∫ 1_______ x7∕2(a+bx2)(c+dx2)3 dx

3.487 \(\int \frac {1}{x^{7/2} (a+b x^2) (c+d x^2)^3} \, dx\)

Optimal. Leaf size=743 \[ \frac {b^{17/4} \log \left (-\sqrt {2} \sqrt [4]{a} \sqrt [4]{b} \sqrt {x}+\sqrt {a}+\sqrt {b} x\right )}{2 \sqrt {2} a^{9/4} (b c-a d)^3}-\frac {b^{17/4} \log \left (\sqrt {2} \sqrt [4]{a} \sqrt [4]{b} \sqrt {x}+\sqrt {a}+\sqrt {b} x\right )}{2 \sqrt {2} a^{9/4} (b c-a d)^3}-\frac {b^{17/4} \tan ^{-1}\left (1-\frac {\sqrt {2} \sqrt [4]{b} \sqrt {x}}{\sqrt [4]{a}}\right )}{\sqrt {2} a^{9/4} (b c-a d)^3}+\frac {b^{17/4} \tan ^{-1}\left (\frac {\sqrt {2} \sqrt [4]{b} \sqrt {x}}{\sqrt [4]{a}}+1\right )}{\sqrt {2} a^{9/4} (b c-a d)^3}-\frac {d^{9/4} \left (117 a^2 d^2-306 a b c d+221 b^2 c^2\right ) \log \left (-\sqrt {2} \sqrt [4]{c} \sqrt [4]{d} \sqrt {x}+\sqrt {c}+\sqrt {d} x\right )}{64 \sqrt {2} c^{17/4} (b c-a d)^3}+\frac {d^{9/4} \left (117 a^2 d^2-306 a b c d+221 b^2 c^2\right ) \log \left (\sqrt {2} \sqrt [4]{c} \sqrt [4]{d} \sqrt {x}+\sqrt {c}+\sqrt {d} x\right )}{64 \sqrt {2} c^{17/4} (b c-a d)^3}+\frac {d^{9/4} \left (117 a^2 d^2-306 a b c d+221 b^2 c^2\right ) \tan ^{-1}\left (1-\frac {\sqrt {2} \sqrt [4]{d} \sqrt {x}}{\sqrt [4]{c}}\right )}{32 \sqrt {2} c^{17/4} (b c-a d)^3}-\frac {d^{9/4} \left (117 a^2 d^2-306 a b c d+221 b^2 c^2\right ) \tan ^{-1}\left (\frac {\sqrt {2} \sqrt [4]{d} \sqrt {x}}{\sqrt [4]{c}}+1\right )}{32 \sqrt {2} c^{17/4} (b c-a d)^3}-\frac {117 a^2 d^2-189 a b c d+32 b^2 c^2}{80 a c^3 x^{5/2} (b c-a d)^2}+\frac {117 a^3 d^3-189 a^2 b c d^2+32 a b^2 c^2 d+32 b^3 c^3}{16 a^2 c^4 \sqrt {x} (b c-a d)^2}-\frac {d (21 b c-13 a d)}{16 c^2 x^{5/2} \left (c+d x^2\right ) (b c-a d)^2}-\frac {d}{4 c x^{5/2} \left (c+d x^2\right )^2 (b c-a d)} \]

[Out]

1/80*(-117*a^2*d^2+189*a*b*c*d-32*b^2*c^2)/a/c^3/(-a*d+b*c)^2/x^(5/2)-1/4*d/c/(-a*d+b*c)/x^(5/2)/(d*x^2+c)^2-1

/16*d*(-13*a*d+21*b*c)/c^2/(-a*d+b*c)^2/x^(5/2)/(d*x^2+c)-1/2*b^(17/4)*arctan(1-b^(1/4)*2^(1/2)*x^(1/2)/a^(1/4

))/a^(9/4)/(-a*d+b*c)^3*2^(1/2)+1/2*b^(17/4)*arctan(1+b^(1/4)*2^(1/2)*x^(1/2)/a^(1/4))/a^(9/4)/(-a*d+b*c)^3*2^

(1/2)+1/64*d^(9/4)*(117*a^2*d^2-306*a*b*c*d+221*b^2*c^2)*arctan(1-d^(1/4)*2^(1/2)*x^(1/2)/c^(1/4))/c^(17/4)/(-

a*d+b*c)^3*2^(1/2)-1/64*d^(9/4)*(117*a^2*d^2-306*a*b*c*d+221*b^2*c^2)*arctan(1+d^(1/4)*2^(1/2)*x^(1/2)/c^(1/4)

)/c^(17/4)/(-a*d+b*c)^3*2^(1/2)+1/4*b^(17/4)*ln(a^(1/2)+x*b^(1/2)-a^(1/4)*b^(1/4)*2^(1/2)*x^(1/2))/a^(9/4)/(-a

*d+b*c)^3*2^(1/2)-1/4*b^(17/4)*ln(a^(1/2)+x*b^(1/2)+a^(1/4)*b^(1/4)*2^(1/2)*x^(1/2))/a^(9/4)/(-a*d+b*c)^3*2^(1

/2)-1/128*d^(9/4)*(117*a^2*d^2-306*a*b*c*d+221*b^2*c^2)*ln(c^(1/2)+x*d^(1/2)-c^(1/4)*d^(1/4)*2^(1/2)*x^(1/2))/

c^(17/4)/(-a*d+b*c)^3*2^(1/2)+1/128*d^(9/4)*(117*a^2*d^2-306*a*b*c*d+221*b^2*c^2)*ln(c^(1/2)+x*d^(1/2)+c^(1/4)

*d^(1/4)*2^(1/2)*x^(1/2))/c^(17/4)/(-a*d+b*c)^3*2^(1/2)+1/16*(117*a^3*d^3-189*a^2*b*c*d^2+32*a*b^2*c^2*d+32*b^

3*c^3)/a^2/c^4/(-a*d+b*c)^2/x^(1/2)

________________________________________________________________________________________

Rubi [A] time = 1.23, antiderivative size = 743, normalized size of antiderivative = 1.00, number of steps used = 25, number of rules used = 11, integrand size = 24, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.458, Rules used = {466, 472, 579, 583, 584, 297, 1162, 617, 204, 1165, 628} \[ -\frac {117 a^2 d^2-189 a b c d+32 b^2 c^2}{80 a c^3 x^{5/2} (b c-a d)^2}+\frac {-189 a^2 b c d^2+117 a^3 d^3+32 a b^2 c^2 d+32 b^3 c^3}{16 a^2 c^4 \sqrt {x} (b c-a d)^2}-\frac {d^{9/4} \left (117 a^2 d^2-306 a b c d+221 b^2 c^2\right ) \log \left (-\sqrt {2} \sqrt [4]{c} \sqrt [4]{d} \sqrt {x}+\sqrt {c}+\sqrt {d} x\right )}{64 \sqrt {2} c^{17/4} (b c-a d)^3}+\frac {d^{9/4} \left (117 a^2 d^2-306 a b c d+221 b^2 c^2\right ) \log \left (\sqrt {2} \sqrt [4]{c} \sqrt [4]{d} \sqrt {x}+\sqrt {c}+\sqrt {d} x\right )}{64 \sqrt {2} c^{17/4} (b c-a d)^3}+\frac {d^{9/4} \left (117 a^2 d^2-306 a b c d+221 b^2 c^2\right ) \tan ^{-1}\left (1-\frac {\sqrt {2} \sqrt [4]{d} \sqrt {x}}{\sqrt [4]{c}}\right )}{32 \sqrt {2} c^{17/4} (b c-a d)^3}-\frac {d^{9/4} \left (117 a^2 d^2-306 a b c d+221 b^2 c^2\right ) \tan ^{-1}\left (\frac {\sqrt {2} \sqrt [4]{d} \sqrt {x}}{\sqrt [4]{c}}+1\right )}{32 \sqrt {2} c^{17/4} (b c-a d)^3}+\frac {b^{17/4} \log \left (-\sqrt {2} \sqrt [4]{a} \sqrt [4]{b} \sqrt {x}+\sqrt {a}+\sqrt {b} x\right )}{2 \sqrt {2} a^{9/4} (b c-a d)^3}-\frac {b^{17/4} \log \left (\sqrt {2} \sqrt [4]{a} \sqrt [4]{b} \sqrt {x}+\sqrt {a}+\sqrt {b} x\right )}{2 \sqrt {2} a^{9/4} (b c-a d)^3}-\frac {b^{17/4} \tan ^{-1}\left (1-\frac {\sqrt {2} \sqrt [4]{b} \sqrt {x}}{\sqrt [4]{a}}\right )}{\sqrt {2} a^{9/4} (b c-a d)^3}+\frac {b^{17/4} \tan ^{-1}\left (\frac {\sqrt {2} \sqrt [4]{b} \sqrt {x}}{\sqrt [4]{a}}+1\right )}{\sqrt {2} a^{9/4} (b c-a d)^3}-\frac {d (21 b c-13 a d)}{16 c^2 x^{5/2} \left (c+d x^2\right ) (b c-a d)^2}-\frac {d}{4 c x^{5/2} \left (c+d x^2\right )^2 (b c-a d)} \]

Antiderivative was successfully veriﬁed.

[In]

Int[1/(x^(7/2)*(a + b*x^2)*(c + d*x^2)^3),x]

[Out]

-(32*b^2*c^2 - 189*a*b*c*d + 117*a^2*d^2)/(80*a*c^3*(b*c - a*d)^2*x^(5/2)) + (32*b^3*c^3 + 32*a*b^2*c^2*d - 18

9*a^2*b*c*d^2 + 117*a^3*d^3)/(16*a^2*c^4*(b*c - a*d)^2*Sqrt[x]) - d/(4*c*(b*c - a*d)*x^(5/2)*(c + d*x^2)^2) -

(d*(21*b*c - 13*a*d))/(16*c^2*(b*c - a*d)^2*x^(5/2)*(c + d*x^2)) - (b^(17/4)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[

x])/a^(1/4)])/(Sqrt[2]*a^(9/4)*(b*c - a*d)^3) + (b^(17/4)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(Sqrt

[2]*a^(9/4)*(b*c - a*d)^3) + (d^(9/4)*(221*b^2*c^2 - 306*a*b*c*d + 117*a^2*d^2)*ArcTan[1 - (Sqrt[2]*d^(1/4)*Sq

rt[x])/c^(1/4)])/(32*Sqrt[2]*c^(17/4)*(b*c - a*d)^3) - (d^(9/4)*(221*b^2*c^2 - 306*a*b*c*d + 117*a^2*d^2)*ArcT

an[1 + (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(32*Sqrt[2]*c^(17/4)*(b*c - a*d)^3) + (b^(17/4)*Log[Sqrt[a] - Sqrt[

2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(2*Sqrt[2]*a^(9/4)*(b*c - a*d)^3) - (b^(17/4)*Log[Sqrt[a] + Sqrt[2]*a

^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(2*Sqrt[2]*a^(9/4)*(b*c - a*d)^3) - (d^(9/4)*(221*b^2*c^2 - 306*a*b*c*d +

117*a^2*d^2)*Log[Sqrt[c] - Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(64*Sqrt[2]*c^(17/4)*(b*c - a*d)^3)

+ (d^(9/4)*(221*b^2*c^2 - 306*a*b*c*d + 117*a^2*d^2)*Log[Sqrt[c] + Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x

])/(64*Sqrt[2]*c^(17/4)*(b*c - a*d)^3)

Rule 204

Int[((a_) + (b_.)*(x_)^2)^(-1), x_Symbol] :> -Simp[ArcTan[(Rt[-b, 2]*x)/Rt[-a, 2]]/(Rt[-a, 2]*Rt[-b, 2]), x] /

; FreeQ[{a, b}, x] && PosQ[a/b] && (LtQ[a, 0] || LtQ[b, 0])

Rule 297

Int[(x_)^2/((a_) + (b_.)*(x_)^4), x_Symbol] :> With[{r = Numerator[Rt[a/b, 2]], s = Denominator[Rt[a/b, 2]]},

Dist[1/(2*s), Int[(r + s*x^2)/(a + b*x^4), x], x] - Dist[1/(2*s), Int[(r - s*x^2)/(a + b*x^4), x], x]] /; Free

Q[{a, b}, x] && (GtQ[a/b, 0] || (PosQ[a/b] && AtomQ[SplitProduct[SumBaseQ, a]] && AtomQ[SplitProduct[SumBaseQ,

b]]))

Rule 466

Int[((e_.)*(x_))^(m_)*((a_) + (b_.)*(x_)^(n_))^(p_)*((c_) + (d_.)*(x_)^(n_))^(q_), x_Symbol] :> With[{k = Deno

minator[m]}, Dist[k/e, Subst[Int[x^(k*(m + 1) - 1)*(a + (b*x^(k*n))/e^n)^p*(c + (d*x^(k*n))/e^n)^q, x], x, (e*

x)^(1/k)], x]] /; FreeQ[{a, b, c, d, e, p, q}, x] && NeQ[b*c - a*d, 0] && IGtQ[n, 0] && FractionQ[m] && Intege

rQ[p]

Rule 472

Int[((e_.)*(x_))^(m_.)*((a_) + (b_.)*(x_)^(n_))^(p_)*((c_) + (d_.)*(x_)^(n_))^(q_), x_Symbol] :> -Simp[(b*(e*x

)^(m + 1)*(a + b*x^n)^(p + 1)*(c + d*x^n)^(q + 1))/(a*e*n*(b*c - a*d)*(p + 1)), x] + Dist[1/(a*n*(b*c - a*d)*(

p + 1)), Int[(e*x)^m*(a + b*x^n)^(p + 1)*(c + d*x^n)^q*Simp[c*b*(m + 1) + n*(b*c - a*d)*(p + 1) + d*b*(m + n*(

p + q + 2) + 1)*x^n, x], x], x] /; FreeQ[{a, b, c, d, e, m, q}, x] && NeQ[b*c - a*d, 0] && IGtQ[n, 0] && LtQ[p

, -1] && IntBinomialQ[a, b, c, d, e, m, n, p, q, x]

Rule 579

Int[((g_.)*(x_))^(m_.)*((a_) + (b_.)*(x_)^(n_))^(p_)*((c_) + (d_.)*(x_)^(n_))^(q_)*((e_) + (f_.)*(x_)^(n_)), x

_Symbol] :> -Simp[((b*e - a*f)*(g*x)^(m + 1)*(a + b*x^n)^(p + 1)*(c + d*x^n)^(q + 1))/(a*g*n*(b*c - a*d)*(p +

1)), x] + Dist[1/(a*n*(b*c - a*d)*(p + 1)), Int[(g*x)^m*(a + b*x^n)^(p + 1)*(c + d*x^n)^q*Simp[c*(b*e - a*f)*(

m + 1) + e*n*(b*c - a*d)*(p + 1) + d*(b*e - a*f)*(m + n*(p + q + 2) + 1)*x^n, x], x], x] /; FreeQ[{a, b, c, d,

e, f, g, m, q}, x] && IGtQ[n, 0] && LtQ[p, -1]

Rule 583

Int[((g_.)*(x_))^(m_)*((a_) + (b_.)*(x_)^(n_))^(p_.)*((c_) + (d_.)*(x_)^(n_))^(q_.)*((e_) + (f_.)*(x_)^(n_)),

x_Symbol] :> Simp[(e*(g*x)^(m + 1)*(a + b*x^n)^(p + 1)*(c + d*x^n)^(q + 1))/(a*c*g*(m + 1)), x] + Dist[1/(a*c*

g^n*(m + 1)), Int[(g*x)^(m + n)*(a + b*x^n)^p*(c + d*x^n)^q*Simp[a*f*c*(m + 1) - e*(b*c + a*d)*(m + n + 1) - e

*n*(b*c*p + a*d*q) - b*e*d*(m + n*(p + q + 2) + 1)*x^n, x], x], x] /; FreeQ[{a, b, c, d, e, f, g, p, q}, x] &&

IGtQ[n, 0] && LtQ[m, -1]

Rule 584

Int[(((g_.)*(x_))^(m_.)*((a_) + (b_.)*(x_)^(n_))^(p_)*((e_) + (f_.)*(x_)^(n_)))/((c_) + (d_.)*(x_)^(n_)), x_Sy

mbol] :> Int[ExpandIntegrand[((g*x)^m*(a + b*x^n)^p*(e + f*x^n))/(c + d*x^n), x], x] /; FreeQ[{a, b, c, d, e,

f, g, m, p}, x] && IGtQ[n, 0]

Rule 617

Int[((a_) + (b_.)*(x_) + (c_.)*(x_)^2)^(-1), x_Symbol] :> With[{q = 1 - 4*Simplify[(a*c)/b^2]}, Dist[-2/b, Sub

st[Int[1/(q - x^2), x], x, 1 + (2*c*x)/b], x] /; RationalQ[q] && (EqQ[q^2, 1] || !RationalQ[b^2 - 4*a*c])] /;

FreeQ[{a, b, c}, x] && NeQ[b^2 - 4*a*c, 0]

Rule 628

Int[((d_) + (e_.)*(x_))/((a_.) + (b_.)*(x_) + (c_.)*(x_)^2), x_Symbol] :> Simp[(d*Log[RemoveContent[a + b*x +

c*x^2, x]])/b, x] /; FreeQ[{a, b, c, d, e}, x] && EqQ[2*c*d - b*e, 0]

Rule 1162

Int[((d_) + (e_.)*(x_)^2)/((a_) + (c_.)*(x_)^4), x_Symbol] :> With[{q = Rt[(2*d)/e, 2]}, Dist[e/(2*c), Int[1/S

imp[d/e + q*x + x^2, x], x], x] + Dist[e/(2*c), Int[1/Simp[d/e - q*x + x^2, x], x], x]] /; FreeQ[{a, c, d, e},

x] && EqQ[c*d^2 - a*e^2, 0] && PosQ[d*e]

Rule 1165

Int[((d_) + (e_.)*(x_)^2)/((a_) + (c_.)*(x_)^4), x_Symbol] :> With[{q = Rt[(-2*d)/e, 2]}, Dist[e/(2*c*q), Int[

(q - 2*x)/Simp[d/e + q*x - x^2, x], x], x] + Dist[e/(2*c*q), Int[(q + 2*x)/Simp[d/e - q*x - x^2, x], x], x]] /

; FreeQ[{a, c, d, e}, x] && EqQ[c*d^2 - a*e^2, 0] && NegQ[d*e]

