3.2179 \(\int \frac {1}{(1-2 x)^{5/2} (2+3 x)^4 (3+5 x)} \, dx\)
Optimal. Leaf size=145 \[ -\frac {446660}{290521 \sqrt {1-2 x}}+\frac {582}{49 (1-2 x)^{3/2} (3 x+2)}-\frac {39520}{11319 (1-2 x)^{3/2}}+\frac {57}{49 (1-2 x)^{3/2} (3 x+2)^2}+\frac {1}{7 (1-2 x)^{3/2} (3 x+2)^3}+\frac {127710 \sqrt {\frac {3}{7}} \tanh ^{-1}\left (\sqrt {\frac {3}{7}} \sqrt {1-2 x}\right )}{2401}-\frac {6250}{121} \sqrt {\frac {5}{11}} \tanh ^{-1}\left (\sqrt {\frac {5}{11}} \sqrt {1-2 x}\right ) \]
[Out]
-39520/11319/(1-2*x)^(3/2)+1/7/(1-2*x)^(3/2)/(2+3*x)^3+57/49/(1-2*x)^(3/2)/(2+3*x)^2+582/49/(1-2*x)^(3/2)/(2+3
*x)+127710/16807*arctanh(1/7*21^(1/2)*(1-2*x)^(1/2))*21^(1/2)-6250/1331*arctanh(1/11*55^(1/2)*(1-2*x)^(1/2))*5
5^(1/2)-446660/290521/(1-2*x)^(1/2)
________________________________________________________________________________________
Rubi [A] time = 0.07, antiderivative size = 145, normalized size of antiderivative = 1.00,
number of steps used = 10, number of rules used = 6, integrand size = 24, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.250, Rules used
= {103, 151, 152, 156, 63, 206} \[ -\frac {446660}{290521 \sqrt {1-2 x}}+\frac {582}{49 (1-2 x)^{3/2} (3 x+2)}-\frac {39520}{11319 (1-2 x)^{3/2}}+\frac {57}{49 (1-2 x)^{3/2} (3 x+2)^2}+\frac {1}{7 (1-2 x)^{3/2} (3 x+2)^3}+\frac {127710 \sqrt {\frac {3}{7}} \tanh ^{-1}\left (\sqrt {\frac {3}{7}} \sqrt {1-2 x}\right )}{2401}-\frac {6250}{121} \sqrt {\frac {5}{11}} \tanh ^{-1}\left (\sqrt {\frac {5}{11}} \sqrt {1-2 x}\right ) \]
Antiderivative was successfully verified.
[In]
Int[1/((1 - 2*x)^(5/2)*(2 + 3*x)^4*(3 + 5*x)),x]
[Out]
-39520/(11319*(1 - 2*x)^(3/2)) - 446660/(290521*Sqrt[1 - 2*x]) + 1/(7*(1 - 2*x)^(3/2)*(2 + 3*x)^3) + 57/(49*(1
- 2*x)^(3/2)*(2 + 3*x)^2) + 582/(49*(1 - 2*x)^(3/2)*(2 + 3*x)) + (127710*Sqrt[3/7]*ArcTanh[Sqrt[3/7]*Sqrt[1 -
2*x]])/2401 - (6250*Sqrt[5/11]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/121
Rule 63
Int[((a_.) + (b_.)*(x_))^(m_)*((c_.) + (d_.)*(x_))^(n_), x_Symbol] :> With[{p = Denominator[m]}, Dist[p/b, Sub
st[Int[x^(p*(m + 1) - 1)*(c - (a*d)/b + (d*x^p)/b)^n, x], x, (a + b*x)^(1/p)], x]] /; FreeQ[{a, b, c, d}, x] &
& NeQ[b*c - a*d, 0] && LtQ[-1, m, 0] && LeQ[-1, n, 0] && LeQ[Denominator[n], Denominator[m]] && IntLinearQ[a,
b, c, d, m, n, x]
Rule 103
Int[((a_.) + (b_.)*(x_))^(m_)*((c_.) + (d_.)*(x_))^(n_.)*((e_.) + (f_.)*(x_))^(p_.), x_Symbol] :> Simp[(b*(a +
b*x)^(m + 1)*(c + d*x)^(n + 1)*(e + f*x)^(p + 1))/((m + 1)*(b*c - a*d)*(b*e - a*f)), x] + Dist[1/((m + 1)*(b*
c - a*d)*(b*e - a*f)), Int[(a + b*x)^(m + 1)*(c + d*x)^n*(e + f*x)^p*Simp[a*d*f*(m + 1) - b*(d*e*(m + n + 2) +
c*f*(m + p + 2)) - b*d*f*(m + n + p + 3)*x, x], x], x] /; FreeQ[{a, b, c, d, e, f, n, p}, x] && LtQ[m, -1] &&
IntegerQ[m] && (IntegerQ[n] || IntegersQ[2*n, 2*p])
Rule 151
Int[((a_.) + (b_.)*(x_))^(m_)*((c_.) + (d_.)*(x_))^(n_)*((e_.) + (f_.)*(x_))^(p_)*((g_.) + (h_.)*(x_)), x_Symb
ol] :> Simp[((b*g - a*h)*(a + b*x)^(m + 1)*(c + d*x)^(n + 1)*(e + f*x)^(p + 1))/((m + 1)*(b*c - a*d)*(b*e - a*
f)), x] + Dist[1/((m + 1)*(b*c - a*d)*(b*e - a*f)), Int[(a + b*x)^(m + 1)*(c + d*x)^n*(e + f*x)^p*Simp[(a*d*f*
g - b*(d*e + c*f)*g + b*c*e*h)*(m + 1) - (b*g - a*h)*(d*e*(n + 1) + c*f*(p + 1)) - d*f*(b*g - a*h)*(m + n + p
+ 3)*x, x], x], x] /; FreeQ[{a, b, c, d, e, f, g, h, n, p}, x] && LtQ[m, -1] && IntegerQ[m]
Rule 152
Int[((a_.) + (b_.)*(x_))^(m_)*((c_.) + (d_.)*(x_))^(n_)*((e_.) + (f_.)*(x_))^(p_)*((g_.) + (h_.)*(x_)), x_Symb
ol] :> Simp[((b*g - a*h)*(a + b*x)^(m + 1)*(c + d*x)^(n + 1)*(e + f*x)^(p + 1))/((m + 1)*(b*c - a*d)*(b*e - a*
