrate((x**2+5*x+2)/(-7*x**2+4*x+1)/(5*x**2+2*x+3)**(1/2),x)","- \int \frac{5 x}{7 x^{2} \sqrt{5 x^{2} + 2 x + 3} - 4 x \sqrt{5 x^{2} + 2 x + 3} - \sqrt{5 x^{2} + 2 x + 3}}\, dx - \int \frac{x^{2}}{7 x^{2} \sqrt{5 x^{2} + 2 x + 3} - 4 x \sqrt{5 x^{2} + 2 x + 3} - \sqrt{5 x^{2} + 2 x + 3}}\, dx - \int \frac{2}{7 x^{2} \sqrt{5 x^{2} + 2 x + 3} - 4 x \sqrt{5 x^{2} + 2 x + 3} - \sqrt{5 x^{2} + 2 x + 3}}\, dx"," ",0,"-Integral(5*x/(7*x**2*sqrt(5*x**2 + 2*x + 3) - 4*x*sqrt(5*x**2 + 2*x + 3) - sqrt(5*x**2 + 2*x + 3)), x) - Integral(x**2/(7*x**2*sqrt(5*x**2 + 2*x + 3) - 4*x*sqrt(5*x**2 + 2*x + 3) - sqrt(5*x**2 + 2*x + 3)), x) - Integral(2/(7*x**2*sqrt(5*x**2 + 2*x + 3) - 4*x*sqrt(5*x**2 + 2*x + 3) - sqrt(5*x**2 + 2*x + 3)), x)","F",0
390,0,0,0,0.000000," ","integrate((x**2+5*x+2)/(-7*x**2+4*x+1)**2/(5*x**2+2*x+3)**(1/2),x)","\int \frac{x^{2} + 5 x + 2}{\sqrt{5 x^{2} + 2 x + 3} \left(7 x^{2} - 4 x - 1\right)^{2}}\, dx"," ",0,"Integral((x**2 + 5*x + 2)/(sqrt(5*x**2 + 2*x + 3)*(7*x**2 - 4*x - 1)**2), x)","F",0
391,0,0,0,0.000000," ","integrate((x**2+5*x+2)/(-7*x**2+4*x+1)**3/(5*x**2+2*x+3)**(1/2),x)","- \int \frac{5 x}{343 x^{6} \sqrt{5 x^{2} + 2 x + 3} - 588 x^{5} \sqrt{5 x^{2} + 2 x + 3} + 189 x^{4} \sqrt{5 x^{2} + 2 x + 3} + 104 x^{3} \sqrt{5 x^{2} + 2 x + 3} - 27 x^{2} \sqrt{5 x^{2} + 2 x + 3} - 12 x \sqrt{5 x^{2} + 2 x + 3} - \sqrt{5 x^{2} + 2 x + 3}}\, dx - \int \frac{x^{2}}{343 x^{6} \sqrt{5 x^{2} + 2 x + 3} - 588 x^{5} \sqrt{5 x^{2} + 2 x + 3} + 189 x^{4} \sqrt{5 x^{2} + 2 x + 3} + 104 x^{3} \sqrt{5 x^{2} + 2 x + 3} - 27 x^{2} \sqrt{5 x^{2} + 2 x + 3} - 12 x \sqrt{5 x^{2} + 2 x + 3} - \sqrt{5 x^{2} + 2 x + 3}}\, dx - \int \frac{2}{343 x^{6} \sqrt{5 x^{2} + 2 x + 3} - 588 x^{5} \sqrt{5 x^{2} + 2 x + 3} + 189 x^{4} \sqrt{5 x^{2} + 2 x + 3} + 104 x^{3} \sqrt{5 x^{2} + 2 x + 3} - 27 x^{2} \sqrt{5 x^{2} + 2 x + 3} - 12 x \sqrt{5 x^{2} + 2 x + 3} - \sqrt{5 x^{2} + 2 x + 3}}\, dx"," ",0,"-Integral(5*x/(343*x**6*sqrt(5*x**2 + 2*x + 3) - 588*x**5*sqrt(5*x**2 + 2*x + 3) + 189*x**4*sqrt(5*x**2 + 2*x + 3) + 104*x**3*sqrt(5*x**2 + 2*x + 3) - 27*x**2*sqrt(5*x**2 + 2*x + 3) - 