Rubi steps

\begin {align*} \int \frac {1}{x^{7/2} \left (a+b x^2\right ) \left (c+d x^2\right )^3} \, dx &=2 \operatorname {Subst}\left (\int \frac {1}{x^6 \left (a+b x^4\right ) \left (c+d x^4\right )^3} \, dx,x,\sqrt {x}\right )\\ &=-\frac {d}{4 c (b c-a d) x^{5/2} \left (c+d x^2\right )^2}+\frac {\operatorname {Subst}\left (\int \frac {8 b c-13 a d-13 b d x^4}{x^6 \left (a+b x^4\right ) \left (c+d x^4\right )^2} \, dx,x,\sqrt {x}\right )}{4 c (b c-a d)}\\ &=-\frac {d}{4 c (b c-a d) x^{5/2} \left (c+d x^2\right )^2}-\frac {d (21 b c-13 a d)}{16 c^2 (b c-a d)^2 x^{5/2} \left (c+d x^2\right )}+\frac {\operatorname {Subst}\left (\int \frac {32 b^2 c^2-189 a b c d+117 a^2 d^2-9 b d (21 b c-13 a d) x^4}{x^6 \left (a+b x^4\right ) \left (c+d x^4\right )} \, dx,x,\sqrt {x}\right )}{16 c^2 (b c-a d)^2}\\ &=-\frac {\frac {32 b^2 c}{a}-189 b d+\frac {117 a d^2}{c}}{80 c^2 (b c-a d)^2 x^{5/2}}-\frac {d}{4 c (b c-a d) x^{5/2} \left (c+d x^2\right )^2}-\frac {d (21 b c-13 a d)}{16 c^2 (b c-a d)^2 x^{5/2} \left (c+d x^2\right )}-\frac {\operatorname {Subst}\left (\int \frac {5 \left (32 b^3 c^3+32 a b^2 c^2 d-189 a^2 b c d^2+117 a^3 d^3\right )+5 b d \left (32 b^2 c^2-189 a b c d+117 a^2 d^2\right ) x^4}{x^2 \left (a+b x^4\right ) \left (c+d x^4\right )} \, dx,x,\sqrt {x}\right )}{80 a c^3 (b c-a d)^2}\\ &=-\frac {\frac {32 b^2 c}{a}-189 b d+\frac {117 a d^2}{c}}{80 c^2 (b c-a d)^2 x^{5/2}}+\frac {32 b^3 c^3+32 a b^2 c^2 d-189 a^2 b c d^2+117 a^3 d^3}{16 a^2 c^4 (b c-a d)^2 \sqrt {x}}-\frac {d}{4 c (b c-a d) x^{5/2} \left (c+d x^2\right )^2}-\frac {d (21 b c-13 a d)}{16 c^2 (b c-a d)^2 x^{5/2} \left (c+d x^2\right )}+\frac {\operatorname {Subst}\left (\int \frac {x^2 \left (5 \left (32 b^4 c^4+32 a b^3 c^3 d+32 a^2 b^2 c^2 d^2-189 a^3 b c d^3+117 a^4 d^4\right )+5 b d \left (32 b^3 c^3+32 a b^2 c^2 d-189 a^2 b c d^2+117 a^3 d^3\right ) x^4\right )}{\left (a+b x^4\right ) \left (c+d x^4\right )} \, dx,x,\sqrt {x}\right )}{80 a^2 c^4 (b c-a d)^2}\\ &=-\frac {\frac {32 b^2 c}{a}-189 b d+\frac {117 a d^2}{c}}{80 c^2 (b c-a d)^2 x^{5/2}}+\frac {32 b^3 c^3+32 a b^2 c^2 d-189 a^2 b c d^2+117 a^3 d^3}{16 a^2 c^4 (b c-a d)^2 \sqrt {x}}-\frac {d}{4 c (b c-a d) x^{5/2} \left (c+d x^2\right )^2}-\frac {d (21 b c-13 a d)}{16 c^2 (b c-a d)^2 x^{5/2} \left (c+d x^2\right )}+\frac {\operatorname {Subst}\left (\int \left (\frac {160 b^5 c^4 x^2}{(b c-a d) \left (a+b x^4\right )}+\frac {5 a^2 d^3 \left (221 b^2 c^2-306 a b c d+117 a^2 d^2\right ) x^2}{(-b c+a d) \left (c+d x^4\right )}\right ) \, dx,x,\sqrt {x}\right )}{80 a^2 c^4 (b c-a d)^2}\\ &=-\frac {\frac {32 b^2 c}{a}-189 b d+\frac {117 a d^2}{c}}{80 c^2 (b c-a d)^2 x^{5/2}}+\frac {32 b^3 c^3+32 a b^2 c^2 d-189 a^2 b c d^2+117 a^3 d^3}{16 a^2 c^4 (b c-a d)^2 \sqrt {x}}-\frac {d}{4 c (b c-a d) x^{5/2} \left (c+d x^2\right )^2}-\frac {d (21 b c-13 a d)}{16 c^2 (b c-a d)^2 x^{5/2} \left (c+d x^2\right )}+\frac {\left (2 b^5\right ) \operatorname {Subst}\left (\int \frac {x^2}{a+b x^4} \, dx,x,\sqrt {x}\right )}{a^2 (b c-a d)^3}-\frac {\left (d^3 \left (221 b^2 c^2-306 a b c d+117 a^2 d^2\right )\right ) \operatorname {Subst}\left (\int \frac {x^2}{c+d x^4} \, dx,x,\sqrt {x}\right )}{16 c^4 (b c-a d)^3}\\ &=-\frac {\frac {32 b^2 c}{a}-189 b d+\frac {117 a d^2}{c}}{80 c^2 (b c-a d)^2 x^{5/2}}+\frac {32 b^3 c^3+32 a b^2 c^2 d-189 a^2 b c d^2+117 a^3 d^3}{16 a^2 c^4 (b c-a d)^2 \sqrt {x}}-\frac {d}{4 c (b c-a d) x^{5/2} \left (c+d x^2\right )^2}-\frac {d (21 b c-13 a d)}{16 c^2 (b c-a d)^2 x^{5/2} \left (c+d x^2\right )}-\frac {b^{9/2} \operatorname {Subst}\left (\int \frac {\sqrt {a}-\sqrt {b} x^2}{a+b x^4} \, dx,x,\sqrt {x}\right )}{a^2 (b c-a d)^3}+\frac {b^{9/2} \operatorname {Subst}\left (\int \frac {\sqrt {a}+\sqrt {b} x^2}{a+b x^4} \, dx,x,\sqrt {x}\right )}{a^2 (b c-a d)^3}+\frac {\left (d^{5/2} \left (221 b^2 c^2-306 a b c d+117 a^2 d^2\right )\right ) \operatorname {Subst}\left (\int \frac {\sqrt {c}-\sqrt {d} x^2}{c+d x^4} \, dx,x,\sqrt {x}\right )}{32 c^4 (b c-a d)^3}-\frac {\left (d^{5/2} \left (221 b^2 c^2-306 a b c d+117 a^2 d^2\right )\right ) \operatorname {Subst}\left (\int \frac {\sqrt {c}+\sqrt {d} x^2}{c+d x^4} \, dx,x,\sqrt {x}\right )}{32 c^4 (b c-a d)^3}\\ &=-\frac {\frac {32 b^2 c}{a}-189 b d+\frac {117 a d^2}{c}}{80 c^2 (b c-a d)^2 x^{5/2}}+\frac {32 b^3 c^3+32 a b^2 c^2 d-189 a^2 b c d^2+117 a^3 d^3}{16 a^2 c^4 (b c-a d)^2 \sqrt {x}}-\frac {d}{4 c (b c-a d) x^{5/2} \left (c+d x^2\right )^2}-\frac {d (21 b c-13 a d)}{16 c^2 (b c-a d)^2 x^{5/2} \left (c+d x^2\right )}+\frac {b^4 \operatorname {Subst}\left (\int \frac {1}{\frac {\sqrt {a}}{\sqrt {b}}-\frac {\sqrt {2} \sqrt [4]{a} x}{\sqrt [4]{b}}+x^2} \, dx,x,\sqrt {x}\right )}{2 a^2 (b c-a d)^3}+\frac {b^4 \operatorname {Subst}\left (\int \frac {1}{\frac {\sqrt {a}}{\sqrt {b}}+\frac {\sqrt {2} \sqrt [4]{a} x}{\sqrt [4]{b}}+x^2} \, dx,x,\sqrt {x}\right )}{2 a^2 (b c-a d)^3}+\frac {b^{17/4} \operatorname {Subst}\left (\int \frac {\frac {\sqrt {2} \sqrt [4]{a}}{\sqrt [4]{b}}+2 x}{-\frac {\sqrt {a}}{\sqrt {b}}-\frac {\sqrt {2} \sqrt [4]{a} x}{\sqrt [4]{b}}-x^2} \, dx,x,\sqrt {x}\right )}{2 \sqrt {2} a^{9/4} (b c-a d)^3}+\frac {b^{17/4} \operatorname {Subst}\left (\int \frac {\frac {\sqrt {2} \sqrt [4]{a}}{\sqrt [4]{b}}-2 x}{-\frac {\sqrt {a}}{\sqrt {b}}+\frac {\sqrt {2} \sqrt [4]{a} x}{\sqrt [4]{b}}-x^2} \, dx,x,\sqrt {x}\right )}{2 \sqrt {2} a^{9/4} (b c-a d)^3}-\frac {\left (d^2 \left (221 b^2 c^2-306 a b c d+117 a^2 d^2\right )\right ) \operatorname {Subst}\left (\int \frac {1}{\frac {\sqrt {c}}{\sqrt {d}}-\frac {\sqrt {2} \sqrt [4]{c} x}{\sqrt [4]{d}}+x^2} \, dx,x,\sqrt {x}\right )}{64 c^4 (b c-a d)^3}-\frac {\left (d^2 \left (221 b^2 c^2-306 a b c d+117 a^2 d^2\right )\right ) \operatorname {Subst}\left (\int \frac {1}{\frac {\sqrt {c}}{\sqrt {d}}+\frac {\sqrt {2} \sqrt [4]{c} x}{\sqrt [4]{d}}+x^2} \, dx,x,\sqrt {x}\right )}{64 c^4 (b c-a d)^3}-\frac {\left (d^{9/4} \left (221 b^2 c^2-306 a b c d+117 a^2 d^2\right )\right ) \operatorname {Subst}\left (\int \frac {\frac {\sqrt {2} \sqrt [4]{c}}{\sqrt [4]{d}}+2 x}{-\frac {\sqrt {c}}{\sqrt {d}}-\frac {\sqrt {2} \sqrt [4]{c} x}{\sqrt [4]{d}}-x^2} \, dx,x,\sqrt {x}\right )}{64 \sqrt {2} c^{17/4} (b c-a d)^3}-\frac {\left (d^{9/4} \left (221 b^2 c^2-306 a b c d+117 a^2 d^2\right )\right ) \operatorname {Subst}\left (\int \frac {\frac {\sqrt {2} \sqrt [4]{c}}{\sqrt [4]{d}}-2 x}{-\frac {\sqrt {c}}{\sqrt {d}}+\frac {\sqrt {2} \sqrt [4]{c} x}{\sqrt [4]{d}}-x^2} \, dx,x,\sqrt {x}\right )}{64 \sqrt {2} c^{17/4} (b c-a d)^3}\\ &=-\frac {\frac {32 b^2 c}{a}-189 b d+\frac {117 a d^2}{c}}{80 c^2 (b c-a d)^2 x^{5/2}}+\frac {32 b^3 c^3+32 a b^2 c^2 d-189 a^2 b c d^2+117 a^3 d^3}{16 a^2 c^4 (b c-a d)^2 \sqrt {x}}-\frac {d}{4 c (b c-a d) x^{5/2} \left (c+d x^2\right )^2}-\frac {d (21 b c-13 a d)}{16 c^2 (b c-a d)^2 x^{5/2} \left (c+d x^2\right )}+\frac {b^{17/4} \log \left (\sqrt {a}-\sqrt {2} \sqrt [4]{a} \sqrt [4]{b} \sqrt {x}+\sqrt {b} x\right )}{2 \sqrt {2} a^{9/4} (b c-a d)^3}-\frac {b^{17/4} \log \left (\sqrt {a}+\sqrt {2} \sqrt [4]{a} \sqrt [4]{b} \sqrt {x}+\sqrt {b} x\right )}{2 \sqrt {2} a^{9/4} (b c-a d)^3}-\frac {d^{9/4} \left (221 b^2 c^2-306 a b c d+117 a^2 d^2\right ) \log \left (\sqrt {c}-\sqrt {2} \sqrt [4]{c} \sqrt [4]{d} \sqrt {x}+\sqrt {d} x\right )}{64 \sqrt {2} c^{17/4} (b c-a d)^3}+\frac {d^{9/4} \left (221 b^2 c^2-306 a b c d+117 a^2 d^2\right ) \log \left (\sqrt {c}+\sqrt {2} \sqrt [4]{c} \sqrt [4]{d} \sqrt {x}+\sqrt {d} x\right )}{64 \sqrt {2} c^{17/4} (b c-a d)^3}+\frac {b^{17/4} \operatorname {Subst}\left (\int \frac {1}{-1-x^2} \, dx,x,1-\frac {\sqrt {2} \sqrt [4]{b} \sqrt {x}}{\sqrt [4]{a}}\right )}{\sqrt {2} a^{9/4} (b c-a d)^3}-\frac {b^{17/4} \operatorname {Subst}\left (\int \frac {1}{-1-x^2} \, dx,x,1+\frac {\sqrt {2} \sqrt [4]{b} \sqrt {x}}{\sqrt [4]{a}}\right )}{\sqrt {2} a^{9/4} (b c-a d)^3}-\frac {\left (d^{9/4} \left (221 b^2 c^2-306 a b c d+117 a^2 d^2\right )\right ) \operatorname {Subst}\left (\int \frac {1}{-1-x^2} \, dx,x,1-\frac {\sqrt {2} \sqrt [4]{d} \sqrt {x}}{\sqrt [4]{c}}\right )}{32 \sqrt {2} c^{17/4} (b c-a d)^3}+\frac {\left (d^{9/4} \left (221 b^2 c^2-306 a b c d+117 a^2 d^2\right )\right ) \operatorname {Subst}\left (\int \frac {1}{-1-x^2} \, dx,x,1+\frac {\sqrt {2} \sqrt [4]{d} \sqrt {x}}{\sqrt [4]{c}}\right )}{32 \sqrt {2} c^{17/4} (b c-a d)^3}\\ &=-\frac {\frac {32 b^2 c}{a}-189 b d+\frac {117 a d^2}{c}}{80 c^2 (b c-a d)^2 x^{5/2}}+\frac {32 b^3 c^3+32 a b^2 c^2 d-189 a^2 b c d^2+117 a^3 d^3}{16 a^2 c^4 (b c-a d)^2 \sqrt {x}}-\frac {d}{4 c (b c-a d) x^{5/2} \left (c+d x^2\right )^2}-\frac {d (21 b c-13 a d)}{16 c^2 (b c-a d)^2 x^{5/2} \left (c+d x^2\right )}-\frac {b^{17/4} \tan ^{-1}\left (1-\frac {\sqrt {2} \sqrt [4]{b} \sqrt {x}}{\sqrt [4]{a}}\right )}{\sqrt {2} a^{9/4} (b c-a d)^3}+\frac {b^{17/4} \tan ^{-1}\left (1+\frac {\sqrt {2} \sqrt [4]{b} \sqrt {x}}{\sqrt [4]{a}}\right )}{\sqrt {2} a^{9/4} (b c-a d)^3}+\frac {d^{9/4} \left (221 b^2 c^2-306 a b c d+117 a^2 d^2\right ) \tan ^{-1}\left (1-\frac {\sqrt {2} \sqrt [4]{d} \sqrt {x}}{\sqrt [4]{c}}\right )}{32 \sqrt {2} c^{17/4} (b c-a d)^3}-\frac {d^{9/4} \left (221 b^2 c^2-306 a b c d+117 a^2 d^2\right ) \tan ^{-1}\left (1+\frac {\sqrt {2} \sqrt [4]{d} \sqrt {x}}{\sqrt [4]{c}}\right )}{32 \sqrt {2} c^{17/4} (b c-a d)^3}+\frac {b^{17/4} \log \left (\sqrt {a}-\sqrt {2} \sqrt [4]{a} \sqrt [4]{b} \sqrt {x}+\sqrt {b} x\right )}{2 \sqrt {2} a^{9/4} (b c-a d)^3}-\frac {b^{17/4} \log \left (\sqrt {a}+\sqrt {2} \sqrt [4]{a} \sqrt [4]{b} \sqrt {x}+\sqrt {b} x\right )}{2 \sqrt {2} a^{9/4} (b c-a d)^3}-\frac {d^{9/4} \left (221 b^2 c^2-306 a b c d+117 a^2 d^2\right ) \log \left (\sqrt {c}-\sqrt {2} \sqrt [4]{c} \sqrt [4]{d} \sqrt {x}+\sqrt {d} x\right )}{64 \sqrt {2} c^{17/4} (b c-a d)^3}+\frac {d^{9/4} \left (221 b^2 c^2-306 a b c d+117 a^2 d^2\right ) \log \left (\sqrt {c}+\sqrt {2} \sqrt [4]{c} \sqrt [4]{d} \sqrt {x}+\sqrt {d} x\right )}{64 \sqrt {2} c^{17/4} (b c-a d)^3}\\ \end {align*}

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Mathematica [A] time = 6.18, size = 720, normalized size = 0.97 \[ \frac {b^{17/4} \log \left (-\sqrt {2} \sqrt [4]{a} \sqrt [4]{b} \sqrt {x}+\sqrt {a}+\sqrt {b} x\right )}{2 \sqrt {2} a^{9/4} (b c-a d)^3}-\frac {b^{17/4} \log \left (\sqrt {2} \sqrt [4]{a} \sqrt [4]{b} \sqrt {x}+\sqrt {a}+\sqrt {b} x\right )}{2 \sqrt {2} a^{9/4} (b c-a d)^3}+\frac {b^{17/4} \tan ^{-1}\left (\frac {2 \sqrt [4]{b} \sqrt {x}-\sqrt {2} \sqrt [4]{a}}{\sqrt {2} \sqrt [4]{a}}\right )}{\sqrt {2} a^{9/4} (b c-a d)^3}+\frac {b^{17/4} \tan ^{-1}\left (\frac {\sqrt {2} \sqrt [4]{a}+2 \sqrt [4]{b} \sqrt {x}}{\sqrt {2} \sqrt [4]{a}}\right )}{\sqrt {2} a^{9/4} (b c-a d)^3}+\frac {d^{9/4} \left (117 a^2 d^2-306 a b c d+221 b^2 c^2\right ) \log \left (-\sqrt {2} \sqrt [4]{c} \sqrt [4]{d} \sqrt {x}+\sqrt {c}+\sqrt {d} x\right )}{64 \sqrt {2} c^{17/4} (a d-b c)^3}-\frac {d^{9/4} \left (117 a^2 d^2-306 a b c d+221 b^2 c^2\right ) \log \left (\sqrt {2} \sqrt [4]{c} \sqrt [4]{d} \sqrt {x}+\sqrt {c}+\sqrt {d} x\right )}{64 \sqrt {2} c^{17/4} (a d-b c)^3}+\frac {d^{9/4} \left (117 a^2 d^2-306 a b c d+221 b^2 c^2\right ) \tan ^{-1}\left (\frac {2 \sqrt [4]{d} \sqrt {x}-\sqrt {2} \sqrt [4]{c}}{\sqrt {2} \sqrt [4]{c}}\right )}{32 \sqrt {2} c^{17/4} (a d-b c)^3}+\frac {d^{9/4} \left (117 a^2 d^2-306 a b c d+221 b^2 c^2\right ) \tan ^{-1}\left (\frac {\sqrt {2} \sqrt [4]{c}+2 \sqrt [4]{d} \sqrt {x}}{\sqrt {2} \sqrt [4]{c}}\right )}{32 \sqrt {2} c^{17/4} (a d-b c)^3}+\frac {2 (3 a d+b c)}{a^2 c^4 \sqrt {x}}-\frac {d^3 x^{3/2} (29 b c-21 a d)}{16 c^4 \left (c+d x^2\right ) (b c-a d)^2}-\frac {d^3 x^{3/2}}{4 c^3 \left (c+d x^2\right )^2 (b c-a d)}-\frac {2}{5 a c^3 x^{5/2}} \]

Antiderivative was successfully veriﬁed.

[In]

Integrate[1/(x^(7/2)*(a + b*x^2)*(c + d*x^2)^3),x]

[Out]

-2/(5*a*c^3*x^(5/2)) + (2*(b*c + 3*a*d))/(a^2*c^4*Sqrt[x]) - (d^3*x^(3/2))/(4*c^3*(b*c - a*d)*(c + d*x^2)^2) -

(d^3*(29*b*c - 21*a*d)*x^(3/2))/(16*c^4*(b*c - a*d)^2*(c + d*x^2)) + (b^(17/4)*ArcTan[(-(Sqrt[2]*a^(1/4)) + 2

*b^(1/4)*Sqrt[x])/(Sqrt[2]*a^(1/4))])/(Sqrt[2]*a^(9/4)*(b*c - a*d)^3) + (b^(17/4)*ArcTan[(Sqrt[2]*a^(1/4) + 2*

b^(1/4)*Sqrt[x])/(Sqrt[2]*a^(1/4))])/(Sqrt[2]*a^(9/4)*(b*c - a*d)^3) + (d^(9/4)*(221*b^2*c^2 - 306*a*b*c*d + 1

17*a^2*d^2)*ArcTan[(-(Sqrt[2]*c^(1/4)) + 2*d^(1/4)*Sqrt[x])/(Sqrt[2]*c^(1/4))])/(32*Sqrt[2]*c^(17/4)*(-(b*c) +

a*d)^3) + (d^(9/4)*(221*b^2*c^2 - 306*a*b*c*d + 117*a^2*d^2)*ArcTan[(Sqrt[2]*c^(1/4) + 2*d^(1/4)*Sqrt[x])/(Sq

rt[2]*c^(1/4))])/(32*Sqrt[2]*c^(17/4)*(-(b*c) + a*d)^3) + (b^(17/4)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt

[x] + Sqrt[b]*x])/(2*Sqrt[2]*a^(9/4)*(b*c - a*d)^3) - (b^(17/4)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x]

+ Sqrt[b]*x])/(2*Sqrt[2]*a^(9/4)*(b*c - a*d)^3) + (d^(9/4)*(221*b^2*c^2 - 306*a*b*c*d + 117*a^2*d^2)*Log[Sqrt[

c] - Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(64*Sqrt[2]*c^(17/4)*(-(b*c) + a*d)^3) - (d^(9/4)*(221*b^2*

c^2 - 306*a*b*c*d + 117*a^2*d^2)*Log[Sqrt[c] + Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(64*Sqrt[2]*c^(17

/4)*(-(b*c) + a*d)^3)

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fricas [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \[ \text {Timed out} \]

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x^(7/2)/(b*x^2+a)/(d*x^2+c)^3,x, algorithm="fricas")

[Out]

Timed out

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giac [A] time = 1.86, size = 1000, normalized size = 1.35 \[ \text {result too large to display} \]

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x^(7/2)/(b*x^2+a)/(d*x^2+c)^3,x, algorithm="giac")

[Out]

(a*b^3)^(3/4)*b^2*arctan(1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) + 2*sqrt(x))/(a/b)^(1/4))/(sqrt(2)*a^3*b^3*c^3 - 3*s

qrt(2)*a^4*b^2*c^2*d + 3*sqrt(2)*a^5*b*c*d^2 - sqrt(2)*a^6*d^3) + (a*b^3)^(3/4)*b^2*arctan(-1/2*sqrt(2)*(sqrt(

2)*(a/b)^(1/4) - 2*sqrt(x))/(a/b)^(1/4))/(sqrt(2)*a^3*b^3*c^3 - 3*sqrt(2)*a^4*b^2*c^2*d + 3*sqrt(2)*a^5*b*c*d^

2 - sqrt(2)*a^6*d^3) - 1/2*(a*b^3)^(3/4)*b^2*log(sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(sqrt(2)*a^3*b^3

*c^3 - 3*sqrt(2)*a^4*b^2*c^2*d + 3*sqrt(2)*a^5*b*c*d^2 - sqrt(2)*a^6*d^3) + 1/2*(a*b^3)^(3/4)*b^2*log(-sqrt(2)

*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(sqrt(2)*a^3*b^3*c^3 - 3*sqrt(2)*a^4*b^2*c^2*d + 3*sqrt(2)*a^5*b*c*d^2 -

sqrt(2)*a^6*d^3) - 1/32*(221*(c*d^3)^(3/4)*b^2*c^2 - 306*(c*d^3)^(3/4)*a*b*c*d + 117*(c*d^3)^(3/4)*a^2*d^2)*a

rctan(1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) + 2*sqrt(x))/(c/d)^(1/4))/(sqrt(2)*b^3*c^8 - 3*sqrt(2)*a*b^2*c^7*d + 3*

sqrt(2)*a^2*b*c^6*d^2 - sqrt(2)*a^3*c^5*d^3) - 1/32*(221*(c*d^3)^(3/4)*b^2*c^2 - 306*(c*d^3)^(3/4)*a*b*c*d + 1

17*(c*d^3)^(3/4)*a^2*d^2)*arctan(-1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) - 2*sqrt(x))/(c/d)^(1/4))/(sqrt(2)*b^3*c^8

- 3*sqrt(2)*a*b^2*c^7*d + 3*sqrt(2)*a^2*b*c^6*d^2 - sqrt(2)*a^3*c^5*d^3) + 1/64*(221*(c*d^3)^(3/4)*b^2*c^2 - 3

06*(c*d^3)^(3/4)*a*b*c*d + 117*(c*d^3)^(3/4)*a^2*d^2)*log(sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(sqrt(2

)*b^3*c^8 - 3*sqrt(2)*a*b^2*c^7*d + 3*sqrt(2)*a^2*b*c^6*d^2 - sqrt(2)*a^3*c^5*d^3) - 1/64*(221*(c*d^3)^(3/4)*b

^2*c^2 - 306*(c*d^3)^(3/4)*a*b*c*d + 117*(c*d^3)^(3/4)*a^2*d^2)*log(-sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/

d))/(sqrt(2)*b^3*c^8 - 3*sqrt(2)*a*b^2*c^7*d + 3*sqrt(2)*a^2*b*c^6*d^2 - sqrt(2)*a^3*c^5*d^3) - 1/16*(29*b*c*d

^4*x^(7/2) - 21*a*d^5*x^(7/2) + 33*b*c^2*d^3*x^(3/2) - 25*a*c*d^4*x^(3/2))/((b^2*c^6 - 2*a*b*c^5*d + a^2*c^4*d

^2)*(d*x^2 + c)^2) + 2/5*(5*b*c*x^2 + 15*a*d*x^2 - a*c)/(a^2*c^4*x^(5/2))

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maple [A] time = 0.03, size = 933, normalized size = 1.26 \[ \text {result too large to display} \]

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

int(1/x^(7/2)/(b*x^2+a)/(d*x^2+c)^3,x)

[Out]

-1/4*b^4/a^2/(a*d-b*c)^3/(a/b)^(1/4)*2^(1/2)*ln((x-(a/b)^(1/4)*2^(1/2)*x^(1/2)+(a/b)^(1/2))/(x+(a/b)^(1/4)*2^(

1/2)*x^(1/2)+(a/b)^(1/2)))-1/2*b^4/a^2/(a*d-b*c)^3/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)+1)-1

/2*b^4/a^2/(a*d-b*c)^3/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x^(1/2)-1)+21/16*d^6/c^4/(a*d-b*c)^3/(d*

x^2+c)^2*x^(7/2)*a^2-25/8*d^5/c^3/(a*d-b*c)^3/(d*x^2+c)^2*x^(7/2)*a*b+29/16*d^4/c^2/(a*d-b*c)^3/(d*x^2+c)^2*x^

(7/2)*b^2+25/16*d^5/c^3/(a*d-b*c)^3/(d*x^2+c)^2*x^(3/2)*a^2-29/8*d^4/c^2/(a*d-b*c)^3/(d*x^2+c)^2*x^(3/2)*a*b+3

3/16*d^3/c/(a*d-b*c)^3/(d*x^2+c)^2*x^(3/2)*b^2+117/128*d^4/c^4/(a*d-b*c)^3/(c/d)^(1/4)*2^(1/2)*a^2*ln((x-(c/d)

^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2))/(x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))+117/64*d^4/c^4/(a*d-b*c)^3/(c

/d)^(1/4)*2^(1/2)*a^2*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)+117/64*d^4/c^4/(a*d-b*c)^3/(c/d)^(1/4)*2^(1/2)*a^2

*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)-1)-153/64*d^3/c^3/(a*d-b*c)^3/(c/d)^(1/4)*2^(1/2)*a*b*ln((x-(c/d)^(1/4)*2^

(1/2)*x^(1/2)+(c/d)^(1/2))/(x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))-153/32*d^3/c^3/(a*d-b*c)^3/(c/d)^(1/4)

*2^(1/2)*a*b*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)-153/32*d^3/c^3/(a*d-b*c)^3/(c/d)^(1/4)*2^(1/2)*a*b*arctan(2

^(1/2)/(c/d)^(1/4)*x^(1/2)-1)+221/128*d^2/c^2/(a*d-b*c)^3/(c/d)^(1/4)*2^(1/2)*b^2*ln((x-(c/d)^(1/4)*2^(1/2)*x^

(1/2)+(c/d)^(1/2))/(x+(c/d)^(1/4)*2^(1/2)*x^(1/2)+(c/d)^(1/2)))+221/64*d^2/c^2/(a*d-b*c)^3/(c/d)^(1/4)*2^(1/2)