f)), x] + Dist[1/((m + 1)*(b*c - a*d)*(b*e - a*f)), Int[(a + b*x)^(m + 1)*(c + d*x)^n*(e + f*x)^p*Simp[(a*d*f*
g - b*(d*e + c*f)*g + b*c*e*h)*(m + 1) - (b*g - a*h)*(d*e*(n + 1) + c*f*(p + 1)) - d*f*(b*g - a*h)*(m + n + p
+ 3)*x, x], x], x] /; FreeQ[{a, b, c, d, e, f, g, h, n, p}, x] && LtQ[m, -1] && IntegersQ[2*m, 2*n, 2*p]
Rule 156
Int[(((e_.) + (f_.)*(x_))^(p_)*((g_.) + (h_.)*(x_)))/(((a_.) + (b_.)*(x_))*((c_.) + (d_.)*(x_))), x_Symbol] :>
Dist[(b*g - a*h)/(b*c - a*d), Int[(e + f*x)^p/(a + b*x), x], x] - Dist[(d*g - c*h)/(b*c - a*d), Int[(e + f*x)
^p/(c + d*x), x], x] /; FreeQ[{a, b, c, d, e, f, g, h}, x]
Rule 206
Int[((a_) + (b_.)*(x_)^2)^(-1), x_Symbol] :> Simp[(1*ArcTanh[(Rt[-b, 2]*x)/Rt[a, 2]])/(Rt[a, 2]*Rt[-b, 2]), x]
/; FreeQ[{a, b}, x] && NegQ[a/b] && (GtQ[a, 0] || LtQ[b, 0])
Rubi steps
\begin {align*} \int \frac {1}{(1-2 x)^{5/2} (2+3 x)^4 (3+5 x)} \, dx &=\frac {1}{7 (1-2 x)^{3/2} (2+3 x)^3}+\frac {1}{21} \int \frac {24-135 x}{(1-2 x)^{5/2} (2+3 x)^3 (3+5 x)} \, dx\\ &=\frac {1}{7 (1-2 x)^{3/2} (2+3 x)^3}+\frac {57}{49 (1-2 x)^{3/2} (2+3 x)^2}+\frac {1}{294} \int \frac {168-11970 x}{(1-2 x)^{5/2} (2+3 x)^2 (3+5 x)} \, dx\\ &=\frac {1}{7 (1-2 x)^{3/2} (2+3 x)^3}+\frac {57}{49 (1-2 x)^{3/2} (2+3 x)^2}+\frac {582}{49 (1-2 x)^{3/2} (2+3 x)}+\frac {\int \frac {-109410-611100 x}{(1-2 x)^{5/2} (2+3 x) (3+5 x)} \, dx}{2058}\\ &=-\frac {39520}{11319 (1-2 x)^{3/2}}+\frac {1}{7 (1-2 x)^{3/2} (2+3 x)^3}+\frac {57}{49 (1-2 x)^{3/2} (2+3 x)^2}+\frac {582}{49 (1-2 x)^{3/2} (2+3 x)}-\frac {\int \frac {-2301705+18673200 x}{(1-2 x)^{3/2} (2+3 x) (3+5 x)} \, dx}{237699}\\ &=-\frac {39520}{11319 (1-2 x)^{3/2}}-\frac {446660}{290521 \sqrt {1-2 x}}+\frac {1}{7 (1-2 x)^{3/2} (2+3 x)^3}+\frac {57}{49 (1-2 x)^{3/2} (2+3 x)^2}+\frac {582}{49 (1-2 x)^{3/2} (2+3 x)}+\frac {2 \int \frac {\frac {346068765}{2}-105523425 x}{\sqrt {1-2 x} (2+3 x) (3+5 x)} \, dx}{18302823}\\ &=-\frac {39520}{11319 (1-2 x)^{3/2}}-\frac {446660}{290521 \sqrt {1-2 x}}+\frac {1}{7 (1-2 x)^{3/2} (2+3 x)^3}+\frac {57}{49 (1-2 x)^{3/2} (2+3 x)^2}+\frac {582}{49 (1-2 x)^{3/2} (2+3 x)}-\frac {191565 \int \frac {1}{\sqrt {1-2 x} (2+3 x)} \, dx}{2401}+\frac {15625}{121} \int \frac {1}{\sqrt {1-2 x} (3+5 x)} \, dx\\ &=-\frac {39520}{11319 (1-2 x)^{3/2}}-\frac {446660}{290521 \sqrt {1-2 x}}+\frac {1}{7 (1-2 x)^{3/2} (2+3 x)^3}+\frac {57}{49 (1-2 x)^{3/2} (2+3 x)^2}+\frac {582}{49 (1-2 x)^{3/2} (2+3 x)}+\frac {191565 \operatorname {Subst}\left (\int \frac {1}{\frac {7}{2}-\frac {3 x^2}{2}} \, dx,x,\sqrt {1-2 x}\right )}{2401}-\frac {15625}{121} \operatorname {Subst}\left (\int \frac {1}{\frac {11}{2}-\frac {5 x^2}{2}} \, dx,x,\sqrt {1-2 x}\right )\\ &=-\frac {39520}{11319 (1-2 x)^{3/2}}-\frac {446660}{290521 \sqrt {1-2 x}}+\frac {1}{7 (1-2 x)^{3/2} (2+3 x)^3}+\frac {57}{49 (1-2 x)^{3/2} (2+3 x)^2}+\frac {582}{49 (1-2 x)^{3/2} (2+3 x)}+\frac {127710 \sqrt {\frac {3}{7}} \tanh ^{-1}\left (\sqrt {\frac {3}{7}} \sqrt {1-2 x}\right )}{2401}-\frac {6250}{121} \sqrt {\frac {5}{11}} \tanh ^{-1}\left (\sqrt {\frac {5}{11}} \sqrt {1-2 x}\right )\\ \end {align*}
________________________________________________________________________________________
Mathematica [C] time = 0.08, size = 71, normalized size = 0.49 \[ \frac {-468270 \, _2F_1\left (-\frac {3}{2},1;-\frac {1}{2};\frac {3}{7}-\frac {6 x}{7}\right )+428750 \, _2F_1\left (-\frac {3}{2},1;-\frac {1}{2};-\frac {5}{11} (2 x-1)\right )+\frac {231 \left (5238 x^2+7155 x+2449\right )}{(3 x+2)^3}}{11319 (1-2 x)^{3/2}} \]
Antiderivative was successfully verified.
