3.12.1 \(\int \frac {A+B x}{(d+e x)^{7/2} (b x+c x^2)^2} \, dx\)
Optimal. Leaf size=457 \[ -\frac {\tanh ^{-1}\left (\frac {\sqrt {d+e x}}{\sqrt {d}}\right ) (-7 A b e-4 A c d+2 b B d)}{b^3 d^{9/2}}-\frac {e \left (b^2 (-e) (2 B d-7 A e)-5 b c d (2 A e+B d)+10 A c^2 d^2\right )}{5 b^2 d^2 (d+e x)^{5/2} (c d-b e)^2}-\frac {c x (2 A c d-b (A e+B d))+A b (c d-b e)}{b^2 d \left (b x+c x^2\right ) (d+e x)^{5/2} (c d-b e)}+\frac {c^{7/2} \left (11 A b c e-4 A c^2 d-9 b^2 B e+2 b B c d\right ) \tanh ^{-1}\left (\frac {\sqrt {c} \sqrt {d+e x}}{\sqrt {c d-b e}}\right )}{b^3 (c d-b e)^{9/2}}-\frac {e \left (b^3 e^2 (2 B d-7 A e)-b^2 c d e (6 B d-17 A e)-3 b c^2 d^2 (3 A e+B d)+6 A c^3 d^3\right )}{3 b^2 d^3 (d+e x)^{3/2} (c d-b e)^3}-\frac {e \left (b^4 \left (-e^3\right ) (2 B d-7 A e)+8 b^3 c d e^2 (B d-3 A e)-2 b^2 c^2 d^2 e (6 B d-13 A e)-b c^3 d^3 (4 A e+B d)+2 A c^4 d^4\right )}{b^2 d^4 \sqrt {d+e x} (c d-b e)^4} \]
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Rubi [A] time = 1.28, antiderivative size = 457, normalized size of antiderivative = 1.00,
number of steps used = 8, number of rules used = 5, integrand size = 26, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.192, Rules used =
{822, 828, 826, 1166, 208} \begin {gather*} -\frac {e \left (-2 b^2 c^2 d^2 e (6 B d-13 A e)+8 b^3 c d e^2 (B d-3 A e)+b^4 \left (-e^3\right ) (2 B d-7 A e)-b c^3 d^3 (4 A e+B d)+2 A c^4 d^4\right )}{b^2 d^4 \sqrt {d+e x} (c d-b e)^4}-\frac {e \left (-b^2 c d e (6 B d-17 A e)+b^3 e^2 (2 B d-7 A e)-3 b c^2 d^2 (3 A e+B d)+6 A c^3 d^3\right )}{3 b^2 d^3 (d+e x)^{3/2} (c d-b e)^3}-\frac {e \left (b^2 (-e) (2 B d-7 A e)-5 b c d (2 A e+B d)+10 A c^2 d^2\right )}{5 b^2 d^2 (d+e x)^{5/2} (c d-b e)^2}+\frac {c^{7/2} \left (11 A b c e-4 A c^2 d-9 b^2 B e+2 b B c d\right ) \tanh ^{-1}\left (\frac {\sqrt {c} \sqrt {d+e x}}{\sqrt {c d-b e}}\right )}{b^3 (c d-b e)^{9/2}}-\frac {\tanh ^{-1}\left (\frac {\sqrt {d+e x}}{\sqrt {d}}\right ) (-7 A b e-4 A c d+2 b B d)}{b^3 d^{9/2}}-\frac {c x (2 A c d-b (A e+B d))+A b (c d-b e)}{b^2 d \left (b x+c x^2\right ) (d+e x)^{5/2} (c d-b e)} \end {gather*}
Antiderivative was successfully verified.
[In]
Int[(A + B*x)/((d + e*x)^(7/2)*(b*x + c*x^2)^2),x]
[Out]
-(e*(10*A*c^2*d^2 - b^2*e*(2*B*d - 7*A*e) - 5*b*c*d*(B*d + 2*A*e)))/(5*b^2*d^2*(c*d - b*e)^2*(d + e*x)^(5/2))
- (e*(6*A*c^3*d^3 - b^2*c*d*e*(6*B*d - 17*A*e) + b^3*e^2*(2*B*d - 7*A*e) - 3*b*c^2*d^2*(B*d + 3*A*e)))/(3*b^2*
d^3*(c*d - b*e)^3*(d + e*x)^(3/2)) - (e*(2*A*c^4*d^4 - 2*b^2*c^2*d^2*e*(6*B*d - 13*A*e) - b^4*e^3*(2*B*d - 7*A
*e) + 8*b^3*c*d*e^2*(B*d - 3*A*e) - b*c^3*d^3*(B*d + 4*A*e)))/(b^2*d^4*(c*d - b*e)^4*Sqrt[d + e*x]) - (A*b*(c*
d - b*e) + c*(2*A*c*d - b*(B*d + A*e))*x)/(b^2*d*(c*d - b*e)*(d + e*x)^(5/2)*(b*x + c*x^2)) - ((2*b*B*d - 4*A*
c*d - 7*A*b*e)*ArcTanh[Sqrt[d + e*x]/Sqrt[d]])/(b^3*d^(9/2)) + (c^(7/2)*(2*b*B*c*d - 4*A*c^2*d - 9*b^2*B*e + 1
1*A*b*c*e)*ArcTanh[(Sqrt[c]*Sqrt[d + e*x])/Sqrt[c*d - b*e]])/(b^3*(c*d - b*e)^(9/2))
Rule 208
Int[((a_) + (b_.)*(x_)^2)^(-1), x_Symbol] :> Simp[(Rt[-(a/b), 2]*ArcTanh[x/Rt[-(a/b), 2]])/a, x] /; FreeQ[{a,
b}, x] && NegQ[a/b]
Rule 822
Int[((d_.) + (e_.)*(x_))^(m_)*((f_.) + (g_.)*(x_))*((a_.) + (b_.)*(x_) + (c_.)*(x_)^2)^(p_), x_Symbol] :> Simp
[((d + e*x)^(m + 1)*(f*(b*c*d - b^2*e + 2*a*c*e) - a*g*(2*c*d - b*e) + c*(f*(2*c*d - b*e) - g*(b*d - 2*a*e))*x
)*(a + b*x + c*x^2)^(p + 1))/((p + 1)*(b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)), x] + Dist[1/((p + 1)*(b^2 - 4*a*
c)*(c*d^2 - b*d*e + a*e^2)), Int[(d + e*x)^m*(a + b*x + c*x^2)^(p + 1)*Simp[f*(b*c*d*e*(2*p - m + 2) + b^2*e^2
*(p + m + 2) - 2*c^2*d^2*(2*p + 3) - 2*a*c*e^2*(m + 2*p + 3)) - g*(a*e*(b*e - 2*c*d*m + b*e*m) - b*d*(3*c*d -
b*e + 2*c*d*p - b*e*p)) + c*e*(g*(b*d - 2*a*e) - f*(2*c*d - b*e))*(m + 2*p + 4)*x, x], x], x] /; FreeQ[{a, b,
c, d, e, f, g, m}, x] && NeQ[b^2 - 4*a*c, 0] && NeQ[c*d^2 - b*d*e + a*e^2, 0] && LtQ[p, -1] && (IntegerQ[m] ||
IntegerQ[p] || IntegersQ[2*m, 2*p])
Rule 826
Int[((f_.) + (g_.)*(x_))/(Sqrt[(d_.) + (e_.)*(x_)]*((a_.) + (b_.)*(x_) + (c_.)*(x_)^2)), x_Symbol] :> Dist[2,
Subst[Int[(e*f - d*g + g*x^2)/(c*d^2 - b*d*e + a*e^2 - (2*c*d - b*e)*x^2 + c*x^4), x], x, Sqrt[d + e*x]], x] /
; FreeQ[{a, b, c, d, e, f, g}, x] && NeQ[b^2 - 4*a*c, 0] && NeQ[c*d^2 - b*d*e + a*e^2, 0]
Rule 828
Int[(((d_.) + (e_.)*(x_))^(m_)*((f_.) + (g_.)*(x_)))/((a_.) + (b_.)*(x_) + (c_.)*(x_)^2), x_Symbol] :> Simp[((
e*f - d*g)*(d + e*x)^(m + 1))/((m + 1)*(c*d^2 - b*d*e + a*e^2)), x] + Dist[1/(c*d^2 - b*d*e + a*e^2), Int[((d
+ e*x)^(m + 1)*Simp[c*d*f - f*b*e + a*e*g - c*(e*f - d*g)*x, x])/(a + b*x + c*x^2), x], x] /; FreeQ[{a, b, c,
d, e, f, g, m}, x] && NeQ[b^2 - 4*a*c, 0] && NeQ[c*d^2 - b*d*e + a*e^2, 0] && FractionQ[m] && LtQ[m, -1]
Rule 1166
Int[((d_) + (e_.)*(x_)^2)/((a_) + (b_.)*(x_)^2 + (c_.)*(x_)^4), x_Symbol] :> With[{q = Rt[b^2 - 4*a*c, 2]}, Di
st[e/2 + (2*c*d - b*e)/(2*q), Int[1/(b/2 - q/2 + c*x^2), x], x] + Dist[e/2 - (2*c*d - b*e)/(2*q), Int[1/(b/2 +
q/2 + c*x^2), x], x]] /; FreeQ[{a, b, c, d, e}, x] && NeQ[b^2 - 4*a*c, 0] && NeQ[c*d^2 - a*e^2, 0] && PosQ[b^
2 - 4*a*c]
Rubi steps
\begin {align*} \int \frac {A+B x}{(d+e x)^{7/2} \left (b x+c x^2\right )^2} \, dx &=-\frac {A b (c d-b e)+c (2 A c d-b (B d+A e)) x}{b^2 d (c d-b e) (d+e x)^{5/2} \left (b x+c x^2\right )}-\frac {\int \frac {-\frac {1}{2} (c d-b e) (2 b B d-4 A c d-7 A b e)-\frac {7}{2} c e (b B d-2 A c d+A b e) x}{(d+e x)^{7/2} \left (b x+c x^2\right )} \, dx}{b^2 d (c d-b e)}\\ &=-\frac {e \left (10 A c^2 d^2-b^2 e (2 B d-7 A e)-5 b c d (B d+2 A e)\right )}{5 b^2 d^2 (c d-b e)^2 (d+e x)^{5/2}}-\frac {A b (c d-b e)+c (2 A c d-b (B d+A e)) x}{b^2 d (c d-b e) (d+e x)^{5/2} \left (b x+c x^2\right )}-\frac {\int \frac {-\frac {1}{2} (c d-b e)^2 (2 b B d-4 A c d-7 A b e)+\frac {1}{2} c e \left (10 A c^2 d^2-b^2 e (2 B d-7 A e)-5 b c d (B d+2 A e)\right ) x}{(d+e x)^{5/2} \left (b x+c x^2\right )} \, dx}{b^2 d^2 (c d-b e)^2}\\ &=-\frac {e \left (10 A c^2 d^2-b^2 e (2 B d-7 A e)-5 b c d (B d+2 A e)\right )}{5 b^2 d^2 (c d-b e)^2 (d+e x)^{5/2}}-\frac {e \left (6 A c^3 d^3-b^2 c d e (6 B d-17 A e)+b^3 e^2 (2 B d-7 A e)-3 b c^2 d^2 (B d+3 A e)\right )}{3 b^2 d^3 (c d-b e)^3 (d+e x)^{3/2}}-\frac {A b (c d-b e)+c (2 A c d-b (B d+A e)) x}{b^2 d (c d-b e) (d+e x)^{5/2} \left (b x+c x^2\right )}-\frac {\int \frac {-\frac {1}{2} (c d-b e)^3 (2 b B d-4 A c d-7 A b e)+\frac {1}{2} c e \left (6 A c^3 d^3-b^2 c d e (6 B d-17 A e)+b^3 e^2 (2 B d-7 A e)-3 b c^2 d^2 (B d+3 A e)\right ) x}{(d+e x)^{3/2} \left (b x+c x^2\right )} \, dx}{b^2 d^3 (c d-b e)^3}\\ &=-\frac {e \left (10 A c^2 d^2-b^2 e (2 B d-7 A e)-5 b c d (B d+2 A e)\right )}{5 b^2 d^2 (c d-b e)^2 (d+e x)^{5/2}}-\frac {e \left (6 A c^3 d^3-b^2 c d e (6 B d-17 A e)+b^3 e^2 (2 B d-7 A e)-3 b c^2 d^2 (B d+3 A e)\right )}{3 b^2 d^3 (c d-b e)^3 (d+e x)^{3/2}}-\frac {e \left (2 A c^4 d^4-2 b^2 c^2 d^2 e (6 B d-13 A e)-b^4 e^3 (2 B d-7 A e)+8 b^3 c d e^2 (B d-3 A e)-b c^3 d^3 (B d+4 A e)\right )}{b^2 d^4 (c d-b e)^4 \sqrt {d+e x}}-\frac {A b (c d-b e)+c (2 A c d-b (B d+A e)) x}{b^2 d (c d-b e) (d+e x)^{5/2} \left (b x+c x^2\right )}-\frac {\int \frac {-\frac {1}{2} (c d-b e)^4 (2 b B d-4 A c d-7 A b e)+\frac {1}{2} c e \left (2 A c^4 d^4-2 b^2 c^2 d^2 e (6 B d-13 A e)-b^4 e^3 (2 B d-7 A e)+8 b^3 c d e^2 (B d-3 A e)-b c^3 d^3 (B d+4 A e)\right ) x}{\sqrt {d+e x} \left (b x+c x^2\right )} \, dx}{b^2 d^4 (c d-b e)^4}\\ &=-\frac {e \left (10 A c^2 d^2-b^2 e (2 B d-7 A e)-5 b c d (B d+2 A e)\right )}{5 b^2 d^2 (c d-b e)^2 (d+e x)^{5/2}}-\frac {e \left (6 A c^3 d^3-b^2 c d e (6 B d-17 A e)+b^3 e^2 (2 B d-7 A e)-3 b c^2 d^2 (B d+3 A e)\right )}{3 b^2 d^3 (c d-b e)^3 (d+e x)^{3/2}}-\frac {e \left (2 A c^4 d^4-2 b^2 c^2 d^2 e (6 B d-13 A e)-b^4 e^3 (2 B d-7 A e)+8 b^3 c d e^2 (B d-3 A e)-b c^3 d^3 (B d+4 A e)\right )}{b^2 d^4 (c d-b e)^4 \sqrt {d+e x}}-\frac {A b (c d-b e)+c (2 A c d-b (B d+A e)) x}{b^2 d (c d-b e) (d+e x)^{5/2} \left (b x+c x^2\right )}-\frac {2 \operatorname {Subst}\left (\int \frac {-\frac {1}{2} e (c d-b e)^4 (2 b B d-4 A c d-7 A b e)-\frac {1}{2} c d e \left (2 A c^4 d^4-2 b^2 c^2 d^2 e (6 B d-13 A e)-b^4 e^3 (2 B d-7 A e)+8 b^3 c d e^2 (B d-3 A e)-b c^3 d^3 (B d+4 A e)\right )+\frac {1}{2} c e \left (2 A c^4 d^4-2 b^2 c^2 d^2 e (6 B d-13 A e)-b^4 e^3 (2 B d-7 A e)+8 b^3 c d e^2 (B d-3 A e)-b c^3 d^3 (B d+4 A e)\right ) x^2}{c d^2-b d e+(-2 c d+b e) x^2+c x^4} \, dx,x,\sqrt {d+e x}\right )}{b^2 d^4 (c d-b e)^4}\\ &=-\frac {e \left (10 A c^2 d^2-b^2 e (2 B d-7 A e)-5 b c d (B d+2 A e)\right )}{5 b^2 d^2 (c d-b e)^2 (d+e x)^{5/2}}-\frac {e \left (6 A c^3 d^3-b^2 c d e (6 B d-17 A e)+b^3 e^2 (2 B d-7 A e)-3 b c^2 d^2 (B d+3 A e)\right )}{3 b^2 d^3 (c d-b e)^3 (d+e x)^{3/2}}-\frac {e \left (2 A c^4 d^4-2 b^2 c^2 d^2 e (6 B d-13 A e)-b^4 e^3 (2 B d-7 A e)+8 b^3 c d e^2 (B d-3 A e)-b c^3 d^3 (B d+4 A e)\right )}{b^2 d^4 (c d-b e)^4 \sqrt {d+e x}}-\frac {A b (c d-b e)+c (2 A c d-b (B d+A e)) x}{b^2 d (c d-b e) (d+e x)^{5/2} \left (b x+c x^2\right )}+\frac {(c (2 b B d-4 A c d-7 A b e)) \operatorname {Subst}\left (\int \frac {1}{-\frac {b e}{2}+\frac {1}{2} (-2 c d+b e)+c x^2} \, dx,x,\sqrt {d+e x}\right )}{b^3 d^4}-\frac {\left (2 \left (\frac {1}{4} c e \left (2 A c^4 d^4-2 b^2 c^2 d^2 e (6 B d-13 A e)-b^4 e^3 (2 B d-7 A e)+8 b^3 c d e^2 (B d-3 A e)-b c^3 d^3 (B d+4 A e)\right )-\frac {-\frac {1}{2} c e (-2 c d+b e) \left (2 A c^4 d^4-2 b^2 c^2 d^2 e (6 B d-13 A e)-b^4 e^3 (2 B d-7 A e)+8 b^3 c d e^2 (B d-3 A e)-b c^3 d^3 (B d+4 A e)\right )+2 c \left (-\frac {1}{2} e (c d-b e)^4 (2 b B d-4 A c d-7 A b e)-\frac {1}{2} c d e \left (2 A c^4 d^4-2 b^2 c^2 d^2 e (6 B d-13 A e)-b^4 e^3 (2 B d-7 A e)+8 b^3 c d e^2 (B d-3 A e)-b c^3 d^3 (B d+4 A e)\right )\right )}{2 b e}\right )\right ) \operatorname {Subst}\left (\int \frac {1}{\frac {b e}{2}+\frac {1}{2} (-2 c d+b e)+c x^2} \, dx,x,\sqrt {d+e x}\right )}{b^2 d^4 (c d-b e)^4}\\ &=-\frac {e \left (10 A c^2 d^2-b^2 e (2 B d-7 A e)-5 b c d (B d+2 A e)\right )}{5 b^2 d^2 (c d-b e)^2 (d+e x)^{5/2}}-\frac {e \left (6 A c^3 d^3-b^2 c d e (6 B d-17 A e)+b^3 e^2 (2 B d-7 A e)-3 b c^2 d^2 (B d+3 A e)\right )}{3 b^2 d^3 (c d-b e)^3 (d+e x)^{3/2}}-\frac {e \left (2 A c^4 d^4-2 b^2 c^2 d^2 e (6 B d-13 A e)-b^4 e^3 (2 B d-7 A e)+8 b^3 c d e^2 (B d-3 A e)-b c^3 d^3 (B d+4 A e)\right )}{b^2 d^4 (c d-b e)^4 \sqrt {d+e x}}-\frac {A b (c d-b e)+c (2 A c d-b (B d+A e)) x}{b^2 d (c d-b e) (d+e x)^{5/2} \left (b x+c x^2\right )}-\frac {(2 b B d-4 A c d-7 A b e) \tanh ^{-1}\left (\frac {\sqrt {d+e x}}{\sqrt {d}}\right )}{b^3 d^{9/2}}+\frac {c^{7/2} \left (2 b B c d-4 A c^2 d-9 b^2 B e+11 A b c e\right ) \tanh ^{-1}\left (\frac {\sqrt {c} \sqrt {d+e x}}{\sqrt {c d-b e}}\right )}{b^3 (c d-b e)^{9/2}}\\ \end {align*}
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Mathematica [C] time = 0.20, size = 194, normalized size = 0.42 \begin {gather*} \frac {-x (b+c x) \left (c d^2 \left (b c (11 A e+2 B d)-4 A c^2 d-9 b^2 B e\right ) \, _2F_1\left (-\frac {5}{2},1;-\frac {3}{2};\frac {c (d+e x)}{c d-b e}\right )+(c d-b e)^2 \, _2F_1\left (-\frac {5}{2},1;-\frac {3}{2};\frac {e x}{d}+1\right ) (7 A b e+4 A c d-2 b B d)\right )-5 A b^2 d (c d-b e)^2-5 b c d x (b e-c d) (A b e-2 A c d+b B d)}{5 b^3 d^2 x (b+c x) (d+e x)^{5/2} (c d-b e)^2} \end {gather*}
Antiderivative was successfully verified.