*b^2*arctan(2^(1/2)/(c/d)^(1/4)*x^(1/2)+1)+221/64*d^2/c^2/(a*d-b*c)^3/(c/d)^(1/4)*2^(1/2)*b^2*arctan(2^(1/2)/(

c/d)^(1/4)*x^(1/2)-1)-2/5/a/c^3/x^(5/2)+6/a/c^4/x^(1/2)*d+2/a^2/c^3/x^(1/2)*b

________________________________________________________________________________________

maxima [A] time = 2.76, size = 756, normalized size = 1.02 \[ \frac {b^{5} {\left (\frac {2 \, \sqrt {2} \arctan \left (\frac {\sqrt {2} {\left (\sqrt {2} a^{\frac {1}{4}} b^{\frac {1}{4}} + 2 \, \sqrt {b} \sqrt {x}\right )}}{2 \, \sqrt {\sqrt {a} \sqrt {b}}}\right )}{\sqrt {\sqrt {a} \sqrt {b}} \sqrt {b}} + \frac {2 \, \sqrt {2} \arctan \left (-\frac {\sqrt {2} {\left (\sqrt {2} a^{\frac {1}{4}} b^{\frac {1}{4}} - 2 \, \sqrt {b} \sqrt {x}\right )}}{2 \, \sqrt {\sqrt {a} \sqrt {b}}}\right )}{\sqrt {\sqrt {a} \sqrt {b}} \sqrt {b}} - \frac {\sqrt {2} \log \left (\sqrt {2} a^{\frac {1}{4}} b^{\frac {1}{4}} \sqrt {x} + \sqrt {b} x + \sqrt {a}\right )}{a^{\frac {1}{4}} b^{\frac {3}{4}}} + \frac {\sqrt {2} \log \left (-\sqrt {2} a^{\frac {1}{4}} b^{\frac {1}{4}} \sqrt {x} + \sqrt {b} x + \sqrt {a}\right )}{a^{\frac {1}{4}} b^{\frac {3}{4}}}\right )}}{4 \, {\left (a^{2} b^{3} c^{3} - 3 \, a^{3} b^{2} c^{2} d + 3 \, a^{4} b c d^{2} - a^{5} d^{3}\right )}} - \frac {{\left (221 \, b^{2} c^{2} d^{3} - 306 \, a b c d^{4} + 117 \, a^{2} d^{5}\right )} {\left (\frac {2 \, \sqrt {2} \arctan \left (\frac {\sqrt {2} {\left (\sqrt {2} c^{\frac {1}{4}} d^{\frac {1}{4}} + 2 \, \sqrt {d} \sqrt {x}\right )}}{2 \, \sqrt {\sqrt {c} \sqrt {d}}}\right )}{\sqrt {\sqrt {c} \sqrt {d}} \sqrt {d}} + \frac {2 \, \sqrt {2} \arctan \left (-\frac {\sqrt {2} {\left (\sqrt {2} c^{\frac {1}{4}} d^{\frac {1}{4}} - 2 \, \sqrt {d} \sqrt {x}\right )}}{2 \, \sqrt {\sqrt {c} \sqrt {d}}}\right )}{\sqrt {\sqrt {c} \sqrt {d}} \sqrt {d}} - \frac {\sqrt {2} \log \left (\sqrt {2} c^{\frac {1}{4}} d^{\frac {1}{4}} \sqrt {x} + \sqrt {d} x + \sqrt {c}\right )}{c^{\frac {1}{4}} d^{\frac {3}{4}}} + \frac {\sqrt {2} \log \left (-\sqrt {2} c^{\frac {1}{4}} d^{\frac {1}{4}} \sqrt {x} + \sqrt {d} x + \sqrt {c}\right )}{c^{\frac {1}{4}} d^{\frac {3}{4}}}\right )}}{128 \, {\left (b^{3} c^{7} - 3 \, a b^{2} c^{6} d + 3 \, a^{2} b c^{5} d^{2} - a^{3} c^{4} d^{3}\right )}} - \frac {32 \, a b^{2} c^{5} - 64 \, a^{2} b c^{4} d + 32 \, a^{3} c^{3} d^{2} - 5 \, {\left (32 \, b^{3} c^{3} d^{2} + 32 \, a b^{2} c^{2} d^{3} - 189 \, a^{2} b c d^{4} + 117 \, a^{3} d^{5}\right )} x^{6} - {\left (320 \, b^{3} c^{4} d + 288 \, a b^{2} c^{3} d^{2} - 1701 \, a^{2} b c^{2} d^{3} + 1053 \, a^{3} c d^{4}\right )} x^{4} - 32 \, {\left (5 \, b^{3} c^{5} + 3 \, a b^{2} c^{4} d - 21 \, a^{2} b c^{3} d^{2} + 13 \, a^{3} c^{2} d^{3}\right )} x^{2}}{80 \, {\left ({\left (a^{2} b^{2} c^{6} d^{2} - 2 \, a^{3} b c^{5} d^{3} + a^{4} c^{4} d^{4}\right )} x^{\frac {13}{2}} + 2 \, {\left (a^{2} b^{2} c^{7} d - 2 \, a^{3} b c^{6} d^{2} + a^{4} c^{5} d^{3}\right )} x^{\frac {9}{2}} + {\left (a^{2} b^{2} c^{8} - 2 \, a^{3} b c^{7} d + a^{4} c^{6} d^{2}\right )} x^{\frac {5}{2}}\right )}} \]

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x^(7/2)/(b*x^2+a)/(d*x^2+c)^3,x, algorithm="maxima")

[Out]

1/4*b^5*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) + 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sq

rt(sqrt(a)*sqrt(b))*sqrt(b)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) - 2*sqrt(b)*sqrt(x))/sqr

t(sqrt(a)*sqrt(b)))/(sqrt(sqrt(a)*sqrt(b))*sqrt(b)) - sqrt(2)*log(sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x

+ sqrt(a))/(a^(1/4)*b^(3/4)) + sqrt(2)*log(-sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(1/4)*b^

(3/4)))/(a^2*b^3*c^3 - 3*a^3*b^2*c^2*d + 3*a^4*b*c*d^2 - a^5*d^3) - 1/128*(221*b^2*c^2*d^3 - 306*a*b*c*d^4 + 1

17*a^2*d^5)*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) + 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))

/(sqrt(sqrt(c)*sqrt(d))*sqrt(d)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) - 2*sqrt(d)*sqrt(x))

/sqrt(sqrt(c)*sqrt(d)))/(sqrt(sqrt(c)*sqrt(d))*sqrt(d)) - sqrt(2)*log(sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d

)*x + sqrt(c))/(c^(1/4)*d^(3/4)) + sqrt(2)*log(-sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(1/4

)*d^(3/4)))/(b^3*c^7 - 3*a*b^2*c^6*d + 3*a^2*b*c^5*d^2 - a^3*c^4*d^3) - 1/80*(32*a*b^2*c^5 - 64*a^2*b*c^4*d +

32*a^3*c^3*d^2 - 5*(32*b^3*c^3*d^2 + 32*a*b^2*c^2*d^3 - 189*a^2*b*c*d^4 + 117*a^3*d^5)*x^6 - (320*b^3*c^4*d +

288*a*b^2*c^3*d^2 - 1701*a^2*b*c^2*d^3 + 1053*a^3*c*d^4)*x^4 - 32*(5*b^3*c^5 + 3*a*b^2*c^4*d - 21*a^2*b*c^3*d^

2 + 13*a^3*c^2*d^3)*x^2)/((a^2*b^2*c^6*d^2 - 2*a^3*b*c^5*d^3 + a^4*c^4*d^4)*x^(13/2) + 2*(a^2*b^2*c^7*d - 2*a^

3*b*c^6*d^2 + a^4*c^5*d^3)*x^(9/2) + (a^2*b^2*c^8 - 2*a^3*b*c^7*d + a^4*c^6*d^2)*x^(5/2))

________________________________________________________________________________________

mupad [B] time = 12.55, size = 36917, normalized size = 49.69 \[ \text {result too large to display} \]

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

int(1/(x^(7/2)*(a + b*x^2)*(c + d*x^2)^3),x)

[Out]

((2*x^2*(13*a*d + 5*b*c))/(5*a^2*c^2) - 2/(5*a*c) + (x^4*(1053*a^3*d^4 + 320*b^3*c^3*d + 288*a*b^2*c^2*d^2 - 1

701*a^2*b*c*d^3))/(80*a^2*c^2*(b^2*c^3 + a^2*c*d^2 - 2*a*b*c^2*d)) + (d^2*x^6*(117*a^3*d^3 + 32*b^3*c^3 + 32*a

*b^2*c^2*d - 189*a^2*b*c*d^2))/(16*a^2*c^3*(b^2*c^3 + a^2*c*d^2 - 2*a*b*c^2*d)))/(c^2*x^(5/2) + d^2*x^(13/2) +

2*c*d*x^(9/2)) - atan((a^11*b^22*c^29*x^(1/2)*(-b^17/(16*a^21*d^12 + 16*a^9*b^12*c^12 - 192*a^10*b^11*c^11*d

+ 1056*a^11*b^10*c^10*d^2 - 3520*a^12*b^9*c^9*d^3 + 7920*a^13*b^8*c^8*d^4 - 12672*a^14*b^7*c^7*d^5 + 14784*a^1

5*b^6*c^6*d^6 - 12672*a^16*b^5*c^5*d^7 + 7920*a^17*b^4*c^4*d^8 - 3520*a^18*b^3*c^3*d^9 + 1056*a^19*b^2*c^2*d^1

0 - 192*a^20*b*c*d^11))^(5/4)*33554432i + a^19*b^10*d^17*x^(1/2)*(-b^17/(16*a^21*d^12 + 16*a^9*b^12*c^12 - 192

*a^10*b^11*c^11*d + 1056*a^11*b^10*c^10*d^2 - 3520*a^12*b^9*c^9*d^3 + 7920*a^13*b^8*c^8*d^4 - 12672*a^14*b^7*c

^7*d^5 + 14784*a^15*b^6*c^6*d^6 - 12672*a^16*b^5*c^5*d^7 + 7920*a^17*b^4*c^4*d^8 - 3520*a^18*b^3*c^3*d^9 + 105

6*a^19*b^2*c^2*d^10 - 192*a^20*b*c*d^11))^(1/4)*374777442i + a^33*c^7*d^22*x^(1/2)*(-b^17/(16*a^21*d^12 + 16*a

^9*b^12*c^12 - 192*a^10*b^11*c^11*d + 1056*a^11*b^10*c^10*d^2 - 3520*a^12*b^9*c^9*d^3 + 7920*a^13*b^8*c^8*d^4

- 12672*a^14*b^7*c^7*d^5 + 14784*a^15*b^6*c^6*d^6 - 12672*a^16*b^5*c^5*d^7 + 7920*a^17*b^4*c^4*d^8 - 3520*a^18

*b^3*c^3*d^9 + 1056*a^19*b^2*c^2*d^10 - 192*a^20*b*c*d^11))^(5/4)*448561152i + a^8*b^21*c^11*d^6*x^(1/2)*(-b^1

7/(16*a^21*d^12 + 16*a^9*b^12*c^12 - 192*a^10*b^11*c^11*d + 1056*a^11*b^10*c^10*d^2 - 3520*a^12*b^9*c^9*d^3 +

7920*a^13*b^8*c^8*d^4 - 12672*a^14*b^7*c^7*d^5 + 14784*a^15*b^6*c^6*d^6 - 12672*a^16*b^5*c^5*d^7 + 7920*a^17*b

^4*c^4*d^8 - 3520*a^18*b^3*c^3*d^9 + 1056*a^19*b^2*c^2*d^10 - 192*a^20*b*c*d^11))^(1/4)*100026368i - a^9*b^20*

c^10*d^7*x^(1/2)*(-b^17/(16*a^21*d^12 + 16*a^9*b^12*c^12 - 192*a^10*b^11*c^11*d + 1056*a^11*b^10*c^10*d^2 - 35

20*a^12*b^9*c^9*d^3 + 7920*a^13*b^8*c^8*d^4 - 12672*a^14*b^7*c^7*d^5 + 14784*a^15*b^6*c^6*d^6 - 12672*a^16*b^5

*c^5*d^7 + 7920*a^17*b^4*c^4*d^8 - 3520*a^18*b^3*c^3*d^9 + 1056*a^19*b^2*c^2*d^10 - 192*a^20*b*c*d^11))^(1/4)*

276996096i + a^10*b^19*c^9*d^8*x^(1/2)*(-b^17/(16*a^21*d^12 + 16*a^9*b^12*c^12 - 192*a^10*b^11*c^11*d + 1056*a

^11*b^10*c^10*d^2 - 3520*a^12*b^9*c^9*d^3 + 7920*a^13*b^8*c^8*d^4 - 12672*a^14*b^7*c^7*d^5 + 14784*a^15*b^6*c^

6*d^6 - 12672*a^16*b^5*c^5*d^7 + 7920*a^17*b^4*c^4*d^8 - 3520*a^18*b^3*c^3*d^9 + 1056*a^19*b^2*c^2*d^10 - 192*

a^20*b*c*d^11))^(1/4)*297676800i + a^11*b^18*c^8*d^9*x^(1/2)*(-b^17/(16*a^21*d^12 + 16*a^9*b^12*c^12 - 192*a^1

0*b^11*c^11*d + 1056*a^11*b^10*c^10*d^2 - 3520*a^12*b^9*c^9*d^3 + 7920*a^13*b^8*c^8*d^4 - 12672*a^14*b^7*c^7*d

^5 + 14784*a^15*b^6*c^6*d^6 - 12672*a^16*b^5*c^5*d^7 + 7920*a^17*b^4*c^4*d^8 - 3520*a^18*b^3*c^3*d^9 + 1056*a^

19*b^2*c^2*d^10 - 192*a^20*b*c*d^11))^(1/4)*4624241570i - a^12*b^17*c^7*d^10*x^(1/2)*(-b^17/(16*a^21*d^12 + 16

*a^9*b^12*c^12 - 192*a^10*b^11*c^11*d + 1056*a^11*b^10*c^10*d^2 - 3520*a^12*b^9*c^9*d^3 + 7920*a^13*b^8*c^8*d^

4 - 12672*a^14*b^7*c^7*d^5 + 14784*a^15*b^6*c^6*d^6 - 12672*a^16*b^5*c^5*d^7 + 7920*a^17*b^4*c^4*d^8 - 3520*a^

18*b^3*c^3*d^9 + 1056*a^19*b^2*c^2*d^10 - 192*a^20*b*c*d^11))^(1/4)*26395336656i + a^13*b^16*c^6*d^11*x^(1/2)*

(-b^17/(16*a^21*d^12 + 16*a^9*b^12*c^12 - 192*a^10*b^11*c^11*d + 1056*a^11*b^10*c^10*d^2 - 3520*a^12*b^9*c^9*d

^3 + 7920*a^13*b^8*c^8*d^4 - 12672*a^14*b^7*c^7*d^5 + 14784*a^15*b^6*c^6*d^6 - 12672*a^16*b^5*c^5*d^7 + 7920*a

^17*b^4*c^4*d^8 - 3520*a^18*b^3*c^3*d^9 + 1056*a^19*b^2*c^2*d^10 - 192*a^20*b*c*d^11))^(1/4)*64982364408i - a^

14*b^15*c^5*d^12*x^(1/2)*(-b^17/(16*a^21*d^12 + 16*a^9*b^12*c^12 - 192*a^10*b^11*c^11*d + 1056*a^11*b^10*c^10*

d^2 - 3520*a^12*b^9*c^9*d^3 + 7920*a^13*b^8*c^8*d^4 - 12672*a^14*b^7*c^7*d^5 + 14784*a^15*b^6*c^6*d^6 - 12672*

a^16*b^5*c^5*d^7 + 7920*a^17*b^4*c^4*d^8 - 3520*a^18*b^3*c^3*d^9 + 1056*a^19*b^2*c^2*d^10 - 192*a^20*b*c*d^11)

)^(1/4)*92624356656i + a^15*b^14*c^4*d^13*x^(1/2)*(-b^17/(16*a^21*d^12 + 16*a^9*b^12*c^12 - 192*a^10*b^11*c^11

*d + 1056*a^11*b^10*c^10*d^2 - 3520*a^12*b^9*c^9*d^3 + 7920*a^13*b^8*c^8*d^4 - 12672*a^14*b^7*c^7*d^5 + 14784*

a^15*b^6*c^6*d^6 - 12672*a^16*b^5*c^5*d^7 + 7920*a^17*b^4*c^4*d^8 - 3520*a^18*b^3*c^3*d^9 + 1056*a^19*b^2*c^2*

d^10 - 192*a^20*b*c*d^11))^(1/4)*83665919628i - a^16*b^13*c^3*d^14*x^(1/2)*(-b^17/(16*a^21*d^12 + 16*a^9*b^12*

c^12 - 192*a^10*b^11*c^11*d + 1056*a^11*b^10*c^10*d^2 - 3520*a^12*b^9*c^9*d^3 + 7920*a^13*b^8*c^8*d^4 - 12672*

a^14*b^7*c^7*d^5 + 14784*a^15*b^6*c^6*d^6 - 12672*a^16*b^5*c^5*d^7 + 7920*a^17*b^4*c^4*d^8 - 3520*a^18*b^3*c^3

*d^9 + 1056*a^19*b^2*c^2*d^10 - 192*a^20*b*c*d^11))^(1/4)*49036424112i + a^17*b^12*c^2*d^15*x^(1/2)*(-b^17/(16

*a^21*d^12 + 16*a^9*b^12*c^12 - 192*a^10*b^11*c^11*d + 1056*a^11*b^10*c^10*d^2 - 3520*a^12*b^9*c^9*d^3 + 7920*

a^13*b^8*c^8*d^4 - 12672*a^14*b^7*c^7*d^5 + 14784*a^15*b^6*c^6*d^6 - 12672*a^16*b^5*c^5*d^7 + 7920*a^17*b^4*c^

4*d^8 - 3520*a^18*b^3*c^3*d^9 + 1056*a^19*b^2*c^2*d^10 - 192*a^20*b*c*d^11))^(1/4)*18213050232i + a^13*b^20*c^

27*d^2*x^(1/2)*(-b^17/(16*a^21*d^12 + 16*a^9*b^12*c^12 - 192*a^10*b^11*c^11*d + 1056*a^11*b^10*c^10*d^2 - 3520

*a^12*b^9*c^9*d^3 + 7920*a^13*b^8*c^8*d^4 - 12672*a^14*b^7*c^7*d^5 + 14784*a^15*b^6*c^6*d^6 - 12672*a^16*b^5*c

^5*d^7 + 7920*a^17*b^4*c^4*d^8 - 3520*a^18*b^3*c^3*d^9 + 1056*a^19*b^2*c^2*d^10 - 192*a^20*b*c*d^11))^(5/4)*22

14592512i - a^14*b^19*c^26*d^3*x^(1/2)*(-b^17/(16*a^21*d^12 + 16*a^9*b^12*c^12 - 192*a^10*b^11*c^11*d + 1056*a

^11*b^10*c^10*d^2 - 3520*a^12*b^9*c^9*d^3 + 7920*a^13*b^8*c^8*d^4 - 12672*a^14*b^7*c^7*d^5 + 14784*a^15*b^6*c^

6*d^6 - 12672*a^16*b^5*c^5*d^7 + 7920*a^17*b^4*c^4*d^8 - 3520*a^18*b^3*c^3*d^9 + 1056*a^19*b^2*c^2*d^10 - 192*

a^20*b*c*d^11))^(5/4)*7381975040i + a^15*b^18*c^25*d^4*x^(1/2)*(-b^17/(16*a^21*d^12 + 16*a^9*b^12*c^12 - 192*a

^10*b^11*c^11*d + 1056*a^11*b^10*c^10*d^2 - 3520*a^12*b^9*c^9*d^3 + 7920*a^13*b^8*c^8*d^4 - 12672*a^14*b^7*c^7

*d^5 + 14784*a^15*b^6*c^6*d^6 - 12672*a^16*b^5*c^5*d^7 + 7920*a^17*b^4*c^4*d^8 - 3520*a^18*b^3*c^3*d^9 + 1056*

a^19*b^2*c^2*d^10 - 192*a^20*b*c*d^11))^(5/4)*16609443840i - a^16*b^17*c^24*d^5*x^(1/2)*(-b^17/(16*a^21*d^12 +

16*a^9*b^12*c^12 - 192*a^10*b^11*c^11*d + 1056*a^11*b^10*c^10*d^2 - 3520*a^12*b^9*c^9*d^3 + 7920*a^13*b^8*c^8

*d^4 - 12672*a^14*b^7*c^7*d^5 + 14784*a^15*b^6*c^6*d^6 - 12672*a^16*b^5*c^5*d^7 + 7920*a^17*b^4*c^4*d^8 - 3520

*a^18*b^3*c^3*d^9 + 1056*a^19*b^2*c^2*d^10 - 192*a^20*b*c*d^11))^(5/4)*26575110144i + a^17*b^16*c^23*d^6*x^(1/

2)*(-b^17/(16*a^21*d^12 + 16*a^9*b^12*c^12 - 192*a^10*b^11*c^11*d + 1056*a^11*b^10*c^10*d^2 - 3520*a^12*b^9*c^

9*d^3 + 7920*a^13*b^8*c^8*d^4 - 12672*a^14*b^7*c^7*d^5 + 14784*a^15*b^6*c^6*d^6 - 12672*a^16*b^5*c^5*d^7 + 792

0*a^17*b^4*c^4*d^8 - 3520*a^18*b^3*c^3*d^9 + 1056*a^19*b^2*c^2*d^10 - 192*a^20*b*c*d^11))^(5/4)*32604717056i -

a^18*b^15*c^22*d^7*x^(1/2)*(-b^17/(16*a^21*d^12 + 16*a^9*b^12*c^12 - 192*a^10*b^11*c^11*d + 1056*a^11*b^10*c^

10*d^2 - 3520*a^12*b^9*c^9*d^3 + 7920*a^13*b^8*c^8*d^4 - 12672*a^14*b^7*c^7*d^5 + 14784*a^15*b^6*c^6*d^6 - 126

72*a^16*b^5*c^5*d^7 + 7920*a^17*b^4*c^4*d^8 - 3520*a^18*b^3*c^3*d^9 + 1056*a^19*b^2*c^2*d^10 - 192*a^20*b*c*d^

11))^(5/4)*50212110336i + a^19*b^14*c^21*d^8*x^(1/2)*(-b^17/(16*a^21*d^12 + 16*a^9*b^12*c^12 - 192*a^10*b^11*c

^11*d + 1056*a^11*b^10*c^10*d^2 - 3520*a^12*b^9*c^9*d^3 + 7920*a^13*b^8*c^8*d^4 - 12672*a^14*b^7*c^7*d^5 + 147

84*a^15*b^6*c^6*d^6 - 12672*a^16*b^5*c^5*d^7 + 7920*a^17*b^4*c^4*d^8 - 3520*a^18*b^3*c^3*d^9 + 1056*a^19*b^2*c

^2*d^10 - 192*a^20*b*c*d^11))^(5/4)*180183367680i - a^20*b^13*c^20*d^9*x^(1/2)*(-b^17/(16*a^21*d^12 + 16*a^9*b

^12*c^12 - 192*a^10*b^11*c^11*d + 1056*a^11*b^10*c^10*d^2 - 3520*a^12*b^9*c^9*d^3 + 7920*a^13*b^8*c^8*d^4 - 12

672*a^14*b^7*c^7*d^5 + 14784*a^15*b^6*c^6*d^6 - 12672*a^16*b^5*c^5*d^7 + 7920*a^17*b^4*c^4*d^8 - 3520*a^18*b^3

*c^3*d^9 + 1056*a^19*b^2*c^2*d^10 - 192*a^20*b*c*d^11))^(5/4)*711482933248i + a^21*b^12*c^19*d^10*x^(1/2)*(-b^

17/(16*a^21*d^12 + 16*a^9*b^12*c^12 - 192*a^10*b^11*c^11*d + 1056*a^11*b^10*c^10*d^2 - 3520*a^12*b^9*c^9*d^3 +

7920*a^13*b^8*c^8*d^4 - 12672*a^14*b^7*c^7*d^5 + 14784*a^15*b^6*c^6*d^6 - 12672*a^16*b^5*c^5*d^7 + 7920*a^17*

b^4*c^4*d^8 - 3520*a^18*b^3*c^3*d^9 + 1056*a^19*b^2*c^2*d^10 - 192*a^20*b*c*d^11))^(5/4)*2112400785408i - a^22

*b^11*c^18*d^11*x^(1/2)*(-b^17/(16*a^21*d^12 + 16*a^9*b^12*c^12 - 192*a^10*b^11*c^11*d + 1056*a^11*b^10*c^10*d

^2 - 3520*a^12*b^9*c^9*d^3 + 7920*a^13*b^8*c^8*d^4 - 12672*a^14*b^7*c^7*d^5 + 14784*a^15*b^6*c^6*d^6 - 12672*a

^16*b^5*c^5*d^7 + 7920*a^17*b^4*c^4*d^8 - 3520*a^18*b^3*c^3*d^9 + 1056*a^19*b^2*c^2*d^10 - 192*a^20*b*c*d^11))

^(5/4)*4669808050176i + a^23*b^10*c^17*d^12*x^(1/2)*(-b^17/(16*a^21*d^12 + 16*a^9*b^12*c^12 - 192*a^10*b^11*c^

11*d + 1056*a^11*b^10*c^10*d^2 - 3520*a^12*b^9*c^9*d^3 + 7920*a^13*b^8*c^8*d^4 - 12672*a^14*b^7*c^7*d^5 + 1478

4*a^15*b^6*c^6*d^6 - 12672*a^16*b^5*c^5*d^7 + 7920*a^17*b^4*c^4*d^8 - 3520*a^18*b^3*c^3*d^9 + 1056*a^19*b^2*c^

2*d^10 - 192*a^20*b*c*d^11))^(5/4)*7892313571328i - a^24*b^9*c^16*d^13*x^(1/2)*(-b^17/(16*a^21*d^12 + 16*a^9*b

^12*c^12 - 192*a^10*b^11*c^11*d + 1056*a^11*b^10*c^10*d^2 - 3520*a^12*b^9*c^9*d^3 + 7920*a^13*b^8*c^8*d^4 - 12

672*a^14*b^7*c^7*d^5 + 14784*a^15*b^6*c^6*d^6 - 12672*a^16*b^5*c^5*d^7 + 7920*a^17*b^4*c^4*d^8 - 3520*a^18*b^3

*c^3*d^9 + 1056*a^19*b^2*c^2*d^10 - 192*a^20*b*c*d^11))^(5/4)*10394916618240i + a^25*b^8*c^15*d^14*x^(1/2)*(-b

^17/(16*a^21*d^12 + 16*a^9*b^12*c^12 - 192*a^10*b^11*c^11*d + 1056*a^11*b^10*c^10*d^2 - 3520*a^12*b^9*c^9*d^3

+ 7920*a^13*b^8*c^8*d^4 - 12672*a^14*b^7*c^7*d^5 + 14784*a^15*b^6*c^6*d^6 - 12672*a^16*b^5*c^5*d^7 + 7920*a^17

*b^4*c^4*d^8 - 3520*a^18*b^3*c^3*d^9 + 1056*a^19*b^2*c^2*d^10 - 192*a^20*b*c*d^11))^(5/4)*10783480283136i - a^