[In]
Integrate[1/((1 - 2*x)^(5/2)*(2 + 3*x)^4*(3 + 5*x)),x]
[Out]
((231*(2449 + 7155*x + 5238*x^2))/(2 + 3*x)^3 - 468270*Hypergeometric2F1[-3/2, 1, -1/2, 3/7 - (6*x)/7] + 42875
0*Hypergeometric2F1[-3/2, 1, -1/2, (-5*(-1 + 2*x))/11])/(11319*(1 - 2*x)^(3/2))
________________________________________________________________________________________
fricas [A] time = 1.00, size = 182, normalized size = 1.26 \[ \frac {157565625 \, \sqrt {11} \sqrt {5} {\left (108 \, x^{5} + 108 \, x^{4} - 45 \, x^{3} - 58 \, x^{2} + 4 \, x + 8\right )} \log \left (\frac {\sqrt {11} \sqrt {5} \sqrt {-2 \, x + 1} + 5 \, x - 8}{5 \, x + 3}\right ) + 254973015 \, \sqrt {7} \sqrt {3} {\left (108 \, x^{5} + 108 \, x^{4} - 45 \, x^{3} - 58 \, x^{2} + 4 \, x + 8\right )} \log \left (-\frac {\sqrt {7} \sqrt {3} \sqrt {-2 \, x + 1} - 3 \, x + 5}{3 \, x + 2}\right ) + 77 \, {\left (72358920 \, x^{4} + 26376300 \, x^{3} - 47036214 \, x^{2} - 9083055 \, x + 8496203\right )} \sqrt {-2 \, x + 1}}{67110351 \, {\left (108 \, x^{5} + 108 \, x^{4} - 45 \, x^{3} - 58 \, x^{2} + 4 \, x + 8\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(1/(1-2*x)^(5/2)/(2+3*x)^4/(3+5*x),x, algorithm="fricas")
[Out]
1/67110351*(157565625*sqrt(11)*sqrt(5)*(108*x^5 + 108*x^4 - 45*x^3 - 58*x^2 + 4*x + 8)*log((sqrt(11)*sqrt(5)*s
qrt(-2*x + 1) + 5*x - 8)/(5*x + 3)) + 254973015*sqrt(7)*sqrt(3)*(108*x^5 + 108*x^4 - 45*x^3 - 58*x^2 + 4*x + 8
)*log(-(sqrt(7)*sqrt(3)*sqrt(-2*x + 1) - 3*x + 5)/(3*x + 2)) + 77*(72358920*x^4 + 26376300*x^3 - 47036214*x^2
- 9083055*x + 8496203)*sqrt(-2*x + 1))/(108*x^5 + 108*x^4 - 45*x^3 - 58*x^2 + 4*x + 8)
________________________________________________________________________________________
giac [A] time = 1.22, size = 134, normalized size = 0.92 \[ \frac {3125}{1331} \, \sqrt {55} \log \left (\frac {{\left | -2 \, \sqrt {55} + 10 \, \sqrt {-2 \, x + 1} \right |}}{2 \, {\left (\sqrt {55} + 5 \, \sqrt {-2 \, x + 1}\right )}}\right ) - \frac {63855}{16807} \, \sqrt {21} \log \left (\frac {{\left | -2 \, \sqrt {21} + 6 \, \sqrt {-2 \, x + 1} \right |}}{2 \, {\left (\sqrt {21} + 3 \, \sqrt {-2 \, x + 1}\right )}}\right ) - \frac {4 \, {\left (9044865 \, {\left (2 \, x - 1\right )}^{4} + 42773535 \, {\left (2 \, x - 1\right )}^{3} + 50533308 \, {\left (2 \, x - 1\right )}^{2} - 315168 \, x + 187768\right )}}{871563 \, {\left (3 \, {\left (-2 \, x + 1\right )}^{\frac {3}{2}} - 7 \, \sqrt {-2 \, x + 1}\right )}^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(1/(1-2*x)^(5/2)/(2+3*x)^4/(3+5*x),x, algorithm="giac")
[Out]
3125/1331*sqrt(55)*log(1/2*abs(-2*sqrt(55) + 10*sqrt(-2*x + 1))/(sqrt(55) + 5*sqrt(-2*x + 1))) - 63855/16807*s
qrt(21)*log(1/2*abs(-2*sqrt(21) + 6*sqrt(-2*x + 1))/(sqrt(21) + 3*sqrt(-2*x + 1))) - 4/871563*(9044865*(2*x -
1)^4 + 42773535*(2*x - 1)^3 + 50533308*(2*x - 1)^2 - 315168*x + 187768)/(3*(-2*x + 1)^(3/2) - 7*sqrt(-2*x + 1)
)^3
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maple [A] time = 0.02, size = 93, normalized size = 0.64 \[ \frac {127710 \sqrt {21}\, \arctanh \left (\frac {\sqrt {21}\, \sqrt {-2 x +1}}{7}\right )}{16807}-\frac {6250 \sqrt {55}\, \arctanh \left (\frac {\sqrt {55}\, \sqrt {-2 x +1}}{11}\right )}{1331}+\frac {32}{79233 \left (-2 x +1\right )^{\frac {3}{2}}}+\frac {5344}{2033647 \sqrt {-2 x +1}}-\frac {1458 \left (\frac {1438 \left (-2 x +1\right )^{\frac {5}{2}}}{3}-\frac {61250 \left (-2 x +1\right )^{\frac {3}{2}}}{27}+\frac {72520 \sqrt {-2 x +1}}{27}\right )}{16807 \left (-6 x -4\right )^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
int(1/(-2*x+1)^(5/2)/(3*x+2)^4/(5*x+3),x)