[In]
Integrate[(A + B*x)/((d + e*x)^(7/2)*(b*x + c*x^2)^2),x]
[Out]
(-5*A*b^2*d*(c*d - b*e)^2 - 5*b*c*d*(-(c*d) + b*e)*(b*B*d - 2*A*c*d + A*b*e)*x - x*(b + c*x)*(c*d^2*(-4*A*c^2*
d - 9*b^2*B*e + b*c*(2*B*d + 11*A*e))*Hypergeometric2F1[-5/2, 1, -3/2, (c*(d + e*x))/(c*d - b*e)] + (c*d - b*e
)^2*(-2*b*B*d + 4*A*c*d + 7*A*b*e)*Hypergeometric2F1[-5/2, 1, -3/2, 1 + (e*x)/d]))/(5*b^3*d^2*(c*d - b*e)^2*x*
(b + c*x)*(d + e*x)^(5/2))
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IntegrateAlgebraic [B] time = 1.36, size = 994, normalized size = 2.18 \begin {gather*} -\frac {-6 b^2 B c^3 e d^7+6 A b^2 c^3 e^2 d^6+18 b^3 B c^2 e^2 d^6-18 b^2 B c^3 e (d+e x) d^6-18 A b^3 c^2 e^3 d^5-18 b^4 B c e^3 d^5-30 A c^5 (d+e x)^3 d^5+15 b B c^4 (d+e x)^3 d^5-126 b^2 B c^3 e (d+e x)^2 d^5+28 A b^2 c^3 e^2 (d+e x) d^5+40 b^3 B c^2 e^2 (d+e x) d^5+6 b^5 B e^4 d^4+18 A b^4 c e^4 d^4+30 A c^5 (d+e x)^4 d^4-15 b B c^4 (d+e x)^4 d^4+75 A b c^4 e (d+e x)^3 d^4+330 b^2 B c^3 e (d+e x)^3 d^4+226 A b^2 c^3 e^2 (d+e x)^2 d^4+202 b^3 B c^2 e^2 (d+e x)^2 d^4-70 A b^3 c^2 e^3 (d+e x) d^4-26 b^4 B c e^3 (d+e x) d^4-6 A b^5 e^5 d^3-60 A b c^4 e (d+e x)^4 d^3-180 b^2 B c^3 e (d+e x)^4 d^3-710 A b^2 c^3 e^2 (d+e x)^3 d^3-380 b^3 B c^2 e^2 (d+e x)^3 d^3-452 A b^3 c^2 e^3 (d+e x)^2 d^3-96 b^4 B c e^3 (d+e x)^2 d^3+4 b^5 B e^4 (d+e x) d^3+56 A b^4 c e^4 (d+e x) d^3+390 A b^2 c^3 e^2 (d+e x)^4 d^2+120 b^3 B c^2 e^2 (d+e x)^4 d^2+990 A b^3 c^2 e^3 (d+e x)^3 d^2+170 b^4 B c e^3 (d+e x)^3 d^2+20 b^5 B e^4 (d+e x)^2 d^2+296 A b^4 c e^4 (d+e x)^2 d^2-14 A b^5 e^5 (d+e x) d^2-360 A b^3 c^2 e^3 (d+e x)^4 d-30 b^4 B c e^3 (d+e x)^4 d-30 b^5 B e^4 (d+e x)^3 d-535 A b^4 c e^4 (d+e x)^3 d-70 A b^5 e^5 (d+e x)^2 d+105 A b^4 c e^4 (d+e x)^4+105 A b^5 e^5 (d+e x)^3}{15 b^2 d^4 (b e-c d)^4 x (d+e x)^{5/2} (-c d+b e+c (d+e x))}+\frac {\left (-4 A d c^{11/2}+2 b B d c^{9/2}+11 A b e c^{9/2}-9 b^2 B e c^{7/2}\right ) \tan ^{-1}\left (\frac {\sqrt {c} \sqrt {b e-c d} \sqrt {d+e x}}{c d-b e}\right )}{b^3 (c d-b e)^4 \sqrt {b e-c d}}+\frac {(-2 b B d+4 A c d+7 A b e) \tanh ^{-1}\left (\frac {\sqrt {d+e x}}{\sqrt {d}}\right )}{b^3 d^{9/2}} \end {gather*}
Antiderivative was successfully verified.
[In]
IntegrateAlgebraic[(A + B*x)/((d + e*x)^(7/2)*(b*x + c*x^2)^2),x]
[Out]
-1/15*(-6*b^2*B*c^3*d^7*e + 18*b^3*B*c^2*d^6*e^2 + 6*A*b^2*c^3*d^6*e^2 - 18*b^4*B*c*d^5*e^3 - 18*A*b^3*c^2*d^5
*e^3 + 6*b^5*B*d^4*e^4 + 18*A*b^4*c*d^4*e^4 - 6*A*b^5*d^3*e^5 - 18*b^2*B*c^3*d^6*e*(d + e*x) + 40*b^3*B*c^2*d^
5*e^2*(d + e*x) + 28*A*b^2*c^3*d^5*e^2*(d + e*x) - 26*b^4*B*c*d^4*e^3*(d + e*x) - 70*A*b^3*c^2*d^4*e^3*(d + e*
x) + 4*b^5*B*d^3*e^4*(d + e*x) + 56*A*b^4*c*d^3*e^4*(d + e*x) - 14*A*b^5*d^2*e^5*(d + e*x) - 126*b^2*B*c^3*d^5
*e*(d + e*x)^2 + 202*b^3*B*c^2*d^4*e^2*(d + e*x)^2 + 226*A*b^2*c^3*d^4*e^2*(d + e*x)^2 - 96*b^4*B*c*d^3*e^3*(d
+ e*x)^2 - 452*A*b^3*c^2*d^3*e^3*(d + e*x)^2 + 20*b^5*B*d^2*e^4*(d + e*x)^2 + 296*A*b^4*c*d^2*e^4*(d + e*x)^2
- 70*A*b^5*d*e^5*(d + e*x)^2 + 15*b*B*c^4*d^5*(d + e*x)^3 - 30*A*c^5*d^5*(d + e*x)^3 + 330*b^2*B*c^3*d^4*e*(d
+ e*x)^3 + 75*A*b*c^4*d^4*e*(d + e*x)^3 - 380*b^3*B*c^2*d^3*e^2*(d + e*x)^3 - 710*A*b^2*c^3*d^3*e^2*(d + e*x)
^3 + 170*b^4*B*c*d^2*e^3*(d + e*x)^3 + 990*A*b^3*c^2*d^2*e^3*(d + e*x)^3 - 30*b^5*B*d*e^4*(d + e*x)^3 - 535*A*
b^4*c*d*e^4*(d + e*x)^3 + 105*A*b^5*e^5*(d + e*x)^3 - 15*b*B*c^4*d^4*(d + e*x)^4 + 30*A*c^5*d^4*(d + e*x)^4 -
180*b^2*B*c^3*d^3*e*(d + e*x)^4 - 60*A*b*c^4*d^3*e*(d + e*x)^4 + 120*b^3*B*c^2*d^2*e^2*(d + e*x)^4 + 390*A*b^2
*c^3*d^2*e^2*(d + e*x)^4 - 30*b^4*B*c*d*e^3*(d + e*x)^4 - 360*A*b^3*c^2*d*e^3*(d + e*x)^4 + 105*A*b^4*c*e^4*(d
+ e*x)^4)/(b^2*d^4*(-(c*d) + b*e)^4*x*(d + e*x)^(5/2)*(-(c*d) + b*e + c*(d + e*x))) + ((2*b*B*c^(9/2)*d - 4*A
*c^(11/2)*d - 9*b^2*B*c^(7/2)*e + 11*A*b*c^(9/2)*e)*ArcTan[(Sqrt[c]*Sqrt[-(c*d) + b*e]*Sqrt[d + e*x])/(c*d - b
*e)])/(b^3*(c*d - b*e)^4*Sqrt[-(c*d) + b*e]) + ((-2*b*B*d + 4*A*c*d + 7*A*b*e)*ArcTanh[Sqrt[d + e*x]/Sqrt[d]])
/(b^3*d^(9/2))
________________________________________________________________________________________
fricas [B] time = 131.54, size = 8537, normalized size = 18.68
result too large to display
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((B*x+A)/(e*x+d)^(7/2)/(c*x^2+b*x)^2,x, algorithm="fricas")
[Out]
[1/30*(15*((2*(B*b*c^5 - 2*A*c^6)*d^6*e^3 - (9*B*b^2*c^4 - 11*A*b*c^5)*d^5*e^4)*x^5 + (6*(B*b*c^5 - 2*A*c^6)*d
^7*e^2 - (25*B*b^2*c^4 - 29*A*b*c^5)*d^6*e^3 - (9*B*b^3*c^3 - 11*A*b^2*c^4)*d^5*e^4)*x^4 + 3*(2*(B*b*c^5 - 2*A
*c^6)*d^8*e - 7*(B*b^2*c^4 - A*b*c^5)*d^7*e^2 - (9*B*b^3*c^3 - 11*A*b^2*c^4)*d^6*e^3)*x^3 + (2*(B*b*c^5 - 2*A*
c^6)*d^9 - (3*B*b^2*c^4 + A*b*c^5)*d^8*e - 3*(9*B*b^3*c^3 - 11*A*b^2*c^4)*d^7*e^2)*x^2 + (2*(B*b^2*c^4 - 2*A*b
*c^5)*d^9 - (9*B*b^3*c^3 - 11*A*b^2*c^4)*d^8*e)*x)*sqrt(c/(c*d - b*e))*log((c*e*x + 2*c*d - b*e + 2*(c*d - b*e
)*sqrt(e*x + d)*sqrt(c/(c*d - b*e)))/(c*x + b)) + 15*((7*A*b^5*c*e^8 - 2*(B*b*c^5 - 2*A*c^6)*d^5*e^3 + (8*B*b^
2*c^4 - 9*A*b*c^5)*d^4*e^4 - 4*(3*B*b^3*c^3 + A*b^2*c^4)*d^3*e^5 + 2*(4*B*b^4*c^2 + 13*A*b^3*c^3)*d^2*e^6 - 2*
(B*b^5*c + 12*A*b^4*c^2)*d*e^7)*x^5 + (7*A*b^6*e^8 - 6*(B*b*c^5 - 2*A*c^6)*d^6*e^2 + (22*B*b^2*c^4 - 23*A*b*c^
5)*d^5*e^3 - 7*(4*B*b^3*c^3 + 3*A*b^2*c^4)*d^4*e^4 + 2*(6*B*b^4*c^2 + 37*A*b^3*c^3)*d^3*e^5 + 2*(B*b^5*c - 23*
A*b^4*c^2)*d^2*e^6 - (2*B*b^6 + 3*A*b^5*c)*d*e^7)*x^4 + 3*(7*A*b^6*d*e^7 - 2*(B*b*c^5 - 2*A*c^6)*d^7*e + (6*B*
b^2*c^4 - 5*A*b*c^5)*d^6*e^2 - (4*B*b^3*c^3 + 13*A*b^2*c^4)*d^5*e^3 - 2*(2*B*b^4*c^2 - 11*A*b^3*c^3)*d^4*e^4 +
2*(3*B*b^5*c + A*b^4*c^2)*d^3*e^5 - (2*B*b^6 + 17*A*b^5*c)*d^2*e^6)*x^3 + (21*A*b^6*d^2*e^6 - 2*(B*b*c^5 - 2*
A*c^6)*d^8 + (2*B*b^2*c^4 + 3*A*b*c^5)*d^7*e + (12*B*b^3*c^3 - 31*A*b^2*c^4)*d^6*e^2 - 14*(2*B*b^4*c^2 - A*b^3
*c^3)*d^5*e^3 + 2*(11*B*b^5*c + 27*A*b^4*c^2)*d^4*e^4 - (6*B*b^6 + 65*A*b^5*c)*d^3*e^5)*x^2 + (7*A*b^6*d^3*e^5
- 2*(B*b^2*c^4 - 2*A*b*c^5)*d^8 + (8*B*b^3*c^3 - 9*A*b^2*c^4)*d^7*e - 4*(3*B*b^4*c^2 + A*b^3*c^3)*d^6*e^2 + 2
*(4*B*b^5*c + 13*A*b^4*c^2)*d^5*e^3 - 2*(B*b^6 + 12*A*b^5*c)*d^4*e^4)*x)*sqrt(d)*log((e*x + 2*sqrt(e*x + d)*sq
rt(d) + 2*d)/x) - 2*(15*A*b^2*c^4*d^8 - 60*A*b^3*c^3*d^7*e + 90*A*b^4*c^2*d^6*e^2 - 60*A*b^5*c*d^5*e^3 + 15*A*
b^6*d^4*e^4 + 15*(7*A*b^5*c*d*e^7 - (B*b^2*c^4 - 2*A*b*c^5)*d^5*e^3 - 4*(3*B*b^3*c^3 + A*b^2*c^4)*d^4*e^4 + 2*
(4*B*b^4*c^2 + 13*A*b^3*c^3)*d^3*e^5 - 2*(B*b^5*c + 12*A*b^4*c^2)*d^2*e^6)*x^4 + 5*(21*A*b^6*d*e^7 - 9*(B*b^2*
c^4 - 2*A*b*c^5)*d^6*e^2 - 3*(26*B*b^3*c^3 + 11*A*b^2*c^4)*d^5*e^3 + 10*(2*B*b^4*c^2 + 17*A*b^3*c^3)*d^4*e^4 +
10*(B*b^5*c - 9*A*b^4*c^2)*d^3*e^5 - (6*B*b^6 + 23*A*b^5*c)*d^2*e^6)*x^3 + (245*A*b^6*d^2*e^6 - 45*(B*b^2*c^4
- 2*A*b*c^5)*d^7*e - 27*(8*B*b^3*c^3 + 5*A*b^2*c^4)*d^6*e^2 - 218*(B*b^4*c^2 - 2*A*b^3*c^3)*d^5*e^3 + 2*(117*
B*b^5*c + 179*A*b^4*c^2)*d^4*e^4 - 7*(10*B*b^6 + 97*A*b^5*c)*d^3*e^5)*x^2 - (15*A*b^2*c^4*d^7*e - 161*A*b^6*d^
3*e^5 + 15*(B*b^2*c^4 - 2*A*b*c^5)*d^8 + 18*(12*B*b^4*c^2 + 5*A*b^3*c^3)*d^6*e^2 - 4*(43*B*b^5*c + 139*A*b^4*c
^2)*d^5*e^3 + (46*B*b^6 + 537*A*b^5*c)*d^4*e^4)*x)*sqrt(e*x + d))/((b^3*c^5*d^9*e^3 - 4*b^4*c^4*d^8*e^4 + 6*b^
5*c^3*d^7*e^5 - 4*b^6*c^2*d^6*e^6 + b^7*c*d^5*e^7)*x^5 + (3*b^3*c^5*d^10*e^2 - 11*b^4*c^4*d^9*e^3 + 14*b^5*c^3
*d^8*e^4 - 6*b^6*c^2*d^7*e^5 - b^7*c*d^6*e^6 + b^8*d^5*e^7)*x^4 + 3*(b^3*c^5*d^11*e - 3*b^4*c^4*d^10*e^2 + 2*b
^5*c^3*d^9*e^3 + 2*b^6*c^2*d^8*e^4 - 3*b^7*c*d^7*e^5 + b^8*d^6*e^6)*x^3 + (b^3*c^5*d^12 - b^4*c^4*d^11*e - 6*b
^5*c^3*d^10*e^2 + 14*b^6*c^2*d^9*e^3 - 11*b^7*c*d^8*e^4 + 3*b^8*d^7*e^5)*x^2 + (b^4*c^4*d^12 - 4*b^5*c^3*d^11*
e + 6*b^6*c^2*d^10*e^2 - 4*b^7*c*d^9*e^3 + b^8*d^8*e^4)*x), 1/30*(30*((2*(B*b*c^5 - 2*A*c^6)*d^6*e^3 - (9*B*b^
2*c^4 - 11*A*b*c^5)*d^5*e^4)*x^5 + (6*(B*b*c^5 - 2*A*c^6)*d^7*e^2 - (25*B*b^2*c^4 - 29*A*b*c^5)*d^6*e^3 - (9*B
*b^3*c^3 - 11*A*b^2*c^4)*d^5*e^4)*x^4 + 3*(2*(B*b*c^5 - 2*A*c^6)*d^8*e - 7*(B*b^2*c^4 - A*b*c^5)*d^7*e^2 - (9*
B*b^3*c^3 - 11*A*b^2*c^4)*d^6*e^3)*x^3 + (2*(B*b*c^5 - 2*A*c^6)*d^9 - (3*B*b^2*c^4 + A*b*c^5)*d^8*e - 3*(9*B*b
^3*c^3 - 11*A*b^2*c^4)*d^7*e^2)*x^2 + (2*(B*b^2*c^4 - 2*A*b*c^5)*d^9 - (9*B*b^3*c^3 - 11*A*b^2*c^4)*d^8*e)*x)*
sqrt(-c/(c*d - b*e))*arctan(-(c*d - b*e)*sqrt(e*x + d)*sqrt(-c/(c*d - b*e))/(c*e*x + c*d)) + 15*((7*A*b^5*c*e^
8 - 2*(B*b*c^5 - 2*A*c^6)*d^5*e^3 + (8*B*b^2*c^4 - 9*A*b*c^5)*d^4*e^4 - 4*(3*B*b^3*c^3 + A*b^2*c^4)*d^3*e^5 +
2*(4*B*b^4*c^2 + 13*A*b^3*c^3)*d^2*e^6 - 2*(B*b^5*c + 12*A*b^4*c^2)*d*e^7)*x^5 + (7*A*b^6*e^8 - 6*(B*b*c^5 - 2
*A*c^6)*d^6*e^2 + (22*B*b^2*c^4 - 23*A*b*c^5)*d^5*e^3 - 7*(4*B*b^3*c^3 + 3*A*b^2*c^4)*d^4*e^4 + 2*(6*B*b^4*c^2
+ 37*A*b^3*c^3)*d^3*e^5 + 2*(B*b^5*c - 23*A*b^4*c^2)*d^2*e^6 - (2*B*b^6 + 3*A*b^5*c)*d*e^7)*x^4 + 3*(7*A*b^6*