26*b^7*c^14*d^15*x^(1/2)*(-b^17/(16*a^21*d^12 + 16*a^9*b^12*c^12 - 192*a^10*b^11*c^11*d + 1056*a^11*b^10*c^10*

d^2 - 3520*a^12*b^9*c^9*d^3 + 7920*a^13*b^8*c^8*d^4 - 12672*a^14*b^7*c^7*d^5 + 14784*a^15*b^6*c^6*d^6 - 12672*

a^16*b^5*c^5*d^7 + 7920*a^17*b^4*c^4*d^8 - 3520*a^18*b^3*c^3*d^9 + 1056*a^19*b^2*c^2*d^10 - 192*a^20*b*c*d^11)

)^(5/4)*8841322299392i + a^27*b^6*c^13*d^16*x^(1/2)*(-b^17/(16*a^21*d^12 + 16*a^9*b^12*c^12 - 192*a^10*b^11*c^

11*d + 1056*a^11*b^10*c^10*d^2 - 3520*a^12*b^9*c^9*d^3 + 7920*a^13*b^8*c^8*d^4 - 12672*a^14*b^7*c^7*d^5 + 1478

4*a^15*b^6*c^6*d^6 - 12672*a^16*b^5*c^5*d^7 + 7920*a^17*b^4*c^4*d^8 - 3520*a^18*b^3*c^3*d^9 + 1056*a^19*b^2*c^

2*d^10 - 192*a^20*b*c*d^11))^(5/4)*5711010201600i - a^28*b^5*c^12*d^17*x^(1/2)*(-b^17/(16*a^21*d^12 + 16*a^9*b

^12*c^12 - 192*a^10*b^11*c^11*d + 1056*a^11*b^10*c^10*d^2 - 3520*a^12*b^9*c^9*d^3 + 7920*a^13*b^8*c^8*d^4 - 12

672*a^14*b^7*c^7*d^5 + 14784*a^15*b^6*c^6*d^6 - 12672*a^16*b^5*c^5*d^7 + 7920*a^17*b^4*c^4*d^8 - 3520*a^18*b^3

*c^3*d^9 + 1056*a^19*b^2*c^2*d^10 - 192*a^20*b*c*d^11))^(5/4)*2876224045056i + a^29*b^4*c^11*d^18*x^(1/2)*(-b^

17/(16*a^21*d^12 + 16*a^9*b^12*c^12 - 192*a^10*b^11*c^11*d + 1056*a^11*b^10*c^10*d^2 - 3520*a^12*b^9*c^9*d^3 +

7920*a^13*b^8*c^8*d^4 - 12672*a^14*b^7*c^7*d^5 + 14784*a^15*b^6*c^6*d^6 - 12672*a^16*b^5*c^5*d^7 + 7920*a^17*

b^4*c^4*d^8 - 3520*a^18*b^3*c^3*d^9 + 1056*a^19*b^2*c^2*d^10 - 192*a^20*b*c*d^11))^(5/4)*1107358515200i - a^30

*b^3*c^10*d^19*x^(1/2)*(-b^17/(16*a^21*d^12 + 16*a^9*b^12*c^12 - 192*a^10*b^11*c^11*d + 1056*a^11*b^10*c^10*d^

2 - 3520*a^12*b^9*c^9*d^3 + 7920*a^13*b^8*c^8*d^4 - 12672*a^14*b^7*c^7*d^5 + 14784*a^15*b^6*c^6*d^6 - 12672*a^

16*b^5*c^5*d^7 + 7920*a^17*b^4*c^4*d^8 - 3520*a^18*b^3*c^3*d^9 + 1056*a^19*b^2*c^2*d^10 - 192*a^20*b*c*d^11))^

(5/4)*315126448128i + a^31*b^2*c^9*d^20*x^(1/2)*(-b^17/(16*a^21*d^12 + 16*a^9*b^12*c^12 - 192*a^10*b^11*c^11*d

+ 1056*a^11*b^10*c^10*d^2 - 3520*a^12*b^9*c^9*d^3 + 7920*a^13*b^8*c^8*d^4 - 12672*a^14*b^7*c^7*d^5 + 14784*a^

15*b^6*c^6*d^6 - 12672*a^16*b^5*c^5*d^7 + 7920*a^17*b^4*c^4*d^8 - 3520*a^18*b^3*c^3*d^9 + 1056*a^19*b^2*c^2*d^

10 - 192*a^20*b*c*d^11))^(5/4)*62523703296i - a^18*b^11*c*d^16*x^(1/2)*(-b^17/(16*a^21*d^12 + 16*a^9*b^12*c^12

- 192*a^10*b^11*c^11*d + 1056*a^11*b^10*c^10*d^2 - 3520*a^12*b^9*c^9*d^3 + 7920*a^13*b^8*c^8*d^4 - 12672*a^14

*b^7*c^7*d^5 + 14784*a^15*b^6*c^6*d^6 - 12672*a^16*b^5*c^5*d^7 + 7920*a^17*b^4*c^4*d^8 - 3520*a^18*b^3*c^3*d^9

+ 1056*a^19*b^2*c^2*d^10 - 192*a^20*b*c*d^11))^(1/4)*3920748624i - a^12*b^21*c^28*d*x^(1/2)*(-b^17/(16*a^21*d

^12 + 16*a^9*b^12*c^12 - 192*a^10*b^11*c^11*d + 1056*a^11*b^10*c^10*d^2 - 3520*a^12*b^9*c^9*d^3 + 7920*a^13*b^

8*c^8*d^4 - 12672*a^14*b^7*c^7*d^5 + 14784*a^15*b^6*c^6*d^6 - 12672*a^16*b^5*c^5*d^7 + 7920*a^17*b^4*c^4*d^8 -

3520*a^18*b^3*c^3*d^9 + 1056*a^19*b^2*c^2*d^10 - 192*a^20*b*c*d^11))^(5/4)*402653184i - a^32*b*c^8*d^21*x^(1/

2)*(-b^17/(16*a^21*d^12 + 16*a^9*b^12*c^12 - 192*a^10*b^11*c^11*d + 1056*a^11*b^10*c^10*d^2 - 3520*a^12*b^9*c^

9*d^3 + 7920*a^13*b^8*c^8*d^4 - 12672*a^14*b^7*c^7*d^5 + 14784*a^15*b^6*c^6*d^6 - 12672*a^16*b^5*c^5*d^7 + 792

0*a^17*b^4*c^4*d^8 - 3520*a^18*b^3*c^3*d^9 + 1056*a^19*b^2*c^2*d^10 - 192*a^20*b*c*d^11))^(5/4)*7729053696i)/(

1048576*b^28*c^14 + 187388721*a^14*b^14*d^14 - 1398208149*a^13*b^15*c*d^13 + 6291456*a^2*b^26*c^12*d^2 + 10485

760*a^3*b^25*c^11*d^3 + 15728640*a^4*b^24*c^10*d^4 + 22020096*a^5*b^23*c^9*d^5 + 29360128*a^6*b^22*c^8*d^6 + 3

7748736*a^7*b^21*c^7*d^7 + 47185920*a^8*b^20*c^6*d^8 - 2327771601*a^9*b^19*c^5*d^9 + 6124562037*a^10*b^18*c^4*

d^10 - 7086995370*a^11*b^17*c^3*d^11 + 4349734506*a^12*b^16*c^2*d^12 + 3145728*a*b^27*c^13*d))*(-b^17/(16*a^21

*d^12 + 16*a^9*b^12*c^12 - 192*a^10*b^11*c^11*d + 1056*a^11*b^10*c^10*d^2 - 3520*a^12*b^9*c^9*d^3 + 7920*a^13*

b^8*c^8*d^4 - 12672*a^14*b^7*c^7*d^5 + 14784*a^15*b^6*c^6*d^6 - 12672*a^16*b^5*c^5*d^7 + 7920*a^17*b^4*c^4*d^8

- 3520*a^18*b^3*c^3*d^9 + 1056*a^19*b^2*c^2*d^10 - 192*a^20*b*c*d^11))^(1/4)*2i - 2*atan((1099511627776*a^3*b

^22*c^43*x^(1/2)*(-(187388721*a^8*d^17 + 2385443281*b^8*c^8*d^9 - 13211685864*a*b^7*c^7*d^10 + 32491182204*a^2

*b^6*c^6*d^11 - 46312178328*a^3*b^5*c^5*d^12 + 41832959814*a^4*b^4*c^4*d^13 - 24518212056*a^5*b^3*c^3*d^14 + 9

106525116*a^6*b^2*c^2*d^15 - 1960374312*a^7*b*c*d^16)/(16777216*b^12*c^29 + 16777216*a^12*c^17*d^12 - 20132659

2*a^11*b*c^18*d^11 + 1107296256*a^2*b^10*c^27*d^2 - 3690987520*a^3*b^9*c^26*d^3 + 8304721920*a^4*b^8*c^25*d^4

- 13287555072*a^5*b^7*c^24*d^5 + 15502147584*a^6*b^6*c^23*d^6 - 13287555072*a^7*b^5*c^22*d^7 + 8304721920*a^8*

b^4*c^21*d^8 - 3690987520*a^9*b^3*c^20*d^9 + 1107296256*a^10*b^2*c^19*d^10 - 201326592*a*b^11*c^28*d))^(5/4) +

14698451828736*a^25*c^21*d^22*x^(1/2)*(-(187388721*a^8*d^17 + 2385443281*b^8*c^8*d^9 - 13211685864*a*b^7*c^7*

d^10 + 32491182204*a^2*b^6*c^6*d^11 - 46312178328*a^3*b^5*c^5*d^12 + 41832959814*a^4*b^4*c^4*d^13 - 2451821205

6*a^5*b^3*c^3*d^14 + 9106525116*a^6*b^2*c^2*d^15 - 1960374312*a^7*b*c*d^16)/(16777216*b^12*c^29 + 16777216*a^1

2*c^17*d^12 - 201326592*a^11*b*c^18*d^11 + 1107296256*a^2*b^10*c^27*d^2 - 3690987520*a^3*b^9*c^26*d^3 + 830472

1920*a^4*b^8*c^25*d^4 - 13287555072*a^5*b^7*c^24*d^5 + 15502147584*a^6*b^6*c^23*d^6 - 13287555072*a^7*b^5*c^22

*d^7 + 8304721920*a^8*b^4*c^21*d^8 - 3690987520*a^9*b^3*c^20*d^9 + 1107296256*a^10*b^2*c^19*d^10 - 201326592*a

*b^11*c^28*d))^(5/4) + 3277664026624*b^21*c^25*d^6*x^(1/2)*(-(187388721*a^8*d^17 + 2385443281*b^8*c^8*d^9 - 13

211685864*a*b^7*c^7*d^10 + 32491182204*a^2*b^6*c^6*d^11 - 46312178328*a^3*b^5*c^5*d^12 + 41832959814*a^4*b^4*c

^4*d^13 - 24518212056*a^5*b^3*c^3*d^14 + 9106525116*a^6*b^2*c^2*d^15 - 1960374312*a^7*b*c*d^16)/(16777216*b^12

*c^29 + 16777216*a^12*c^17*d^12 - 201326592*a^11*b*c^18*d^11 + 1107296256*a^2*b^10*c^27*d^2 - 3690987520*a^3*b

^9*c^26*d^3 + 8304721920*a^4*b^8*c^25*d^4 - 13287555072*a^5*b^7*c^24*d^5 + 15502147584*a^6*b^6*c^23*d^6 - 1328

7555072*a^7*b^5*c^22*d^7 + 8304721920*a^8*b^4*c^21*d^8 - 3690987520*a^9*b^3*c^20*d^9 + 1107296256*a^10*b^2*c^1

9*d^10 - 201326592*a*b^11*c^28*d))^(1/4) + 9754273382400*a^2*b^19*c^23*d^8*x^(1/2)*(-(187388721*a^8*d^17 + 238

5443281*b^8*c^8*d^9 - 13211685864*a*b^7*c^7*d^10 + 32491182204*a^2*b^6*c^6*d^11 - 46312178328*a^3*b^5*c^5*d^12

+ 41832959814*a^4*b^4*c^4*d^13 - 24518212056*a^5*b^3*c^3*d^14 + 9106525116*a^6*b^2*c^2*d^15 - 1960374312*a^7*

b*c*d^16)/(16777216*b^12*c^29 + 16777216*a^12*c^17*d^12 - 201326592*a^11*b*c^18*d^11 + 1107296256*a^2*b^10*c^2

7*d^2 - 3690987520*a^3*b^9*c^26*d^3 + 8304721920*a^4*b^8*c^25*d^4 - 13287555072*a^5*b^7*c^24*d^5 + 15502147584

*a^6*b^6*c^23*d^6 - 13287555072*a^7*b^5*c^22*d^7 + 8304721920*a^8*b^4*c^21*d^8 - 3690987520*a^9*b^3*c^20*d^9 +

1107296256*a^10*b^2*c^19*d^10 - 201326592*a*b^11*c^28*d))^(1/4) + 151527147765760*a^3*b^18*c^22*d^9*x^(1/2)*(

-(187388721*a^8*d^17 + 2385443281*b^8*c^8*d^9 - 13211685864*a*b^7*c^7*d^10 + 32491182204*a^2*b^6*c^6*d^11 - 46

312178328*a^3*b^5*c^5*d^12 + 41832959814*a^4*b^4*c^4*d^13 - 24518212056*a^5*b^3*c^3*d^14 + 9106525116*a^6*b^2*

c^2*d^15 - 1960374312*a^7*b*c*d^16)/(16777216*b^12*c^29 + 16777216*a^12*c^17*d^12 - 201326592*a^11*b*c^18*d^11

+ 1107296256*a^2*b^10*c^27*d^2 - 3690987520*a^3*b^9*c^26*d^3 + 8304721920*a^4*b^8*c^25*d^4 - 13287555072*a^5*

b^7*c^24*d^5 + 15502147584*a^6*b^6*c^23*d^6 - 13287555072*a^7*b^5*c^22*d^7 + 8304721920*a^8*b^4*c^21*d^8 - 369

0987520*a^9*b^3*c^20*d^9 + 1107296256*a^10*b^2*c^19*d^10 - 201326592*a*b^11*c^28*d))^(1/4) - 864922391543808*a

^4*b^17*c^21*d^10*x^(1/2)*(-(187388721*a^8*d^17 + 2385443281*b^8*c^8*d^9 - 13211685864*a*b^7*c^7*d^10 + 324911

82204*a^2*b^6*c^6*d^11 - 46312178328*a^3*b^5*c^5*d^12 + 41832959814*a^4*b^4*c^4*d^13 - 24518212056*a^5*b^3*c^3

*d^14 + 9106525116*a^6*b^2*c^2*d^15 - 1960374312*a^7*b*c*d^16)/(16777216*b^12*c^29 + 16777216*a^12*c^17*d^12 -

201326592*a^11*b*c^18*d^11 + 1107296256*a^2*b^10*c^27*d^2 - 3690987520*a^3*b^9*c^26*d^3 + 8304721920*a^4*b^8*

c^25*d^4 - 13287555072*a^5*b^7*c^24*d^5 + 15502147584*a^6*b^6*c^23*d^6 - 13287555072*a^7*b^5*c^22*d^7 + 830472

1920*a^8*b^4*c^21*d^8 - 3690987520*a^9*b^3*c^20*d^9 + 1107296256*a^10*b^2*c^19*d^10 - 201326592*a*b^11*c^28*d)

)^(1/4) + 2129342116921344*a^5*b^16*c^20*d^11*x^(1/2)*(-(187388721*a^8*d^17 + 2385443281*b^8*c^8*d^9 - 1321168

5864*a*b^7*c^7*d^10 + 32491182204*a^2*b^6*c^6*d^11 - 46312178328*a^3*b^5*c^5*d^12 + 41832959814*a^4*b^4*c^4*d^

13 - 24518212056*a^5*b^3*c^3*d^14 + 9106525116*a^6*b^2*c^2*d^15 - 1960374312*a^7*b*c*d^16)/(16777216*b^12*c^29

+ 16777216*a^12*c^17*d^12 - 201326592*a^11*b*c^18*d^11 + 1107296256*a^2*b^10*c^27*d^2 - 3690987520*a^3*b^9*c^

26*d^3 + 8304721920*a^4*b^8*c^25*d^4 - 13287555072*a^5*b^7*c^24*d^5 + 15502147584*a^6*b^6*c^23*d^6 - 132875550

72*a^7*b^5*c^22*d^7 + 8304721920*a^8*b^4*c^21*d^8 - 3690987520*a^9*b^3*c^20*d^9 + 1107296256*a^10*b^2*c^19*d^1

0 - 201326592*a*b^11*c^28*d))^(1/4) - 3035114918903808*a^6*b^15*c^19*d^12*x^(1/2)*(-(187388721*a^8*d^17 + 2385

443281*b^8*c^8*d^9 - 13211685864*a*b^7*c^7*d^10 + 32491182204*a^2*b^6*c^6*d^11 - 46312178328*a^3*b^5*c^5*d^12

+ 41832959814*a^4*b^4*c^4*d^13 - 24518212056*a^5*b^3*c^3*d^14 + 9106525116*a^6*b^2*c^2*d^15 - 1960374312*a^7*b

*c*d^16)/(16777216*b^12*c^29 + 16777216*a^12*c^17*d^12 - 201326592*a^11*b*c^18*d^11 + 1107296256*a^2*b^10*c^27

*d^2 - 3690987520*a^3*b^9*c^26*d^3 + 8304721920*a^4*b^8*c^25*d^4 - 13287555072*a^5*b^7*c^24*d^5 + 15502147584*

a^6*b^6*c^23*d^6 - 13287555072*a^7*b^5*c^22*d^7 + 8304721920*a^8*b^4*c^21*d^8 - 3690987520*a^9*b^3*c^20*d^9 +

1107296256*a^10*b^2*c^19*d^10 - 201326592*a*b^11*c^28*d))^(1/4) + 2741564854370304*a^7*b^14*c^18*d^13*x^(1/2)*

(-(187388721*a^8*d^17 + 2385443281*b^8*c^8*d^9 - 13211685864*a*b^7*c^7*d^10 + 32491182204*a^2*b^6*c^6*d^11 - 4

6312178328*a^3*b^5*c^5*d^12 + 41832959814*a^4*b^4*c^4*d^13 - 24518212056*a^5*b^3*c^3*d^14 + 9106525116*a^6*b^2

*c^2*d^15 - 1960374312*a^7*b*c*d^16)/(16777216*b^12*c^29 + 16777216*a^12*c^17*d^12 - 201326592*a^11*b*c^18*d^1

1 + 1107296256*a^2*b^10*c^27*d^2 - 3690987520*a^3*b^9*c^26*d^3 + 8304721920*a^4*b^8*c^25*d^4 - 13287555072*a^5

*b^7*c^24*d^5 + 15502147584*a^6*b^6*c^23*d^6 - 13287555072*a^7*b^5*c^22*d^7 + 8304721920*a^8*b^4*c^21*d^8 - 36

90987520*a^9*b^3*c^20*d^9 + 1107296256*a^10*b^2*c^19*d^10 - 201326592*a*b^11*c^28*d))^(1/4) - 1606825545302016

*a^8*b^13*c^17*d^14*x^(1/2)*(-(187388721*a^8*d^17 + 2385443281*b^8*c^8*d^9 - 13211685864*a*b^7*c^7*d^10 + 3249

1182204*a^2*b^6*c^6*d^11 - 46312178328*a^3*b^5*c^5*d^12 + 41832959814*a^4*b^4*c^4*d^13 - 24518212056*a^5*b^3*c

^3*d^14 + 9106525116*a^6*b^2*c^2*d^15 - 1960374312*a^7*b*c*d^16)/(16777216*b^12*c^29 + 16777216*a^12*c^17*d^12

- 201326592*a^11*b*c^18*d^11 + 1107296256*a^2*b^10*c^27*d^2 - 3690987520*a^3*b^9*c^26*d^3 + 8304721920*a^4*b^

8*c^25*d^4 - 13287555072*a^5*b^7*c^24*d^5 + 15502147584*a^6*b^6*c^23*d^6 - 13287555072*a^7*b^5*c^22*d^7 + 8304

721920*a^8*b^4*c^21*d^8 - 3690987520*a^9*b^3*c^20*d^9 + 1107296256*a^10*b^2*c^19*d^10 - 201326592*a*b^11*c^28*

d))^(1/4) + 596805230002176*a^9*b^12*c^16*d^15*x^(1/2)*(-(187388721*a^8*d^17 + 2385443281*b^8*c^8*d^9 - 132116

85864*a*b^7*c^7*d^10 + 32491182204*a^2*b^6*c^6*d^11 - 46312178328*a^3*b^5*c^5*d^12 + 41832959814*a^4*b^4*c^4*d

^13 - 24518212056*a^5*b^3*c^3*d^14 + 9106525116*a^6*b^2*c^2*d^15 - 1960374312*a^7*b*c*d^16)/(16777216*b^12*c^2

9 + 16777216*a^12*c^17*d^12 - 201326592*a^11*b*c^18*d^11 + 1107296256*a^2*b^10*c^27*d^2 - 3690987520*a^3*b^9*c

^26*d^3 + 8304721920*a^4*b^8*c^25*d^4 - 13287555072*a^5*b^7*c^24*d^5 + 15502147584*a^6*b^6*c^23*d^6 - 13287555

072*a^7*b^5*c^22*d^7 + 8304721920*a^8*b^4*c^21*d^8 - 3690987520*a^9*b^3*c^20*d^9 + 1107296256*a^10*b^2*c^19*d^

10 - 201326592*a*b^11*c^28*d))^(1/4) - 128475090911232*a^10*b^11*c^15*d^16*x^(1/2)*(-(187388721*a^8*d^17 + 238

5443281*b^8*c^8*d^9 - 13211685864*a*b^7*c^7*d^10 + 32491182204*a^2*b^6*c^6*d^11 - 46312178328*a^3*b^5*c^5*d^12

+ 41832959814*a^4*b^4*c^4*d^13 - 24518212056*a^5*b^3*c^3*d^14 + 9106525116*a^6*b^2*c^2*d^15 - 1960374312*a^7*

b*c*d^16)/(16777216*b^12*c^29 + 16777216*a^12*c^17*d^12 - 201326592*a^11*b*c^18*d^11 + 1107296256*a^2*b^10*c^2

7*d^2 - 3690987520*a^3*b^9*c^26*d^3 + 8304721920*a^4*b^8*c^25*d^4 - 13287555072*a^5*b^7*c^24*d^5 + 15502147584

*a^6*b^6*c^23*d^6 - 13287555072*a^7*b^5*c^22*d^7 + 8304721920*a^8*b^4*c^21*d^8 - 3690987520*a^9*b^3*c^20*d^9 +

1107296256*a^10*b^2*c^19*d^10 - 201326592*a*b^11*c^28*d))^(1/4) + 12280707219456*a^11*b^10*c^14*d^17*x^(1/2)*

(-(187388721*a^8*d^17 + 2385443281*b^8*c^8*d^9 - 13211685864*a*b^7*c^7*d^10 + 32491182204*a^2*b^6*c^6*d^11 - 4

6312178328*a^3*b^5*c^5*d^12 + 41832959814*a^4*b^4*c^4*d^13 - 24518212056*a^5*b^3*c^3*d^14 + 9106525116*a^6*b^2

*c^2*d^15 - 1960374312*a^7*b*c*d^16)/(16777216*b^12*c^29 + 16777216*a^12*c^17*d^12 - 201326592*a^11*b*c^18*d^1

1 + 1107296256*a^2*b^10*c^27*d^2 - 3690987520*a^3*b^9*c^26*d^3 + 8304721920*a^4*b^8*c^25*d^4 - 13287555072*a^5

*b^7*c^24*d^5 + 15502147584*a^6*b^6*c^23*d^6 - 13287555072*a^7*b^5*c^22*d^7 + 8304721920*a^8*b^4*c^21*d^8 - 36

90987520*a^9*b^3*c^20*d^9 + 1107296256*a^10*b^2*c^19*d^10 - 201326592*a*b^11*c^28*d))^(1/4) + 72567767433216*a

^5*b^20*c^41*d^2*x^(1/2)*(-(187388721*a^8*d^17 + 2385443281*b^8*c^8*d^9 - 13211685864*a*b^7*c^7*d^10 + 3249118

2204*a^2*b^6*c^6*d^11 - 46312178328*a^3*b^5*c^5*d^12 + 41832959814*a^4*b^4*c^4*d^13 - 24518212056*a^5*b^3*c^3*

d^14 + 9106525116*a^6*b^2*c^2*d^15 - 1960374312*a^7*b*c*d^16)/(16777216*b^12*c^29 + 16777216*a^12*c^17*d^12 -

201326592*a^11*b*c^18*d^11 + 1107296256*a^2*b^10*c^27*d^2 - 3690987520*a^3*b^9*c^26*d^3 + 8304721920*a^4*b^8*c

^25*d^4 - 13287555072*a^5*b^7*c^24*d^5 + 15502147584*a^6*b^6*c^23*d^6 - 13287555072*a^7*b^5*c^22*d^7 + 8304721

920*a^8*b^4*c^21*d^8 - 3690987520*a^9*b^3*c^20*d^9 + 1107296256*a^10*b^2*c^19*d^10 - 201326592*a*b^11*c^28*d))

^(5/4) - 241892558110720*a^6*b^19*c^40*d^3*x^(1/2)*(-(187388721*a^8*d^17 + 2385443281*b^8*c^8*d^9 - 1321168586