[Out]
32/79233/(-2*x+1)^(3/2)+5344/2033647/(-2*x+1)^(1/2)-6250/1331*arctanh(1/11*55^(1/2)*(-2*x+1)^(1/2))*55^(1/2)-1
458/16807*(1438/3*(-2*x+1)^(5/2)-61250/27*(-2*x+1)^(3/2)+72520/27*(-2*x+1)^(1/2))/(-6*x-4)^3+127710/16807*arct
anh(1/7*21^(1/2)*(-2*x+1)^(1/2))*21^(1/2)
________________________________________________________________________________________
maxima [A] time = 1.16, size = 146, normalized size = 1.01 \[ \frac {3125}{1331} \, \sqrt {55} \log \left (-\frac {\sqrt {55} - 5 \, \sqrt {-2 \, x + 1}}{\sqrt {55} + 5 \, \sqrt {-2 \, x + 1}}\right ) - \frac {63855}{16807} \, \sqrt {21} \log \left (-\frac {\sqrt {21} - 3 \, \sqrt {-2 \, x + 1}}{\sqrt {21} + 3 \, \sqrt {-2 \, x + 1}}\right ) - \frac {4 \, {\left (9044865 \, {\left (2 \, x - 1\right )}^{4} + 42773535 \, {\left (2 \, x - 1\right )}^{3} + 50533308 \, {\left (2 \, x - 1\right )}^{2} - 315168 \, x + 187768\right )}}{871563 \, {\left (27 \, {\left (-2 \, x + 1\right )}^{\frac {9}{2}} - 189 \, {\left (-2 \, x + 1\right )}^{\frac {7}{2}} + 441 \, {\left (-2 \, x + 1\right )}^{\frac {5}{2}} - 343 \, {\left (-2 \, x + 1\right )}^{\frac {3}{2}}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(1/(1-2*x)^(5/2)/(2+3*x)^4/(3+5*x),x, algorithm="maxima")
[Out]
3125/1331*sqrt(55)*log(-(sqrt(55) - 5*sqrt(-2*x + 1))/(sqrt(55) + 5*sqrt(-2*x + 1))) - 63855/16807*sqrt(21)*lo
g(-(sqrt(21) - 3*sqrt(-2*x + 1))/(sqrt(21) + 3*sqrt(-2*x + 1))) - 4/871563*(9044865*(2*x - 1)^4 + 42773535*(2*
x - 1)^3 + 50533308*(2*x - 1)^2 - 315168*x + 187768)/(27*(-2*x + 1)^(9/2) - 189*(-2*x + 1)^(7/2) + 441*(-2*x +
1)^(5/2) - 343*(-2*x + 1)^(3/2))
________________________________________________________________________________________
mupad [B] time = 1.23, size = 109, normalized size = 0.75 \[ \frac {\frac {50928\,{\left (2\,x-1\right )}^2}{5929}-\frac {8576\,x}{160083}+\frac {905260\,{\left (2\,x-1\right )}^3}{124509}+\frac {446660\,{\left (2\,x-1\right )}^4}{290521}+\frac {15328}{480249}}{\frac {343\,{\left (1-2\,x\right )}^{3/2}}{27}-\frac {49\,{\left (1-2\,x\right )}^{5/2}}{3}+7\,{\left (1-2\,x\right )}^{7/2}-{\left (1-2\,x\right )}^{9/2}}+\frac {127710\,\sqrt {21}\,\mathrm {atanh}\left (\frac {\sqrt {21}\,\sqrt {1-2\,x}}{7}\right )}{16807}-\frac {6250\,\sqrt {55}\,\mathrm {atanh}\left (\frac {\sqrt {55}\,\sqrt {1-2\,x}}{11}\right )}{1331} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
int(1/((1 - 2*x)^(5/2)*(3*x + 2)^4*(5*x + 3)),x)
[Out]
((50928*(2*x - 1)^2)/5929 - (8576*x)/160083 + (905260*(2*x - 1)^3)/124509 + (446660*(2*x - 1)^4)/290521 + 1532
8/480249)/((343*(1 - 2*x)^(3/2))/27 - (49*(1 - 2*x)^(5/2))/3 + 7*(1 - 2*x)^(7/2) - (1 - 2*x)^(9/2)) + (127710*
21^(1/2)*atanh((21^(1/2)*(1 - 2*x)^(1/2))/7))/16807 - (6250*55^(1/2)*atanh((55^(1/2)*(1 - 2*x)^(1/2))/11))/133
1
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sympy [C] time = 29.35, size = 5593, normalized size = 38.57 \[ \text {result too large to display} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(1/(1-2*x)**(5/2)/(2+3*x)**4/(3+5*x),x)
[Out]
-519900576814080*sqrt(2)*I*(x - 1/2)**(23/2)/(-676317715831296*(x - 1/2)**12 - 7101336016228608*(x - 1/2)**11
- 33139568075733504*(x - 1/2)**10 - 90213268650607872*(x - 1/2)**9 - 157873220138563776*(x - 1/2)**8 - 1841854
23494991072*(x - 1/2)**7 - 143255329384993056*(x - 1/2)**6 - 71627664692496528*(x - 1/2)**5 - 2089140220197815
4*(x - 1/2)**4 - 2708144729886057*(x - 1/2)**3) - 4868619539857920*sqrt(2)*I*(x - 1/2)**(21/2)/(-6763177158312
96*(x - 1/2)**12 - 7101336016228608*(x - 1/2)**11 - 33139568075733504*(x - 1/2)**10 - 90213268650607872*(x - 1