d*e^7 - 2*(B*b*c^5 - 2*A*c^6)*d^7*e + (6*B*b^2*c^4 - 5*A*b*c^5)*d^6*e^2 - (4*B*b^3*c^3 + 13*A*b^2*c^4)*d^5*e^3
- 2*(2*B*b^4*c^2 - 11*A*b^3*c^3)*d^4*e^4 + 2*(3*B*b^5*c + A*b^4*c^2)*d^3*e^5 - (2*B*b^6 + 17*A*b^5*c)*d^2*e^6
)*x^3 + (21*A*b^6*d^2*e^6 - 2*(B*b*c^5 - 2*A*c^6)*d^8 + (2*B*b^2*c^4 + 3*A*b*c^5)*d^7*e + (12*B*b^3*c^3 - 31*A
*b^2*c^4)*d^6*e^2 - 14*(2*B*b^4*c^2 - A*b^3*c^3)*d^5*e^3 + 2*(11*B*b^5*c + 27*A*b^4*c^2)*d^4*e^4 - (6*B*b^6 +
65*A*b^5*c)*d^3*e^5)*x^2 + (7*A*b^6*d^3*e^5 - 2*(B*b^2*c^4 - 2*A*b*c^5)*d^8 + (8*B*b^3*c^3 - 9*A*b^2*c^4)*d^7*
e - 4*(3*B*b^4*c^2 + A*b^3*c^3)*d^6*e^2 + 2*(4*B*b^5*c + 13*A*b^4*c^2)*d^5*e^3 - 2*(B*b^6 + 12*A*b^5*c)*d^4*e^
4)*x)*sqrt(d)*log((e*x + 2*sqrt(e*x + d)*sqrt(d) + 2*d)/x) - 2*(15*A*b^2*c^4*d^8 - 60*A*b^3*c^3*d^7*e + 90*A*b
^4*c^2*d^6*e^2 - 60*A*b^5*c*d^5*e^3 + 15*A*b^6*d^4*e^4 + 15*(7*A*b^5*c*d*e^7 - (B*b^2*c^4 - 2*A*b*c^5)*d^5*e^3
- 4*(3*B*b^3*c^3 + A*b^2*c^4)*d^4*e^4 + 2*(4*B*b^4*c^2 + 13*A*b^3*c^3)*d^3*e^5 - 2*(B*b^5*c + 12*A*b^4*c^2)*d
^2*e^6)*x^4 + 5*(21*A*b^6*d*e^7 - 9*(B*b^2*c^4 - 2*A*b*c^5)*d^6*e^2 - 3*(26*B*b^3*c^3 + 11*A*b^2*c^4)*d^5*e^3
+ 10*(2*B*b^4*c^2 + 17*A*b^3*c^3)*d^4*e^4 + 10*(B*b^5*c - 9*A*b^4*c^2)*d^3*e^5 - (6*B*b^6 + 23*A*b^5*c)*d^2*e^
6)*x^3 + (245*A*b^6*d^2*e^6 - 45*(B*b^2*c^4 - 2*A*b*c^5)*d^7*e - 27*(8*B*b^3*c^3 + 5*A*b^2*c^4)*d^6*e^2 - 218*
(B*b^4*c^2 - 2*A*b^3*c^3)*d^5*e^3 + 2*(117*B*b^5*c + 179*A*b^4*c^2)*d^4*e^4 - 7*(10*B*b^6 + 97*A*b^5*c)*d^3*e^
5)*x^2 - (15*A*b^2*c^4*d^7*e - 161*A*b^6*d^3*e^5 + 15*(B*b^2*c^4 - 2*A*b*c^5)*d^8 + 18*(12*B*b^4*c^2 + 5*A*b^3
*c^3)*d^6*e^2 - 4*(43*B*b^5*c + 139*A*b^4*c^2)*d^5*e^3 + (46*B*b^6 + 537*A*b^5*c)*d^4*e^4)*x)*sqrt(e*x + d))/(
(b^3*c^5*d^9*e^3 - 4*b^4*c^4*d^8*e^4 + 6*b^5*c^3*d^7*e^5 - 4*b^6*c^2*d^6*e^6 + b^7*c*d^5*e^7)*x^5 + (3*b^3*c^5
*d^10*e^2 - 11*b^4*c^4*d^9*e^3 + 14*b^5*c^3*d^8*e^4 - 6*b^6*c^2*d^7*e^5 - b^7*c*d^6*e^6 + b^8*d^5*e^7)*x^4 + 3
*(b^3*c^5*d^11*e - 3*b^4*c^4*d^10*e^2 + 2*b^5*c^3*d^9*e^3 + 2*b^6*c^2*d^8*e^4 - 3*b^7*c*d^7*e^5 + b^8*d^6*e^6)
*x^3 + (b^3*c^5*d^12 - b^4*c^4*d^11*e - 6*b^5*c^3*d^10*e^2 + 14*b^6*c^2*d^9*e^3 - 11*b^7*c*d^8*e^4 + 3*b^8*d^7
*e^5)*x^2 + (b^4*c^4*d^12 - 4*b^5*c^3*d^11*e + 6*b^6*c^2*d^10*e^2 - 4*b^7*c*d^9*e^3 + b^8*d^8*e^4)*x), -1/30*(
30*((7*A*b^5*c*e^8 - 2*(B*b*c^5 - 2*A*c^6)*d^5*e^3 + (8*B*b^2*c^4 - 9*A*b*c^5)*d^4*e^4 - 4*(3*B*b^3*c^3 + A*b^
2*c^4)*d^3*e^5 + 2*(4*B*b^4*c^2 + 13*A*b^3*c^3)*d^2*e^6 - 2*(B*b^5*c + 12*A*b^4*c^2)*d*e^7)*x^5 + (7*A*b^6*e^8
- 6*(B*b*c^5 - 2*A*c^6)*d^6*e^2 + (22*B*b^2*c^4 - 23*A*b*c^5)*d^5*e^3 - 7*(4*B*b^3*c^3 + 3*A*b^2*c^4)*d^4*e^4
+ 2*(6*B*b^4*c^2 + 37*A*b^3*c^3)*d^3*e^5 + 2*(B*b^5*c - 23*A*b^4*c^2)*d^2*e^6 - (2*B*b^6 + 3*A*b^5*c)*d*e^7)*
x^4 + 3*(7*A*b^6*d*e^7 - 2*(B*b*c^5 - 2*A*c^6)*d^7*e + (6*B*b^2*c^4 - 5*A*b*c^5)*d^6*e^2 - (4*B*b^3*c^3 + 13*A
*b^2*c^4)*d^5*e^3 - 2*(2*B*b^4*c^2 - 11*A*b^3*c^3)*d^4*e^4 + 2*(3*B*b^5*c + A*b^4*c^2)*d^3*e^5 - (2*B*b^6 + 17
*A*b^5*c)*d^2*e^6)*x^3 + (21*A*b^6*d^2*e^6 - 2*(B*b*c^5 - 2*A*c^6)*d^8 + (2*B*b^2*c^4 + 3*A*b*c^5)*d^7*e + (12
*B*b^3*c^3 - 31*A*b^2*c^4)*d^6*e^2 - 14*(2*B*b^4*c^2 - A*b^3*c^3)*d^5*e^3 + 2*(11*B*b^5*c + 27*A*b^4*c^2)*d^4*
e^4 - (6*B*b^6 + 65*A*b^5*c)*d^3*e^5)*x^2 + (7*A*b^6*d^3*e^5 - 2*(B*b^2*c^4 - 2*A*b*c^5)*d^8 + (8*B*b^3*c^3 -
9*A*b^2*c^4)*d^7*e - 4*(3*B*b^4*c^2 + A*b^3*c^3)*d^6*e^2 + 2*(4*B*b^5*c + 13*A*b^4*c^2)*d^5*e^3 - 2*(B*b^6 + 1
2*A*b^5*c)*d^4*e^4)*x)*sqrt(-d)*arctan(sqrt(e*x + d)*sqrt(-d)/d) - 15*((2*(B*b*c^5 - 2*A*c^6)*d^6*e^3 - (9*B*b
^2*c^4 - 11*A*b*c^5)*d^5*e^4)*x^5 + (6*(B*b*c^5 - 2*A*c^6)*d^7*e^2 - (25*B*b^2*c^4 - 29*A*b*c^5)*d^6*e^3 - (9*
B*b^3*c^3 - 11*A*b^2*c^4)*d^5*e^4)*x^4 + 3*(2*(B*b*c^5 - 2*A*c^6)*d^8*e - 7*(B*b^2*c^4 - A*b*c^5)*d^7*e^2 - (9
*B*b^3*c^3 - 11*A*b^2*c^4)*d^6*e^3)*x^3 + (2*(B*b*c^5 - 2*A*c^6)*d^9 - (3*B*b^2*c^4 + A*b*c^5)*d^8*e - 3*(9*B*
b^3*c^3 - 11*A*b^2*c^4)*d^7*e^2)*x^2 + (2*(B*b^2*c^4 - 2*A*b*c^5)*d^9 - (9*B*b^3*c^3 - 11*A*b^2*c^4)*d^8*e)*x)
*sqrt(c/(c*d - b*e))*log((c*e*x + 2*c*d - b*e + 2*(c*d - b*e)*sqrt(e*x + d)*sqrt(c/(c*d - b*e)))/(c*x + b)) +
2*(15*A*b^2*c^4*d^8 - 60*A*b^3*c^3*d^7*e + 90*A*b^4*c^2*d^6*e^2 - 60*A*b^5*c*d^5*e^3 + 15*A*b^6*d^4*e^4 + 15*(
7*A*b^5*c*d*e^7 - (B*b^2*c^4 - 2*A*b*c^5)*d^5*e^3 - 4*(3*B*b^3*c^3 + A*b^2*c^4)*d^4*e^4 + 2*(4*B*b^4*c^2 + 13*
A*b^3*c^3)*d^3*e^5 - 2*(B*b^5*c + 12*A*b^4*c^2)*d^2*e^6)*x^4 + 5*(21*A*b^6*d*e^7 - 9*(B*b^2*c^4 - 2*A*b*c^5)*d
^6*e^2 - 3*(26*B*b^3*c^3 + 11*A*b^2*c^4)*d^5*e^3 + 10*(2*B*b^4*c^2 + 17*A*b^3*c^3)*d^4*e^4 + 10*(B*b^5*c - 9*A
*b^4*c^2)*d^3*e^5 - (6*B*b^6 + 23*A*b^5*c)*d^2*e^6)*x^3 + (245*A*b^6*d^2*e^6 - 45*(B*b^2*c^4 - 2*A*b*c^5)*d^7*
e - 27*(8*B*b^3*c^3 + 5*A*b^2*c^4)*d^6*e^2 - 218*(B*b^4*c^2 - 2*A*b^3*c^3)*d^5*e^3 + 2*(117*B*b^5*c + 179*A*b^
4*c^2)*d^4*e^4 - 7*(10*B*b^6 + 97*A*b^5*c)*d^3*e^5)*x^2 - (15*A*b^2*c^4*d^7*e - 161*A*b^6*d^3*e^5 + 15*(B*b^2*
c^4 - 2*A*b*c^5)*d^8 + 18*(12*B*b^4*c^2 + 5*A*b^3*c^3)*d^6*e^2 - 4*(43*B*b^5*c + 139*A*b^4*c^2)*d^5*e^3 + (46*
B*b^6 + 537*A*b^5*c)*d^4*e^4)*x)*sqrt(e*x + d))/((b^3*c^5*d^9*e^3 - 4*b^4*c^4*d^8*e^4 + 6*b^5*c^3*d^7*e^5 - 4*
b^6*c^2*d^6*e^6 + b^7*c*d^5*e^7)*x^5 + (3*b^3*c^5*d^10*e^2 - 11*b^4*c^4*d^9*e^3 + 14*b^5*c^3*d^8*e^4 - 6*b^6*c
^2*d^7*e^5 - b^7*c*d^6*e^6 + b^8*d^5*e^7)*x^4 + 3*(b^3*c^5*d^11*e - 3*b^4*c^4*d^10*e^2 + 2*b^5*c^3*d^9*e^3 + 2
*b^6*c^2*d^8*e^4 - 3*b^7*c*d^7*e^5 + b^8*d^6*e^6)*x^3 + (b^3*c^5*d^12 - b^4*c^4*d^11*e - 6*b^5*c^3*d^10*e^2 +
14*b^6*c^2*d^9*e^3 - 11*b^7*c*d^8*e^4 + 3*b^8*d^7*e^5)*x^2 + (b^4*c^4*d^12 - 4*b^5*c^3*d^11*e + 6*b^6*c^2*d^10
*e^2 - 4*b^7*c*d^9*e^3 + b^8*d^8*e^4)*x), 1/15*(15*((2*(B*b*c^5 - 2*A*c^6)*d^6*e^3 - (9*B*b^2*c^4 - 11*A*b*c^5
)*d^5*e^4)*x^5 + (6*(B*b*c^5 - 2*A*c^6)*d^7*e^2 - (25*B*b^2*c^4 - 29*A*b*c^5)*d^6*e^3 - (9*B*b^3*c^3 - 11*A*b^
2*c^4)*d^5*e^4)*x^4 + 3*(2*(B*b*c^5 - 2*A*c^6)*d^8*e - 7*(B*b^2*c^4 - A*b*c^5)*d^7*e^2 - (9*B*b^3*c^3 - 11*A*b
^2*c^4)*d^6*e^3)*x^3 + (2*(B*b*c^5 - 2*A*c^6)*d^9 - (3*B*b^2*c^4 + A*b*c^5)*d^8*e - 3*(9*B*b^3*c^3 - 11*A*b^2*
c^4)*d^7*e^2)*x^2 + (2*(B*b^2*c^4 - 2*A*b*c^5)*d^9 - (9*B*b^3*c^3 - 11*A*b^2*c^4)*d^8*e)*x)*sqrt(-c/(c*d - b*e
))*arctan(-(c*d - b*e)*sqrt(e*x + d)*sqrt(-c/(c*d - b*e))/(c*e*x + c*d)) - 15*((7*A*b^5*c*e^8 - 2*(B*b*c^5 - 2
*A*c^6)*d^5*e^3 + (8*B*b^2*c^4 - 9*A*b*c^5)*d^4*e^4 - 4*(3*B*b^3*c^3 + A*b^2*c^4)*d^3*e^5 + 2*(4*B*b^4*c^2 + 1
3*A*b^3*c^3)*d^2*e^6 - 2*(B*b^5*c + 12*A*b^4*c^2)*d*e^7)*x^5 + (7*A*b^6*e^8 - 6*(B*b*c^5 - 2*A*c^6)*d^6*e^2 +
(22*B*b^2*c^4 - 23*A*b*c^5)*d^5*e^3 - 7*(4*B*b^3*c^3 + 3*A*b^2*c^4)*d^4*e^4 + 2*(6*B*b^4*c^2 + 37*A*b^3*c^3)*d
^3*e^5 + 2*(B*b^5*c - 23*A*b^4*c^2)*d^2*e^6 - (2*B*b^6 + 3*A*b^5*c)*d*e^7)*x^4 + 3*(7*A*b^6*d*e^7 - 2*(B*b*c^5
- 2*A*c^6)*d^7*e + (6*B*b^2*c^4 - 5*A*b*c^5)*d^6*e^2 - (4*B*b^3*c^3 + 13*A*b^2*c^4)*d^5*e^3 - 2*(2*B*b^4*c^2
- 11*A*b^3*c^3)*d^4*e^4 + 2*(3*B*b^5*c + A*b^4*c^2)*d^3*e^5 - (2*B*b^6 + 17*A*b^5*c)*d^2*e^6)*x^3 + (21*A*b^6*
d^2*e^6 - 2*(B*b*c^5 - 2*A*c^6)*d^8 + (2*B*b^2*c^4 + 3*A*b*c^5)*d^7*e + (12*B*b^3*c^3 - 31*A*b^2*c^4)*d^6*e^2
- 14*(2*B*b^4*c^2 - A*b^3*c^3)*d^5*e^3 + 2*(11*B*b^5*c + 27*A*b^4*c^2)*d^4*e^4 - (6*B*b^6 + 65*A*b^5*c)*d^3*e^
5)*x^2 + (7*A*b^6*d^3*e^5 - 2*(B*b^2*c^4 - 2*A*b*c^5)*d^8 + (8*B*b^3*c^3 - 9*A*b^2*c^4)*d^7*e - 4*(3*B*b^4*c^2
+ A*b^3*c^3)*d^6*e^2 + 2*(4*B*b^5*c + 13*A*b^4*c^2)*d^5*e^3 - 2*(B*b^6 + 12*A*b^5*c)*d^4*e^4)*x)*sqrt(-d)*arc
tan(sqrt(e*x + d)*sqrt(-d)/d) - (15*A*b^2*c^4*d^8 - 60*A*b^3*c^3*d^7*e + 90*A*b^4*c^2*d^6*e^2 - 60*A*b^5*c*d^5
*e^3 + 15*A*b^6*d^4*e^4 + 15*(7*A*b^5*c*d*e^7 - (B*b^2*c^4 - 2*A*b*c^5)*d^5*e^3 - 4*(3*B*b^3*c^3 + A*b^2*c^4)*
d^4*e^4 + 2*(4*B*b^4*c^2 + 13*A*b^3*c^3)*d^3*e^5 - 2*(B*b^5*c + 12*A*b^4*c^2)*d^2*e^6)*x^4 + 5*(21*A*b^6*d*e^7
- 9*(B*b^2*c^4 - 2*A*b*c^5)*d^6*e^2 - 3*(26*B*b^3*c^3 + 11*A*b^2*c^4)*d^5*e^3 + 10*(2*B*b^4*c^2 + 17*A*b^3*c^
3)*d^4*e^4 + 10*(B*b^5*c - 9*A*b^4*c^2)*d^3*e^5 - (6*B*b^6 + 23*A*b^5*c)*d^2*e^6)*x^3 + (245*A*b^6*d^2*e^6 - 4
5*(B*b^2*c^4 - 2*A*b*c^5)*d^7*e - 27*(8*B*b^3*c^3 + 5*A*b^2*c^4)*d^6*e^2 - 218*(B*b^4*c^2 - 2*A*b^3*c^3)*d^5*e
^3 + 2*(117*B*b^5*c + 179*A*b^4*c^2)*d^4*e^4 - 7*(10*B*b^6 + 97*A*b^5*c)*d^3*e^5)*x^2 - (15*A*b^2*c^4*d^7*e -
161*A*b^6*d^3*e^5 + 15*(B*b^2*c^4 - 2*A*b*c^5)*d^8 + 18*(12*B*b^4*c^2 + 5*A*b^3*c^3)*d^6*e^2 - 4*(43*B*b^5*c +
139*A*b^4*c^2)*d^5*e^3 + (46*B*b^6 + 537*A*b^5*c)*d^4*e^4)*x)*sqrt(e*x + d))/((b^3*c^5*d^9*e^3 - 4*b^4*c^4*d^
8*e^4 + 6*b^5*c^3*d^7*e^5 - 4*b^6*c^2*d^6*e^6 + b^7*c*d^5*e^7)*x^5 + (3*b^3*c^5*d^10*e^2 - 11*b^4*c^4*d^9*e^3
+ 14*b^5*c^3*d^8*e^4 - 6*b^6*c^2*d^7*e^5 - b^7*c*d^6*e^6 + b^8*d^5*e^7)*x^4 + 3*(b^3*c^5*d^11*e - 3*b^4*c^4*d^
10*e^2 + 2*b^5*c^3*d^9*e^3 + 2*b^6*c^2*d^8*e^4 - 3*b^7*c*d^7*e^5 + b^8*d^6*e^6)*x^3 + (b^3*c^5*d^12 - b^4*c^4*
d^11*e - 6*b^5*c^3*d^10*e^2 + 14*b^6*c^2*d^9*e^3 - 11*b^7*c*d^8*e^4 + 3*b^8*d^7*e^5)*x^2 + (b^4*c^4*d^12 - 4*b