4*a*b^7*c^7*d^10 + 32491182204*a^2*b^6*c^6*d^11 - 46312178328*a^3*b^5*c^5*d^12 + 41832959814*a^4*b^4*c^4*d^13

- 24518212056*a^5*b^3*c^3*d^14 + 9106525116*a^6*b^2*c^2*d^15 - 1960374312*a^7*b*c*d^16)/(16777216*b^12*c^29 +

16777216*a^12*c^17*d^12 - 201326592*a^11*b*c^18*d^11 + 1107296256*a^2*b^10*c^27*d^2 - 3690987520*a^3*b^9*c^26*

d^3 + 8304721920*a^4*b^8*c^25*d^4 - 13287555072*a^5*b^7*c^24*d^5 + 15502147584*a^6*b^6*c^23*d^6 - 13287555072*

a^7*b^5*c^22*d^7 + 8304721920*a^8*b^4*c^21*d^8 - 3690987520*a^9*b^3*c^20*d^9 + 1107296256*a^10*b^2*c^19*d^10 -

201326592*a*b^11*c^28*d))^(5/4) + 544258255749120*a^7*b^18*c^39*d^4*x^(1/2)*(-(187388721*a^8*d^17 + 238544328

1*b^8*c^8*d^9 - 13211685864*a*b^7*c^7*d^10 + 32491182204*a^2*b^6*c^6*d^11 - 46312178328*a^3*b^5*c^5*d^12 + 418

32959814*a^4*b^4*c^4*d^13 - 24518212056*a^5*b^3*c^3*d^14 + 9106525116*a^6*b^2*c^2*d^15 - 1960374312*a^7*b*c*d^

16)/(16777216*b^12*c^29 + 16777216*a^12*c^17*d^12 - 201326592*a^11*b*c^18*d^11 + 1107296256*a^2*b^10*c^27*d^2

- 3690987520*a^3*b^9*c^26*d^3 + 8304721920*a^4*b^8*c^25*d^4 - 13287555072*a^5*b^7*c^24*d^5 + 15502147584*a^6*b

^6*c^23*d^6 - 13287555072*a^7*b^5*c^22*d^7 + 8304721920*a^8*b^4*c^21*d^8 - 3690987520*a^9*b^3*c^20*d^9 + 11072

96256*a^10*b^2*c^19*d^10 - 201326592*a*b^11*c^28*d))^(5/4) - 870813209198592*a^8*b^17*c^38*d^5*x^(1/2)*(-(1873

88721*a^8*d^17 + 2385443281*b^8*c^8*d^9 - 13211685864*a*b^7*c^7*d^10 + 32491182204*a^2*b^6*c^6*d^11 - 46312178

328*a^3*b^5*c^5*d^12 + 41832959814*a^4*b^4*c^4*d^13 - 24518212056*a^5*b^3*c^3*d^14 + 9106525116*a^6*b^2*c^2*d^

15 - 1960374312*a^7*b*c*d^16)/(16777216*b^12*c^29 + 16777216*a^12*c^17*d^12 - 201326592*a^11*b*c^18*d^11 + 110

7296256*a^2*b^10*c^27*d^2 - 3690987520*a^3*b^9*c^26*d^3 + 8304721920*a^4*b^8*c^25*d^4 - 13287555072*a^5*b^7*c^

24*d^5 + 15502147584*a^6*b^6*c^23*d^6 - 13287555072*a^7*b^5*c^22*d^7 + 8304721920*a^8*b^4*c^21*d^8 - 369098752

0*a^9*b^3*c^20*d^9 + 1107296256*a^10*b^2*c^19*d^10 - 201326592*a*b^11*c^28*d))^(5/4) + 1068391368491008*a^9*b^

16*c^37*d^6*x^(1/2)*(-(187388721*a^8*d^17 + 2385443281*b^8*c^8*d^9 - 13211685864*a*b^7*c^7*d^10 + 32491182204*

a^2*b^6*c^6*d^11 - 46312178328*a^3*b^5*c^5*d^12 + 41832959814*a^4*b^4*c^4*d^13 - 24518212056*a^5*b^3*c^3*d^14

+ 9106525116*a^6*b^2*c^2*d^15 - 1960374312*a^7*b*c*d^16)/(16777216*b^12*c^29 + 16777216*a^12*c^17*d^12 - 20132

6592*a^11*b*c^18*d^11 + 1107296256*a^2*b^10*c^27*d^2 - 3690987520*a^3*b^9*c^26*d^3 + 8304721920*a^4*b^8*c^25*d

^4 - 13287555072*a^5*b^7*c^24*d^5 + 15502147584*a^6*b^6*c^23*d^6 - 13287555072*a^7*b^5*c^22*d^7 + 8304721920*a

^8*b^4*c^21*d^8 - 3690987520*a^9*b^3*c^20*d^9 + 1107296256*a^10*b^2*c^19*d^10 - 201326592*a*b^11*c^28*d))^(5/4

) - 1645350431490048*a^10*b^15*c^36*d^7*x^(1/2)*(-(187388721*a^8*d^17 + 2385443281*b^8*c^8*d^9 - 13211685864*a

*b^7*c^7*d^10 + 32491182204*a^2*b^6*c^6*d^11 - 46312178328*a^3*b^5*c^5*d^12 + 41832959814*a^4*b^4*c^4*d^13 - 2

4518212056*a^5*b^3*c^3*d^14 + 9106525116*a^6*b^2*c^2*d^15 - 1960374312*a^7*b*c*d^16)/(16777216*b^12*c^29 + 167

77216*a^12*c^17*d^12 - 201326592*a^11*b*c^18*d^11 + 1107296256*a^2*b^10*c^27*d^2 - 3690987520*a^3*b^9*c^26*d^3

+ 8304721920*a^4*b^8*c^25*d^4 - 13287555072*a^5*b^7*c^24*d^5 + 15502147584*a^6*b^6*c^23*d^6 - 13287555072*a^7

*b^5*c^22*d^7 + 8304721920*a^8*b^4*c^21*d^8 - 3690987520*a^9*b^3*c^20*d^9 + 1107296256*a^10*b^2*c^19*d^10 - 20

1326592*a*b^11*c^28*d))^(5/4) + 5904248592138240*a^11*b^14*c^35*d^8*x^(1/2)*(-(187388721*a^8*d^17 + 2385443281

*b^8*c^8*d^9 - 13211685864*a*b^7*c^7*d^10 + 32491182204*a^2*b^6*c^6*d^11 - 46312178328*a^3*b^5*c^5*d^12 + 4183

2959814*a^4*b^4*c^4*d^13 - 24518212056*a^5*b^3*c^3*d^14 + 9106525116*a^6*b^2*c^2*d^15 - 1960374312*a^7*b*c*d^1

6)/(16777216*b^12*c^29 + 16777216*a^12*c^17*d^12 - 201326592*a^11*b*c^18*d^11 + 1107296256*a^2*b^10*c^27*d^2 -

3690987520*a^3*b^9*c^26*d^3 + 8304721920*a^4*b^8*c^25*d^4 - 13287555072*a^5*b^7*c^24*d^5 + 15502147584*a^6*b^

6*c^23*d^6 - 13287555072*a^7*b^5*c^22*d^7 + 8304721920*a^8*b^4*c^21*d^8 - 3690987520*a^9*b^3*c^20*d^9 + 110729

6256*a^10*b^2*c^19*d^10 - 201326592*a*b^11*c^28*d))^(5/4) - 23313872756670464*a^12*b^13*c^34*d^9*x^(1/2)*(-(18

7388721*a^8*d^17 + 2385443281*b^8*c^8*d^9 - 13211685864*a*b^7*c^7*d^10 + 32491182204*a^2*b^6*c^6*d^11 - 463121

78328*a^3*b^5*c^5*d^12 + 41832959814*a^4*b^4*c^4*d^13 - 24518212056*a^5*b^3*c^3*d^14 + 9106525116*a^6*b^2*c^2*

d^15 - 1960374312*a^7*b*c*d^16)/(16777216*b^12*c^29 + 16777216*a^12*c^17*d^12 - 201326592*a^11*b*c^18*d^11 + 1

107296256*a^2*b^10*c^27*d^2 - 3690987520*a^3*b^9*c^26*d^3 + 8304721920*a^4*b^8*c^25*d^4 - 13287555072*a^5*b^7*

c^24*d^5 + 15502147584*a^6*b^6*c^23*d^6 - 13287555072*a^7*b^5*c^22*d^7 + 8304721920*a^8*b^4*c^21*d^8 - 3690987

520*a^9*b^3*c^20*d^9 + 1107296256*a^10*b^2*c^19*d^10 - 201326592*a*b^11*c^28*d))^(5/4) + 69219148936249344*a^1

3*b^12*c^33*d^10*x^(1/2)*(-(187388721*a^8*d^17 + 2385443281*b^8*c^8*d^9 - 13211685864*a*b^7*c^7*d^10 + 3249118

2204*a^2*b^6*c^6*d^11 - 46312178328*a^3*b^5*c^5*d^12 + 41832959814*a^4*b^4*c^4*d^13 - 24518212056*a^5*b^3*c^3*

d^14 + 9106525116*a^6*b^2*c^2*d^15 - 1960374312*a^7*b*c*d^16)/(16777216*b^12*c^29 + 16777216*a^12*c^17*d^12 -

201326592*a^11*b*c^18*d^11 + 1107296256*a^2*b^10*c^27*d^2 - 3690987520*a^3*b^9*c^26*d^3 + 8304721920*a^4*b^8*c

^25*d^4 - 13287555072*a^5*b^7*c^24*d^5 + 15502147584*a^6*b^6*c^23*d^6 - 13287555072*a^7*b^5*c^22*d^7 + 8304721

920*a^8*b^4*c^21*d^8 - 3690987520*a^9*b^3*c^20*d^9 + 1107296256*a^10*b^2*c^19*d^10 - 201326592*a*b^11*c^28*d))

^(5/4) - 153020270188167168*a^14*b^11*c^32*d^11*x^(1/2)*(-(187388721*a^8*d^17 + 2385443281*b^8*c^8*d^9 - 13211

685864*a*b^7*c^7*d^10 + 32491182204*a^2*b^6*c^6*d^11 - 46312178328*a^3*b^5*c^5*d^12 + 41832959814*a^4*b^4*c^4*

d^13 - 24518212056*a^5*b^3*c^3*d^14 + 9106525116*a^6*b^2*c^2*d^15 - 1960374312*a^7*b*c*d^16)/(16777216*b^12*c^

29 + 16777216*a^12*c^17*d^12 - 201326592*a^11*b*c^18*d^11 + 1107296256*a^2*b^10*c^27*d^2 - 3690987520*a^3*b^9*

c^26*d^3 + 8304721920*a^4*b^8*c^25*d^4 - 13287555072*a^5*b^7*c^24*d^5 + 15502147584*a^6*b^6*c^23*d^6 - 1328755

5072*a^7*b^5*c^22*d^7 + 8304721920*a^8*b^4*c^21*d^8 - 3690987520*a^9*b^3*c^20*d^9 + 1107296256*a^10*b^2*c^19*d

^10 - 201326592*a*b^11*c^28*d))^(5/4) + 258615331105275904*a^15*b^10*c^31*d^12*x^(1/2)*(-(187388721*a^8*d^17 +

2385443281*b^8*c^8*d^9 - 13211685864*a*b^7*c^7*d^10 + 32491182204*a^2*b^6*c^6*d^11 - 46312178328*a^3*b^5*c^5*

d^12 + 41832959814*a^4*b^4*c^4*d^13 - 24518212056*a^5*b^3*c^3*d^14 + 9106525116*a^6*b^2*c^2*d^15 - 1960374312*

a^7*b*c*d^16)/(16777216*b^12*c^29 + 16777216*a^12*c^17*d^12 - 201326592*a^11*b*c^18*d^11 + 1107296256*a^2*b^10

*c^27*d^2 - 3690987520*a^3*b^9*c^26*d^3 + 8304721920*a^4*b^8*c^25*d^4 - 13287555072*a^5*b^7*c^24*d^5 + 1550214

7584*a^6*b^6*c^23*d^6 - 13287555072*a^7*b^5*c^22*d^7 + 8304721920*a^8*b^4*c^21*d^8 - 3690987520*a^9*b^3*c^20*d

^9 + 1107296256*a^10*b^2*c^19*d^10 - 201326592*a*b^11*c^28*d))^(5/4) - 340620627746488320*a^16*b^9*c^30*d^13*x

^(1/2)*(-(187388721*a^8*d^17 + 2385443281*b^8*c^8*d^9 - 13211685864*a*b^7*c^7*d^10 + 32491182204*a^2*b^6*c^6*d

^11 - 46312178328*a^3*b^5*c^5*d^12 + 41832959814*a^4*b^4*c^4*d^13 - 24518212056*a^5*b^3*c^3*d^14 + 9106525116*

a^6*b^2*c^2*d^15 - 1960374312*a^7*b*c*d^16)/(16777216*b^12*c^29 + 16777216*a^12*c^17*d^12 - 201326592*a^11*b*c

^18*d^11 + 1107296256*a^2*b^10*c^27*d^2 - 3690987520*a^3*b^9*c^26*d^3 + 8304721920*a^4*b^8*c^25*d^4 - 13287555

072*a^5*b^7*c^24*d^5 + 15502147584*a^6*b^6*c^23*d^6 - 13287555072*a^7*b^5*c^22*d^7 + 8304721920*a^8*b^4*c^21*d

^8 - 3690987520*a^9*b^3*c^20*d^9 + 1107296256*a^10*b^2*c^19*d^10 - 201326592*a*b^11*c^28*d))^(5/4) + 353353081

917800448*a^17*b^8*c^29*d^14*x^(1/2)*(-(187388721*a^8*d^17 + 2385443281*b^8*c^8*d^9 - 13211685864*a*b^7*c^7*d^

10 + 32491182204*a^2*b^6*c^6*d^11 - 46312178328*a^3*b^5*c^5*d^12 + 41832959814*a^4*b^4*c^4*d^13 - 24518212056*

a^5*b^3*c^3*d^14 + 9106525116*a^6*b^2*c^2*d^15 - 1960374312*a^7*b*c*d^16)/(16777216*b^12*c^29 + 16777216*a^12*

c^17*d^12 - 201326592*a^11*b*c^18*d^11 + 1107296256*a^2*b^10*c^27*d^2 - 3690987520*a^3*b^9*c^26*d^3 + 83047219

20*a^4*b^8*c^25*d^4 - 13287555072*a^5*b^7*c^24*d^5 + 15502147584*a^6*b^6*c^23*d^6 - 13287555072*a^7*b^5*c^22*d

^7 + 8304721920*a^8*b^4*c^21*d^8 - 3690987520*a^9*b^3*c^20*d^9 + 1107296256*a^10*b^2*c^19*d^10 - 201326592*a*b

^11*c^28*d))^(5/4) - 289712449106477056*a^18*b^7*c^28*d^15*x^(1/2)*(-(187388721*a^8*d^17 + 2385443281*b^8*c^8*

d^9 - 13211685864*a*b^7*c^7*d^10 + 32491182204*a^2*b^6*c^6*d^11 - 46312178328*a^3*b^5*c^5*d^12 + 41832959814*a

^4*b^4*c^4*d^13 - 24518212056*a^5*b^3*c^3*d^14 + 9106525116*a^6*b^2*c^2*d^15 - 1960374312*a^7*b*c*d^16)/(16777

216*b^12*c^29 + 16777216*a^12*c^17*d^12 - 201326592*a^11*b*c^18*d^11 + 1107296256*a^2*b^10*c^27*d^2 - 36909875

20*a^3*b^9*c^26*d^3 + 8304721920*a^4*b^8*c^25*d^4 - 13287555072*a^5*b^7*c^24*d^5 + 15502147584*a^6*b^6*c^23*d^

6 - 13287555072*a^7*b^5*c^22*d^7 + 8304721920*a^8*b^4*c^21*d^8 - 3690987520*a^9*b^3*c^20*d^9 + 1107296256*a^10

*b^2*c^19*d^10 - 201326592*a*b^11*c^28*d))^(5/4) + 187138382286028800*a^19*b^6*c^27*d^16*x^(1/2)*(-(187388721*

a^8*d^17 + 2385443281*b^8*c^8*d^9 - 13211685864*a*b^7*c^7*d^10 + 32491182204*a^2*b^6*c^6*d^11 - 46312178328*a^

3*b^5*c^5*d^12 + 41832959814*a^4*b^4*c^4*d^13 - 24518212056*a^5*b^3*c^3*d^14 + 9106525116*a^6*b^2*c^2*d^15 - 1

960374312*a^7*b*c*d^16)/(16777216*b^12*c^29 + 16777216*a^12*c^17*d^12 - 201326592*a^11*b*c^18*d^11 + 110729625

6*a^2*b^10*c^27*d^2 - 3690987520*a^3*b^9*c^26*d^3 + 8304721920*a^4*b^8*c^25*d^4 - 13287555072*a^5*b^7*c^24*d^5

+ 15502147584*a^6*b^6*c^23*d^6 - 13287555072*a^7*b^5*c^22*d^7 + 8304721920*a^8*b^4*c^21*d^8 - 3690987520*a^9*

b^3*c^20*d^9 + 1107296256*a^10*b^2*c^19*d^10 - 201326592*a*b^11*c^28*d))^(5/4) - 94248109508395008*a^20*b^5*c^

26*d^17*x^(1/2)*(-(187388721*a^8*d^17 + 2385443281*b^8*c^8*d^9 - 13211685864*a*b^7*c^7*d^10 + 32491182204*a^2*

b^6*c^6*d^11 - 46312178328*a^3*b^5*c^5*d^12 + 41832959814*a^4*b^4*c^4*d^13 - 24518212056*a^5*b^3*c^3*d^14 + 91

06525116*a^6*b^2*c^2*d^15 - 1960374312*a^7*b*c*d^16)/(16777216*b^12*c^29 + 16777216*a^12*c^17*d^12 - 201326592

*a^11*b*c^18*d^11 + 1107296256*a^2*b^10*c^27*d^2 - 3690987520*a^3*b^9*c^26*d^3 + 8304721920*a^4*b^8*c^25*d^4 -

13287555072*a^5*b^7*c^24*d^5 + 15502147584*a^6*b^6*c^23*d^6 - 13287555072*a^7*b^5*c^22*d^7 + 8304721920*a^8*b

^4*c^21*d^8 - 3690987520*a^9*b^3*c^20*d^9 + 1107296256*a^10*b^2*c^19*d^10 - 201326592*a*b^11*c^28*d))^(5/4) +

36285923826073600*a^21*b^4*c^25*d^18*x^(1/2)*(-(187388721*a^8*d^17 + 2385443281*b^8*c^8*d^9 - 13211685864*a*b^

7*c^7*d^10 + 32491182204*a^2*b^6*c^6*d^11 - 46312178328*a^3*b^5*c^5*d^12 + 41832959814*a^4*b^4*c^4*d^13 - 2451

8212056*a^5*b^3*c^3*d^14 + 9106525116*a^6*b^2*c^2*d^15 - 1960374312*a^7*b*c*d^16)/(16777216*b^12*c^29 + 167772

16*a^12*c^17*d^12 - 201326592*a^11*b*c^18*d^11 + 1107296256*a^2*b^10*c^27*d^2 - 3690987520*a^3*b^9*c^26*d^3 +

8304721920*a^4*b^8*c^25*d^4 - 13287555072*a^5*b^7*c^24*d^5 + 15502147584*a^6*b^6*c^23*d^6 - 13287555072*a^7*b^

5*c^22*d^7 + 8304721920*a^8*b^4*c^21*d^8 - 3690987520*a^9*b^3*c^20*d^9 + 1107296256*a^10*b^2*c^19*d^10 - 20132

6592*a*b^11*c^28*d))^(5/4) - 10326063452258304*a^22*b^3*c^24*d^19*x^(1/2)*(-(187388721*a^8*d^17 + 2385443281*b

^8*c^8*d^9 - 13211685864*a*b^7*c^7*d^10 + 32491182204*a^2*b^6*c^6*d^11 - 46312178328*a^3*b^5*c^5*d^12 + 418329

59814*a^4*b^4*c^4*d^13 - 24518212056*a^5*b^3*c^3*d^14 + 9106525116*a^6*b^2*c^2*d^15 - 1960374312*a^7*b*c*d^16)

/(16777216*b^12*c^29 + 16777216*a^12*c^17*d^12 - 201326592*a^11*b*c^18*d^11 + 1107296256*a^2*b^10*c^27*d^2 - 3

690987520*a^3*b^9*c^26*d^3 + 8304721920*a^4*b^8*c^25*d^4 - 13287555072*a^5*b^7*c^24*d^5 + 15502147584*a^6*b^6*

c^23*d^6 - 13287555072*a^7*b^5*c^22*d^7 + 8304721920*a^8*b^4*c^21*d^8 - 3690987520*a^9*b^3*c^20*d^9 + 11072962

56*a^10*b^2*c^19*d^10 - 201326592*a*b^11*c^28*d))^(5/4) + 2048776709603328*a^23*b^2*c^23*d^20*x^(1/2)*(-(18738

8721*a^8*d^17 + 2385443281*b^8*c^8*d^9 - 13211685864*a*b^7*c^7*d^10 + 32491182204*a^2*b^6*c^6*d^11 - 463121783

28*a^3*b^5*c^5*d^12 + 41832959814*a^4*b^4*c^4*d^13 - 24518212056*a^5*b^3*c^3*d^14 + 9106525116*a^6*b^2*c^2*d^1

5 - 1960374312*a^7*b*c*d^16)/(16777216*b^12*c^29 + 16777216*a^12*c^17*d^12 - 201326592*a^11*b*c^18*d^11 + 1107

296256*a^2*b^10*c^27*d^2 - 3690987520*a^3*b^9*c^26*d^3 + 8304721920*a^4*b^8*c^25*d^4 - 13287555072*a^5*b^7*c^2

4*d^5 + 15502147584*a^6*b^6*c^23*d^6 - 13287555072*a^7*b^5*c^22*d^7 + 8304721920*a^8*b^4*c^21*d^8 - 3690987520

*a^9*b^3*c^20*d^9 + 1107296256*a^10*b^2*c^19*d^10 - 201326592*a*b^11*c^28*d))^(5/4) - 9076608073728*a*b^20*c^2

4*d^7*x^(1/2)*(-(187388721*a^8*d^17 + 2385443281*b^8*c^8*d^9 - 13211685864*a*b^7*c^7*d^10 + 32491182204*a^2*b^

6*c^6*d^11 - 46312178328*a^3*b^5*c^5*d^12 + 41832959814*a^4*b^4*c^4*d^13 - 24518212056*a^5*b^3*c^3*d^14 + 9106

525116*a^6*b^2*c^2*d^15 - 1960374312*a^7*b*c*d^16)/(16777216*b^12*c^29 + 16777216*a^12*c^17*d^12 - 201326592*a

^11*b*c^18*d^11 + 1107296256*a^2*b^10*c^27*d^2 - 3690987520*a^3*b^9*c^26*d^3 + 8304721920*a^4*b^8*c^25*d^4 - 1

3287555072*a^5*b^7*c^24*d^5 + 15502147584*a^6*b^6*c^23*d^6 - 13287555072*a^7*b^5*c^22*d^7 + 8304721920*a^8*b^4

*c^21*d^8 - 3690987520*a^9*b^3*c^20*d^9 + 1107296256*a^10*b^2*c^19*d^10 - 201326592*a*b^11*c^28*d))^(1/4) - 13

194139533312*a^4*b^21*c^42*d*x^(1/2)*(-(187388721*a^8*d^17 + 2385443281*b^8*c^8*d^9 - 13211685864*a*b^7*c^7*d^

10 + 32491182204*a^2*b^6*c^6*d^11 - 46312178328*a^3*b^5*c^5*d^12 + 41832959814*a^4*b^4*c^4*d^13 - 24518212056*

a^5*b^3*c^3*d^14 + 9106525116*a^6*b^2*c^2*d^15 - 1960374312*a^7*b*c*d^16)/(16777216*b^12*c^29 + 16777216*a^12*

c^17*d^12 - 201326592*a^11*b*c^18*d^11 + 1107296256*a^2*b^10*c^27*d^2 - 3690987520*a^3*b^9*c^26*d^3 + 83047219

20*a^4*b^8*c^25*d^4 - 13287555072*a^5*b^7*c^24*d^5 + 15502147584*a^6*b^6*c^23*d^6 - 13287555072*a^7*b^5*c^22*d

^7 + 8304721920*a^8*b^4*c^21*d^8 - 3690987520*a^9*b^3*c^20*d^9 + 1107296256*a^10*b^2*c^19*d^10 - 201326592*a*b

^11*c^28*d))^(5/4) - 253265631510528*a^24*b*c^22*d^21*x^(1/2)*(-(187388721*a^8*d^17 + 2385443281*b^8*c^8*d^9 -

13211685864*a*b^7*c^7*d^10 + 32491182204*a^2*b^6*c^6*d^11 - 46312178328*a^3*b^5*c^5*d^12 + 41832959814*a^4*b^

4*c^4*d^13 - 24518212056*a^5*b^3*c^3*d^14 + 9106525116*a^6*b^2*c^2*d^15 - 1960374312*a^7*b*c*d^16)/(16777216*b