/2)**9 - 157873220138563776*(x - 1/2)**8 - 184185423494991072*(x - 1/2)**7 - 143255329384993056*(x - 1/2)**6 -
71627664692496528*(x - 1/2)**5 - 20891402201978154*(x - 1/2)**4 - 2708144729886057*(x - 1/2)**3) - 1994601135
3295104*sqrt(2)*I*(x - 1/2)**(19/2)/(-676317715831296*(x - 1/2)**12 - 7101336016228608*(x - 1/2)**11 - 3313956
8075733504*(x - 1/2)**10 - 90213268650607872*(x - 1/2)**9 - 157873220138563776*(x - 1/2)**8 - 1841854234949910
72*(x - 1/2)**7 - 143255329384993056*(x - 1/2)**6 - 71627664692496528*(x - 1/2)**5 - 20891402201978154*(x - 1/
2)**4 - 2708144729886057*(x - 1/2)**3) - 46692212229919872*sqrt(2)*I*(x - 1/2)**(17/2)/(-676317715831296*(x -
1/2)**12 - 7101336016228608*(x - 1/2)**11 - 33139568075733504*(x - 1/2)**10 - 90213268650607872*(x - 1/2)**9 -
157873220138563776*(x - 1/2)**8 - 184185423494991072*(x - 1/2)**7 - 143255329384993056*(x - 1/2)**6 - 7162766
4692496528*(x - 1/2)**5 - 20891402201978154*(x - 1/2)**4 - 2708144729886057*(x - 1/2)**3) - 68307922947692736*
sqrt(2)*I*(x - 1/2)**(15/2)/(-676317715831296*(x - 1/2)**12 - 7101336016228608*(x - 1/2)**11 - 331395680757335
04*(x - 1/2)**10 - 90213268650607872*(x - 1/2)**9 - 157873220138563776*(x - 1/2)**8 - 184185423494991072*(x -
1/2)**7 - 143255329384993056*(x - 1/2)**6 - 71627664692496528*(x - 1/2)**5 - 20891402201978154*(x - 1/2)**4 -
2708144729886057*(x - 1/2)**3) - 63944279656953696*sqrt(2)*I*(x - 1/2)**(13/2)/(-676317715831296*(x - 1/2)**12
- 7101336016228608*(x - 1/2)**11 - 33139568075733504*(x - 1/2)**10 - 90213268650607872*(x - 1/2)**9 - 1578732
20138563776*(x - 1/2)**8 - 184185423494991072*(x - 1/2)**7 - 143255329384993056*(x - 1/2)**6 - 716276646924965
28*(x - 1/2)**5 - 20891402201978154*(x - 1/2)**4 - 2708144729886057*(x - 1/2)**3) - 37399144991004720*sqrt(2)*
I*(x - 1/2)**(11/2)/(-676317715831296*(x - 1/2)**12 - 7101336016228608*(x - 1/2)**11 - 33139568075733504*(x -
1/2)**10 - 90213268650607872*(x - 1/2)**9 - 157873220138563776*(x - 1/2)**8 - 184185423494991072*(x - 1/2)**7
- 143255329384993056*(x - 1/2)**6 - 71627664692496528*(x - 1/2)**5 - 20891402201978154*(x - 1/2)**4 - 27081447
29886057*(x - 1/2)**3) - 12489039853051608*sqrt(2)*I*(x - 1/2)**(9/2)/(-676317715831296*(x - 1/2)**12 - 710133
6016228608*(x - 1/2)**11 - 33139568075733504*(x - 1/2)**10 - 90213268650607872*(x - 1/2)**9 - 1578732201385637
76*(x - 1/2)**8 - 184185423494991072*(x - 1/2)**7 - 143255329384993056*(x - 1/2)**6 - 71627664692496528*(x - 1
/2)**5 - 20891402201978154*(x - 1/2)**4 - 2708144729886057*(x - 1/2)**3) - 1819449504656784*sqrt(2)*I*(x - 1/2
)**(7/2)/(-676317715831296*(x - 1/2)**12 - 7101336016228608*(x - 1/2)**11 - 33139568075733504*(x - 1/2)**10 -
90213268650607872*(x - 1/2)**9 - 157873220138563776*(x - 1/2)**8 - 184185423494991072*(x - 1/2)**7 - 143255329
384993056*(x - 1/2)**6 - 71627664692496528*(x - 1/2)**5 - 20891402201978154*(x - 1/2)**4 - 2708144729886057*(x
- 1/2)**3) + 1448855905728*sqrt(2)*I*(x - 1/2)**(5/2)/(-676317715831296*(x - 1/2)**12 - 7101336016228608*(x -
1/2)**11 - 33139568075733504*(x - 1/2)**10 - 90213268650607872*(x - 1/2)**9 - 157873220138563776*(x - 1/2)**8
- 184185423494991072*(x - 1/2)**7 - 143255329384993056*(x - 1/2)**6 - 71627664692496528*(x - 1/2)**5 - 208914
02201978154*(x - 1/2)**4 - 2708144729886057*(x - 1/2)**3) - 273436041032*sqrt(2)*I*(x - 1/2)**(3/2)/(-67631771
5831296*(x - 1/2)**12 - 7101336016228608*(x - 1/2)**11 - 33139568075733504*(x - 1/2)**10 - 90213268650607872*(
x - 1/2)**9 - 157873220138563776*(x - 1/2)**8 - 184185423494991072*(x - 1/2)**7 - 143255329384993056*(x - 1/2)