^5*c^3*d^11*e + 6*b^6*c^2*d^10*e^2 - 4*b^7*c*d^9*e^3 + b^8*d^8*e^4)*x)]
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giac [B] time = 0.49, size = 867, normalized size = 1.90 \begin {gather*} -\frac {{\left (2 \, B b c^{5} d - 4 \, A c^{6} d - 9 \, B b^{2} c^{4} e + 11 \, A b c^{5} e\right )} \arctan \left (\frac {\sqrt {x e + d} c}{\sqrt {-c^{2} d + b c e}}\right )}{{\left (b^{3} c^{4} d^{4} - 4 \, b^{4} c^{3} d^{3} e + 6 \, b^{5} c^{2} d^{2} e^{2} - 4 \, b^{6} c d e^{3} + b^{7} e^{4}\right )} \sqrt {-c^{2} d + b c e}} + \frac {{\left (x e + d\right )}^{\frac {3}{2}} B b c^{4} d^{4} e - 2 \, {\left (x e + d\right )}^{\frac {3}{2}} A c^{5} d^{4} e - \sqrt {x e + d} B b c^{4} d^{5} e + 2 \, \sqrt {x e + d} A c^{5} d^{5} e + 4 \, {\left (x e + d\right )}^{\frac {3}{2}} A b c^{4} d^{3} e^{2} - 5 \, \sqrt {x e + d} A b c^{4} d^{4} e^{2} - 6 \, {\left (x e + d\right )}^{\frac {3}{2}} A b^{2} c^{3} d^{2} e^{3} + 10 \, \sqrt {x e + d} A b^{2} c^{3} d^{3} e^{3} + 4 \, {\left (x e + d\right )}^{\frac {3}{2}} A b^{3} c^{2} d e^{4} - 10 \, \sqrt {x e + d} A b^{3} c^{2} d^{2} e^{4} - {\left (x e + d\right )}^{\frac {3}{2}} A b^{4} c e^{5} + 5 \, \sqrt {x e + d} A b^{4} c d e^{5} - \sqrt {x e + d} A b^{5} e^{6}}{{\left (b^{2} c^{4} d^{8} - 4 \, b^{3} c^{3} d^{7} e + 6 \, b^{4} c^{2} d^{6} e^{2} - 4 \, b^{5} c d^{5} e^{3} + b^{6} d^{4} e^{4}\right )} {\left ({\left (x e + d\right )}^{2} c - 2 \, {\left (x e + d\right )} c d + c d^{2} + {\left (x e + d\right )} b e - b d e\right )}} + \frac {2 \, {\left (90 \, {\left (x e + d\right )}^{2} B c^{2} d^{3} e^{2} + 15 \, {\left (x e + d\right )} B c^{2} d^{4} e^{2} + 3 \, B c^{2} d^{5} e^{2} - 60 \, {\left (x e + d\right )}^{2} B b c d^{2} e^{3} - 150 \, {\left (x e + d\right )}^{2} A c^{2} d^{2} e^{3} - 20 \, {\left (x e + d\right )} B b c d^{3} e^{3} - 20 \, {\left (x e + d\right )} A c^{2} d^{3} e^{3} - 6 \, B b c d^{4} e^{3} - 3 \, A c^{2} d^{4} e^{3} + 15 \, {\left (x e + d\right )}^{2} B b^{2} d e^{4} + 150 \, {\left (x e + d\right )}^{2} A b c d e^{4} + 5 \, {\left (x e + d\right )} B b^{2} d^{2} e^{4} + 30 \, {\left (x e + d\right )} A b c d^{2} e^{4} + 3 \, B b^{2} d^{3} e^{4} + 6 \, A b c d^{3} e^{4} - 45 \, {\left (x e + d\right )}^{2} A b^{2} e^{5} - 10 \, {\left (x e + d\right )} A b^{2} d e^{5} - 3 \, A b^{2} d^{2} e^{5}\right )}}{15 \, {\left (c^{4} d^{8} - 4 \, b c^{3} d^{7} e + 6 \, b^{2} c^{2} d^{6} e^{2} - 4 \, b^{3} c d^{5} e^{3} + b^{4} d^{4} e^{4}\right )} {\left (x e + d\right )}^{\frac {5}{2}}} + \frac {{\left (2 \, B b d - 4 \, A c d - 7 \, A b e\right )} \arctan \left (\frac {\sqrt {x e + d}}{\sqrt {-d}}\right )}{b^{3} \sqrt {-d} d^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((B*x+A)/(e*x+d)^(7/2)/(c*x^2+b*x)^2,x, algorithm="giac")
[Out]
-(2*B*b*c^5*d - 4*A*c^6*d - 9*B*b^2*c^4*e + 11*A*b*c^5*e)*arctan(sqrt(x*e + d)*c/sqrt(-c^2*d + b*c*e))/((b^3*c
^4*d^4 - 4*b^4*c^3*d^3*e + 6*b^5*c^2*d^2*e^2 - 4*b^6*c*d*e^3 + b^7*e^4)*sqrt(-c^2*d + b*c*e)) + ((x*e + d)^(3/
2)*B*b*c^4*d^4*e - 2*(x*e + d)^(3/2)*A*c^5*d^4*e - sqrt(x*e + d)*B*b*c^4*d^5*e + 2*sqrt(x*e + d)*A*c^5*d^5*e +
4*(x*e + d)^(3/2)*A*b*c^4*d^3*e^2 - 5*sqrt(x*e + d)*A*b*c^4*d^4*e^2 - 6*(x*e + d)^(3/2)*A*b^2*c^3*d^2*e^3 + 1
0*sqrt(x*e + d)*A*b^2*c^3*d^3*e^3 + 4*(x*e + d)^(3/2)*A*b^3*c^2*d*e^4 - 10*sqrt(x*e + d)*A*b^3*c^2*d^2*e^4 - (
x*e + d)^(3/2)*A*b^4*c*e^5 + 5*sqrt(x*e + d)*A*b^4*c*d*e^5 - sqrt(x*e + d)*A*b^5*e^6)/((b^2*c^4*d^8 - 4*b^3*c^
3*d^7*e + 6*b^4*c^2*d^6*e^2 - 4*b^5*c*d^5*e^3 + b^6*d^4*e^4)*((x*e + d)^2*c - 2*(x*e + d)*c*d + c*d^2 + (x*e +
d)*b*e - b*d*e)) + 2/15*(90*(x*e + d)^2*B*c^2*d^3*e^2 + 15*(x*e + d)*B*c^2*d^4*e^2 + 3*B*c^2*d^5*e^2 - 60*(x*
e + d)^2*B*b*c*d^2*e^3 - 150*(x*e + d)^2*A*c^2*d^2*e^3 - 20*(x*e + d)*B*b*c*d^3*e^3 - 20*(x*e + d)*A*c^2*d^3*e
^3 - 6*B*b*c*d^4*e^3 - 3*A*c^2*d^4*e^3 + 15*(x*e + d)^2*B*b^2*d*e^4 + 150*(x*e + d)^2*A*b*c*d*e^4 + 5*(x*e + d
)*B*b^2*d^2*e^4 + 30*(x*e + d)*A*b*c*d^2*e^4 + 3*B*b^2*d^3*e^4 + 6*A*b*c*d^3*e^4 - 45*(x*e + d)^2*A*b^2*e^5 -
10*(x*e + d)*A*b^2*d*e^5 - 3*A*b^2*d^2*e^5)/((c^4*d^8 - 4*b*c^3*d^7*e + 6*b^2*c^2*d^6*e^2 - 4*b^3*c*d^5*e^3 +
b^4*d^4*e^4)*(x*e + d)^(5/2)) + (2*B*b*d - 4*A*c*d - 7*A*b*e)*arctan(sqrt(x*e + d)/sqrt(-d))/(b^3*sqrt(-d)*d^4
)
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maple [A] time = 0.10, size = 707, normalized size = 1.55 \begin {gather*} -\frac {11 A \,c^{5} e \arctan \left (\frac {\sqrt {e x +d}\, c}{\sqrt {\left (b e -c d \right ) c}}\right )}{\left (b e -c d \right )^{4} \sqrt {\left (b e -c d \right ) c}\, b^{2}}+\frac {4 A \,c^{6} d \arctan \left (\frac {\sqrt {e x +d}\, c}{\sqrt {\left (b e -c d \right ) c}}\right )}{\left (b e -c d \right )^{4} \sqrt {\left (b e -c d \right ) c}\, b^{3}}+\frac {9 B \,c^{4} e \arctan \left (\frac {\sqrt {e x +d}\, c}{\sqrt {\left (b e -c d \right ) c}}\right )}{\left (b e -c d \right )^{4} \sqrt {\left (b e -c d \right ) c}\, b}-\frac {2 B \,c^{5} d \arctan \left (\frac {\sqrt {e x +d}\, c}{\sqrt {\left (b e -c d \right ) c}}\right )}{\left (b e -c d \right )^{4} \sqrt {\left (b e -c d \right ) c}\, b^{2}}-\frac {\sqrt {e x +d}\, A \,c^{5} e}{\left (b e -c d \right )^{4} \left (c e x +b e \right ) b^{2}}+\frac {\sqrt {e x +d}\, B \,c^{4} e}{\left (b e -c d \right )^{4} \left (c e x +b e \right ) b}-\frac {6 A \,b^{2} e^{5}}{\left (b e -c d \right )^{4} \sqrt {e x +d}\, d^{4}}+\frac {20 A b c \,e^{4}}{\left (b e -c d \right )^{4} \sqrt {e x +d}\, d^{3}}-\frac {20 A \,c^{2} e^{3}}{\left (b e -c d \right )^{4} \sqrt {e x +d}\, d^{2}}+\frac {2 B \,b^{2} e^{4}}{\left (b e -c d \right )^{4} \sqrt {e x +d}\, d^{3}}-\frac {8 B b c \,e^{3}}{\left (b e -c d \right )^{4} \sqrt {e x +d}\, d^{2}}+\frac {12 B \,c^{2} e^{2}}{\left (b e -c d \right )^{4} \sqrt {e x +d}\, d}-\frac {4 A b \,e^{4}}{3 \left (b e -c d \right )^{3} \left (e x +d \right )^{\frac {3}{2}} d^{3}}+\frac {8 A c \,e^{3}}{3 \left (b e -c d \right )^{3} \left (e x +d \right )^{\frac {3}{2}} d^{2}}+\frac {2 B b \,e^{3}}{3 \left (b e -c d \right )^{3} \left (e x +d \right )^{\frac {3}{2}} d^{2}}-\frac {2 B c \,e^{2}}{\left (b e -c d \right )^{3} \left (e x +d \right )^{\frac {3}{2}} d}-\frac {2 A \,e^{3}}{5 \left (b e -c d \right )^{2} \left (e x +d \right )^{\frac {5}{2}} d^{2}}+\frac {2 B \,e^{2}}{5 \left (b e -c d \right )^{2} \left (e x +d \right )^{\frac {5}{2}} d}+\frac {7 A e \arctanh \left (\frac {\sqrt {e x +d}}{\sqrt {d}}\right )}{b^{2} d^{\frac {9}{2}}}+\frac {4 A c \arctanh \left (\frac {\sqrt {e x +d}}{\sqrt {d}}\right )}{b^{3} d^{\frac {7}{2}}}-\frac {2 B \arctanh \left (\frac {\sqrt {e x +d}}{\sqrt {d}}\right )}{b^{2} d^{\frac {7}{2}}}-\frac {\sqrt {e x +d}\, A}{b^{2} d^{4} x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
int((B*x+A)/(e*x+d)^(7/2)/(c*x^2+b*x)^2,x)
[Out]
-e*c^5/(b*e-c*d)^4/b^2*(e*x+d)^(1/2)/(c*e*x+b*e)*A+e*c^4/(b*e-c*d)^4/b*(e*x+d)^(1/2)/(c*e*x+b*e)*B-11*e*c^5/(b
*e-c*d)^4/b^2/((b*e-c*d)*c)^(1/2)*arctan((e*x+d)^(1/2)/((b*e-c*d)*c)^(1/2)*c)*A+4*c^6/(b*e-c*d)^4/b^3/((b*e-c*
d)*c)^(1/2)*arctan((e*x+d)^(1/2)/((b*e-c*d)*c)^(1/2)*c)*A*d+9*e*c^4/(b*e-c*d)^4/b/((b*e-c*d)*c)^(1/2)*arctan((
e*x+d)^(1/2)/((b*e-c*d)*c)^(1/2)*c)*B-2*c^5/(b*e-c*d)^4/b^2/((b*e-c*d)*c)^(1/2)*arctan((e*x+d)^(1/2)/((b*e-c*d
)*c)^(1/2)*c)*B*d-1/b^2/d^4*A*(e*x+d)^(1/2)/x+7*e/b^2/d^(9/2)*arctanh((e*x+d)^(1/2)/d^(1/2))*A+4/b^3/d^(7/2)*a
rctanh((e*x+d)^(1/2)/d^(1/2))*A*c-2/b^2/d^(7/2)*arctanh((e*x+d)^(1/2)/d^(1/2))*B-2/5*e^3/(b*e-c*d)^2/d^2/(e*x+
d)^(5/2)*A+2/5*e^2/(b*e-c*d)^2/d/(e*x+d)^(5/2)*B-4/3*e^4/(b*e-c*d)^3/d^3/(e*x+d)^(3/2)*A*b+8/3*e^3/(b*e-c*d)^3
/d^2/(e*x+d)^(3/2)*A*c+2/3*e^3/(b*e-c*d)^3/d^2/(e*x+d)^(3/2)*B*b-2*e^2/(b*e-c*d)^3/d/(e*x+d)^(3/2)*B*c-6*e^5/(
b*e-c*d)^4/d^4/(e*x+d)^(1/2)*A*b^2+20*e^4/(b*e-c*d)^4/d^3/(e*x+d)^(1/2)*A*b*c-20*e^3/(b*e-c*d)^4/d^2/(e*x+d)^(
1/2)*A*c^2+2*e^4/(b*e-c*d)^4/d^3/(e*x+d)^(1/2)*B*b^2-8*e^3/(b*e-c*d)^4/d^2/(e*x+d)^(1/2)*B*b*c+12*e^2/(b*e-c*d
)^4/d/(e*x+d)^(1/2)*B*c^2
________________________________________________________________________________________
maxima [F(-2)] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: ValueError} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((B*x+A)/(e*x+d)^(7/2)/(c*x^2+b*x)^2,x, algorithm="maxima")
[Out]
Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'a
ssume' command before evaluation *may* help (example of legal syntax is 'assume(b*e-c*d>0)', see `assume?` for
more details)Is b*e-c*d positive or negative?
________________________________________________________________________________________
mupad [B] time = 7.16, size = 20597, normalized size = 45.07
result too large to display
Verification of antiderivative is not currently implemented for this CAS.