^12*c^29 + 16777216*a^12*c^17*d^12 - 201326592*a^11*b*c^18*d^11 + 1107296256*a^2*b^10*c^27*d^2 - 3690987520*a^

3*b^9*c^26*d^3 + 8304721920*a^4*b^8*c^25*d^4 - 13287555072*a^5*b^7*c^24*d^5 + 15502147584*a^6*b^6*c^23*d^6 - 1

3287555072*a^7*b^5*c^22*d^7 + 8304721920*a^8*b^4*c^21*d^8 - 3690987520*a^9*b^3*c^20*d^9 + 1107296256*a^10*b^2*

c^19*d^10 - 201326592*a*b^11*c^28*d))^(5/4))/(300124211606973*a^20*d^28 + 11318183591936*b^20*c^20*d^8 - 13059

442606080*a*b^19*c^19*d^9 + 9939358580736*a^2*b^18*c^18*d^10 + 490619273216*a^3*b^17*c^17*d^11 + 2573759152128

*a^4*b^16*c^16*d^12 + 3011845816320*a^5*b^15*c^15*d^13 + 3484292218880*a^6*b^14*c^14*d^14 + 3991098359808*a^7*

b^13*c^13*d^15 + 4532264239104*a^8*b^12*c^12*d^16 - 25743035408641173*a^9*b^11*c^11*d^17 + 172320214465160559*

a^10*b^10*c^10*d^18 - 537854694138813555*a^11*b^9*c^9*d^19 + 1028670489683926929*a^12*b^8*c^8*d^20 - 133597887

3710775378*a^13*b^7*c^7*d^21 + 1235024770525419510*a^14*b^6*c^6*d^22 - 828236972743874694*a^15*b^5*c^5*d^23 +

402590417597719650*a^16*b^4*c^4*d^24 - 138920444110237257*a^17*b^3*c^3*d^25 + 32396642626079979*a^18*b^2*c^2*d

^26 - 4594209085368279*a^19*b*c*d^27))*(-(187388721*a^8*d^17 + 2385443281*b^8*c^8*d^9 - 13211685864*a*b^7*c^7*

d^10 + 32491182204*a^2*b^6*c^6*d^11 - 46312178328*a^3*b^5*c^5*d^12 + 41832959814*a^4*b^4*c^4*d^13 - 2451821205

6*a^5*b^3*c^3*d^14 + 9106525116*a^6*b^2*c^2*d^15 - 1960374312*a^7*b*c*d^16)/(16777216*b^12*c^29 + 16777216*a^1

2*c^17*d^12 - 201326592*a^11*b*c^18*d^11 + 1107296256*a^2*b^10*c^27*d^2 - 3690987520*a^3*b^9*c^26*d^3 + 830472

1920*a^4*b^8*c^25*d^4 - 13287555072*a^5*b^7*c^24*d^5 + 15502147584*a^6*b^6*c^23*d^6 - 13287555072*a^7*b^5*c^22

*d^7 + 8304721920*a^8*b^4*c^21*d^8 - 3690987520*a^9*b^3*c^20*d^9 + 1107296256*a^10*b^2*c^19*d^10 - 201326592*a

*b^11*c^28*d))^(1/4) - atan((a^3*b^22*c^43*x^(1/2)*(-(187388721*a^8*d^17 + 2385443281*b^8*c^8*d^9 - 1321168586

4*a*b^7*c^7*d^10 + 32491182204*a^2*b^6*c^6*d^11 - 46312178328*a^3*b^5*c^5*d^12 + 41832959814*a^4*b^4*c^4*d^13

- 24518212056*a^5*b^3*c^3*d^14 + 9106525116*a^6*b^2*c^2*d^15 - 1960374312*a^7*b*c*d^16)/(16777216*b^12*c^29 +

16777216*a^12*c^17*d^12 - 201326592*a^11*b*c^18*d^11 + 1107296256*a^2*b^10*c^27*d^2 - 3690987520*a^3*b^9*c^26*

d^3 + 8304721920*a^4*b^8*c^25*d^4 - 13287555072*a^5*b^7*c^24*d^5 + 15502147584*a^6*b^6*c^23*d^6 - 13287555072*

a^7*b^5*c^22*d^7 + 8304721920*a^8*b^4*c^21*d^8 - 3690987520*a^9*b^3*c^20*d^9 + 1107296256*a^10*b^2*c^19*d^10 -

201326592*a*b^11*c^28*d))^(5/4)*1099511627776i + a^25*c^21*d^22*x^(1/2)*(-(187388721*a^8*d^17 + 2385443281*b^

8*c^8*d^9 - 13211685864*a*b^7*c^7*d^10 + 32491182204*a^2*b^6*c^6*d^11 - 46312178328*a^3*b^5*c^5*d^12 + 4183295

9814*a^4*b^4*c^4*d^13 - 24518212056*a^5*b^3*c^3*d^14 + 9106525116*a^6*b^2*c^2*d^15 - 1960374312*a^7*b*c*d^16)/

(16777216*b^12*c^29 + 16777216*a^12*c^17*d^12 - 201326592*a^11*b*c^18*d^11 + 1107296256*a^2*b^10*c^27*d^2 - 36

90987520*a^3*b^9*c^26*d^3 + 8304721920*a^4*b^8*c^25*d^4 - 13287555072*a^5*b^7*c^24*d^5 + 15502147584*a^6*b^6*c

^23*d^6 - 13287555072*a^7*b^5*c^22*d^7 + 8304721920*a^8*b^4*c^21*d^8 - 3690987520*a^9*b^3*c^20*d^9 + 110729625

6*a^10*b^2*c^19*d^10 - 201326592*a*b^11*c^28*d))^(5/4)*14698451828736i + b^21*c^25*d^6*x^(1/2)*(-(187388721*a^

8*d^17 + 2385443281*b^8*c^8*d^9 - 13211685864*a*b^7*c^7*d^10 + 32491182204*a^2*b^6*c^6*d^11 - 46312178328*a^3*

b^5*c^5*d^12 + 41832959814*a^4*b^4*c^4*d^13 - 24518212056*a^5*b^3*c^3*d^14 + 9106525116*a^6*b^2*c^2*d^15 - 196

0374312*a^7*b*c*d^16)/(16777216*b^12*c^29 + 16777216*a^12*c^17*d^12 - 201326592*a^11*b*c^18*d^11 + 1107296256*

a^2*b^10*c^27*d^2 - 3690987520*a^3*b^9*c^26*d^3 + 8304721920*a^4*b^8*c^25*d^4 - 13287555072*a^5*b^7*c^24*d^5 +

15502147584*a^6*b^6*c^23*d^6 - 13287555072*a^7*b^5*c^22*d^7 + 8304721920*a^8*b^4*c^21*d^8 - 3690987520*a^9*b^

3*c^20*d^9 + 1107296256*a^10*b^2*c^19*d^10 - 201326592*a*b^11*c^28*d))^(1/4)*3277664026624i + a^2*b^19*c^23*d^

8*x^(1/2)*(-(187388721*a^8*d^17 + 2385443281*b^8*c^8*d^9 - 13211685864*a*b^7*c^7*d^10 + 32491182204*a^2*b^6*c^

6*d^11 - 46312178328*a^3*b^5*c^5*d^12 + 41832959814*a^4*b^4*c^4*d^13 - 24518212056*a^5*b^3*c^3*d^14 + 91065251

16*a^6*b^2*c^2*d^15 - 1960374312*a^7*b*c*d^16)/(16777216*b^12*c^29 + 16777216*a^12*c^17*d^12 - 201326592*a^11*

b*c^18*d^11 + 1107296256*a^2*b^10*c^27*d^2 - 3690987520*a^3*b^9*c^26*d^3 + 8304721920*a^4*b^8*c^25*d^4 - 13287

555072*a^5*b^7*c^24*d^5 + 15502147584*a^6*b^6*c^23*d^6 - 13287555072*a^7*b^5*c^22*d^7 + 8304721920*a^8*b^4*c^2

1*d^8 - 3690987520*a^9*b^3*c^20*d^9 + 1107296256*a^10*b^2*c^19*d^10 - 201326592*a*b^11*c^28*d))^(1/4)*97542733

82400i + a^3*b^18*c^22*d^9*x^(1/2)*(-(187388721*a^8*d^17 + 2385443281*b^8*c^8*d^9 - 13211685864*a*b^7*c^7*d^10

+ 32491182204*a^2*b^6*c^6*d^11 - 46312178328*a^3*b^5*c^5*d^12 + 41832959814*a^4*b^4*c^4*d^13 - 24518212056*a^

5*b^3*c^3*d^14 + 9106525116*a^6*b^2*c^2*d^15 - 1960374312*a^7*b*c*d^16)/(16777216*b^12*c^29 + 16777216*a^12*c^

17*d^12 - 201326592*a^11*b*c^18*d^11 + 1107296256*a^2*b^10*c^27*d^2 - 3690987520*a^3*b^9*c^26*d^3 + 8304721920

*a^4*b^8*c^25*d^4 - 13287555072*a^5*b^7*c^24*d^5 + 15502147584*a^6*b^6*c^23*d^6 - 13287555072*a^7*b^5*c^22*d^7

+ 8304721920*a^8*b^4*c^21*d^8 - 3690987520*a^9*b^3*c^20*d^9 + 1107296256*a^10*b^2*c^19*d^10 - 201326592*a*b^1

1*c^28*d))^(1/4)*151527147765760i - a^4*b^17*c^21*d^10*x^(1/2)*(-(187388721*a^8*d^17 + 2385443281*b^8*c^8*d^9

- 13211685864*a*b^7*c^7*d^10 + 32491182204*a^2*b^6*c^6*d^11 - 46312178328*a^3*b^5*c^5*d^12 + 41832959814*a^4*b

^4*c^4*d^13 - 24518212056*a^5*b^3*c^3*d^14 + 9106525116*a^6*b^2*c^2*d^15 - 1960374312*a^7*b*c*d^16)/(16777216*

b^12*c^29 + 16777216*a^12*c^17*d^12 - 201326592*a^11*b*c^18*d^11 + 1107296256*a^2*b^10*c^27*d^2 - 3690987520*a

^3*b^9*c^26*d^3 + 8304721920*a^4*b^8*c^25*d^4 - 13287555072*a^5*b^7*c^24*d^5 + 15502147584*a^6*b^6*c^23*d^6 -

13287555072*a^7*b^5*c^22*d^7 + 8304721920*a^8*b^4*c^21*d^8 - 3690987520*a^9*b^3*c^20*d^9 + 1107296256*a^10*b^2

*c^19*d^10 - 201326592*a*b^11*c^28*d))^(1/4)*864922391543808i + a^5*b^16*c^20*d^11*x^(1/2)*(-(187388721*a^8*d^

17 + 2385443281*b^8*c^8*d^9 - 13211685864*a*b^7*c^7*d^10 + 32491182204*a^2*b^6*c^6*d^11 - 46312178328*a^3*b^5*

c^5*d^12 + 41832959814*a^4*b^4*c^4*d^13 - 24518212056*a^5*b^3*c^3*d^14 + 9106525116*a^6*b^2*c^2*d^15 - 1960374

312*a^7*b*c*d^16)/(16777216*b^12*c^29 + 16777216*a^12*c^17*d^12 - 201326592*a^11*b*c^18*d^11 + 1107296256*a^2*

b^10*c^27*d^2 - 3690987520*a^3*b^9*c^26*d^3 + 8304721920*a^4*b^8*c^25*d^4 - 13287555072*a^5*b^7*c^24*d^5 + 155

02147584*a^6*b^6*c^23*d^6 - 13287555072*a^7*b^5*c^22*d^7 + 8304721920*a^8*b^4*c^21*d^8 - 3690987520*a^9*b^3*c^

20*d^9 + 1107296256*a^10*b^2*c^19*d^10 - 201326592*a*b^11*c^28*d))^(1/4)*2129342116921344i - a^6*b^15*c^19*d^1

2*x^(1/2)*(-(187388721*a^8*d^17 + 2385443281*b^8*c^8*d^9 - 13211685864*a*b^7*c^7*d^10 + 32491182204*a^2*b^6*c^

6*d^11 - 46312178328*a^3*b^5*c^5*d^12 + 41832959814*a^4*b^4*c^4*d^13 - 24518212056*a^5*b^3*c^3*d^14 + 91065251

16*a^6*b^2*c^2*d^15 - 1960374312*a^7*b*c*d^16)/(16777216*b^12*c^29 + 16777216*a^12*c^17*d^12 - 201326592*a^11*

b*c^18*d^11 + 1107296256*a^2*b^10*c^27*d^2 - 3690987520*a^3*b^9*c^26*d^3 + 8304721920*a^4*b^8*c^25*d^4 - 13287

555072*a^5*b^7*c^24*d^5 + 15502147584*a^6*b^6*c^23*d^6 - 13287555072*a^7*b^5*c^22*d^7 + 8304721920*a^8*b^4*c^2

1*d^8 - 3690987520*a^9*b^3*c^20*d^9 + 1107296256*a^10*b^2*c^19*d^10 - 201326592*a*b^11*c^28*d))^(1/4)*30351149

18903808i + a^7*b^14*c^18*d^13*x^(1/2)*(-(187388721*a^8*d^17 + 2385443281*b^8*c^8*d^9 - 13211685864*a*b^7*c^7*

d^10 + 32491182204*a^2*b^6*c^6*d^11 - 46312178328*a^3*b^5*c^5*d^12 + 41832959814*a^4*b^4*c^4*d^13 - 2451821205

6*a^5*b^3*c^3*d^14 + 9106525116*a^6*b^2*c^2*d^15 - 1960374312*a^7*b*c*d^16)/(16777216*b^12*c^29 + 16777216*a^1

2*c^17*d^12 - 201326592*a^11*b*c^18*d^11 + 1107296256*a^2*b^10*c^27*d^2 - 3690987520*a^3*b^9*c^26*d^3 + 830472

1920*a^4*b^8*c^25*d^4 - 13287555072*a^5*b^7*c^24*d^5 + 15502147584*a^6*b^6*c^23*d^6 - 13287555072*a^7*b^5*c^22

*d^7 + 8304721920*a^8*b^4*c^21*d^8 - 3690987520*a^9*b^3*c^20*d^9 + 1107296256*a^10*b^2*c^19*d^10 - 201326592*a

*b^11*c^28*d))^(1/4)*2741564854370304i - a^8*b^13*c^17*d^14*x^(1/2)*(-(187388721*a^8*d^17 + 2385443281*b^8*c^8

*d^9 - 13211685864*a*b^7*c^7*d^10 + 32491182204*a^2*b^6*c^6*d^11 - 46312178328*a^3*b^5*c^5*d^12 + 41832959814*

a^4*b^4*c^4*d^13 - 24518212056*a^5*b^3*c^3*d^14 + 9106525116*a^6*b^2*c^2*d^15 - 1960374312*a^7*b*c*d^16)/(1677

7216*b^12*c^29 + 16777216*a^12*c^17*d^12 - 201326592*a^11*b*c^18*d^11 + 1107296256*a^2*b^10*c^27*d^2 - 3690987

520*a^3*b^9*c^26*d^3 + 8304721920*a^4*b^8*c^25*d^4 - 13287555072*a^5*b^7*c^24*d^5 + 15502147584*a^6*b^6*c^23*d

^6 - 13287555072*a^7*b^5*c^22*d^7 + 8304721920*a^8*b^4*c^21*d^8 - 3690987520*a^9*b^3*c^20*d^9 + 1107296256*a^1

0*b^2*c^19*d^10 - 201326592*a*b^11*c^28*d))^(1/4)*1606825545302016i + a^9*b^12*c^16*d^15*x^(1/2)*(-(187388721*

a^8*d^17 + 2385443281*b^8*c^8*d^9 - 13211685864*a*b^7*c^7*d^10 + 32491182204*a^2*b^6*c^6*d^11 - 46312178328*a^

3*b^5*c^5*d^12 + 41832959814*a^4*b^4*c^4*d^13 - 24518212056*a^5*b^3*c^3*d^14 + 9106525116*a^6*b^2*c^2*d^15 - 1

960374312*a^7*b*c*d^16)/(16777216*b^12*c^29 + 16777216*a^12*c^17*d^12 - 201326592*a^11*b*c^18*d^11 + 110729625

6*a^2*b^10*c^27*d^2 - 3690987520*a^3*b^9*c^26*d^3 + 8304721920*a^4*b^8*c^25*d^4 - 13287555072*a^5*b^7*c^24*d^5

+ 15502147584*a^6*b^6*c^23*d^6 - 13287555072*a^7*b^5*c^22*d^7 + 8304721920*a^8*b^4*c^21*d^8 - 3690987520*a^9*

b^3*c^20*d^9 + 1107296256*a^10*b^2*c^19*d^10 - 201326592*a*b^11*c^28*d))^(1/4)*596805230002176i - a^10*b^11*c^

15*d^16*x^(1/2)*(-(187388721*a^8*d^17 + 2385443281*b^8*c^8*d^9 - 13211685864*a*b^7*c^7*d^10 + 32491182204*a^2*

b^6*c^6*d^11 - 46312178328*a^3*b^5*c^5*d^12 + 41832959814*a^4*b^4*c^4*d^13 - 24518212056*a^5*b^3*c^3*d^14 + 91

06525116*a^6*b^2*c^2*d^15 - 1960374312*a^7*b*c*d^16)/(16777216*b^12*c^29 + 16777216*a^12*c^17*d^12 - 201326592

*a^11*b*c^18*d^11 + 1107296256*a^2*b^10*c^27*d^2 - 3690987520*a^3*b^9*c^26*d^3 + 8304721920*a^4*b^8*c^25*d^4 -

13287555072*a^5*b^7*c^24*d^5 + 15502147584*a^6*b^6*c^23*d^6 - 13287555072*a^7*b^5*c^22*d^7 + 8304721920*a^8*b

^4*c^21*d^8 - 3690987520*a^9*b^3*c^20*d^9 + 1107296256*a^10*b^2*c^19*d^10 - 201326592*a*b^11*c^28*d))^(1/4)*12

8475090911232i + a^11*b^10*c^14*d^17*x^(1/2)*(-(187388721*a^8*d^17 + 2385443281*b^8*c^8*d^9 - 13211685864*a*b^

7*c^7*d^10 + 32491182204*a^2*b^6*c^6*d^11 - 46312178328*a^3*b^5*c^5*d^12 + 41832959814*a^4*b^4*c^4*d^13 - 2451

8212056*a^5*b^3*c^3*d^14 + 9106525116*a^6*b^2*c^2*d^15 - 1960374312*a^7*b*c*d^16)/(16777216*b^12*c^29 + 167772

16*a^12*c^17*d^12 - 201326592*a^11*b*c^18*d^11 + 1107296256*a^2*b^10*c^27*d^2 - 3690987520*a^3*b^9*c^26*d^3 +

8304721920*a^4*b^8*c^25*d^4 - 13287555072*a^5*b^7*c^24*d^5 + 15502147584*a^6*b^6*c^23*d^6 - 13287555072*a^7*b^

5*c^22*d^7 + 8304721920*a^8*b^4*c^21*d^8 - 3690987520*a^9*b^3*c^20*d^9 + 1107296256*a^10*b^2*c^19*d^10 - 20132

6592*a*b^11*c^28*d))^(1/4)*12280707219456i + a^5*b^20*c^41*d^2*x^(1/2)*(-(187388721*a^8*d^17 + 2385443281*b^8*

c^8*d^9 - 13211685864*a*b^7*c^7*d^10 + 32491182204*a^2*b^6*c^6*d^11 - 46312178328*a^3*b^5*c^5*d^12 + 418329598

14*a^4*b^4*c^4*d^13 - 24518212056*a^5*b^3*c^3*d^14 + 9106525116*a^6*b^2*c^2*d^15 - 1960374312*a^7*b*c*d^16)/(1

6777216*b^12*c^29 + 16777216*a^12*c^17*d^12 - 201326592*a^11*b*c^18*d^11 + 1107296256*a^2*b^10*c^27*d^2 - 3690

987520*a^3*b^9*c^26*d^3 + 8304721920*a^4*b^8*c^25*d^4 - 13287555072*a^5*b^7*c^24*d^5 + 15502147584*a^6*b^6*c^2

3*d^6 - 13287555072*a^7*b^5*c^22*d^7 + 8304721920*a^8*b^4*c^21*d^8 - 3690987520*a^9*b^3*c^20*d^9 + 1107296256*

a^10*b^2*c^19*d^10 - 201326592*a*b^11*c^28*d))^(5/4)*72567767433216i - a^6*b^19*c^40*d^3*x^(1/2)*(-(187388721*

a^8*d^17 + 2385443281*b^8*c^8*d^9 - 13211685864*a*b^7*c^7*d^10 + 32491182204*a^2*b^6*c^6*d^11 - 46312178328*a^

3*b^5*c^5*d^12 + 41832959814*a^4*b^4*c^4*d^13 - 24518212056*a^5*b^3*c^3*d^14 + 9106525116*a^6*b^2*c^2*d^15 - 1

960374312*a^7*b*c*d^16)/(16777216*b^12*c^29 + 16777216*a^12*c^17*d^12 - 201326592*a^11*b*c^18*d^11 + 110729625

6*a^2*b^10*c^27*d^2 - 3690987520*a^3*b^9*c^26*d^3 + 8304721920*a^4*b^8*c^25*d^4 - 13287555072*a^5*b^7*c^24*d^5

+ 15502147584*a^6*b^6*c^23*d^6 - 13287555072*a^7*b^5*c^22*d^7 + 8304721920*a^8*b^4*c^21*d^8 - 3690987520*a^9*

b^3*c^20*d^9 + 1107296256*a^10*b^2*c^19*d^10 - 201326592*a*b^11*c^28*d))^(5/4)*241892558110720i + a^7*b^18*c^3

9*d^4*x^(1/2)*(-(187388721*a^8*d^17 + 2385443281*b^8*c^8*d^9 - 13211685864*a*b^7*c^7*d^10 + 32491182204*a^2*b^

6*c^6*d^11 - 46312178328*a^3*b^5*c^5*d^12 + 41832959814*a^4*b^4*c^4*d^13 - 24518212056*a^5*b^3*c^3*d^14 + 9106

525116*a^6*b^2*c^2*d^15 - 1960374312*a^7*b*c*d^16)/(16777216*b^12*c^29 + 16777216*a^12*c^17*d^12 - 201326592*a

^11*b*c^18*d^11 + 1107296256*a^2*b^10*c^27*d^2 - 3690987520*a^3*b^9*c^26*d^3 + 8304721920*a^4*b^8*c^25*d^4 - 1

3287555072*a^5*b^7*c^24*d^5 + 15502147584*a^6*b^6*c^23*d^6 - 13287555072*a^7*b^5*c^22*d^7 + 8304721920*a^8*b^4

*c^21*d^8 - 3690987520*a^9*b^3*c^20*d^9 + 1107296256*a^10*b^2*c^19*d^10 - 201326592*a*b^11*c^28*d))^(5/4)*5442

58255749120i - a^8*b^17*c^38*d^5*x^(1/2)*(-(187388721*a^8*d^17 + 2385443281*b^8*c^8*d^9 - 13211685864*a*b^7*c^

7*d^10 + 32491182204*a^2*b^6*c^6*d^11 - 46312178328*a^3*b^5*c^5*d^12 + 41832959814*a^4*b^4*c^4*d^13 - 24518212

056*a^5*b^3*c^3*d^14 + 9106525116*a^6*b^2*c^2*d^15 - 1960374312*a^7*b*c*d^16)/(16777216*b^12*c^29 + 16777216*a

^12*c^17*d^12 - 201326592*a^11*b*c^18*d^11 + 1107296256*a^2*b^10*c^27*d^2 - 3690987520*a^3*b^9*c^26*d^3 + 8304

721920*a^4*b^8*c^25*d^4 - 13287555072*a^5*b^7*c^24*d^5 + 15502147584*a^6*b^6*c^23*d^6 - 13287555072*a^7*b^5*c^

22*d^7 + 8304721920*a^8*b^4*c^21*d^8 - 3690987520*a^9*b^3*c^20*d^9 + 1107296256*a^10*b^2*c^19*d^10 - 201326592

*a*b^11*c^28*d))^(5/4)*870813209198592i + a^9*b^16*c^37*d^6*x^(1/2)*(-(187388721*a^8*d^17 + 2385443281*b^8*c^8

*d^9 - 13211685864*a*b^7*c^7*d^10 + 32491182204*a^2*b^6*c^6*d^11 - 46312178328*a^3*b^5*c^5*d^12 + 41832959814*

a^4*b^4*c^4*d^13 - 24518212056*a^5*b^3*c^3*d^14 + 9106525116*a^6*b^2*c^2*d^15 - 1960374312*a^7*b*c*d^16)/(1677

7216*b^12*c^29 + 16777216*a^12*c^17*d^12 - 201326592*a^11*b*c^18*d^11 + 1107296256*a^2*b^10*c^27*d^2 - 3690987

520*a^3*b^9*c^26*d^3 + 8304721920*a^4*b^8*c^25*d^4 - 13287555072*a^5*b^7*c^24*d^5 + 15502147584*a^6*b^6*c^23*d