**6 - 71627664692496528*(x - 1/2)**5 - 20891402201978154*(x - 1/2)**4 - 2708144729886057*(x - 1/2)**3) + 31757
96937600000*sqrt(55)*I*(x - 1/2)**12*atan(sqrt(110)*sqrt(x - 1/2)/11)/(-676317715831296*(x - 1/2)**12 - 710133
6016228608*(x - 1/2)**11 - 33139568075733504*(x - 1/2)**10 - 90213268650607872*(x - 1/2)**9 - 1578732201385637
76*(x - 1/2)**8 - 184185423494991072*(x - 1/2)**7 - 143255329384993056*(x - 1/2)**6 - 71627664692496528*(x - 1
/2)**5 - 20891402201978154*(x - 1/2)**4 - 2708144729886057*(x - 1/2)**3) - 5139081066746880*sqrt(21)*I*(x - 1/
2)**12*atan(sqrt(42)*sqrt(x - 1/2)/7)/(-676317715831296*(x - 1/2)**12 - 7101336016228608*(x - 1/2)**11 - 33139
568075733504*(x - 1/2)**10 - 90213268650607872*(x - 1/2)**9 - 157873220138563776*(x - 1/2)**8 - 18418542349499
1072*(x - 1/2)**7 - 143255329384993056*(x - 1/2)**6 - 71627664692496528*(x - 1/2)**5 - 20891402201978154*(x -
1/2)**4 - 2708144729886057*(x - 1/2)**3) - 1587898468800000*sqrt(55)*I*pi*(x - 1/2)**12/(-676317715831296*(x -
1/2)**12 - 7101336016228608*(x - 1/2)**11 - 33139568075733504*(x - 1/2)**10 - 90213268650607872*(x - 1/2)**9
- 157873220138563776*(x - 1/2)**8 - 184185423494991072*(x - 1/2)**7 - 143255329384993056*(x - 1/2)**6 - 716276
64692496528*(x - 1/2)**5 - 20891402201978154*(x - 1/2)**4 - 2708144729886057*(x - 1/2)**3) + 2569540533373440*
sqrt(21)*I*pi*(x - 1/2)**12/(-676317715831296*(x - 1/2)**12 - 7101336016228608*(x - 1/2)**11 - 331395680757335
04*(x - 1/2)**10 - 90213268650607872*(x - 1/2)**9 - 157873220138563776*(x - 1/2)**8 - 184185423494991072*(x -
1/2)**7 - 143255329384993056*(x - 1/2)**6 - 71627664692496528*(x - 1/2)**5 - 20891402201978154*(x - 1/2)**4 -
2708144729886057*(x - 1/2)**3) + 33345867844800000*sqrt(55)*I*(x - 1/2)**11*atan(sqrt(110)*sqrt(x - 1/2)/11)/(
-676317715831296*(x - 1/2)**12 - 7101336016228608*(x - 1/2)**11 - 33139568075733504*(x - 1/2)**10 - 9021326865
0607872*(x - 1/2)**9 - 157873220138563776*(x - 1/2)**8 - 184185423494991072*(x - 1/2)**7 - 143255329384993056*
(x - 1/2)**6 - 71627664692496528*(x - 1/2)**5 - 20891402201978154*(x - 1/2)**4 - 2708144729886057*(x - 1/2)**3
) - 53960351200842240*sqrt(21)*I*(x - 1/2)**11*atan(sqrt(42)*sqrt(x - 1/2)/7)/(-676317715831296*(x - 1/2)**12
- 7101336016228608*(x - 1/2)**11 - 33139568075733504*(x - 1/2)**10 - 90213268650607872*(x - 1/2)**9 - 15787322
0138563776*(x - 1/2)**8 - 184185423494991072*(x - 1/2)**7 - 143255329384993056*(x - 1/2)**6 - 7162766469249652
8*(x - 1/2)**5 - 20891402201978154*(x - 1/2)**4 - 2708144729886057*(x - 1/2)**3) - 16672933922400000*sqrt(55)*
I*pi*(x - 1/2)**11/(-676317715831296*(x - 1/2)**12 - 7101336016228608*(x - 1/2)**11 - 33139568075733504*(x - 1
/2)**10 - 90213268650607872*(x - 1/2)**9 - 157873220138563776*(x - 1/2)**8 - 184185423494991072*(x - 1/2)**7 -
143255329384993056*(x - 1/2)**6 - 71627664692496528*(x - 1/2)**5 - 20891402201978154*(x - 1/2)**4 - 270814472
9886057*(x - 1/2)**3) + 26980175600421120*sqrt(21)*I*pi*(x - 1/2)**11/(-676317715831296*(x - 1/2)**12 - 710133
6016228608*(x - 1/2)**11 - 33139568075733504*(x - 1/2)**10 - 90213268650607872*(x - 1/2)**9 - 1578732201385637
76*(x - 1/2)**8 - 184185423494991072*(x - 1/2)**7 - 143255329384993056*(x - 1/2)**6 - 71627664692496528*(x - 1
/2)**5 - 20891402201978154*(x - 1/2)**4 - 2708144729886057*(x - 1/2)**3) + 155614049942400000*sqrt(55)*I*(x -
1/2)**10*atan(sqrt(110)*sqrt(x - 1/2)/11)/(-676317715831296*(x - 1/2)**12 - 7101336016228608*(x - 1/2)**11 - 3
3139568075733504*(x - 1/2)**10 - 90213268650607872*(x - 1/2)**9 - 157873220138563776*(x - 1/2)**8 - 1841854234
94991072*(x - 1/2)**7 - 143255329384993056*(x - 1/2)**6 - 71627664692496528*(x - 1/2)**5 - 20891402201978154*(