[In]
int((A + B*x)/((b*x + c*x^2)^2*(d + e*x)^(7/2)),x)
[Out]
log((((49*A^2*b^2*e^2 + 16*A^2*c^2*d^2 + 4*B^2*b^2*d^2 - 16*A*B*b*c*d^2 - 28*A*B*b^2*d*e + 56*A^2*b*c*d*e)/(4*
b^6*d^9))^(1/2)*((d + e*x)^(1/2)*((49*A^2*b^2*e^2 + 16*A^2*c^2*d^2 + 4*B^2*b^2*d^2 - 16*A*B*b*c*d^2 - 28*A*B*b
^2*d*e + 56*A^2*b*c*d*e)/(4*b^6*d^9))^(1/2)*(16*b^12*c^23*d^41*e^2 - 328*b^13*c^22*d^40*e^3 + 3200*b^14*c^21*d
^39*e^4 - 19760*b^15*c^20*d^38*e^5 + 86640*b^16*c^19*d^37*e^6 - 286824*b^17*c^18*d^36*e^7 + 744192*b^18*c^17*d
^35*e^8 - 1550400*b^19*c^16*d^34*e^9 + 2635680*b^20*c^15*d^33*e^10 - 3695120*b^21*c^14*d^32*e^11 + 4299776*b^2
2*c^13*d^31*e^12 - 4165408*b^23*c^12*d^30*e^13 + 3359200*b^24*c^11*d^29*e^14 - 2248080*b^25*c^10*d^28*e^15 + 1
240320*b^26*c^9*d^27*e^16 - 558144*b^27*c^8*d^26*e^17 + 201552*b^28*c^7*d^25*e^18 - 57000*b^29*c^6*d^24*e^19 +
12160*b^30*c^5*d^23*e^20 - 1840*b^31*c^4*d^22*e^21 + 176*b^32*c^3*d^21*e^22 - 8*b^33*c^2*d^20*e^23) - 8*A*b^1
0*c^23*d^37*e^3 + 148*A*b^11*c^22*d^36*e^4 - 1160*A*b^12*c^21*d^35*e^5 + 4760*A*b^13*c^20*d^34*e^6 - 8036*A*b^
14*c^19*d^33*e^7 - 21868*A*b^15*c^18*d^32*e^8 + 194304*A*b^16*c^17*d^31*e^9 - 709280*A*b^17*c^16*d^30*e^10 + 1
744160*A*b^18*c^15*d^29*e^11 - 3218072*A*b^19*c^14*d^28*e^12 + 4654832*A*b^20*c^13*d^27*e^13 - 5394480*A*b^21*
c^12*d^26*e^14 + 5063240*A*b^22*c^11*d^25*e^15 - 3863800*A*b^23*c^10*d^24*e^16 + 2393152*A*b^24*c^9*d^23*e^17
- 1194528*A*b^25*c^8*d^22*e^18 + 474056*A*b^26*c^7*d^21*e^19 - 146300*A*b^27*c^6*d^20*e^20 + 33880*A*b^28*c^5*
d^19*e^21 - 5544*A*b^29*c^4*d^18*e^22 + 572*A*b^30*c^3*d^17*e^23 - 28*A*b^31*c^2*d^16*e^24 + 4*B*b^11*c^22*d^3
7*e^3 - 144*B*b^12*c^21*d^36*e^4 + 1840*B*b^13*c^20*d^35*e^5 - 13160*B*b^14*c^19*d^34*e^6 + 62328*B*b^15*c^18*
d^33*e^7 - 212800*B*b^16*c^17*d^32*e^8 + 550432*B*b^17*c^16*d^31*e^9 - 1113120*B*b^18*c^15*d^30*e^10 + 1796600
*B*b^19*c^14*d^29*e^11 - 2345824*B*b^20*c^13*d^28*e^12 + 2498496*B*b^21*c^12*d^27*e^13 - 2179632*B*b^22*c^11*d
^26*e^14 + 1557920*B*b^23*c^10*d^25*e^15 - 909120*B*b^24*c^9*d^24*e^16 + 429664*B*b^25*c^8*d^23*e^17 - 162208*
B*b^26*c^7*d^22*e^18 + 47844*B*b^27*c^6*d^21*e^19 - 10640*B*b^28*c^5*d^20*e^20 + 1680*B*b^29*c^4*d^19*e^21 - 1
68*B*b^30*c^3*d^18*e^22 + 8*B*b^31*c^2*d^17*e^23) + (d + e*x)^(1/2)*(1088*A^2*b^7*c^24*d^33*e^3 - 64*A^2*b^6*c
^25*d^34*e^2 - 8404*A^2*b^8*c^23*d^32*e^4 + 38720*A^2*b^9*c^22*d^31*e^5 - 116512*A^2*b^10*c^21*d^30*e^6 + 2309
12*A^2*b^11*c^20*d^29*e^7 - 267432*A^2*b^12*c^19*d^28*e^8 + 38544*A^2*b^13*c^18*d^27*e^9 + 473880*A^2*b^14*c^1
7*d^26*e^10 - 851136*A^2*b^15*c^16*d^25*e^11 + 393646*A^2*b^16*c^15*d^24*e^12 + 1207368*A^2*b^17*c^14*d^23*e^1
3 - 3343724*A^2*b^18*c^13*d^22*e^14 + 4835160*A^2*b^19*c^12*d^21*e^15 - 4903382*A^2*b^20*c^11*d^20*e^16 + 3751
968*A^2*b^21*c^10*d^19*e^17 - 2217072*A^2*b^22*c^9*d^18*e^18 + 1013232*A^2*b^23*c^8*d^17*e^19 - 353210*A^2*b^2
4*c^7*d^16*e^20 + 91080*A^2*b^25*c^6*d^15*e^21 - 16412*A^2*b^26*c^5*d^14*e^22 + 1848*A^2*b^27*c^4*d^13*e^23 -
98*A^2*b^28*c^3*d^12*e^24 - 16*B^2*b^8*c^23*d^34*e^2 + 328*B^2*b^9*c^22*d^33*e^3 - 3074*B^2*b^10*c^21*d^32*e^4
+ 17576*B^2*b^11*c^20*d^31*e^5 - 69252*B^2*b^12*c^19*d^30*e^6 + 201648*B^2*b^13*c^18*d^29*e^7 - 454686*B^2*b^
14*c^17*d^28*e^8 + 821328*B^2*b^15*c^16*d^27*e^9 - 1218432*B^2*b^16*c^15*d^26*e^10 + 1509384*B^2*b^17*c^14*d^2
5*e^11 - 1574606*B^2*b^18*c^13*d^24*e^12 + 1384168*B^2*b^19*c^12*d^23*e^13 - 1019324*B^2*b^20*c^11*d^22*e^14 +
622176*B^2*b^21*c^10*d^21*e^15 - 310242*B^2*b^22*c^9*d^20*e^16 + 124032*B^2*b^23*c^8*d^19*e^17 - 38760*B^2*b^
24*c^7*d^18*e^18 + 9120*B^2*b^25*c^6*d^17*e^19 - 1520*B^2*b^26*c^5*d^16*e^20 + 160*B^2*b^27*c^4*d^15*e^21 - 8*
B^2*b^28*c^3*d^14*e^22 + 64*A*B*b^7*c^24*d^34*e^2 - 1200*A*B*b^8*c^23*d^33*e^3 + 10252*A*B*b^9*c^22*d^32*e^4 -
52944*A*B*b^10*c^21*d^31*e^5 + 184216*A*B*b^11*c^20*d^30*e^6 - 452112*A*B*b^12*c^19*d^29*e^7 + 781428*A*B*b^1
3*c^18*d^28*e^8 - 863424*A*B*b^14*c^17*d^27*e^9 + 255408*A*B*b^15*c^16*d^26*e^10 + 1244088*A*B*b^16*c^15*d^25*
e^11 - 3244396*A*B*b^17*c^14*d^24*e^12 + 4868800*A*B*b^18*c^13*d^23*e^13 - 5345768*A*B*b^19*c^12*d^22*e^14 + 4
568696*A*B*b^20*c^11*d^21*e^15 - 3100404*A*B*b^21*c^10*d^20*e^16 + 1674432*A*B*b^22*c^9*d^19*e^17 - 713184*A*B
*b^23*c^8*d^18*e^18 + 234840*A*B*b^24*c^7*d^17*e^19 - 57760*A*B*b^25*c^6*d^16*e^20 + 10000*A*B*b^26*c^5*d^15*e
^21 - 1088*A*B*b^27*c^4*d^14*e^22 + 56*A*B*b^28*c^3*d^13*e^23))*((49*A^2*b^2*e^2 + 16*A^2*c^2*d^2 + 4*B^2*b^2*
d^2 - 16*A*B*b*c*d^2 - 28*A*B*b^2*d*e + 56*A^2*b*c*d*e)/(4*b^6*d^9))^(1/2) + 32*A^3*b^4*c^25*d^30*e^3 - 480*A^
3*b^5*c^24*d^29*e^4 + 3590*A^3*b^6*c^23*d^28*e^5 - 17780*A^3*b^7*c^22*d^27*e^6 + 62874*A^3*b^8*c^21*d^26*e^7 -
157248*A^3*b^9*c^20*d^25*e^8 + 254443*A^3*b^10*c^19*d^24*e^9 - 163416*A^3*b^11*c^18*d^23*e^10 - 380204*A^3*b^
12*c^17*d^22*e^11 + 1403292*A^3*b^13*c^16*d^21*e^12 - 2458995*A^3*b^14*c^15*d^20*e^13 + 2901724*A^3*b^15*c^14*
d^19*e^14 - 2487478*A^3*b^16*c^13*d^18*e^15 + 1581048*A^3*b^17*c^12*d^17*e^16 - 741891*A^3*b^18*c^11*d^16*e^17
+ 250736*A^3*b^19*c^10*d^15*e^18 - 57912*A^3*b^20*c^9*d^14*e^19 + 8204*A^3*b^21*c^8*d^13*e^20 - 539*A^3*b^22*
c^7*d^12*e^21 - 4*B^3*b^7*c^22*d^30*e^3 + 18*B^3*b^8*c^21*d^29*e^4 + 344*B^3*b^9*c^20*d^28*e^5 - 4228*B^3*b^10
*c^19*d^27*e^6 + 22848*B^3*b^11*c^18*d^26*e^7 - 76706*B^3*b^12*c^17*d^25*e^8 + 178640*B^3*b^13*c^16*d^24*e^9 -
304128*B^3*b^14*c^15*d^23*e^10 + 389136*B^3*b^15*c^14*d^22*e^11 - 379346*B^3*b^16*c^13*d^21*e^12 + 282744*B^3
*b^17*c^12*d^20*e^13 - 160244*B^3*b^18*c^11*d^19*e^14 + 67984*B^3*b^19*c^10*d^18*e^15 - 20958*B^3*b^20*c^9*d^1
7*e^16 + 4448*B^3*b^21*c^8*d^16*e^17 - 584*B^3*b^22*c^7*d^15*e^18 + 36*B^3*b^23*c^6*d^14*e^19 + 24*A*B^2*b^6*c
^23*d^30*e^3 - 192*A*B^2*b^7*c^22*d^29*e^4 - 111*A*B^2*b^8*c^21*d^28*e^5 + 6636*A*B^2*b^9*c^20*d^27*e^6 - 3297
0*A*B^2*b^10*c^19*d^26*e^7 + 75432*A*B^2*b^11*c^18*d^25*e^8 - 55881*A*B^2*b^12*c^17*d^24*e^9 - 172920*A*B^2*b^
13*c^16*d^23*e^10 + 664488*A*B^2*b^14*c^15*d^22*e^11 - 1211100*A*B^2*b^15*c^14*d^21*e^12 + 1461999*A*B^2*b^16*
c^13*d^20*e^13 - 1264452*A*B^2*b^17*c^12*d^19*e^14 + 802158*A*B^2*b^18*c^11*d^18*e^15 - 372624*A*B^2*b^19*c^10
*d^17*e^16 + 123945*A*B^2*b^20*c^9*d^16*e^17 - 28080*A*B^2*b^21*c^8*d^15*e^18 + 3900*A*B^2*b^22*c^7*d^14*e^19
- 252*A*B^2*b^23*c^6*d^13*e^20 - 48*A^2*B*b^5*c^24*d^30*e^3 + 552*A^2*B*b^6*c^23*d^29*e^4 - 2949*A^2*B*b^7*c^2
2*d^28*e^5 + 11844*A^2*B*b^8*c^21*d^27*e^6 - 47628*A^2*B*b^9*c^20*d^26*e^7 + 176274*A^2*B*b^10*c^19*d^25*e^8 -
502782*A^2*B*b^11*c^18*d^24*e^9 + 1030776*A^2*B*b^12*c^17*d^23*e^10 - 1480512*A^2*B*b^13*c^16*d^22*e^11 + 141
1806*A^2*B*b^14*c^15*d^21*e^12 - 703164*A^2*B*b^15*c^14*d^20*e^13 - 205212*A^2*B*b^16*c^13*d^19*e^14 + 729540*
A^2*B*b^17*c^12*d^18*e^15 - 708498*A^2*B*b^18*c^11*d^17*e^16 + 417222*A^2*B*b^19*c^10*d^16*e^17 - 162912*A^2*B
*b^20*c^9*d^15*e^18 + 41592*A^2*B*b^21*c^8*d^14*e^19 - 6342*A^2*B*b^22*c^7*d^13*e^20 + 441*A^2*B*b^23*c^6*d^12
*e^21)*((49*A^2*b^2*e^2 + 16*A^2*c^2*d^2 + 4*B^2*b^2*d^2 - 16*A*B*b*c*d^2 - 28*A*B*b^2*d*e + 56*A^2*b*c*d*e)/(
4*b^6*d^9))^(1/2) - log(32*A^3*b^4*c^25*d^30*e^3 - ((((49*A^2*b^2*e^2)/4 + 4*A^2*c^2*d^2 + B^2*b^2*d^2 - 4*A*B
*b*c*d^2 - 7*A*B*b^2*d*e + 14*A^2*b*c*d*e)/(b^6*d^9))^(1/2)*((d + e*x)^(1/2)*(((49*A^2*b^2*e^2)/4 + 4*A^2*c^2*
d^2 + B^2*b^2*d^2 - 4*A*B*b*c*d^2 - 7*A*B*b^2*d*e + 14*A^2*b*c*d*e)/(b^6*d^9))^(1/2)*(16*b^12*c^23*d^41*e^2 -
328*b^13*c^22*d^40*e^3 + 3200*b^14*c^21*d^39*e^4 - 19760*b^15*c^20*d^38*e^5 + 86640*b^16*c^19*d^37*e^6 - 28682
4*b^17*c^18*d^36*e^7 + 744192*b^18*c^17*d^35*e^8 - 1550400*b^19*c^16*d^34*e^9 + 2635680*b^20*c^15*d^33*e^10 -
3695120*b^21*c^14*d^32*e^11 + 4299776*b^22*c^13*d^31*e^12 - 4165408*b^23*c^12*d^30*e^13 + 3359200*b^24*c^11*d^
29*e^14 - 2248080*b^25*c^10*d^28*e^15 + 1240320*b^26*c^9*d^27*e^16 - 558144*b^27*c^8*d^26*e^17 + 201552*b^28*c
^7*d^25*e^18 - 57000*b^29*c^6*d^24*e^19 + 12160*b^30*c^5*d^23*e^20 - 1840*b^31*c^4*d^22*e^21 + 176*b^32*c^3*d^
21*e^22 - 8*b^33*c^2*d^20*e^23) + 8*A*b^10*c^23*d^37*e^3 - 148*A*b^11*c^22*d^36*e^4 + 1160*A*b^12*c^21*d^35*e^
5 - 4760*A*b^13*c^20*d^34*e^6 + 8036*A*b^14*c^19*d^33*e^7 + 21868*A*b^15*c^18*d^32*e^8 - 194304*A*b^16*c^17*d^
31*e^9 + 709280*A*b^17*c^16*d^30*e^10 - 1744160*A*b^18*c^15*d^29*e^11 + 3218072*A*b^19*c^14*d^28*e^12 - 465483
2*A*b^20*c^13*d^27*e^13 + 5394480*A*b^21*c^12*d^26*e^14 - 5063240*A*b^22*c^11*d^25*e^15 + 3863800*A*b^23*c^10*
d^24*e^16 - 2393152*A*b^24*c^9*d^23*e^17 + 1194528*A*b^25*c^8*d^22*e^18 - 474056*A*b^26*c^7*d^21*e^19 + 146300
*A*b^27*c^6*d^20*e^20 - 33880*A*b^28*c^5*d^19*e^21 + 5544*A*b^29*c^4*d^18*e^22 - 572*A*b^30*c^3*d^17*e^23 + 28
*A*b^31*c^2*d^16*e^24 - 4*B*b^11*c^22*d^37*e^3 + 144*B*b^12*c^21*d^36*e^4 - 1840*B*b^13*c^20*d^35*e^5 + 13160*
B*b^14*c^19*d^34*e^6 - 62328*B*b^15*c^18*d^33*e^7 + 212800*B*b^16*c^17*d^32*e^8 - 550432*B*b^17*c^16*d^31*e^9
+ 1113120*B*b^18*c^15*d^30*e^10 - 1796600*B*b^19*c^14*d^29*e^11 + 2345824*B*b^20*c^13*d^28*e^12 - 2498496*B*b^
21*c^12*d^27*e^13 + 2179632*B*b^22*c^11*d^26*e^14 - 1557920*B*b^23*c^10*d^25*e^15 + 909120*B*b^24*c^9*d^24*e^1
6 - 429664*B*b^25*c^8*d^23*e^17 + 162208*B*b^26*c^7*d^22*e^18 - 47844*B*b^27*c^6*d^21*e^19 + 10640*B*b^28*c^5*
d^20*e^20 - 1680*B*b^29*c^4*d^19*e^21 + 168*B*b^30*c^3*d^18*e^22 - 8*B*b^31*c^2*d^17*e^23) + (d + e*x)^(1/2)*(
1088*A^2*b^7*c^24*d^33*e^3 - 64*A^2*b^6*c^25*d^34*e^2 - 8404*A^2*b^8*c^23*d^32*e^4 + 38720*A^2*b^9*c^22*d^31*e
^5 - 116512*A^2*b^10*c^21*d^30*e^6 + 230912*A^2*b^11*c^20*d^29*e^7 - 267432*A^2*b^12*c^19*d^28*e^8 + 38544*A^2
*b^13*c^18*d^27*e^9 + 473880*A^2*b^14*c^17*d^26*e^10 - 851136*A^2*b^15*c^16*d^25*e^11 + 393646*A^2*b^16*c^15*d
^24*e^12 + 1207368*A^2*b^17*c^14*d^23*e^13 - 3343724*A^2*b^18*c^13*d^22*e^14 + 4835160*A^2*b^19*c^12*d^21*e^15
- 4903382*A^2*b^20*c^11*d^20*e^16 + 3751968*A^2*b^21*c^10*d^19*e^17 - 2217072*A^2*b^22*c^9*d^18*e^18 + 101323