12*x*sqrt(5*x**2 + 2*x + 3) - sqrt(5*x**2 + 2*x + 3)), x) - Integral(x**2/(343*x**6*sqrt(5*x**2 + 2*x + 3) - 588*x**5*sqrt(5*x**2 + 2*x + 3) + 189*x**4*sqrt(5*x**2 + 2*x + 3) + 104*x**3*sqrt(5*x**2 + 2*x + 3) - 27*x**2*sqrt(5*x**2 + 2*x + 3) - 12*x*sqrt(5*x**2 + 2*x + 3) - sqrt(5*x**2 + 2*x + 3)), x) - Integral(2/(343*x**6*sqrt(5*x**2 + 2*x + 3) - 588*x**5*sqrt(5*x**2 + 2*x + 3) + 189*x**4*sqrt(5*x**2 + 2*x + 3) + 104*x**3*sqrt(5*x**2 + 2*x + 3) - 27*x**2*sqrt(5*x**2 + 2*x + 3) - 12*x*sqrt(5*x**2 + 2*x + 3) - sqrt(5*x**2 + 2*x + 3)), x)","F",0
392,0,0,0,0.000000," ","integrate((-7*x**2+4*x+1)**3*(x**2+5*x+2)/(5*x**2+2*x+3)**(3/2),x)","- \int \left(- \frac{29 x}{5 x^{2} \sqrt{5 x^{2} + 2 x + 3} + 2 x \sqrt{5 x^{2} + 2 x + 3} + 3 \sqrt{5 x^{2} + 2 x + 3}}\right)\, dx - \int \left(- \frac{115 x^{2}}{5 x^{2} \sqrt{5 x^{2} + 2 x + 3} + 2 x \sqrt{5 x^{2} + 2 x + 3} + 3 \sqrt{5 x^{2} + 2 x + 3}}\right)\, dx - \int \frac{61 x^{3}}{5 x^{2} \sqrt{5 x^{2} + 2 x + 3} + 2 x \sqrt{5 x^{2} + 2 x + 3} + 3 \sqrt{5 x^{2} + 2 x + 3}}\, dx - \int \frac{871 x^{4}}{5 x^{2} \sqrt{5 x^{2} + 2 x + 3} + 2 x \sqrt{5 x^{2} + 2 x + 3} + 3 \sqrt{5 x^{2} + 2 x + 3}}\, dx - \int \left(- \frac{127 x^{5}}{5 x^{2} \sqrt{5 x^{2} + 2 x + 3} + 2 x \sqrt{5 x^{2} + 2 x + 3} + 3 \sqrt{5 x^{2} + 2 x + 3}}\right)\, dx - \int \left(- \frac{2065 x^{6}}{5 x^{2} \sqrt{5 x^{2} + 2 x + 3} + 2 x \sqrt{5 x^{2} + 2 x + 3} + 3 \sqrt{5 x^{2} + 2 x + 3}}\right)\, dx - \int \frac{1127 x^{7}}{5 x^{2} \sqrt{5 x^{2} + 2 x + 3} + 2 x \sqrt{5 x^{2} + 2 x + 3} + 3 \sqrt{5 x^{2} + 2 x + 3}}\, dx - \int \frac{343 x^{8}}{5 x^{2} \sqrt{5 x^{2} + 2 x + 3} + 2 x \sqrt{5 x^{2} + 2 x + 3} + 3 \sqrt{5 x^{2} + 2 x + 3}}\, dx - \int \left(- \frac{2}{5 x^{2} \sqrt{5 x^{2} + 2 x + 3} + 2 x \sqrt{5 x^{2} + 2 x + 3} + 3 \sqrt{5 x^{2} + 2 x + 3}}\right)\, dx"," ",0,"-Integral(-29*x/(5*x**2*sqrt(5*x**2 + 2*x + 3) + 2*x*sqrt(5*x**2 + 2*x + 3) + 3*sqrt(5*x**2 + 2*x + 3)), x) - Integral(-115*x**2/(5*x**2*sqrt(5*x**2 + 2*x + 3) + 2*x*sqrt(5*x**2 + 2*x + 3) + 3*sqrt(5*x**2 + 2*x + 3)), x) - Integral(61*x**3/(5*x**2*sqrt(5*x**2 + 2*x + 3) + 2*x*sqrt(5*x**2 + 2*x + 3) + 3*sqrt(5*x**2 + 2*x + 3)), x) - Integral(871*x**4/(5*x**2*sqrt(5*x**2 + 2*x + 3) + 2*x*sqrt(5*x**2 + 2*x + 3) + 3*sqrt(5*x**2 + 2*x + 3)), x) - Integral(-127*x**5/(5*x**2*sqrt(5*x**2 + 2*x + 3) + 2*x*sqrt(5*x**2 + 2*x + 3) + 3*sqrt(5*x**2 + 2*x + 3)), x) - Integral(-2065*x**6/(5*x**2*sqrt(5*x**2 + 2*x + 3) + 2*x*sqrt(5*x**2 + 2*x + 3) + 3*sqrt(5*x**2 + 2*x + 3)), x) - Integral(1127*x**7/(5*x**2*sqrt(5*x**2 + 2*x + 3) + 2*x*sqrt(5*x**2 + 2*x + 3) + 3*sqrt(5*x**2 + 2*x + 3)), x) - Integral(343*x**8/(5*x**2*sqrt(5*x**2 + 2*x + 3) + 2*x*sqrt(5*x**2 + 2*x + 3) + 3*sqrt(5*x**2 + 2*x + 3)), x) - Integral(-2/(5*x**2*sqrt(5*x**2 + 2*x + 3) + 2*x*sqrt(5*x**2 + 2*x + 3) + 3*sqrt(5*x**2 + 2*x + 3)), x)","F",0
393,0,0,0,0.000000," ","integrate((-7*x**2+4*x+1)**2*(x**2+5*x+2)/(5*x**2+2*x+3)**(3/2),x)","\int \frac{\left(x^{2} + 5 x + 2\right) \left(7 x^{2} - 4 x - 1\right)^{2}}{\left(5 x^{2} + 2 x + 3\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((x**2 + 5*x + 2)*(7*x**2 - 4*x - 1)**2/(5*x**2 + 2*x + 3)**(3/2), x)","F",0
394,0,0,0,0.000000," ","integrate((-7*x**2+4*x+1)*(x**2+5*x+2)/(5*x**2+2*x+3)**(3/2),x)","- \int \left(- \frac{13 x}{5 x^{2} \sqrt{5 x^{2} + 2 x + 3} + 2 x \sqrt{5 x^{2} + 2 x + 3} + 3 \sqrt{5 x^{2} + 2 x + 3}}\right)\, dx - \int \left(- \frac{7 x^{2}}{5 x^{2} \sqrt{5 x^{2} + 2 x + 3} + 2 x \sqrt{5 x^{2} + 2 x + 3} + 3 \sqrt{5 x^{2} + 2 x + 3}}\right)\, dx - \int \frac{31 x^{3}}{5 x^{2} \sqrt{5 x^{2} + 2 x + 3} + 2 x \sqrt{5 x^{2} + 2 x + 3} + 3 \sqrt{5 x^{2} + 2 x + 3}}\, dx - \int \frac{7 x^{4}}{5 x^{2} \sqrt{5 x^{2} + 2 x + 3} + 2 x \sqrt{5 x^{2} + 2 x + 3} + 3 \sqrt{5 x^{2} + 2 x + 3}}\, dx - \int \left(- \frac{2}{5 x^{2} \sqrt{5 x^{2} + 2 x + 3} + 2 x \sqrt{5 x^{2} + 2 x + 3} + 3 \sqrt{5 x^{2} + 2 x + 3}}\right)\, dx"," ",0,"-Integral(-13*x/(5*x**2*sqrt(5*x**2 + 2*x + 3) + 2*x*sqrt(5*x**2 + 2*x + 3) + 3*sqrt(5*x**2 + 2*x + 3)), x) - Integral(-7*x**2/(5*x**2*sqrt(5*x**2 + 2*x + 3) + 2*x*sqrt(5*x**2 + 2*x + 3) + 3*sqrt(5*x**2 + 2*x + 3)), x) - Integral(31*x**3/(5*x**2*sqrt(5*x**2 + 2*x + 3) + 2*x*sqrt(5*x**2 + 2*x + 3) + 3*sqrt(5*x**2 + 2*x + 3)), x) - Integral(7*x**4/(5*x**2*sqrt(5*x**2 + 2*x + 3) + 2*x*sqrt(5*x**2 + 2*x + 3) + 3*sqrt(5*x**2 + 2*x + 3)), x) - Integral(-2/(5*x**2*sqrt(5*x**2 + 2*x + 3) + 2*x*sqrt(5*x**2 + 2*x + 3) + 3*sqrt(5*x**2 + 2*x + 3)), x)","F",0