x - 1/2)**4 - 2708144729886057*(x - 1/2)**3) - 251814972270597120*sqrt(21)*I*(x - 1/2)**10*atan(sqrt(42)*sqrt(
x - 1/2)/7)/(-676317715831296*(x - 1/2)**12 - 7101336016228608*(x - 1/2)**11 - 33139568075733504*(x - 1/2)**10
- 90213268650607872*(x - 1/2)**9 - 157873220138563776*(x - 1/2)**8 - 184185423494991072*(x - 1/2)**7 - 143255
329384993056*(x - 1/2)**6 - 71627664692496528*(x - 1/2)**5 - 20891402201978154*(x - 1/2)**4 - 2708144729886057
*(x - 1/2)**3) - 77807024971200000*sqrt(55)*I*pi*(x - 1/2)**10/(-676317715831296*(x - 1/2)**12 - 7101336016228
608*(x - 1/2)**11 - 33139568075733504*(x - 1/2)**10 - 90213268650607872*(x - 1/2)**9 - 157873220138563776*(x -
1/2)**8 - 184185423494991072*(x - 1/2)**7 - 143255329384993056*(x - 1/2)**6 - 71627664692496528*(x - 1/2)**5
- 20891402201978154*(x - 1/2)**4 - 2708144729886057*(x - 1/2)**3) + 125907486135298560*sqrt(21)*I*pi*(x - 1/2)
**10/(-676317715831296*(x - 1/2)**12 - 7101336016228608*(x - 1/2)**11 - 33139568075733504*(x - 1/2)**10 - 9021
3268650607872*(x - 1/2)**9 - 157873220138563776*(x - 1/2)**8 - 184185423494991072*(x - 1/2)**7 - 1432553293849
93056*(x - 1/2)**6 - 71627664692496528*(x - 1/2)**5 - 20891402201978154*(x - 1/2)**4 - 2708144729886057*(x - 1
/2)**3) + 423616024843200000*sqrt(55)*I*(x - 1/2)**9*atan(sqrt(110)*sqrt(x - 1/2)/11)/(-676317715831296*(x - 1
/2)**12 - 7101336016228608*(x - 1/2)**11 - 33139568075733504*(x - 1/2)**10 - 90213268650607872*(x - 1/2)**9 -
157873220138563776*(x - 1/2)**8 - 184185423494991072*(x - 1/2)**7 - 143255329384993056*(x - 1/2)**6 - 71627664
692496528*(x - 1/2)**5 - 20891402201978154*(x - 1/2)**4 - 2708144729886057*(x - 1/2)**3) - 685496313403292160*
sqrt(21)*I*(x - 1/2)**9*atan(sqrt(42)*sqrt(x - 1/2)/7)/(-676317715831296*(x - 1/2)**12 - 7101336016228608*(x -
1/2)**11 - 33139568075733504*(x - 1/2)**10 - 90213268650607872*(x - 1/2)**9 - 157873220138563776*(x - 1/2)**8
- 184185423494991072*(x - 1/2)**7 - 143255329384993056*(x - 1/2)**6 - 71627664692496528*(x - 1/2)**5 - 208914
02201978154*(x - 1/2)**4 - 2708144729886057*(x - 1/2)**3) - 211808012421600000*sqrt(55)*I*pi*(x - 1/2)**9/(-67
6317715831296*(x - 1/2)**12 - 7101336016228608*(x - 1/2)**11 - 33139568075733504*(x - 1/2)**10 - 9021326865060
7872*(x - 1/2)**9 - 157873220138563776*(x - 1/2)**8 - 184185423494991072*(x - 1/2)**7 - 143255329384993056*(x
- 1/2)**6 - 71627664692496528*(x - 1/2)**5 - 20891402201978154*(x - 1/2)**4 - 2708144729886057*(x - 1/2)**3) +
342748156701646080*sqrt(21)*I*pi*(x - 1/2)**9/(-676317715831296*(x - 1/2)**12 - 7101336016228608*(x - 1/2)**1
1 - 33139568075733504*(x - 1/2)**10 - 90213268650607872*(x - 1/2)**9 - 157873220138563776*(x - 1/2)**8 - 18418
5423494991072*(x - 1/2)**7 - 143255329384993056*(x - 1/2)**6 - 71627664692496528*(x - 1/2)**5 - 20891402201978
154*(x - 1/2)**4 - 2708144729886057*(x - 1/2)**3) + 741328043475600000*sqrt(55)*I*(x - 1/2)**8*atan(sqrt(110)*
sqrt(x - 1/2)/11)/(-676317715831296*(x - 1/2)**12 - 7101336016228608*(x - 1/2)**11 - 33139568075733504*(x - 1/
2)**10 - 90213268650607872*(x - 1/2)**9 - 157873220138563776*(x - 1/2)**8 - 184185423494991072*(x - 1/2)**7 -
143255329384993056*(x - 1/2)**6 - 71627664692496528*(x - 1/2)**5 - 20891402201978154*(x - 1/2)**4 - 2708144729
886057*(x - 1/2)**3) - 1199618548455761280*sqrt(21)*I*(x - 1/2)**8*atan(sqrt(42)*sqrt(x - 1/2)/7)/(-6763177158
31296*(x - 1/2)**12 - 7101336016228608*(x - 1/2)**11 - 33139568075733504*(x - 1/2)**10 - 90213268650607872*(x
- 1/2)**9 - 157873220138563776*(x - 1/2)**8 - 184185423494991072*(x - 1/2)**7 - 143255329384993056*(x - 1/2)**