2*A^2*b^23*c^8*d^17*e^19 - 353210*A^2*b^24*c^7*d^16*e^20 + 91080*A^2*b^25*c^6*d^15*e^21 - 16412*A^2*b^26*c^5*d
^14*e^22 + 1848*A^2*b^27*c^4*d^13*e^23 - 98*A^2*b^28*c^3*d^12*e^24 - 16*B^2*b^8*c^23*d^34*e^2 + 328*B^2*b^9*c^
22*d^33*e^3 - 3074*B^2*b^10*c^21*d^32*e^4 + 17576*B^2*b^11*c^20*d^31*e^5 - 69252*B^2*b^12*c^19*d^30*e^6 + 2016
48*B^2*b^13*c^18*d^29*e^7 - 454686*B^2*b^14*c^17*d^28*e^8 + 821328*B^2*b^15*c^16*d^27*e^9 - 1218432*B^2*b^16*c
^15*d^26*e^10 + 1509384*B^2*b^17*c^14*d^25*e^11 - 1574606*B^2*b^18*c^13*d^24*e^12 + 1384168*B^2*b^19*c^12*d^23
*e^13 - 1019324*B^2*b^20*c^11*d^22*e^14 + 622176*B^2*b^21*c^10*d^21*e^15 - 310242*B^2*b^22*c^9*d^20*e^16 + 124
032*B^2*b^23*c^8*d^19*e^17 - 38760*B^2*b^24*c^7*d^18*e^18 + 9120*B^2*b^25*c^6*d^17*e^19 - 1520*B^2*b^26*c^5*d^
16*e^20 + 160*B^2*b^27*c^4*d^15*e^21 - 8*B^2*b^28*c^3*d^14*e^22 + 64*A*B*b^7*c^24*d^34*e^2 - 1200*A*B*b^8*c^23
*d^33*e^3 + 10252*A*B*b^9*c^22*d^32*e^4 - 52944*A*B*b^10*c^21*d^31*e^5 + 184216*A*B*b^11*c^20*d^30*e^6 - 45211
2*A*B*b^12*c^19*d^29*e^7 + 781428*A*B*b^13*c^18*d^28*e^8 - 863424*A*B*b^14*c^17*d^27*e^9 + 255408*A*B*b^15*c^1
6*d^26*e^10 + 1244088*A*B*b^16*c^15*d^25*e^11 - 3244396*A*B*b^17*c^14*d^24*e^12 + 4868800*A*B*b^18*c^13*d^23*e
^13 - 5345768*A*B*b^19*c^12*d^22*e^14 + 4568696*A*B*b^20*c^11*d^21*e^15 - 3100404*A*B*b^21*c^10*d^20*e^16 + 16
74432*A*B*b^22*c^9*d^19*e^17 - 713184*A*B*b^23*c^8*d^18*e^18 + 234840*A*B*b^24*c^7*d^17*e^19 - 57760*A*B*b^25*
c^6*d^16*e^20 + 10000*A*B*b^26*c^5*d^15*e^21 - 1088*A*B*b^27*c^4*d^14*e^22 + 56*A*B*b^28*c^3*d^13*e^23))*(((49
*A^2*b^2*e^2)/4 + 4*A^2*c^2*d^2 + B^2*b^2*d^2 - 4*A*B*b*c*d^2 - 7*A*B*b^2*d*e + 14*A^2*b*c*d*e)/(b^6*d^9))^(1/
2) - 480*A^3*b^5*c^24*d^29*e^4 + 3590*A^3*b^6*c^23*d^28*e^5 - 17780*A^3*b^7*c^22*d^27*e^6 + 62874*A^3*b^8*c^21
*d^26*e^7 - 157248*A^3*b^9*c^20*d^25*e^8 + 254443*A^3*b^10*c^19*d^24*e^9 - 163416*A^3*b^11*c^18*d^23*e^10 - 38
0204*A^3*b^12*c^17*d^22*e^11 + 1403292*A^3*b^13*c^16*d^21*e^12 - 2458995*A^3*b^14*c^15*d^20*e^13 + 2901724*A^3
*b^15*c^14*d^19*e^14 - 2487478*A^3*b^16*c^13*d^18*e^15 + 1581048*A^3*b^17*c^12*d^17*e^16 - 741891*A^3*b^18*c^1
1*d^16*e^17 + 250736*A^3*b^19*c^10*d^15*e^18 - 57912*A^3*b^20*c^9*d^14*e^19 + 8204*A^3*b^21*c^8*d^13*e^20 - 53
9*A^3*b^22*c^7*d^12*e^21 - 4*B^3*b^7*c^22*d^30*e^3 + 18*B^3*b^8*c^21*d^29*e^4 + 344*B^3*b^9*c^20*d^28*e^5 - 42
28*B^3*b^10*c^19*d^27*e^6 + 22848*B^3*b^11*c^18*d^26*e^7 - 76706*B^3*b^12*c^17*d^25*e^8 + 178640*B^3*b^13*c^16
*d^24*e^9 - 304128*B^3*b^14*c^15*d^23*e^10 + 389136*B^3*b^15*c^14*d^22*e^11 - 379346*B^3*b^16*c^13*d^21*e^12 +
282744*B^3*b^17*c^12*d^20*e^13 - 160244*B^3*b^18*c^11*d^19*e^14 + 67984*B^3*b^19*c^10*d^18*e^15 - 20958*B^3*b
^20*c^9*d^17*e^16 + 4448*B^3*b^21*c^8*d^16*e^17 - 584*B^3*b^22*c^7*d^15*e^18 + 36*B^3*b^23*c^6*d^14*e^19 + 24*
A*B^2*b^6*c^23*d^30*e^3 - 192*A*B^2*b^7*c^22*d^29*e^4 - 111*A*B^2*b^8*c^21*d^28*e^5 + 6636*A*B^2*b^9*c^20*d^27
*e^6 - 32970*A*B^2*b^10*c^19*d^26*e^7 + 75432*A*B^2*b^11*c^18*d^25*e^8 - 55881*A*B^2*b^12*c^17*d^24*e^9 - 1729
20*A*B^2*b^13*c^16*d^23*e^10 + 664488*A*B^2*b^14*c^15*d^22*e^11 - 1211100*A*B^2*b^15*c^14*d^21*e^12 + 1461999*
A*B^2*b^16*c^13*d^20*e^13 - 1264452*A*B^2*b^17*c^12*d^19*e^14 + 802158*A*B^2*b^18*c^11*d^18*e^15 - 372624*A*B^
2*b^19*c^10*d^17*e^16 + 123945*A*B^2*b^20*c^9*d^16*e^17 - 28080*A*B^2*b^21*c^8*d^15*e^18 + 3900*A*B^2*b^22*c^7
*d^14*e^19 - 252*A*B^2*b^23*c^6*d^13*e^20 - 48*A^2*B*b^5*c^24*d^30*e^3 + 552*A^2*B*b^6*c^23*d^29*e^4 - 2949*A^
2*B*b^7*c^22*d^28*e^5 + 11844*A^2*B*b^8*c^21*d^27*e^6 - 47628*A^2*B*b^9*c^20*d^26*e^7 + 176274*A^2*B*b^10*c^19
*d^25*e^8 - 502782*A^2*B*b^11*c^18*d^24*e^9 + 1030776*A^2*B*b^12*c^17*d^23*e^10 - 1480512*A^2*B*b^13*c^16*d^22
*e^11 + 1411806*A^2*B*b^14*c^15*d^21*e^12 - 703164*A^2*B*b^15*c^14*d^20*e^13 - 205212*A^2*B*b^16*c^13*d^19*e^1
4 + 729540*A^2*B*b^17*c^12*d^18*e^15 - 708498*A^2*B*b^18*c^11*d^17*e^16 + 417222*A^2*B*b^19*c^10*d^16*e^17 - 1
62912*A^2*B*b^20*c^9*d^15*e^18 + 41592*A^2*B*b^21*c^8*d^14*e^19 - 6342*A^2*B*b^22*c^7*d^13*e^20 + 441*A^2*B*b^
23*c^6*d^12*e^21)*(((49*A^2*b^2*e^2)/4 + 4*A^2*c^2*d^2 + B^2*b^2*d^2 - 4*A*B*b*c*d^2 - 7*A*B*b^2*d*e + 14*A^2*
b*c*d*e)/(b^6*d^9))^(1/2) + atan((((d + e*x)^(1/2)*(1088*A^2*b^7*c^24*d^33*e^3 - 64*A^2*b^6*c^25*d^34*e^2 - 84
04*A^2*b^8*c^23*d^32*e^4 + 38720*A^2*b^9*c^22*d^31*e^5 - 116512*A^2*b^10*c^21*d^30*e^6 + 230912*A^2*b^11*c^20*
d^29*e^7 - 267432*A^2*b^12*c^19*d^28*e^8 + 38544*A^2*b^13*c^18*d^27*e^9 + 473880*A^2*b^14*c^17*d^26*e^10 - 851
136*A^2*b^15*c^16*d^25*e^11 + 393646*A^2*b^16*c^15*d^24*e^12 + 1207368*A^2*b^17*c^14*d^23*e^13 - 3343724*A^2*b
^18*c^13*d^22*e^14 + 4835160*A^2*b^19*c^12*d^21*e^15 - 4903382*A^2*b^20*c^11*d^20*e^16 + 3751968*A^2*b^21*c^10
*d^19*e^17 - 2217072*A^2*b^22*c^9*d^18*e^18 + 1013232*A^2*b^23*c^8*d^17*e^19 - 353210*A^2*b^24*c^7*d^16*e^20 +
91080*A^2*b^25*c^6*d^15*e^21 - 16412*A^2*b^26*c^5*d^14*e^22 + 1848*A^2*b^27*c^4*d^13*e^23 - 98*A^2*b^28*c^3*d
^12*e^24 - 16*B^2*b^8*c^23*d^34*e^2 + 328*B^2*b^9*c^22*d^33*e^3 - 3074*B^2*b^10*c^21*d^32*e^4 + 17576*B^2*b^11
*c^20*d^31*e^5 - 69252*B^2*b^12*c^19*d^30*e^6 + 201648*B^2*b^13*c^18*d^29*e^7 - 454686*B^2*b^14*c^17*d^28*e^8
+ 821328*B^2*b^15*c^16*d^27*e^9 - 1218432*B^2*b^16*c^15*d^26*e^10 + 1509384*B^2*b^17*c^14*d^25*e^11 - 1574606*
B^2*b^18*c^13*d^24*e^12 + 1384168*B^2*b^19*c^12*d^23*e^13 - 1019324*B^2*b^20*c^11*d^22*e^14 + 622176*B^2*b^21*
c^10*d^21*e^15 - 310242*B^2*b^22*c^9*d^20*e^16 + 124032*B^2*b^23*c^8*d^19*e^17 - 38760*B^2*b^24*c^7*d^18*e^18
+ 9120*B^2*b^25*c^6*d^17*e^19 - 1520*B^2*b^26*c^5*d^16*e^20 + 160*B^2*b^27*c^4*d^15*e^21 - 8*B^2*b^28*c^3*d^14
*e^22 + 64*A*B*b^7*c^24*d^34*e^2 - 1200*A*B*b^8*c^23*d^33*e^3 + 10252*A*B*b^9*c^22*d^32*e^4 - 52944*A*B*b^10*c
^21*d^31*e^5 + 184216*A*B*b^11*c^20*d^30*e^6 - 452112*A*B*b^12*c^19*d^29*e^7 + 781428*A*B*b^13*c^18*d^28*e^8 -
863424*A*B*b^14*c^17*d^27*e^9 + 255408*A*B*b^15*c^16*d^26*e^10 + 1244088*A*B*b^16*c^15*d^25*e^11 - 3244396*A*
B*b^17*c^14*d^24*e^12 + 4868800*A*B*b^18*c^13*d^23*e^13 - 5345768*A*B*b^19*c^12*d^22*e^14 + 4568696*A*B*b^20*c
^11*d^21*e^15 - 3100404*A*B*b^21*c^10*d^20*e^16 + 1674432*A*B*b^22*c^9*d^19*e^17 - 713184*A*B*b^23*c^8*d^18*e^
18 + 234840*A*B*b^24*c^7*d^17*e^19 - 57760*A*B*b^25*c^6*d^16*e^20 + 10000*A*B*b^26*c^5*d^15*e^21 - 1088*A*B*b^
27*c^4*d^14*e^22 + 56*A*B*b^28*c^3*d^13*e^23) + (-(16*A^2*c^11*d^2 + 121*A^2*b^2*c^9*e^2 + 4*B^2*b^2*c^9*d^2 +
81*B^2*b^4*c^7*e^2 - 198*A*B*b^3*c^8*e^2 - 36*B^2*b^3*c^8*d*e - 16*A*B*b*c^10*d^2 - 88*A^2*b*c^10*d*e + 116*A
*B*b^2*c^9*d*e)/(4*(b^15*e^9 - b^6*c^9*d^9 + 9*b^7*c^8*d^8*e - 36*b^8*c^7*d^7*e^2 + 84*b^9*c^6*d^6*e^3 - 126*b
^10*c^5*d^5*e^4 + 126*b^11*c^4*d^4*e^5 - 84*b^12*c^3*d^3*e^6 + 36*b^13*c^2*d^2*e^7 - 9*b^14*c*d*e^8)))^(1/2)*(
(d + e*x)^(1/2)*(-(16*A^2*c^11*d^2 + 121*A^2*b^2*c^9*e^2 + 4*B^2*b^2*c^9*d^2 + 81*B^2*b^4*c^7*e^2 - 198*A*B*b^
3*c^8*e^2 - 36*B^2*b^3*c^8*d*e - 16*A*B*b*c^10*d^2 - 88*A^2*b*c^10*d*e + 116*A*B*b^2*c^9*d*e)/(4*(b^15*e^9 - b
^6*c^9*d^9 + 9*b^7*c^8*d^8*e - 36*b^8*c^7*d^7*e^2 + 84*b^9*c^6*d^6*e^3 - 126*b^10*c^5*d^5*e^4 + 126*b^11*c^4*d
^4*e^5 - 84*b^12*c^3*d^3*e^6 + 36*b^13*c^2*d^2*e^7 - 9*b^14*c*d*e^8)))^(1/2)*(16*b^12*c^23*d^41*e^2 - 328*b^13
*c^22*d^40*e^3 + 3200*b^14*c^21*d^39*e^4 - 19760*b^15*c^20*d^38*e^5 + 86640*b^16*c^19*d^37*e^6 - 286824*b^17*c
^18*d^36*e^7 + 744192*b^18*c^17*d^35*e^8 - 1550400*b^19*c^16*d^34*e^9 + 2635680*b^20*c^15*d^33*e^10 - 3695120*
b^21*c^14*d^32*e^11 + 4299776*b^22*c^13*d^31*e^12 - 4165408*b^23*c^12*d^30*e^13 + 3359200*b^24*c^11*d^29*e^14
- 2248080*b^25*c^10*d^28*e^15 + 1240320*b^26*c^9*d^27*e^16 - 558144*b^27*c^8*d^26*e^17 + 201552*b^28*c^7*d^25*
e^18 - 57000*b^29*c^6*d^24*e^19 + 12160*b^30*c^5*d^23*e^20 - 1840*b^31*c^4*d^22*e^21 + 176*b^32*c^3*d^21*e^22
- 8*b^33*c^2*d^20*e^23) - 8*A*b^10*c^23*d^37*e^3 + 148*A*b^11*c^22*d^36*e^4 - 1160*A*b^12*c^21*d^35*e^5 + 4760
*A*b^13*c^20*d^34*e^6 - 8036*A*b^14*c^19*d^33*e^7 - 21868*A*b^15*c^18*d^32*e^8 + 194304*A*b^16*c^17*d^31*e^9 -
709280*A*b^17*c^16*d^30*e^10 + 1744160*A*b^18*c^15*d^29*e^11 - 3218072*A*b^19*c^14*d^28*e^12 + 4654832*A*b^20
*c^13*d^27*e^13 - 5394480*A*b^21*c^12*d^26*e^14 + 5063240*A*b^22*c^11*d^25*e^15 - 3863800*A*b^23*c^10*d^24*e^1
6 + 2393152*A*b^24*c^9*d^23*e^17 - 1194528*A*b^25*c^8*d^22*e^18 + 474056*A*b^26*c^7*d^21*e^19 - 146300*A*b^27*
c^6*d^20*e^20 + 33880*A*b^28*c^5*d^19*e^21 - 5544*A*b^29*c^4*d^18*e^22 + 572*A*b^30*c^3*d^17*e^23 - 28*A*b^31*
c^2*d^16*e^24 + 4*B*b^11*c^22*d^37*e^3 - 144*B*b^12*c^21*d^36*e^4 + 1840*B*b^13*c^20*d^35*e^5 - 13160*B*b^14*c
^19*d^34*e^6 + 62328*B*b^15*c^18*d^33*e^7 - 212800*B*b^16*c^17*d^32*e^8 + 550432*B*b^17*c^16*d^31*e^9 - 111312
0*B*b^18*c^15*d^30*e^10 + 1796600*B*b^19*c^14*d^29*e^11 - 2345824*B*b^20*c^13*d^28*e^12 + 2498496*B*b^21*c^12*
d^27*e^13 - 2179632*B*b^22*c^11*d^26*e^14 + 1557920*B*b^23*c^10*d^25*e^15 - 909120*B*b^24*c^9*d^24*e^16 + 4296
64*B*b^25*c^8*d^23*e^17 - 162208*B*b^26*c^7*d^22*e^18 + 47844*B*b^27*c^6*d^21*e^19 - 10640*B*b^28*c^5*d^20*e^2
0 + 1680*B*b^29*c^4*d^19*e^21 - 168*B*b^30*c^3*d^18*e^22 + 8*B*b^31*c^2*d^17*e^23))*(-(16*A^2*c^11*d^2 + 121*A
^2*b^2*c^9*e^2 + 4*B^2*b^2*c^9*d^2 + 81*B^2*b^4*c^7*e^2 - 198*A*B*b^3*c^8*e^2 - 36*B^2*b^3*c^8*d*e - 16*A*B*b*
c^10*d^2 - 88*A^2*b*c^10*d*e + 116*A*B*b^2*c^9*d*e)/(4*(b^15*e^9 - b^6*c^9*d^9 + 9*b^7*c^8*d^8*e - 36*b^8*c^7*
d^7*e^2 + 84*b^9*c^6*d^6*e^3 - 126*b^10*c^5*d^5*e^4 + 126*b^11*c^4*d^4*e^5 - 84*b^12*c^3*d^3*e^6 + 36*b^13*c^2
*d^2*e^7 - 9*b^14*c*d*e^8)))^(1/2)*1i + ((d + e*x)^(1/2)*(1088*A^2*b^7*c^24*d^33*e^3 - 64*A^2*b^6*c^25*d^34*e^
2 - 8404*A^2*b^8*c^23*d^32*e^4 + 38720*A^2*b^9*c^22*d^31*e^5 - 116512*A^2*b^10*c^21*d^30*e^6 + 230912*A^2*b^11
*c^20*d^29*e^7 - 267432*A^2*b^12*c^19*d^28*e^8 + 38544*A^2*b^13*c^18*d^27*e^9 + 473880*A^2*b^14*c^17*d^26*e^10