^6 - 13287555072*a^7*b^5*c^22*d^7 + 8304721920*a^8*b^4*c^21*d^8 - 3690987520*a^9*b^3*c^20*d^9 + 1107296256*a^1

0*b^2*c^19*d^10 - 201326592*a*b^11*c^28*d))^(5/4)*1068391368491008i - a^10*b^15*c^36*d^7*x^(1/2)*(-(187388721*

a^8*d^17 + 2385443281*b^8*c^8*d^9 - 13211685864*a*b^7*c^7*d^10 + 32491182204*a^2*b^6*c^6*d^11 - 46312178328*a^

3*b^5*c^5*d^12 + 41832959814*a^4*b^4*c^4*d^13 - 24518212056*a^5*b^3*c^3*d^14 + 9106525116*a^6*b^2*c^2*d^15 - 1

960374312*a^7*b*c*d^16)/(16777216*b^12*c^29 + 16777216*a^12*c^17*d^12 - 201326592*a^11*b*c^18*d^11 + 110729625

6*a^2*b^10*c^27*d^2 - 3690987520*a^3*b^9*c^26*d^3 + 8304721920*a^4*b^8*c^25*d^4 - 13287555072*a^5*b^7*c^24*d^5

+ 15502147584*a^6*b^6*c^23*d^6 - 13287555072*a^7*b^5*c^22*d^7 + 8304721920*a^8*b^4*c^21*d^8 - 3690987520*a^9*

b^3*c^20*d^9 + 1107296256*a^10*b^2*c^19*d^10 - 201326592*a*b^11*c^28*d))^(5/4)*1645350431490048i + a^11*b^14*c

^35*d^8*x^(1/2)*(-(187388721*a^8*d^17 + 2385443281*b^8*c^8*d^9 - 13211685864*a*b^7*c^7*d^10 + 32491182204*a^2*

b^6*c^6*d^11 - 46312178328*a^3*b^5*c^5*d^12 + 41832959814*a^4*b^4*c^4*d^13 - 24518212056*a^5*b^3*c^3*d^14 + 91

06525116*a^6*b^2*c^2*d^15 - 1960374312*a^7*b*c*d^16)/(16777216*b^12*c^29 + 16777216*a^12*c^17*d^12 - 201326592

*a^11*b*c^18*d^11 + 1107296256*a^2*b^10*c^27*d^2 - 3690987520*a^3*b^9*c^26*d^3 + 8304721920*a^4*b^8*c^25*d^4 -

13287555072*a^5*b^7*c^24*d^5 + 15502147584*a^6*b^6*c^23*d^6 - 13287555072*a^7*b^5*c^22*d^7 + 8304721920*a^8*b

^4*c^21*d^8 - 3690987520*a^9*b^3*c^20*d^9 + 1107296256*a^10*b^2*c^19*d^10 - 201326592*a*b^11*c^28*d))^(5/4)*59

04248592138240i - a^12*b^13*c^34*d^9*x^(1/2)*(-(187388721*a^8*d^17 + 2385443281*b^8*c^8*d^9 - 13211685864*a*b^

7*c^7*d^10 + 32491182204*a^2*b^6*c^6*d^11 - 46312178328*a^3*b^5*c^5*d^12 + 41832959814*a^4*b^4*c^4*d^13 - 2451

8212056*a^5*b^3*c^3*d^14 + 9106525116*a^6*b^2*c^2*d^15 - 1960374312*a^7*b*c*d^16)/(16777216*b^12*c^29 + 167772

16*a^12*c^17*d^12 - 201326592*a^11*b*c^18*d^11 + 1107296256*a^2*b^10*c^27*d^2 - 3690987520*a^3*b^9*c^26*d^3 +

8304721920*a^4*b^8*c^25*d^4 - 13287555072*a^5*b^7*c^24*d^5 + 15502147584*a^6*b^6*c^23*d^6 - 13287555072*a^7*b^

5*c^22*d^7 + 8304721920*a^8*b^4*c^21*d^8 - 3690987520*a^9*b^3*c^20*d^9 + 1107296256*a^10*b^2*c^19*d^10 - 20132

6592*a*b^11*c^28*d))^(5/4)*23313872756670464i + a^13*b^12*c^33*d^10*x^(1/2)*(-(187388721*a^8*d^17 + 2385443281

*b^8*c^8*d^9 - 13211685864*a*b^7*c^7*d^10 + 32491182204*a^2*b^6*c^6*d^11 - 46312178328*a^3*b^5*c^5*d^12 + 4183

2959814*a^4*b^4*c^4*d^13 - 24518212056*a^5*b^3*c^3*d^14 + 9106525116*a^6*b^2*c^2*d^15 - 1960374312*a^7*b*c*d^1

6)/(16777216*b^12*c^29 + 16777216*a^12*c^17*d^12 - 201326592*a^11*b*c^18*d^11 + 1107296256*a^2*b^10*c^27*d^2 -

3690987520*a^3*b^9*c^26*d^3 + 8304721920*a^4*b^8*c^25*d^4 - 13287555072*a^5*b^7*c^24*d^5 + 15502147584*a^6*b^

6*c^23*d^6 - 13287555072*a^7*b^5*c^22*d^7 + 8304721920*a^8*b^4*c^21*d^8 - 3690987520*a^9*b^3*c^20*d^9 + 110729

6256*a^10*b^2*c^19*d^10 - 201326592*a*b^11*c^28*d))^(5/4)*69219148936249344i - a^14*b^11*c^32*d^11*x^(1/2)*(-(

187388721*a^8*d^17 + 2385443281*b^8*c^8*d^9 - 13211685864*a*b^7*c^7*d^10 + 32491182204*a^2*b^6*c^6*d^11 - 4631

2178328*a^3*b^5*c^5*d^12 + 41832959814*a^4*b^4*c^4*d^13 - 24518212056*a^5*b^3*c^3*d^14 + 9106525116*a^6*b^2*c^

2*d^15 - 1960374312*a^7*b*c*d^16)/(16777216*b^12*c^29 + 16777216*a^12*c^17*d^12 - 201326592*a^11*b*c^18*d^11 +

1107296256*a^2*b^10*c^27*d^2 - 3690987520*a^3*b^9*c^26*d^3 + 8304721920*a^4*b^8*c^25*d^4 - 13287555072*a^5*b^

7*c^24*d^5 + 15502147584*a^6*b^6*c^23*d^6 - 13287555072*a^7*b^5*c^22*d^7 + 8304721920*a^8*b^4*c^21*d^8 - 36909

87520*a^9*b^3*c^20*d^9 + 1107296256*a^10*b^2*c^19*d^10 - 201326592*a*b^11*c^28*d))^(5/4)*153020270188167168i +

a^15*b^10*c^31*d^12*x^(1/2)*(-(187388721*a^8*d^17 + 2385443281*b^8*c^8*d^9 - 13211685864*a*b^7*c^7*d^10 + 324

91182204*a^2*b^6*c^6*d^11 - 46312178328*a^3*b^5*c^5*d^12 + 41832959814*a^4*b^4*c^4*d^13 - 24518212056*a^5*b^3*

c^3*d^14 + 9106525116*a^6*b^2*c^2*d^15 - 1960374312*a^7*b*c*d^16)/(16777216*b^12*c^29 + 16777216*a^12*c^17*d^1

2 - 201326592*a^11*b*c^18*d^11 + 1107296256*a^2*b^10*c^27*d^2 - 3690987520*a^3*b^9*c^26*d^3 + 8304721920*a^4*b

^8*c^25*d^4 - 13287555072*a^5*b^7*c^24*d^5 + 15502147584*a^6*b^6*c^23*d^6 - 13287555072*a^7*b^5*c^22*d^7 + 830

4721920*a^8*b^4*c^21*d^8 - 3690987520*a^9*b^3*c^20*d^9 + 1107296256*a^10*b^2*c^19*d^10 - 201326592*a*b^11*c^28

*d))^(5/4)*258615331105275904i - a^16*b^9*c^30*d^13*x^(1/2)*(-(187388721*a^8*d^17 + 2385443281*b^8*c^8*d^9 - 1

3211685864*a*b^7*c^7*d^10 + 32491182204*a^2*b^6*c^6*d^11 - 46312178328*a^3*b^5*c^5*d^12 + 41832959814*a^4*b^4*

c^4*d^13 - 24518212056*a^5*b^3*c^3*d^14 + 9106525116*a^6*b^2*c^2*d^15 - 1960374312*a^7*b*c*d^16)/(16777216*b^1

2*c^29 + 16777216*a^12*c^17*d^12 - 201326592*a^11*b*c^18*d^11 + 1107296256*a^2*b^10*c^27*d^2 - 3690987520*a^3*

b^9*c^26*d^3 + 8304721920*a^4*b^8*c^25*d^4 - 13287555072*a^5*b^7*c^24*d^5 + 15502147584*a^6*b^6*c^23*d^6 - 132

87555072*a^7*b^5*c^22*d^7 + 8304721920*a^8*b^4*c^21*d^8 - 3690987520*a^9*b^3*c^20*d^9 + 1107296256*a^10*b^2*c^

19*d^10 - 201326592*a*b^11*c^28*d))^(5/4)*340620627746488320i + a^17*b^8*c^29*d^14*x^(1/2)*(-(187388721*a^8*d^

17 + 2385443281*b^8*c^8*d^9 - 13211685864*a*b^7*c^7*d^10 + 32491182204*a^2*b^6*c^6*d^11 - 46312178328*a^3*b^5*

c^5*d^12 + 41832959814*a^4*b^4*c^4*d^13 - 24518212056*a^5*b^3*c^3*d^14 + 9106525116*a^6*b^2*c^2*d^15 - 1960374

312*a^7*b*c*d^16)/(16777216*b^12*c^29 + 16777216*a^12*c^17*d^12 - 201326592*a^11*b*c^18*d^11 + 1107296256*a^2*

b^10*c^27*d^2 - 3690987520*a^3*b^9*c^26*d^3 + 8304721920*a^4*b^8*c^25*d^4 - 13287555072*a^5*b^7*c^24*d^5 + 155

02147584*a^6*b^6*c^23*d^6 - 13287555072*a^7*b^5*c^22*d^7 + 8304721920*a^8*b^4*c^21*d^8 - 3690987520*a^9*b^3*c^

20*d^9 + 1107296256*a^10*b^2*c^19*d^10 - 201326592*a*b^11*c^28*d))^(5/4)*353353081917800448i - a^18*b^7*c^28*d

^15*x^(1/2)*(-(187388721*a^8*d^17 + 2385443281*b^8*c^8*d^9 - 13211685864*a*b^7*c^7*d^10 + 32491182204*a^2*b^6*

c^6*d^11 - 46312178328*a^3*b^5*c^5*d^12 + 41832959814*a^4*b^4*c^4*d^13 - 24518212056*a^5*b^3*c^3*d^14 + 910652

5116*a^6*b^2*c^2*d^15 - 1960374312*a^7*b*c*d^16)/(16777216*b^12*c^29 + 16777216*a^12*c^17*d^12 - 201326592*a^1

1*b*c^18*d^11 + 1107296256*a^2*b^10*c^27*d^2 - 3690987520*a^3*b^9*c^26*d^3 + 8304721920*a^4*b^8*c^25*d^4 - 132

87555072*a^5*b^7*c^24*d^5 + 15502147584*a^6*b^6*c^23*d^6 - 13287555072*a^7*b^5*c^22*d^7 + 8304721920*a^8*b^4*c

^21*d^8 - 3690987520*a^9*b^3*c^20*d^9 + 1107296256*a^10*b^2*c^19*d^10 - 201326592*a*b^11*c^28*d))^(5/4)*289712

449106477056i + a^19*b^6*c^27*d^16*x^(1/2)*(-(187388721*a^8*d^17 + 2385443281*b^8*c^8*d^9 - 13211685864*a*b^7*

c^7*d^10 + 32491182204*a^2*b^6*c^6*d^11 - 46312178328*a^3*b^5*c^5*d^12 + 41832959814*a^4*b^4*c^4*d^13 - 245182

12056*a^5*b^3*c^3*d^14 + 9106525116*a^6*b^2*c^2*d^15 - 1960374312*a^7*b*c*d^16)/(16777216*b^12*c^29 + 16777216

*a^12*c^17*d^12 - 201326592*a^11*b*c^18*d^11 + 1107296256*a^2*b^10*c^27*d^2 - 3690987520*a^3*b^9*c^26*d^3 + 83

04721920*a^4*b^8*c^25*d^4 - 13287555072*a^5*b^7*c^24*d^5 + 15502147584*a^6*b^6*c^23*d^6 - 13287555072*a^7*b^5*

c^22*d^7 + 8304721920*a^8*b^4*c^21*d^8 - 3690987520*a^9*b^3*c^20*d^9 + 1107296256*a^10*b^2*c^19*d^10 - 2013265

92*a*b^11*c^28*d))^(5/4)*187138382286028800i - a^20*b^5*c^26*d^17*x^(1/2)*(-(187388721*a^8*d^17 + 2385443281*b

^8*c^8*d^9 - 13211685864*a*b^7*c^7*d^10 + 32491182204*a^2*b^6*c^6*d^11 - 46312178328*a^3*b^5*c^5*d^12 + 418329

59814*a^4*b^4*c^4*d^13 - 24518212056*a^5*b^3*c^3*d^14 + 9106525116*a^6*b^2*c^2*d^15 - 1960374312*a^7*b*c*d^16)

/(16777216*b^12*c^29 + 16777216*a^12*c^17*d^12 - 201326592*a^11*b*c^18*d^11 + 1107296256*a^2*b^10*c^27*d^2 - 3

690987520*a^3*b^9*c^26*d^3 + 8304721920*a^4*b^8*c^25*d^4 - 13287555072*a^5*b^7*c^24*d^5 + 15502147584*a^6*b^6*

c^23*d^6 - 13287555072*a^7*b^5*c^22*d^7 + 8304721920*a^8*b^4*c^21*d^8 - 3690987520*a^9*b^3*c^20*d^9 + 11072962

56*a^10*b^2*c^19*d^10 - 201326592*a*b^11*c^28*d))^(5/4)*94248109508395008i + a^21*b^4*c^25*d^18*x^(1/2)*(-(187

388721*a^8*d^17 + 2385443281*b^8*c^8*d^9 - 13211685864*a*b^7*c^7*d^10 + 32491182204*a^2*b^6*c^6*d^11 - 4631217

8328*a^3*b^5*c^5*d^12 + 41832959814*a^4*b^4*c^4*d^13 - 24518212056*a^5*b^3*c^3*d^14 + 9106525116*a^6*b^2*c^2*d

^15 - 1960374312*a^7*b*c*d^16)/(16777216*b^12*c^29 + 16777216*a^12*c^17*d^12 - 201326592*a^11*b*c^18*d^11 + 11

07296256*a^2*b^10*c^27*d^2 - 3690987520*a^3*b^9*c^26*d^3 + 8304721920*a^4*b^8*c^25*d^4 - 13287555072*a^5*b^7*c

^24*d^5 + 15502147584*a^6*b^6*c^23*d^6 - 13287555072*a^7*b^5*c^22*d^7 + 8304721920*a^8*b^4*c^21*d^8 - 36909875

20*a^9*b^3*c^20*d^9 + 1107296256*a^10*b^2*c^19*d^10 - 201326592*a*b^11*c^28*d))^(5/4)*36285923826073600i - a^2

2*b^3*c^24*d^19*x^(1/2)*(-(187388721*a^8*d^17 + 2385443281*b^8*c^8*d^9 - 13211685864*a*b^7*c^7*d^10 + 32491182

204*a^2*b^6*c^6*d^11 - 46312178328*a^3*b^5*c^5*d^12 + 41832959814*a^4*b^4*c^4*d^13 - 24518212056*a^5*b^3*c^3*d

^14 + 9106525116*a^6*b^2*c^2*d^15 - 1960374312*a^7*b*c*d^16)/(16777216*b^12*c^29 + 16777216*a^12*c^17*d^12 - 2

01326592*a^11*b*c^18*d^11 + 1107296256*a^2*b^10*c^27*d^2 - 3690987520*a^3*b^9*c^26*d^3 + 8304721920*a^4*b^8*c^

25*d^4 - 13287555072*a^5*b^7*c^24*d^5 + 15502147584*a^6*b^6*c^23*d^6 - 13287555072*a^7*b^5*c^22*d^7 + 83047219

20*a^8*b^4*c^21*d^8 - 3690987520*a^9*b^3*c^20*d^9 + 1107296256*a^10*b^2*c^19*d^10 - 201326592*a*b^11*c^28*d))^

(5/4)*10326063452258304i + a^23*b^2*c^23*d^20*x^(1/2)*(-(187388721*a^8*d^17 + 2385443281*b^8*c^8*d^9 - 1321168

5864*a*b^7*c^7*d^10 + 32491182204*a^2*b^6*c^6*d^11 - 46312178328*a^3*b^5*c^5*d^12 + 41832959814*a^4*b^4*c^4*d^

13 - 24518212056*a^5*b^3*c^3*d^14 + 9106525116*a^6*b^2*c^2*d^15 - 1960374312*a^7*b*c*d^16)/(16777216*b^12*c^29

+ 16777216*a^12*c^17*d^12 - 201326592*a^11*b*c^18*d^11 + 1107296256*a^2*b^10*c^27*d^2 - 3690987520*a^3*b^9*c^

26*d^3 + 8304721920*a^4*b^8*c^25*d^4 - 13287555072*a^5*b^7*c^24*d^5 + 15502147584*a^6*b^6*c^23*d^6 - 132875550

72*a^7*b^5*c^22*d^7 + 8304721920*a^8*b^4*c^21*d^8 - 3690987520*a^9*b^3*c^20*d^9 + 1107296256*a^10*b^2*c^19*d^1

0 - 201326592*a*b^11*c^28*d))^(5/4)*2048776709603328i - a*b^20*c^24*d^7*x^(1/2)*(-(187388721*a^8*d^17 + 238544

3281*b^8*c^8*d^9 - 13211685864*a*b^7*c^7*d^10 + 32491182204*a^2*b^6*c^6*d^11 - 46312178328*a^3*b^5*c^5*d^12 +

41832959814*a^4*b^4*c^4*d^13 - 24518212056*a^5*b^3*c^3*d^14 + 9106525116*a^6*b^2*c^2*d^15 - 1960374312*a^7*b*c

*d^16)/(16777216*b^12*c^29 + 16777216*a^12*c^17*d^12 - 201326592*a^11*b*c^18*d^11 + 1107296256*a^2*b^10*c^27*d

^2 - 3690987520*a^3*b^9*c^26*d^3 + 8304721920*a^4*b^8*c^25*d^4 - 13287555072*a^5*b^7*c^24*d^5 + 15502147584*a^

6*b^6*c^23*d^6 - 13287555072*a^7*b^5*c^22*d^7 + 8304721920*a^8*b^4*c^21*d^8 - 3690987520*a^9*b^3*c^20*d^9 + 11

07296256*a^10*b^2*c^19*d^10 - 201326592*a*b^11*c^28*d))^(1/4)*9076608073728i - a^4*b^21*c^42*d*x^(1/2)*(-(1873

88721*a^8*d^17 + 2385443281*b^8*c^8*d^9 - 13211685864*a*b^7*c^7*d^10 + 32491182204*a^2*b^6*c^6*d^11 - 46312178

328*a^3*b^5*c^5*d^12 + 41832959814*a^4*b^4*c^4*d^13 - 24518212056*a^5*b^3*c^3*d^14 + 9106525116*a^6*b^2*c^2*d^

15 - 1960374312*a^7*b*c*d^16)/(16777216*b^12*c^29 + 16777216*a^12*c^17*d^12 - 201326592*a^11*b*c^18*d^11 + 110

7296256*a^2*b^10*c^27*d^2 - 3690987520*a^3*b^9*c^26*d^3 + 8304721920*a^4*b^8*c^25*d^4 - 13287555072*a^5*b^7*c^

24*d^5 + 15502147584*a^6*b^6*c^23*d^6 - 13287555072*a^7*b^5*c^22*d^7 + 8304721920*a^8*b^4*c^21*d^8 - 369098752

0*a^9*b^3*c^20*d^9 + 1107296256*a^10*b^2*c^19*d^10 - 201326592*a*b^11*c^28*d))^(5/4)*13194139533312i - a^24*b*

c^22*d^21*x^(1/2)*(-(187388721*a^8*d^17 + 2385443281*b^8*c^8*d^9 - 13211685864*a*b^7*c^7*d^10 + 32491182204*a^

2*b^6*c^6*d^11 - 46312178328*a^3*b^5*c^5*d^12 + 41832959814*a^4*b^4*c^4*d^13 - 24518212056*a^5*b^3*c^3*d^14 +

9106525116*a^6*b^2*c^2*d^15 - 1960374312*a^7*b*c*d^16)/(16777216*b^12*c^29 + 16777216*a^12*c^17*d^12 - 2013265

92*a^11*b*c^18*d^11 + 1107296256*a^2*b^10*c^27*d^2 - 3690987520*a^3*b^9*c^26*d^3 + 8304721920*a^4*b^8*c^25*d^4

- 13287555072*a^5*b^7*c^24*d^5 + 15502147584*a^6*b^6*c^23*d^6 - 13287555072*a^7*b^5*c^22*d^7 + 8304721920*a^8

*b^4*c^21*d^8 - 3690987520*a^9*b^3*c^20*d^9 + 1107296256*a^10*b^2*c^19*d^10 - 201326592*a*b^11*c^28*d))^(5/4)*

253265631510528i)/(300124211606973*a^20*d^28 + 11318183591936*b^20*c^20*d^8 - 13059442606080*a*b^19*c^19*d^9 +

9939358580736*a^2*b^18*c^18*d^10 + 490619273216*a^3*b^17*c^17*d^11 + 2573759152128*a^4*b^16*c^16*d^12 + 30118

45816320*a^5*b^15*c^15*d^13 + 3484292218880*a^6*b^14*c^14*d^14 + 3991098359808*a^7*b^13*c^13*d^15 + 4532264239

104*a^8*b^12*c^12*d^16 - 25743035408641173*a^9*b^11*c^11*d^17 + 172320214465160559*a^10*b^10*c^10*d^18 - 53785

4694138813555*a^11*b^9*c^9*d^19 + 1028670489683926929*a^12*b^8*c^8*d^20 - 1335978873710775378*a^13*b^7*c^7*d^2

1 + 1235024770525419510*a^14*b^6*c^6*d^22 - 828236972743874694*a^15*b^5*c^5*d^23 + 402590417597719650*a^16*b^4

*c^4*d^24 - 138920444110237257*a^17*b^3*c^3*d^25 + 32396642626079979*a^18*b^2*c^2*d^26 - 4594209085368279*a^19

*b*c*d^27))*(-(187388721*a^8*d^17 + 2385443281*b^8*c^8*d^9 - 13211685864*a*b^7*c^7*d^10 + 32491182204*a^2*b^6*

c^6*d^11 - 46312178328*a^3*b^5*c^5*d^12 + 41832959814*a^4*b^4*c^4*d^13 - 24518212056*a^5*b^3*c^3*d^14 + 910652

5116*a^6*b^2*c^2*d^15 - 1960374312*a^7*b*c*d^16)/(16777216*b^12*c^29 + 16777216*a^12*c^17*d^12 - 201326592*a^1

1*b*c^18*d^11 + 1107296256*a^2*b^10*c^27*d^2 - 3690987520*a^3*b^9*c^26*d^3 + 8304721920*a^4*b^8*c^25*d^4 - 132

87555072*a^5*b^7*c^24*d^5 + 15502147584*a^6*b^6*c^23*d^6 - 13287555072*a^7*b^5*c^22*d^7 + 8304721920*a^8*b^4*c

^21*d^8 - 3690987520*a^9*b^3*c^20*d^9 + 1107296256*a^10*b^2*c^19*d^10 - 201326592*a*b^11*c^28*d))^(1/4)*2i - 2

*atan((33554432*a^11*b^22*c^29*x^(1/2)*(-b^17/(16*a^21*d^12 + 16*a^9*b^12*c^12 - 192*a^10*b^11*c^11*d + 1056*a

^11*b^10*c^10*d^2 - 3520*a^12*b^9*c^9*d^3 + 7920*a^13*b^8*c^8*d^4 - 12672*a^14*b^7*c^7*d^5 + 14784*a^15*b^6*c^

6*d^6 - 12672*a^16*b^5*c^5*d^7 + 7920*a^17*b^4*c^4*d^8 - 3520*a^18*b^3*c^3*d^9 + 1056*a^19*b^2*c^2*d^10 - 192*

a^20*b*c*d^11))^(5/4) + 374777442*a^19*b^10*d^17*x^(1/2)*(-b^17/(16*a^21*d^12 + 16*a^9*b^12*c^12 - 192*a^10*b^

11*c^11*d + 1056*a^11*b^10*c^10*d^2 - 3520*a^12*b^9*c^9*d^3 + 7920*a^13*b^8*c^8*d^4 - 12672*a^14*b^7*c^7*d^5 +

14784*a^15*b^6*c^6*d^6 - 12672*a^16*b^5*c^5*d^7 + 7920*a^17*b^4*c^4*d^8 - 3520*a^18*b^3*c^3*d^9 + 1056*a^19*b

^2*c^2*d^10 - 192*a^20*b*c*d^11))^(1/4) + 448561152*a^33*c^7*d^22*x^(1/2)*(-b^17/(16*a^21*d^12 + 16*a^9*b^12*c