395,0,0,0,0.000000," ","integrate((x**2+5*x+2)/(-7*x**2+4*x+1)/(5*x**2+2*x+3)**(3/2),x)","- \int \frac{5 x}{35 x^{4} \sqrt{5 x^{2} + 2 x + 3} - 6 x^{3} \sqrt{5 x^{2} + 2 x + 3} + 8 x^{2} \sqrt{5 x^{2} + 2 x + 3} - 14 x \sqrt{5 x^{2} + 2 x + 3} - 3 \sqrt{5 x^{2} + 2 x + 3}}\, dx - \int \frac{x^{2}}{35 x^{4} \sqrt{5 x^{2} + 2 x + 3} - 6 x^{3} \sqrt{5 x^{2} + 2 x + 3} + 8 x^{2} \sqrt{5 x^{2} + 2 x + 3} - 14 x \sqrt{5 x^{2} + 2 x + 3} - 3 \sqrt{5 x^{2} + 2 x + 3}}\, dx - \int \frac{2}{35 x^{4} \sqrt{5 x^{2} + 2 x + 3} - 6 x^{3} \sqrt{5 x^{2} + 2 x + 3} + 8 x^{2} \sqrt{5 x^{2} + 2 x + 3} - 14 x \sqrt{5 x^{2} + 2 x + 3} - 3 \sqrt{5 x^{2} + 2 x + 3}}\, dx"," ",0,"-Integral(5*x/(35*x**4*sqrt(5*x**2 + 2*x + 3) - 6*x**3*sqrt(5*x**2 + 2*x + 3) + 8*x**2*sqrt(5*x**2 + 2*x + 3) - 14*x*sqrt(5*x**2 + 2*x + 3) - 3*sqrt(5*x**2 + 2*x + 3)), x) - Integral(x**2/(35*x**4*sqrt(5*x**2 + 2*x + 3) - 6*x**3*sqrt(5*x**2 + 2*x + 3) + 8*x**2*sqrt(5*x**2 + 2*x + 3) - 14*x*sqrt(5*x**2 + 2*x + 3) - 3*sqrt(5*x**2 + 2*x + 3)), x) - Integral(2/(35*x**4*sqrt(5*x**2 + 2*x + 3) - 6*x**3*sqrt(5*x**2 + 2*x + 3) + 8*x**2*sqrt(5*x**2 + 2*x + 3) - 14*x*sqrt(5*x**2 + 2*x + 3) - 3*sqrt(5*x**2 + 2*x + 3)), x)","F",0
396,0,0,0,0.000000," ","integrate((x**2+5*x+2)/(-7*x**2+4*x+1)**2/(5*x**2+2*x+3)**(3/2),x)","\int \frac{x^{2} + 5 x + 2}{\left(5 x^{2} + 2 x + 3\right)^{\frac{3}{2}} \left(7 x^{2} - 4 x - 1\right)^{2}}\, dx"," ",0,"Integral((x**2 + 5*x + 2)/((5*x**2 + 2*x + 3)**(3/2)*(7*x**2 - 4*x - 1)**2), x)","F",0
397,0,0,0,0.000000," ","integrate((x**2+5*x+2)/(-7*x**2+4*x+1)**3/(5*x**2+2*x+3)**(3/2),x)","- \int \frac{5 x}{1715 x^{8} \sqrt{5 x^{2} + 2 x + 3} - 2254 x^{7} \sqrt{5 x^{2} + 2 x + 3} + 798 x^{6} \sqrt{5 x^{2} + 2 x + 3} - 866 x^{5} \sqrt{5 x^{2} + 2 x + 3} + 640 x^{4} \sqrt{5 x^{2} + 2 x + 3} + 198 x^{3} \sqrt{5 x^{2} + 2 x + 3} - 110 x^{2} \sqrt{5 x^{2} + 2 x + 3} - 