- 851136*A^2*b^15*c^16*d^25*e^11 + 393646*A^2*b^16*c^15*d^24*e^12 + 1207368*A^2*b^17*c^14*d^23*e^13 - 3343724
*A^2*b^18*c^13*d^22*e^14 + 4835160*A^2*b^19*c^12*d^21*e^15 - 4903382*A^2*b^20*c^11*d^20*e^16 + 3751968*A^2*b^2
1*c^10*d^19*e^17 - 2217072*A^2*b^22*c^9*d^18*e^18 + 1013232*A^2*b^23*c^8*d^17*e^19 - 353210*A^2*b^24*c^7*d^16*
e^20 + 91080*A^2*b^25*c^6*d^15*e^21 - 16412*A^2*b^26*c^5*d^14*e^22 + 1848*A^2*b^27*c^4*d^13*e^23 - 98*A^2*b^28
*c^3*d^12*e^24 - 16*B^2*b^8*c^23*d^34*e^2 + 328*B^2*b^9*c^22*d^33*e^3 - 3074*B^2*b^10*c^21*d^32*e^4 + 17576*B^
2*b^11*c^20*d^31*e^5 - 69252*B^2*b^12*c^19*d^30*e^6 + 201648*B^2*b^13*c^18*d^29*e^7 - 454686*B^2*b^14*c^17*d^2
8*e^8 + 821328*B^2*b^15*c^16*d^27*e^9 - 1218432*B^2*b^16*c^15*d^26*e^10 + 1509384*B^2*b^17*c^14*d^25*e^11 - 15
74606*B^2*b^18*c^13*d^24*e^12 + 1384168*B^2*b^19*c^12*d^23*e^13 - 1019324*B^2*b^20*c^11*d^22*e^14 + 622176*B^2
*b^21*c^10*d^21*e^15 - 310242*B^2*b^22*c^9*d^20*e^16 + 124032*B^2*b^23*c^8*d^19*e^17 - 38760*B^2*b^24*c^7*d^18
*e^18 + 9120*B^2*b^25*c^6*d^17*e^19 - 1520*B^2*b^26*c^5*d^16*e^20 + 160*B^2*b^27*c^4*d^15*e^21 - 8*B^2*b^28*c^
3*d^14*e^22 + 64*A*B*b^7*c^24*d^34*e^2 - 1200*A*B*b^8*c^23*d^33*e^3 + 10252*A*B*b^9*c^22*d^32*e^4 - 52944*A*B*
b^10*c^21*d^31*e^5 + 184216*A*B*b^11*c^20*d^30*e^6 - 452112*A*B*b^12*c^19*d^29*e^7 + 781428*A*B*b^13*c^18*d^28
*e^8 - 863424*A*B*b^14*c^17*d^27*e^9 + 255408*A*B*b^15*c^16*d^26*e^10 + 1244088*A*B*b^16*c^15*d^25*e^11 - 3244
396*A*B*b^17*c^14*d^24*e^12 + 4868800*A*B*b^18*c^13*d^23*e^13 - 5345768*A*B*b^19*c^12*d^22*e^14 + 4568696*A*B*
b^20*c^11*d^21*e^15 - 3100404*A*B*b^21*c^10*d^20*e^16 + 1674432*A*B*b^22*c^9*d^19*e^17 - 713184*A*B*b^23*c^8*d
^18*e^18 + 234840*A*B*b^24*c^7*d^17*e^19 - 57760*A*B*b^25*c^6*d^16*e^20 + 10000*A*B*b^26*c^5*d^15*e^21 - 1088*
A*B*b^27*c^4*d^14*e^22 + 56*A*B*b^28*c^3*d^13*e^23) + (-(16*A^2*c^11*d^2 + 121*A^2*b^2*c^9*e^2 + 4*B^2*b^2*c^9
*d^2 + 81*B^2*b^4*c^7*e^2 - 198*A*B*b^3*c^8*e^2 - 36*B^2*b^3*c^8*d*e - 16*A*B*b*c^10*d^2 - 88*A^2*b*c^10*d*e +
116*A*B*b^2*c^9*d*e)/(4*(b^15*e^9 - b^6*c^9*d^9 + 9*b^7*c^8*d^8*e - 36*b^8*c^7*d^7*e^2 + 84*b^9*c^6*d^6*e^3 -
126*b^10*c^5*d^5*e^4 + 126*b^11*c^4*d^4*e^5 - 84*b^12*c^3*d^3*e^6 + 36*b^13*c^2*d^2*e^7 - 9*b^14*c*d*e^8)))^(
1/2)*((d + e*x)^(1/2)*(-(16*A^2*c^11*d^2 + 121*A^2*b^2*c^9*e^2 + 4*B^2*b^2*c^9*d^2 + 81*B^2*b^4*c^7*e^2 - 198*
A*B*b^3*c^8*e^2 - 36*B^2*b^3*c^8*d*e - 16*A*B*b*c^10*d^2 - 88*A^2*b*c^10*d*e + 116*A*B*b^2*c^9*d*e)/(4*(b^15*e
^9 - b^6*c^9*d^9 + 9*b^7*c^8*d^8*e - 36*b^8*c^7*d^7*e^2 + 84*b^9*c^6*d^6*e^3 - 126*b^10*c^5*d^5*e^4 + 126*b^11
*c^4*d^4*e^5 - 84*b^12*c^3*d^3*e^6 + 36*b^13*c^2*d^2*e^7 - 9*b^14*c*d*e^8)))^(1/2)*(16*b^12*c^23*d^41*e^2 - 32
8*b^13*c^22*d^40*e^3 + 3200*b^14*c^21*d^39*e^4 - 19760*b^15*c^20*d^38*e^5 + 86640*b^16*c^19*d^37*e^6 - 286824*
b^17*c^18*d^36*e^7 + 744192*b^18*c^17*d^35*e^8 - 1550400*b^19*c^16*d^34*e^9 + 2635680*b^20*c^15*d^33*e^10 - 36
95120*b^21*c^14*d^32*e^11 + 4299776*b^22*c^13*d^31*e^12 - 4165408*b^23*c^12*d^30*e^13 + 3359200*b^24*c^11*d^29
*e^14 - 2248080*b^25*c^10*d^28*e^15 + 1240320*b^26*c^9*d^27*e^16 - 558144*b^27*c^8*d^26*e^17 + 201552*b^28*c^7
*d^25*e^18 - 57000*b^29*c^6*d^24*e^19 + 12160*b^30*c^5*d^23*e^20 - 1840*b^31*c^4*d^22*e^21 + 176*b^32*c^3*d^21
*e^22 - 8*b^33*c^2*d^20*e^23) + 8*A*b^10*c^23*d^37*e^3 - 148*A*b^11*c^22*d^36*e^4 + 1160*A*b^12*c^21*d^35*e^5
- 4760*A*b^13*c^20*d^34*e^6 + 8036*A*b^14*c^19*d^33*e^7 + 21868*A*b^15*c^18*d^32*e^8 - 194304*A*b^16*c^17*d^31
*e^9 + 709280*A*b^17*c^16*d^30*e^10 - 1744160*A*b^18*c^15*d^29*e^11 + 3218072*A*b^19*c^14*d^28*e^12 - 4654832*
A*b^20*c^13*d^27*e^13 + 5394480*A*b^21*c^12*d^26*e^14 - 5063240*A*b^22*c^11*d^25*e^15 + 3863800*A*b^23*c^10*d^
24*e^16 - 2393152*A*b^24*c^9*d^23*e^17 + 1194528*A*b^25*c^8*d^22*e^18 - 474056*A*b^26*c^7*d^21*e^19 + 146300*A
*b^27*c^6*d^20*e^20 - 33880*A*b^28*c^5*d^19*e^21 + 5544*A*b^29*c^4*d^18*e^22 - 572*A*b^30*c^3*d^17*e^23 + 28*A
*b^31*c^2*d^16*e^24 - 4*B*b^11*c^22*d^37*e^3 + 144*B*b^12*c^21*d^36*e^4 - 1840*B*b^13*c^20*d^35*e^5 + 13160*B*
b^14*c^19*d^34*e^6 - 62328*B*b^15*c^18*d^33*e^7 + 212800*B*b^16*c^17*d^32*e^8 - 550432*B*b^17*c^16*d^31*e^9 +
1113120*B*b^18*c^15*d^30*e^10 - 1796600*B*b^19*c^14*d^29*e^11 + 2345824*B*b^20*c^13*d^28*e^12 - 2498496*B*b^21
*c^12*d^27*e^13 + 2179632*B*b^22*c^11*d^26*e^14 - 1557920*B*b^23*c^10*d^25*e^15 + 909120*B*b^24*c^9*d^24*e^16
- 429664*B*b^25*c^8*d^23*e^17 + 162208*B*b^26*c^7*d^22*e^18 - 47844*B*b^27*c^6*d^21*e^19 + 10640*B*b^28*c^5*d^
20*e^20 - 1680*B*b^29*c^4*d^19*e^21 + 168*B*b^30*c^3*d^18*e^22 - 8*B*b^31*c^2*d^17*e^23))*(-(16*A^2*c^11*d^2 +
121*A^2*b^2*c^9*e^2 + 4*B^2*b^2*c^9*d^2 + 81*B^2*b^4*c^7*e^2 - 198*A*B*b^3*c^8*e^2 - 36*B^2*b^3*c^8*d*e - 16*
A*B*b*c^10*d^2 - 88*A^2*b*c^10*d*e + 116*A*B*b^2*c^9*d*e)/(4*(b^15*e^9 - b^6*c^9*d^9 + 9*b^7*c^8*d^8*e - 36*b^
8*c^7*d^7*e^2 + 84*b^9*c^6*d^6*e^3 - 126*b^10*c^5*d^5*e^4 + 126*b^11*c^4*d^4*e^5 - 84*b^12*c^3*d^3*e^6 + 36*b^
13*c^2*d^2*e^7 - 9*b^14*c*d*e^8)))^(1/2)*1i)/(((d + e*x)^(1/2)*(1088*A^2*b^7*c^24*d^33*e^3 - 64*A^2*b^6*c^25*d
^34*e^2 - 8404*A^2*b^8*c^23*d^32*e^4 + 38720*A^2*b^9*c^22*d^31*e^5 - 116512*A^2*b^10*c^21*d^30*e^6 + 230912*A^
2*b^11*c^20*d^29*e^7 - 267432*A^2*b^12*c^19*d^28*e^8 + 38544*A^2*b^13*c^18*d^27*e^9 + 473880*A^2*b^14*c^17*d^2
6*e^10 - 851136*A^2*b^15*c^16*d^25*e^11 + 393646*A^2*b^16*c^15*d^24*e^12 + 1207368*A^2*b^17*c^14*d^23*e^13 - 3
343724*A^2*b^18*c^13*d^22*e^14 + 4835160*A^2*b^19*c^12*d^21*e^15 - 4903382*A^2*b^20*c^11*d^20*e^16 + 3751968*A
^2*b^21*c^10*d^19*e^17 - 2217072*A^2*b^22*c^9*d^18*e^18 + 1013232*A^2*b^23*c^8*d^17*e^19 - 353210*A^2*b^24*c^7
*d^16*e^20 + 91080*A^2*b^25*c^6*d^15*e^21 - 16412*A^2*b^26*c^5*d^14*e^22 + 1848*A^2*b^27*c^4*d^13*e^23 - 98*A^
2*b^28*c^3*d^12*e^24 - 16*B^2*b^8*c^23*d^34*e^2 + 328*B^2*b^9*c^22*d^33*e^3 - 3074*B^2*b^10*c^21*d^32*e^4 + 17
576*B^2*b^11*c^20*d^31*e^5 - 69252*B^2*b^12*c^19*d^30*e^6 + 201648*B^2*b^13*c^18*d^29*e^7 - 454686*B^2*b^14*c^
17*d^28*e^8 + 821328*B^2*b^15*c^16*d^27*e^9 - 1218432*B^2*b^16*c^15*d^26*e^10 + 1509384*B^2*b^17*c^14*d^25*e^1
1 - 1574606*B^2*b^18*c^13*d^24*e^12 + 1384168*B^2*b^19*c^12*d^23*e^13 - 1019324*B^2*b^20*c^11*d^22*e^14 + 6221
76*B^2*b^21*c^10*d^21*e^15 - 310242*B^2*b^22*c^9*d^20*e^16 + 124032*B^2*b^23*c^8*d^19*e^17 - 38760*B^2*b^24*c^
7*d^18*e^18 + 9120*B^2*b^25*c^6*d^17*e^19 - 1520*B^2*b^26*c^5*d^16*e^20 + 160*B^2*b^27*c^4*d^15*e^21 - 8*B^2*b
^28*c^3*d^14*e^22 + 64*A*B*b^7*c^24*d^34*e^2 - 1200*A*B*b^8*c^23*d^33*e^3 + 10252*A*B*b^9*c^22*d^32*e^4 - 5294
4*A*B*b^10*c^21*d^31*e^5 + 184216*A*B*b^11*c^20*d^30*e^6 - 452112*A*B*b^12*c^19*d^29*e^7 + 781428*A*B*b^13*c^1
8*d^28*e^8 - 863424*A*B*b^14*c^17*d^27*e^9 + 255408*A*B*b^15*c^16*d^26*e^10 + 1244088*A*B*b^16*c^15*d^25*e^11
- 3244396*A*B*b^17*c^14*d^24*e^12 + 4868800*A*B*b^18*c^13*d^23*e^13 - 5345768*A*B*b^19*c^12*d^22*e^14 + 456869
6*A*B*b^20*c^11*d^21*e^15 - 3100404*A*B*b^21*c^10*d^20*e^16 + 1674432*A*B*b^22*c^9*d^19*e^17 - 713184*A*B*b^23
*c^8*d^18*e^18 + 234840*A*B*b^24*c^7*d^17*e^19 - 57760*A*B*b^25*c^6*d^16*e^20 + 10000*A*B*b^26*c^5*d^15*e^21 -
1088*A*B*b^27*c^4*d^14*e^22 + 56*A*B*b^28*c^3*d^13*e^23) + (-(16*A^2*c^11*d^2 + 121*A^2*b^2*c^9*e^2 + 4*B^2*b
^2*c^9*d^2 + 81*B^2*b^4*c^7*e^2 - 198*A*B*b^3*c^8*e^2 - 36*B^2*b^3*c^8*d*e - 16*A*B*b*c^10*d^2 - 88*A^2*b*c^10
*d*e + 116*A*B*b^2*c^9*d*e)/(4*(b^15*e^9 - b^6*c^9*d^9 + 9*b^7*c^8*d^8*e - 36*b^8*c^7*d^7*e^2 + 84*b^9*c^6*d^6
*e^3 - 126*b^10*c^5*d^5*e^4 + 126*b^11*c^4*d^4*e^5 - 84*b^12*c^3*d^3*e^6 + 36*b^13*c^2*d^2*e^7 - 9*b^14*c*d*e^
8)))^(1/2)*((d + e*x)^(1/2)*(-(16*A^2*c^11*d^2 + 121*A^2*b^2*c^9*e^2 + 4*B^2*b^2*c^9*d^2 + 81*B^2*b^4*c^7*e^2
- 198*A*B*b^3*c^8*e^2 - 36*B^2*b^3*c^8*d*e - 16*A*B*b*c^10*d^2 - 88*A^2*b*c^10*d*e + 116*A*B*b^2*c^9*d*e)/(4*(
b^15*e^9 - b^6*c^9*d^9 + 9*b^7*c^8*d^8*e - 36*b^8*c^7*d^7*e^2 + 84*b^9*c^6*d^6*e^3 - 126*b^10*c^5*d^5*e^4 + 12
6*b^11*c^4*d^4*e^5 - 84*b^12*c^3*d^3*e^6 + 36*b^13*c^2*d^2*e^7 - 9*b^14*c*d*e^8)))^(1/2)*(16*b^12*c^23*d^41*e^
2 - 328*b^13*c^22*d^40*e^3 + 3200*b^14*c^21*d^39*e^4 - 19760*b^15*c^20*d^38*e^5 + 86640*b^16*c^19*d^37*e^6 - 2
86824*b^17*c^18*d^36*e^7 + 744192*b^18*c^17*d^35*e^8 - 1550400*b^19*c^16*d^34*e^9 + 2635680*b^20*c^15*d^33*e^1
0 - 3695120*b^21*c^14*d^32*e^11 + 4299776*b^22*c^13*d^31*e^12 - 4165408*b^23*c^12*d^30*e^13 + 3359200*b^24*c^1
1*d^29*e^14 - 2248080*b^25*c^10*d^28*e^15 + 1240320*b^26*c^9*d^27*e^16 - 558144*b^27*c^8*d^26*e^17 + 201552*b^
28*c^7*d^25*e^18 - 57000*b^29*c^6*d^24*e^19 + 12160*b^30*c^5*d^23*e^20 - 1840*b^31*c^4*d^22*e^21 + 176*b^32*c^
3*d^21*e^22 - 8*b^33*c^2*d^20*e^23) + 8*A*b^10*c^23*d^37*e^3 - 148*A*b^11*c^22*d^36*e^4 + 1160*A*b^12*c^21*d^3
5*e^5 - 4760*A*b^13*c^20*d^34*e^6 + 8036*A*b^14*c^19*d^33*e^7 + 21868*A*b^15*c^18*d^32*e^8 - 194304*A*b^16*c^1
7*d^31*e^9 + 709280*A*b^17*c^16*d^30*e^10 - 1744160*A*b^18*c^15*d^29*e^11 + 3218072*A*b^19*c^14*d^28*e^12 - 46
54832*A*b^20*c^13*d^27*e^13 + 5394480*A*b^21*c^12*d^26*e^14 - 5063240*A*b^22*c^11*d^25*e^15 + 3863800*A*b^23*c
^10*d^24*e^16 - 2393152*A*b^24*c^9*d^23*e^17 + 1194528*A*b^25*c^8*d^22*e^18 - 474056*A*b^26*c^7*d^21*e^19 + 14
6300*A*b^27*c^6*d^20*e^20 - 33880*A*b^28*c^5*d^19*e^21 + 5544*A*b^29*c^4*d^18*e^22 - 572*A*b^30*c^3*d^17*e^23
+ 28*A*b^31*c^2*d^16*e^24 - 4*B*b^11*c^22*d^37*e^3 + 144*B*b^12*c^21*d^36*e^4 - 1840*B*b^13*c^20*d^35*e^5 + 13
160*B*b^14*c^19*d^34*e^6 - 62328*B*b^15*c^18*d^33*e^7 + 212800*B*b^16*c^17*d^32*e^8 - 550432*B*b^17*c^16*d^31*
e^9 + 1113120*B*b^18*c^15*d^30*e^10 - 1796600*B*b^19*c^14*d^29*e^11 + 2345824*B*b^20*c^13*d^28*e^12 - 2498496*
B*b^21*c^12*d^27*e^13 + 2179632*B*b^22*c^11*d^26*e^14 - 1557920*B*b^23*c^10*d^25*e^15 + 909120*B*b^24*c^9*d^24
*e^16 - 429664*B*b^25*c^8*d^23*e^17 + 162208*B*b^26*c^7*d^22*e^18 - 47844*B*b^27*c^6*d^21*e^19 + 10640*B*b^28*