^12 - 192*a^10*b^11*c^11*d + 1056*a^11*b^10*c^10*d^2 - 3520*a^12*b^9*c^9*d^3 + 7920*a^13*b^8*c^8*d^4 - 12672*a

^14*b^7*c^7*d^5 + 14784*a^15*b^6*c^6*d^6 - 12672*a^16*b^5*c^5*d^7 + 7920*a^17*b^4*c^4*d^8 - 3520*a^18*b^3*c^3*

d^9 + 1056*a^19*b^2*c^2*d^10 - 192*a^20*b*c*d^11))^(5/4) + 100026368*a^8*b^21*c^11*d^6*x^(1/2)*(-b^17/(16*a^21

*d^12 + 16*a^9*b^12*c^12 - 192*a^10*b^11*c^11*d + 1056*a^11*b^10*c^10*d^2 - 3520*a^12*b^9*c^9*d^3 + 7920*a^13*

b^8*c^8*d^4 - 12672*a^14*b^7*c^7*d^5 + 14784*a^15*b^6*c^6*d^6 - 12672*a^16*b^5*c^5*d^7 + 7920*a^17*b^4*c^4*d^8

- 3520*a^18*b^3*c^3*d^9 + 1056*a^19*b^2*c^2*d^10 - 192*a^20*b*c*d^11))^(1/4) - 276996096*a^9*b^20*c^10*d^7*x^

(1/2)*(-b^17/(16*a^21*d^12 + 16*a^9*b^12*c^12 - 192*a^10*b^11*c^11*d + 1056*a^11*b^10*c^10*d^2 - 3520*a^12*b^9

*c^9*d^3 + 7920*a^13*b^8*c^8*d^4 - 12672*a^14*b^7*c^7*d^5 + 14784*a^15*b^6*c^6*d^6 - 12672*a^16*b^5*c^5*d^7 +

7920*a^17*b^4*c^4*d^8 - 3520*a^18*b^3*c^3*d^9 + 1056*a^19*b^2*c^2*d^10 - 192*a^20*b*c*d^11))^(1/4) + 297676800

*a^10*b^19*c^9*d^8*x^(1/2)*(-b^17/(16*a^21*d^12 + 16*a^9*b^12*c^12 - 192*a^10*b^11*c^11*d + 1056*a^11*b^10*c^1

0*d^2 - 3520*a^12*b^9*c^9*d^3 + 7920*a^13*b^8*c^8*d^4 - 12672*a^14*b^7*c^7*d^5 + 14784*a^15*b^6*c^6*d^6 - 1267

2*a^16*b^5*c^5*d^7 + 7920*a^17*b^4*c^4*d^8 - 3520*a^18*b^3*c^3*d^9 + 1056*a^19*b^2*c^2*d^10 - 192*a^20*b*c*d^1

1))^(1/4) + 4624241570*a^11*b^18*c^8*d^9*x^(1/2)*(-b^17/(16*a^21*d^12 + 16*a^9*b^12*c^12 - 192*a^10*b^11*c^11*

d + 1056*a^11*b^10*c^10*d^2 - 3520*a^12*b^9*c^9*d^3 + 7920*a^13*b^8*c^8*d^4 - 12672*a^14*b^7*c^7*d^5 + 14784*a

^15*b^6*c^6*d^6 - 12672*a^16*b^5*c^5*d^7 + 7920*a^17*b^4*c^4*d^8 - 3520*a^18*b^3*c^3*d^9 + 1056*a^19*b^2*c^2*d

^10 - 192*a^20*b*c*d^11))^(1/4) - 26395336656*a^12*b^17*c^7*d^10*x^(1/2)*(-b^17/(16*a^21*d^12 + 16*a^9*b^12*c^

12 - 192*a^10*b^11*c^11*d + 1056*a^11*b^10*c^10*d^2 - 3520*a^12*b^9*c^9*d^3 + 7920*a^13*b^8*c^8*d^4 - 12672*a^

14*b^7*c^7*d^5 + 14784*a^15*b^6*c^6*d^6 - 12672*a^16*b^5*c^5*d^7 + 7920*a^17*b^4*c^4*d^8 - 3520*a^18*b^3*c^3*d

^9 + 1056*a^19*b^2*c^2*d^10 - 192*a^20*b*c*d^11))^(1/4) + 64982364408*a^13*b^16*c^6*d^11*x^(1/2)*(-b^17/(16*a^

21*d^12 + 16*a^9*b^12*c^12 - 192*a^10*b^11*c^11*d + 1056*a^11*b^10*c^10*d^2 - 3520*a^12*b^9*c^9*d^3 + 7920*a^1

3*b^8*c^8*d^4 - 12672*a^14*b^7*c^7*d^5 + 14784*a^15*b^6*c^6*d^6 - 12672*a^16*b^5*c^5*d^7 + 7920*a^17*b^4*c^4*d

^8 - 3520*a^18*b^3*c^3*d^9 + 1056*a^19*b^2*c^2*d^10 - 192*a^20*b*c*d^11))^(1/4) - 92624356656*a^14*b^15*c^5*d^

12*x^(1/2)*(-b^17/(16*a^21*d^12 + 16*a^9*b^12*c^12 - 192*a^10*b^11*c^11*d + 1056*a^11*b^10*c^10*d^2 - 3520*a^1

2*b^9*c^9*d^3 + 7920*a^13*b^8*c^8*d^4 - 12672*a^14*b^7*c^7*d^5 + 14784*a^15*b^6*c^6*d^6 - 12672*a^16*b^5*c^5*d

^7 + 7920*a^17*b^4*c^4*d^8 - 3520*a^18*b^3*c^3*d^9 + 1056*a^19*b^2*c^2*d^10 - 192*a^20*b*c*d^11))^(1/4) + 8366

5919628*a^15*b^14*c^4*d^13*x^(1/2)*(-b^17/(16*a^21*d^12 + 16*a^9*b^12*c^12 - 192*a^10*b^11*c^11*d + 1056*a^11*

b^10*c^10*d^2 - 3520*a^12*b^9*c^9*d^3 + 7920*a^13*b^8*c^8*d^4 - 12672*a^14*b^7*c^7*d^5 + 14784*a^15*b^6*c^6*d^

6 - 12672*a^16*b^5*c^5*d^7 + 7920*a^17*b^4*c^4*d^8 - 3520*a^18*b^3*c^3*d^9 + 1056*a^19*b^2*c^2*d^10 - 192*a^20

*b*c*d^11))^(1/4) - 49036424112*a^16*b^13*c^3*d^14*x^(1/2)*(-b^17/(16*a^21*d^12 + 16*a^9*b^12*c^12 - 192*a^10*

b^11*c^11*d + 1056*a^11*b^10*c^10*d^2 - 3520*a^12*b^9*c^9*d^3 + 7920*a^13*b^8*c^8*d^4 - 12672*a^14*b^7*c^7*d^5

+ 14784*a^15*b^6*c^6*d^6 - 12672*a^16*b^5*c^5*d^7 + 7920*a^17*b^4*c^4*d^8 - 3520*a^18*b^3*c^3*d^9 + 1056*a^19

*b^2*c^2*d^10 - 192*a^20*b*c*d^11))^(1/4) + 18213050232*a^17*b^12*c^2*d^15*x^(1/2)*(-b^17/(16*a^21*d^12 + 16*a

^9*b^12*c^12 - 192*a^10*b^11*c^11*d + 1056*a^11*b^10*c^10*d^2 - 3520*a^12*b^9*c^9*d^3 + 7920*a^13*b^8*c^8*d^4

- 12672*a^14*b^7*c^7*d^5 + 14784*a^15*b^6*c^6*d^6 - 12672*a^16*b^5*c^5*d^7 + 7920*a^17*b^4*c^4*d^8 - 3520*a^18

*b^3*c^3*d^9 + 1056*a^19*b^2*c^2*d^10 - 192*a^20*b*c*d^11))^(1/4) + 2214592512*a^13*b^20*c^27*d^2*x^(1/2)*(-b^

17/(16*a^21*d^12 + 16*a^9*b^12*c^12 - 192*a^10*b^11*c^11*d + 1056*a^11*b^10*c^10*d^2 - 3520*a^12*b^9*c^9*d^3 +

7920*a^13*b^8*c^8*d^4 - 12672*a^14*b^7*c^7*d^5 + 14784*a^15*b^6*c^6*d^6 - 12672*a^16*b^5*c^5*d^7 + 7920*a^17*

b^4*c^4*d^8 - 3520*a^18*b^3*c^3*d^9 + 1056*a^19*b^2*c^2*d^10 - 192*a^20*b*c*d^11))^(5/4) - 7381975040*a^14*b^1

9*c^26*d^3*x^(1/2)*(-b^17/(16*a^21*d^12 + 16*a^9*b^12*c^12 - 192*a^10*b^11*c^11*d + 1056*a^11*b^10*c^10*d^2 -

3520*a^12*b^9*c^9*d^3 + 7920*a^13*b^8*c^8*d^4 - 12672*a^14*b^7*c^7*d^5 + 14784*a^15*b^6*c^6*d^6 - 12672*a^16*b

^5*c^5*d^7 + 7920*a^17*b^4*c^4*d^8 - 3520*a^18*b^3*c^3*d^9 + 1056*a^19*b^2*c^2*d^10 - 192*a^20*b*c*d^11))^(5/4

) + 16609443840*a^15*b^18*c^25*d^4*x^(1/2)*(-b^17/(16*a^21*d^12 + 16*a^9*b^12*c^12 - 192*a^10*b^11*c^11*d + 10

56*a^11*b^10*c^10*d^2 - 3520*a^12*b^9*c^9*d^3 + 7920*a^13*b^8*c^8*d^4 - 12672*a^14*b^7*c^7*d^5 + 14784*a^15*b^

6*c^6*d^6 - 12672*a^16*b^5*c^5*d^7 + 7920*a^17*b^4*c^4*d^8 - 3520*a^18*b^3*c^3*d^9 + 1056*a^19*b^2*c^2*d^10 -

192*a^20*b*c*d^11))^(5/4) - 26575110144*a^16*b^17*c^24*d^5*x^(1/2)*(-b^17/(16*a^21*d^12 + 16*a^9*b^12*c^12 - 1

92*a^10*b^11*c^11*d + 1056*a^11*b^10*c^10*d^2 - 3520*a^12*b^9*c^9*d^3 + 7920*a^13*b^8*c^8*d^4 - 12672*a^14*b^7

*c^7*d^5 + 14784*a^15*b^6*c^6*d^6 - 12672*a^16*b^5*c^5*d^7 + 7920*a^17*b^4*c^4*d^8 - 3520*a^18*b^3*c^3*d^9 + 1

056*a^19*b^2*c^2*d^10 - 192*a^20*b*c*d^11))^(5/4) + 32604717056*a^17*b^16*c^23*d^6*x^(1/2)*(-b^17/(16*a^21*d^1

2 + 16*a^9*b^12*c^12 - 192*a^10*b^11*c^11*d + 1056*a^11*b^10*c^10*d^2 - 3520*a^12*b^9*c^9*d^3 + 7920*a^13*b^8*

c^8*d^4 - 12672*a^14*b^7*c^7*d^5 + 14784*a^15*b^6*c^6*d^6 - 12672*a^16*b^5*c^5*d^7 + 7920*a^17*b^4*c^4*d^8 - 3

520*a^18*b^3*c^3*d^9 + 1056*a^19*b^2*c^2*d^10 - 192*a^20*b*c*d^11))^(5/4) - 50212110336*a^18*b^15*c^22*d^7*x^(

1/2)*(-b^17/(16*a^21*d^12 + 16*a^9*b^12*c^12 - 192*a^10*b^11*c^11*d + 1056*a^11*b^10*c^10*d^2 - 3520*a^12*b^9*

c^9*d^3 + 7920*a^13*b^8*c^8*d^4 - 12672*a^14*b^7*c^7*d^5 + 14784*a^15*b^6*c^6*d^6 - 12672*a^16*b^5*c^5*d^7 + 7

920*a^17*b^4*c^4*d^8 - 3520*a^18*b^3*c^3*d^9 + 1056*a^19*b^2*c^2*d^10 - 192*a^20*b*c*d^11))^(5/4) + 1801833676

80*a^19*b^14*c^21*d^8*x^(1/2)*(-b^17/(16*a^21*d^12 + 16*a^9*b^12*c^12 - 192*a^10*b^11*c^11*d + 1056*a^11*b^10*

c^10*d^2 - 3520*a^12*b^9*c^9*d^3 + 7920*a^13*b^8*c^8*d^4 - 12672*a^14*b^7*c^7*d^5 + 14784*a^15*b^6*c^6*d^6 - 1

2672*a^16*b^5*c^5*d^7 + 7920*a^17*b^4*c^4*d^8 - 3520*a^18*b^3*c^3*d^9 + 1056*a^19*b^2*c^2*d^10 - 192*a^20*b*c*

d^11))^(5/4) - 711482933248*a^20*b^13*c^20*d^9*x^(1/2)*(-b^17/(16*a^21*d^12 + 16*a^9*b^12*c^12 - 192*a^10*b^11

*c^11*d + 1056*a^11*b^10*c^10*d^2 - 3520*a^12*b^9*c^9*d^3 + 7920*a^13*b^8*c^8*d^4 - 12672*a^14*b^7*c^7*d^5 + 1

4784*a^15*b^6*c^6*d^6 - 12672*a^16*b^5*c^5*d^7 + 7920*a^17*b^4*c^4*d^8 - 3520*a^18*b^3*c^3*d^9 + 1056*a^19*b^2

*c^2*d^10 - 192*a^20*b*c*d^11))^(5/4) + 2112400785408*a^21*b^12*c^19*d^10*x^(1/2)*(-b^17/(16*a^21*d^12 + 16*a^

9*b^12*c^12 - 192*a^10*b^11*c^11*d + 1056*a^11*b^10*c^10*d^2 - 3520*a^12*b^9*c^9*d^3 + 7920*a^13*b^8*c^8*d^4 -

12672*a^14*b^7*c^7*d^5 + 14784*a^15*b^6*c^6*d^6 - 12672*a^16*b^5*c^5*d^7 + 7920*a^17*b^4*c^4*d^8 - 3520*a^18*

b^3*c^3*d^9 + 1056*a^19*b^2*c^2*d^10 - 192*a^20*b*c*d^11))^(5/4) - 4669808050176*a^22*b^11*c^18*d^11*x^(1/2)*(

-b^17/(16*a^21*d^12 + 16*a^9*b^12*c^12 - 192*a^10*b^11*c^11*d + 1056*a^11*b^10*c^10*d^2 - 3520*a^12*b^9*c^9*d^

3 + 7920*a^13*b^8*c^8*d^4 - 12672*a^14*b^7*c^7*d^5 + 14784*a^15*b^6*c^6*d^6 - 12672*a^16*b^5*c^5*d^7 + 7920*a^

17*b^4*c^4*d^8 - 3520*a^18*b^3*c^3*d^9 + 1056*a^19*b^2*c^2*d^10 - 192*a^20*b*c*d^11))^(5/4) + 7892313571328*a^

23*b^10*c^17*d^12*x^(1/2)*(-b^17/(16*a^21*d^12 + 16*a^9*b^12*c^12 - 192*a^10*b^11*c^11*d + 1056*a^11*b^10*c^10

*d^2 - 3520*a^12*b^9*c^9*d^3 + 7920*a^13*b^8*c^8*d^4 - 12672*a^14*b^7*c^7*d^5 + 14784*a^15*b^6*c^6*d^6 - 12672

*a^16*b^5*c^5*d^7 + 7920*a^17*b^4*c^4*d^8 - 3520*a^18*b^3*c^3*d^9 + 1056*a^19*b^2*c^2*d^10 - 192*a^20*b*c*d^11

))^(5/4) - 10394916618240*a^24*b^9*c^16*d^13*x^(1/2)*(-b^17/(16*a^21*d^12 + 16*a^9*b^12*c^12 - 192*a^10*b^11*c

^11*d + 1056*a^11*b^10*c^10*d^2 - 3520*a^12*b^9*c^9*d^3 + 7920*a^13*b^8*c^8*d^4 - 12672*a^14*b^7*c^7*d^5 + 147

84*a^15*b^6*c^6*d^6 - 12672*a^16*b^5*c^5*d^7 + 7920*a^17*b^4*c^4*d^8 - 3520*a^18*b^3*c^3*d^9 + 1056*a^19*b^2*c

^2*d^10 - 192*a^20*b*c*d^11))^(5/4) + 10783480283136*a^25*b^8*c^15*d^14*x^(1/2)*(-b^17/(16*a^21*d^12 + 16*a^9*

b^12*c^12 - 192*a^10*b^11*c^11*d + 1056*a^11*b^10*c^10*d^2 - 3520*a^12*b^9*c^9*d^3 + 7920*a^13*b^8*c^8*d^4 - 1

2672*a^14*b^7*c^7*d^5 + 14784*a^15*b^6*c^6*d^6 - 12672*a^16*b^5*c^5*d^7 + 7920*a^17*b^4*c^4*d^8 - 3520*a^18*b^

3*c^3*d^9 + 1056*a^19*b^2*c^2*d^10 - 192*a^20*b*c*d^11))^(5/4) - 8841322299392*a^26*b^7*c^14*d^15*x^(1/2)*(-b^

17/(16*a^21*d^12 + 16*a^9*b^12*c^12 - 192*a^10*b^11*c^11*d + 1056*a^11*b^10*c^10*d^2 - 3520*a^12*b^9*c^9*d^3 +

7920*a^13*b^8*c^8*d^4 - 12672*a^14*b^7*c^7*d^5 + 14784*a^15*b^6*c^6*d^6 - 12672*a^16*b^5*c^5*d^7 + 7920*a^17*

b^4*c^4*d^8 - 3520*a^18*b^3*c^3*d^9 + 1056*a^19*b^2*c^2*d^10 - 192*a^20*b*c*d^11))^(5/4) + 5711010201600*a^27*

b^6*c^13*d^16*x^(1/2)*(-b^17/(16*a^21*d^12 + 16*a^9*b^12*c^12 - 192*a^10*b^11*c^11*d + 1056*a^11*b^10*c^10*d^2

- 3520*a^12*b^9*c^9*d^3 + 7920*a^13*b^8*c^8*d^4 - 12672*a^14*b^7*c^7*d^5 + 14784*a^15*b^6*c^6*d^6 - 12672*a^1

6*b^5*c^5*d^7 + 7920*a^17*b^4*c^4*d^8 - 3520*a^18*b^3*c^3*d^9 + 1056*a^19*b^2*c^2*d^10 - 192*a^20*b*c*d^11))^(

5/4) - 2876224045056*a^28*b^5*c^12*d^17*x^(1/2)*(-b^17/(16*a^21*d^12 + 16*a^9*b^12*c^12 - 192*a^10*b^11*c^11*d

+ 1056*a^11*b^10*c^10*d^2 - 3520*a^12*b^9*c^9*d^3 + 7920*a^13*b^8*c^8*d^4 - 12672*a^14*b^7*c^7*d^5 + 14784*a^

15*b^6*c^6*d^6 - 12672*a^16*b^5*c^5*d^7 + 7920*a^17*b^4*c^4*d^8 - 3520*a^18*b^3*c^3*d^9 + 1056*a^19*b^2*c^2*d^

10 - 192*a^20*b*c*d^11))^(5/4) + 1107358515200*a^29*b^4*c^11*d^18*x^(1/2)*(-b^17/(16*a^21*d^12 + 16*a^9*b^12*c

^12 - 192*a^10*b^11*c^11*d + 1056*a^11*b^10*c^10*d^2 - 3520*a^12*b^9*c^9*d^3 + 7920*a^13*b^8*c^8*d^4 - 12672*a

^14*b^7*c^7*d^5 + 14784*a^15*b^6*c^6*d^6 - 12672*a^16*b^5*c^5*d^7 + 7920*a^17*b^4*c^4*d^8 - 3520*a^18*b^3*c^3*

d^9 + 1056*a^19*b^2*c^2*d^10 - 192*a^20*b*c*d^11))^(5/4) - 315126448128*a^30*b^3*c^10*d^19*x^(1/2)*(-b^17/(16*

a^21*d^12 + 16*a^9*b^12*c^12 - 192*a^10*b^11*c^11*d + 1056*a^11*b^10*c^10*d^2 - 3520*a^12*b^9*c^9*d^3 + 7920*a

^13*b^8*c^8*d^4 - 12672*a^14*b^7*c^7*d^5 + 14784*a^15*b^6*c^6*d^6 - 12672*a^16*b^5*c^5*d^7 + 7920*a^17*b^4*c^4

*d^8 - 3520*a^18*b^3*c^3*d^9 + 1056*a^19*b^2*c^2*d^10 - 192*a^20*b*c*d^11))^(5/4) + 62523703296*a^31*b^2*c^9*d

^20*x^(1/2)*(-b^17/(16*a^21*d^12 + 16*a^9*b^12*c^12 - 192*a^10*b^11*c^11*d + 1056*a^11*b^10*c^10*d^2 - 3520*a^

12*b^9*c^9*d^3 + 7920*a^13*b^8*c^8*d^4 - 12672*a^14*b^7*c^7*d^5 + 14784*a^15*b^6*c^6*d^6 - 12672*a^16*b^5*c^5*

d^7 + 7920*a^17*b^4*c^4*d^8 - 3520*a^18*b^3*c^3*d^9 + 1056*a^19*b^2*c^2*d^10 - 192*a^20*b*c*d^11))^(5/4) - 392

0748624*a^18*b^11*c*d^16*x^(1/2)*(-b^17/(16*a^21*d^12 + 16*a^9*b^12*c^12 - 192*a^10*b^11*c^11*d + 1056*a^11*b^

10*c^10*d^2 - 3520*a^12*b^9*c^9*d^3 + 7920*a^13*b^8*c^8*d^4 - 12672*a^14*b^7*c^7*d^5 + 14784*a^15*b^6*c^6*d^6

- 12672*a^16*b^5*c^5*d^7 + 7920*a^17*b^4*c^4*d^8 - 3520*a^18*b^3*c^3*d^9 + 1056*a^19*b^2*c^2*d^10 - 192*a^20*b

*c*d^11))^(1/4) - 402653184*a^12*b^21*c^28*d*x^(1/2)*(-b^17/(16*a^21*d^12 + 16*a^9*b^12*c^12 - 192*a^10*b^11*c

^11*d + 1056*a^11*b^10*c^10*d^2 - 3520*a^12*b^9*c^9*d^3 + 7920*a^13*b^8*c^8*d^4 - 12672*a^14*b^7*c^7*d^5 + 147

84*a^15*b^6*c^6*d^6 - 12672*a^16*b^5*c^5*d^7 + 7920*a^17*b^4*c^4*d^8 - 3520*a^18*b^3*c^3*d^9 + 1056*a^19*b^2*c

^2*d^10 - 192*a^20*b*c*d^11))^(5/4) - 7729053696*a^32*b*c^8*d^21*x^(1/2)*(-b^17/(16*a^21*d^12 + 16*a^9*b^12*c^

12 - 192*a^10*b^11*c^11*d + 1056*a^11*b^10*c^10*d^2 - 3520*a^12*b^9*c^9*d^3 + 7920*a^13*b^8*c^8*d^4 - 12672*a^

14*b^7*c^7*d^5 + 14784*a^15*b^6*c^6*d^6 - 12672*a^16*b^5*c^5*d^7 + 7920*a^17*b^4*c^4*d^8 - 3520*a^18*b^3*c^3*d

^9 + 1056*a^19*b^2*c^2*d^10 - 192*a^20*b*c*d^11))^(5/4))/(1048576*b^28*c^14 + 187388721*a^14*b^14*d^14 - 13982

08149*a^13*b^15*c*d^13 + 6291456*a^2*b^26*c^12*d^2 + 10485760*a^3*b^25*c^11*d^3 + 15728640*a^4*b^24*c^10*d^4 +

22020096*a^5*b^23*c^9*d^5 + 29360128*a^6*b^22*c^8*d^6 + 37748736*a^7*b^21*c^7*d^7 + 47185920*a^8*b^20*c^6*d^8

- 2327771601*a^9*b^19*c^5*d^9 + 6124562037*a^10*b^18*c^4*d^10 - 7086995370*a^11*b^17*c^3*d^11 + 4349734506*a^

12*b^16*c^2*d^12 + 3145728*a*b^27*c^13*d))*(-b^17/(16*a^21*d^12 + 16*a^9*b^12*c^12 - 192*a^10*b^11*c^11*d + 10

56*a^11*b^10*c^10*d^2 - 3520*a^12*b^9*c^9*d^3 + 7920*a^13*b^8*c^8*d^4 - 12672*a^14*b^7*c^7*d^5 + 14784*a^15*b^

6*c^6*d^6 - 12672*a^16*b^5*c^5*d^7 + 7920*a^17*b^4*c^4*d^8 - 3520*a^18*b^3*c^3*d^9 + 1056*a^19*b^2*c^2*d^10 -

192*a^20*b*c*d^11))^(1/4)

________________________________________________________________________________________

sympy [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \[ \text {Timed out} \]

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x**(7/2)/(b*x**2+a)/(d*x**2+c)**3,x)

[Out]

Timed out

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