38 x \sqrt{5 x^{2} + 2 x + 3} - 3 \sqrt{5 x^{2} + 2 x + 3}}\, dx - \int \frac{x^{2}}{1715 x^{8} \sqrt{5 x^{2} + 2 x + 3} - 2254 x^{7} \sqrt{5 x^{2} + 2 x + 3} + 798 x^{6} \sqrt{5 x^{2} + 2 x + 3} - 866 x^{5} \sqrt{5 x^{2} + 2 x + 3} + 640 x^{4} \sqrt{5 x^{2} + 2 x + 3} + 198 x^{3} \sqrt{5 x^{2} + 2 x + 3} - 110 x^{2} \sqrt{5 x^{2} + 2 x + 3} - 38 x \sqrt{5 x^{2} + 2 x + 3} - 3 \sqrt{5 x^{2} + 2 x + 3}}\, dx - \int \frac{2}{1715 x^{8} \sqrt{5 x^{2} + 2 x + 3} - 2254 x^{7} \sqrt{5 x^{2} + 2 x + 3} + 798 x^{6} \sqrt{5 x^{2} + 2 x + 3} - 866 x^{5} \sqrt{5 x^{2} + 2 x + 3} + 640 x^{4} \sqrt{5 x^{2} + 2 x + 3} + 198 x^{3} \sqrt{5 x^{2} + 2 x + 3} - 110 x^{2} \sqrt{5 x^{2} + 2 x + 3} - 38 x \sqrt{5 x^{2} + 2 x + 3} - 3 \sqrt{5 x^{2} + 2 x + 3}}\, dx"," ",0,"-Integral(5*x/(1715*x**8*sqrt(5*x**2 + 2*x + 3) - 2254*x**7*sqrt(5*x**2 + 2*x + 3) + 798*x**6*sqrt(5*x**2 + 2*x + 3) - 866*x**5*sqrt(5*x**2 + 2*x + 3) + 640*x**4*sqrt(5*x**2 + 2*x + 3) + 198*x**3*sqrt(5*x**2 + 2*x + 3) - 110*x**2*sqrt(5*x**2 + 2*x + 3) - 38*x*sqrt(5*x**2 + 2*x + 3) - 3*sqrt(5*x**2 + 2*x + 3)), x) - Integral(x**2/(1715*x**8*sqrt(5*x**2 + 2*x + 3) - 2254*x**7*sqrt(5*x**2 + 2*x + 3) + 798*x**6*sqrt(5*x**2 + 2*x + 3) - 866*x**5*sqrt(5*x**2 + 2*x + 3) + 640*x**4*sqrt(5*x**2 + 2*x + 3) + 198*x**3*sqrt(5*x**2 + 2*x + 3) - 110*x**2*sqrt(5*x**2 + 2*x + 3) - 38*x*sqrt(5*x**2 + 2*x + 3) - 3*sqrt(5*x**2 + 2*x + 3)), x) - Integral(2/(1715*x**8*sqrt(5*x**2 + 2*x + 3) - 2254*x**7*sqrt(5*x**2 + 2*x + 3) + 798*x**6*sqrt(5*x**2 + 2*x + 3) - 866*x**5*sqrt(5*x**2 + 2*x + 3) + 640*x**4*sqrt(5*x**2 + 2*x + 3) + 198*x**3*sqrt(5*x**2 + 2*x + 3) - 110*x**2*sqrt(5*x**2 + 2*x + 3) - 38*x*sqrt(5*x**2 + 2*x + 3) - 3*sqrt(5*x**2 + 2*x + 3)), x)","F",0
398,-1,0,0,0.000000," ","integrate((c*x**2+a)**p*(C*x**2+A)*(f*x**2+d)**q,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
399,-1,0,0,0.000000," ","integrate((B*x+A)*(c*x**2+a)**p*(f*x**2+d)**q,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
400,-1,0,0,0.000000," ","integrate((c*x**2+a)**p*(C*x**2+B*x+A)*(f*x**2+d)**q,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