c^5*d^20*e^20 - 1680*B*b^29*c^4*d^19*e^21 + 168*B*b^30*c^3*d^18*e^22 - 8*B*b^31*c^2*d^17*e^23))*(-(16*A^2*c^11
*d^2 + 121*A^2*b^2*c^9*e^2 + 4*B^2*b^2*c^9*d^2 + 81*B^2*b^4*c^7*e^2 - 198*A*B*b^3*c^8*e^2 - 36*B^2*b^3*c^8*d*e
- 16*A*B*b*c^10*d^2 - 88*A^2*b*c^10*d*e + 116*A*B*b^2*c^9*d*e)/(4*(b^15*e^9 - b^6*c^9*d^9 + 9*b^7*c^8*d^8*e -
36*b^8*c^7*d^7*e^2 + 84*b^9*c^6*d^6*e^3 - 126*b^10*c^5*d^5*e^4 + 126*b^11*c^4*d^4*e^5 - 84*b^12*c^3*d^3*e^6 +
36*b^13*c^2*d^2*e^7 - 9*b^14*c*d*e^8)))^(1/2) - ((d + e*x)^(1/2)*(1088*A^2*b^7*c^24*d^33*e^3 - 64*A^2*b^6*c^2
5*d^34*e^2 - 8404*A^2*b^8*c^23*d^32*e^4 + 38720*A^2*b^9*c^22*d^31*e^5 - 116512*A^2*b^10*c^21*d^30*e^6 + 230912
*A^2*b^11*c^20*d^29*e^7 - 267432*A^2*b^12*c^19*d^28*e^8 + 38544*A^2*b^13*c^18*d^27*e^9 + 473880*A^2*b^14*c^17*
d^26*e^10 - 851136*A^2*b^15*c^16*d^25*e^11 + 393646*A^2*b^16*c^15*d^24*e^12 + 1207368*A^2*b^17*c^14*d^23*e^13
- 3343724*A^2*b^18*c^13*d^22*e^14 + 4835160*A^2*b^19*c^12*d^21*e^15 - 4903382*A^2*b^20*c^11*d^20*e^16 + 375196
8*A^2*b^21*c^10*d^19*e^17 - 2217072*A^2*b^22*c^9*d^18*e^18 + 1013232*A^2*b^23*c^8*d^17*e^19 - 353210*A^2*b^24*
c^7*d^16*e^20 + 91080*A^2*b^25*c^6*d^15*e^21 - 16412*A^2*b^26*c^5*d^14*e^22 + 1848*A^2*b^27*c^4*d^13*e^23 - 98
*A^2*b^28*c^3*d^12*e^24 - 16*B^2*b^8*c^23*d^34*e^2 + 328*B^2*b^9*c^22*d^33*e^3 - 3074*B^2*b^10*c^21*d^32*e^4 +
17576*B^2*b^11*c^20*d^31*e^5 - 69252*B^2*b^12*c^19*d^30*e^6 + 201648*B^2*b^13*c^18*d^29*e^7 - 454686*B^2*b^14
*c^17*d^28*e^8 + 821328*B^2*b^15*c^16*d^27*e^9 - 1218432*B^2*b^16*c^15*d^26*e^10 + 1509384*B^2*b^17*c^14*d^25*
e^11 - 1574606*B^2*b^18*c^13*d^24*e^12 + 1384168*B^2*b^19*c^12*d^23*e^13 - 1019324*B^2*b^20*c^11*d^22*e^14 + 6
22176*B^2*b^21*c^10*d^21*e^15 - 310242*B^2*b^22*c^9*d^20*e^16 + 124032*B^2*b^23*c^8*d^19*e^17 - 38760*B^2*b^24
*c^7*d^18*e^18 + 9120*B^2*b^25*c^6*d^17*e^19 - 1520*B^2*b^26*c^5*d^16*e^20 + 160*B^2*b^27*c^4*d^15*e^21 - 8*B^
2*b^28*c^3*d^14*e^22 + 64*A*B*b^7*c^24*d^34*e^2 - 1200*A*B*b^8*c^23*d^33*e^3 + 10252*A*B*b^9*c^22*d^32*e^4 - 5
2944*A*B*b^10*c^21*d^31*e^5 + 184216*A*B*b^11*c^20*d^30*e^6 - 452112*A*B*b^12*c^19*d^29*e^7 + 781428*A*B*b^13*
c^18*d^28*e^8 - 863424*A*B*b^14*c^17*d^27*e^9 + 255408*A*B*b^15*c^16*d^26*e^10 + 1244088*A*B*b^16*c^15*d^25*e^
11 - 3244396*A*B*b^17*c^14*d^24*e^12 + 4868800*A*B*b^18*c^13*d^23*e^13 - 5345768*A*B*b^19*c^12*d^22*e^14 + 456
8696*A*B*b^20*c^11*d^21*e^15 - 3100404*A*B*b^21*c^10*d^20*e^16 + 1674432*A*B*b^22*c^9*d^19*e^17 - 713184*A*B*b
^23*c^8*d^18*e^18 + 234840*A*B*b^24*c^7*d^17*e^19 - 57760*A*B*b^25*c^6*d^16*e^20 + 10000*A*B*b^26*c^5*d^15*e^2
1 - 1088*A*B*b^27*c^4*d^14*e^22 + 56*A*B*b^28*c^3*d^13*e^23) + (-(16*A^2*c^11*d^2 + 121*A^2*b^2*c^9*e^2 + 4*B^
2*b^2*c^9*d^2 + 81*B^2*b^4*c^7*e^2 - 198*A*B*b^3*c^8*e^2 - 36*B^2*b^3*c^8*d*e - 16*A*B*b*c^10*d^2 - 88*A^2*b*c
^10*d*e + 116*A*B*b^2*c^9*d*e)/(4*(b^15*e^9 - b^6*c^9*d^9 + 9*b^7*c^8*d^8*e - 36*b^8*c^7*d^7*e^2 + 84*b^9*c^6*
d^6*e^3 - 126*b^10*c^5*d^5*e^4 + 126*b^11*c^4*d^4*e^5 - 84*b^12*c^3*d^3*e^6 + 36*b^13*c^2*d^2*e^7 - 9*b^14*c*d
*e^8)))^(1/2)*((d + e*x)^(1/2)*(-(16*A^2*c^11*d^2 + 121*A^2*b^2*c^9*e^2 + 4*B^2*b^2*c^9*d^2 + 81*B^2*b^4*c^7*e
^2 - 198*A*B*b^3*c^8*e^2 - 36*B^2*b^3*c^8*d*e - 16*A*B*b*c^10*d^2 - 88*A^2*b*c^10*d*e + 116*A*B*b^2*c^9*d*e)/(
4*(b^15*e^9 - b^6*c^9*d^9 + 9*b^7*c^8*d^8*e - 36*b^8*c^7*d^7*e^2 + 84*b^9*c^6*d^6*e^3 - 126*b^10*c^5*d^5*e^4 +
126*b^11*c^4*d^4*e^5 - 84*b^12*c^3*d^3*e^6 + 36*b^13*c^2*d^2*e^7 - 9*b^14*c*d*e^8)))^(1/2)*(16*b^12*c^23*d^41
*e^2 - 328*b^13*c^22*d^40*e^3 + 3200*b^14*c^21*d^39*e^4 - 19760*b^15*c^20*d^38*e^5 + 86640*b^16*c^19*d^37*e^6
- 286824*b^17*c^18*d^36*e^7 + 744192*b^18*c^17*d^35*e^8 - 1550400*b^19*c^16*d^34*e^9 + 2635680*b^20*c^15*d^33*
e^10 - 3695120*b^21*c^14*d^32*e^11 + 4299776*b^22*c^13*d^31*e^12 - 4165408*b^23*c^12*d^30*e^13 + 3359200*b^24*
c^11*d^29*e^14 - 2248080*b^25*c^10*d^28*e^15 + 1240320*b^26*c^9*d^27*e^16 - 558144*b^27*c^8*d^26*e^17 + 201552
*b^28*c^7*d^25*e^18 - 57000*b^29*c^6*d^24*e^19 + 12160*b^30*c^5*d^23*e^20 - 1840*b^31*c^4*d^22*e^21 + 176*b^32
*c^3*d^21*e^22 - 8*b^33*c^2*d^20*e^23) - 8*A*b^10*c^23*d^37*e^3 + 148*A*b^11*c^22*d^36*e^4 - 1160*A*b^12*c^21*
d^35*e^5 + 4760*A*b^13*c^20*d^34*e^6 - 8036*A*b^14*c^19*d^33*e^7 - 21868*A*b^15*c^18*d^32*e^8 + 194304*A*b^16*
c^17*d^31*e^9 - 709280*A*b^17*c^16*d^30*e^10 + 1744160*A*b^18*c^15*d^29*e^11 - 3218072*A*b^19*c^14*d^28*e^12 +
4654832*A*b^20*c^13*d^27*e^13 - 5394480*A*b^21*c^12*d^26*e^14 + 5063240*A*b^22*c^11*d^25*e^15 - 3863800*A*b^2
3*c^10*d^24*e^16 + 2393152*A*b^24*c^9*d^23*e^17 - 1194528*A*b^25*c^8*d^22*e^18 + 474056*A*b^26*c^7*d^21*e^19 -
146300*A*b^27*c^6*d^20*e^20 + 33880*A*b^28*c^5*d^19*e^21 - 5544*A*b^29*c^4*d^18*e^22 + 572*A*b^30*c^3*d^17*e^
23 - 28*A*b^31*c^2*d^16*e^24 + 4*B*b^11*c^22*d^37*e^3 - 144*B*b^12*c^21*d^36*e^4 + 1840*B*b^13*c^20*d^35*e^5 -
13160*B*b^14*c^19*d^34*e^6 + 62328*B*b^15*c^18*d^33*e^7 - 212800*B*b^16*c^17*d^32*e^8 + 550432*B*b^17*c^16*d^
31*e^9 - 1113120*B*b^18*c^15*d^30*e^10 + 1796600*B*b^19*c^14*d^29*e^11 - 2345824*B*b^20*c^13*d^28*e^12 + 24984
96*B*b^21*c^12*d^27*e^13 - 2179632*B*b^22*c^11*d^26*e^14 + 1557920*B*b^23*c^10*d^25*e^15 - 909120*B*b^24*c^9*d
^24*e^16 + 429664*B*b^25*c^8*d^23*e^17 - 162208*B*b^26*c^7*d^22*e^18 + 47844*B*b^27*c^6*d^21*e^19 - 10640*B*b^
28*c^5*d^20*e^20 + 1680*B*b^29*c^4*d^19*e^21 - 168*B*b^30*c^3*d^18*e^22 + 8*B*b^31*c^2*d^17*e^23))*(-(16*A^2*c
^11*d^2 + 121*A^2*b^2*c^9*e^2 + 4*B^2*b^2*c^9*d^2 + 81*B^2*b^4*c^7*e^2 - 198*A*B*b^3*c^8*e^2 - 36*B^2*b^3*c^8*
d*e - 16*A*B*b*c^10*d^2 - 88*A^2*b*c^10*d*e + 116*A*B*b^2*c^9*d*e)/(4*(b^15*e^9 - b^6*c^9*d^9 + 9*b^7*c^8*d^8*
e - 36*b^8*c^7*d^7*e^2 + 84*b^9*c^6*d^6*e^3 - 126*b^10*c^5*d^5*e^4 + 126*b^11*c^4*d^4*e^5 - 84*b^12*c^3*d^3*e^
6 + 36*b^13*c^2*d^2*e^7 - 9*b^14*c*d*e^8)))^(1/2) - 64*A^3*b^4*c^25*d^30*e^3 + 960*A^3*b^5*c^24*d^29*e^4 - 718
0*A^3*b^6*c^23*d^28*e^5 + 35560*A^3*b^7*c^22*d^27*e^6 - 125748*A^3*b^8*c^21*d^26*e^7 + 314496*A^3*b^9*c^20*d^2
5*e^8 - 508886*A^3*b^10*c^19*d^24*e^9 + 326832*A^3*b^11*c^18*d^23*e^10 + 760408*A^3*b^12*c^17*d^22*e^11 - 2806
584*A^3*b^13*c^16*d^21*e^12 + 4917990*A^3*b^14*c^15*d^20*e^13 - 5803448*A^3*b^15*c^14*d^19*e^14 + 4974956*A^3*
b^16*c^13*d^18*e^15 - 3162096*A^3*b^17*c^12*d^17*e^16 + 1483782*A^3*b^18*c^11*d^16*e^17 - 501472*A^3*b^19*c^10
*d^15*e^18 + 115824*A^3*b^20*c^9*d^14*e^19 - 16408*A^3*b^21*c^8*d^13*e^20 + 1078*A^3*b^22*c^7*d^12*e^21 + 8*B^
3*b^7*c^22*d^30*e^3 - 36*B^3*b^8*c^21*d^29*e^4 - 688*B^3*b^9*c^20*d^28*e^5 + 8456*B^3*b^10*c^19*d^27*e^6 - 456
96*B^3*b^11*c^18*d^26*e^7 + 153412*B^3*b^12*c^17*d^25*e^8 - 357280*B^3*b^13*c^16*d^24*e^9 + 608256*B^3*b^14*c^
15*d^23*e^10 - 778272*B^3*b^15*c^14*d^22*e^11 + 758692*B^3*b^16*c^13*d^21*e^12 - 565488*B^3*b^17*c^12*d^20*e^1
3 + 320488*B^3*b^18*c^11*d^19*e^14 - 135968*B^3*b^19*c^10*d^18*e^15 + 41916*B^3*b^20*c^9*d^17*e^16 - 8896*B^3*
b^21*c^8*d^16*e^17 + 1168*B^3*b^22*c^7*d^15*e^18 - 72*B^3*b^23*c^6*d^14*e^19 - 48*A*B^2*b^6*c^23*d^30*e^3 + 38
4*A*B^2*b^7*c^22*d^29*e^4 + 222*A*B^2*b^8*c^21*d^28*e^5 - 13272*A*B^2*b^9*c^20*d^27*e^6 + 65940*A*B^2*b^10*c^1
9*d^26*e^7 - 150864*A*B^2*b^11*c^18*d^25*e^8 + 111762*A*B^2*b^12*c^17*d^24*e^9 + 345840*A*B^2*b^13*c^16*d^23*e
^10 - 1328976*A*B^2*b^14*c^15*d^22*e^11 + 2422200*A*B^2*b^15*c^14*d^21*e^12 - 2923998*A*B^2*b^16*c^13*d^20*e^1
3 + 2528904*A*B^2*b^17*c^12*d^19*e^14 - 1604316*A*B^2*b^18*c^11*d^18*e^15 + 745248*A*B^2*b^19*c^10*d^17*e^16 -
247890*A*B^2*b^20*c^9*d^16*e^17 + 56160*A*B^2*b^21*c^8*d^15*e^18 - 7800*A*B^2*b^22*c^7*d^14*e^19 + 504*A*B^2*
b^23*c^6*d^13*e^20 + 96*A^2*B*b^5*c^24*d^30*e^3 - 1104*A^2*B*b^6*c^23*d^29*e^4 + 5898*A^2*B*b^7*c^22*d^28*e^5
- 23688*A^2*B*b^8*c^21*d^27*e^6 + 95256*A^2*B*b^9*c^20*d^26*e^7 - 352548*A^2*B*b^10*c^19*d^25*e^8 + 1005564*A^
2*B*b^11*c^18*d^24*e^9 - 2061552*A^2*B*b^12*c^17*d^23*e^10 + 2961024*A^2*B*b^13*c^16*d^22*e^11 - 2823612*A^2*B
*b^14*c^15*d^21*e^12 + 1406328*A^2*B*b^15*c^14*d^20*e^13 + 410424*A^2*B*b^16*c^13*d^19*e^14 - 1459080*A^2*B*b^
17*c^12*d^18*e^15 + 1416996*A^2*B*b^18*c^11*d^17*e^16 - 834444*A^2*B*b^19*c^10*d^16*e^17 + 325824*A^2*B*b^20*c
^9*d^15*e^18 - 83184*A^2*B*b^21*c^8*d^14*e^19 + 12684*A^2*B*b^22*c^7*d^13*e^20 - 882*A^2*B*b^23*c^6*d^12*e^21)
)*(-(16*A^2*c^11*d^2 + 121*A^2*b^2*c^9*e^2 + 4*B^2*b^2*c^9*d^2 + 81*B^2*b^4*c^7*e^2 - 198*A*B*b^3*c^8*e^2 - 36
*B^2*b^3*c^8*d*e - 16*A*B*b*c^10*d^2 - 88*A^2*b*c^10*d*e + 116*A*B*b^2*c^9*d*e)/(4*(b^15*e^9 - b^6*c^9*d^9 + 9
*b^7*c^8*d^8*e - 36*b^8*c^7*d^7*e^2 + 84*b^9*c^6*d^6*e^3 - 126*b^10*c^5*d^5*e^4 + 126*b^11*c^4*d^4*e^5 - 84*b^
12*c^3*d^3*e^6 + 36*b^13*c^2*d^2*e^7 - 9*b^14*c*d*e^8)))^(1/2)*2i - ((2*(A*e^3 - B*d*e^2))/(5*(c*d^2 - b*d*e))
- (2*(d + e*x)*(7*A*b*e^4 - 14*A*c*d*e^3 - 2*B*b*d*e^3 + 9*B*c*d^2*e^2))/(15*(c*d^2 - b*d*e)^2) + (2*(d + e*x
)^2*(35*A*b^2*e^5 - 10*B*b^2*d*e^4 + 113*A*c^2*d^2*e^3 - 63*B*c^2*d^3*e^2 - 113*A*b*c*d*e^4 + 38*B*b*c*d^2*e^3
))/(15*(c*d^2 - b*d*e)^3) + ((d + e*x)^3*(21*A*b^5*e^6 - 6*A*c^5*d^5*e - 6*B*b^5*d*e^5 + 15*A*b*c^4*d^4*e^2 +
34*B*b^4*c*d^2*e^4 - 142*A*b^2*c^3*d^3*e^3 + 198*A*b^3*c^2*d^2*e^4 + 66*B*b^2*c^3*d^4*e^2 - 76*B*b^3*c^2*d^3*e
^3 - 107*A*b^4*c*d*e^5 + 3*B*b*c^4*d^5*e))/(3*b^2*(c*d^2 - b*d*e)^4) - ((d + e*x)^4*(4*A*b*c^4*d^3*e^2 - 2*A*c
^5*d^4*e - 7*A*b^4*c*e^5 + 24*A*b^3*c^2*d*e^4 - 26*A*b^2*c^3*d^2*e^3 + 12*B*b^2*c^3*d^3*e^2 - 8*B*b^3*c^2*d^2*
e^3 + B*b*c^4*d^4*e + 2*B*b^4*c*d*e^4))/(b^2*(c*d^2 - b*d*e)^4))/(c*(d + e*x)^(9/2) + (c*d^2 - b*d*e)*(d + e*x
)^(5/2) + (b*e - 2*c*d)*(d + e*x)^(7/2))
________________________________________________________________________________________
sympy [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((B*x+A)/(e*x+d)**(7/2)/(c*x**2+b*x)**2,x)
[Out]
Timed out
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