6 - 71627664692496528*(x - 1/2)**5 - 20891402201978154*(x - 1/2)**4 - 2708144729886057*(x - 1/2)**3) - 3706640
21737800000*sqrt(55)*I*pi*(x - 1/2)**8/(-676317715831296*(x - 1/2)**12 - 7101336016228608*(x - 1/2)**11 - 3313
9568075733504*(x - 1/2)**10 - 90213268650607872*(x - 1/2)**9 - 157873220138563776*(x - 1/2)**8 - 1841854234949
91072*(x - 1/2)**7 - 143255329384993056*(x - 1/2)**6 - 71627664692496528*(x - 1/2)**5 - 20891402201978154*(x -
1/2)**4 - 2708144729886057*(x - 1/2)**3) + 599809274227880640*sqrt(21)*I*pi*(x - 1/2)**8/(-676317715831296*(x
- 1/2)**12 - 7101336016228608*(x - 1/2)**11 - 33139568075733504*(x - 1/2)**10 - 90213268650607872*(x - 1/2)**
9 - 157873220138563776*(x - 1/2)**8 - 184185423494991072*(x - 1/2)**7 - 143255329384993056*(x - 1/2)**6 - 7162
7664692496528*(x - 1/2)**5 - 20891402201978154*(x - 1/2)**4 - 2708144729886057*(x - 1/2)**3) + 864882717388200
000*sqrt(55)*I*(x - 1/2)**7*atan(sqrt(110)*sqrt(x - 1/2)/11)/(-676317715831296*(x - 1/2)**12 - 710133601622860
8*(x - 1/2)**11 - 33139568075733504*(x - 1/2)**10 - 90213268650607872*(x - 1/2)**9 - 157873220138563776*(x - 1
/2)**8 - 184185423494991072*(x - 1/2)**7 - 143255329384993056*(x - 1/2)**6 - 71627664692496528*(x - 1/2)**5 -
20891402201978154*(x - 1/2)**4 - 2708144729886057*(x - 1/2)**3) - 1399554973198388160*sqrt(21)*I*(x - 1/2)**7*
atan(sqrt(42)*sqrt(x - 1/2)/7)/(-676317715831296*(x - 1/2)**12 - 7101336016228608*(x - 1/2)**11 - 331395680757
33504*(x - 1/2)**10 - 90213268650607872*(x - 1/2)**9 - 157873220138563776*(x - 1/2)**8 - 184185423494991072*(x
- 1/2)**7 - 143255329384993056*(x - 1/2)**6 - 71627664692496528*(x - 1/2)**5 - 20891402201978154*(x - 1/2)**4
- 2708144729886057*(x - 1/2)**3) - 432441358694100000*sqrt(55)*I*pi*(x - 1/2)**7/(-676317715831296*(x - 1/2)*
*12 - 7101336016228608*(x - 1/2)**11 - 33139568075733504*(x - 1/2)**10 - 90213268650607872*(x - 1/2)**9 - 1578
73220138563776*(x - 1/2)**8 - 184185423494991072*(x - 1/2)**7 - 143255329384993056*(x - 1/2)**6 - 716276646924
96528*(x - 1/2)**5 - 20891402201978154*(x - 1/2)**4 - 2708144729886057*(x - 1/2)**3) + 699777486599194080*sqrt
(21)*I*pi*(x - 1/2)**7/(-676317715831296*(x - 1/2)**12 - 7101336016228608*(x - 1/2)**11 - 33139568075733504*(x
- 1/2)**10 - 90213268650607872*(x - 1/2)**9 - 157873220138563776*(x - 1/2)**8 - 184185423494991072*(x - 1/2)*
*7 - 143255329384993056*(x - 1/2)**6 - 71627664692496528*(x - 1/2)**5 - 20891402201978154*(x - 1/2)**4 - 27081
44729886057*(x - 1/2)**3) + 672686557968600000*sqrt(55)*I*(x - 1/2)**6*atan(sqrt(110)*sqrt(x - 1/2)/11)/(-6763
17715831296*(x - 1/2)**12 - 7101336016228608*(x - 1/2)**11 - 33139568075733504*(x - 1/2)**10 - 902132686506078
72*(x - 1/2)**9 - 157873220138563776*(x - 1/2)**8 - 184185423494991072*(x - 1/2)**7 - 143255329384993056*(x -
1/2)**6 - 71627664692496528*(x - 1/2)**5 - 20891402201978154*(x - 1/2)**4 - 2708144729886057*(x - 1/2)**3) - 1
088542756932079680*sqrt(21)*I*(x - 1/2)**6*atan(sqrt(42)*sqrt(x - 1/2)/7)/(-676317715831296*(x - 1/2)**12 - 71
01336016228608*(x - 1/2)**11 - 33139568075733504*(x - 1/2)**10 - 90213268650607872*(x - 1/2)**9 - 157873220138
563776*(x - 1/2)**8 - 184185423494991072*(x - 1/2)**7 - 143255329384993056*(x - 1/2)**6 - 71627664692496528*(x
- 1/2)**5 - 20891402201978154*(x - 1/2)**4 - 2708144729886057*(x - 1/2)**3) - 336343278984300000*sqrt(55)*I*p
i*(x - 1/2)**6/(-676317715831296*(x - 1/2)**12 - 7101336016228608*(x - 1/2)**11 - 33139568075733504*(x - 1/2)*
*10 - 90213268650607872*(x - 1/2)**9 - 157873220138563776*(x - 1/2)**8 - 184185423494991072*(x - 1/2)**7 - 143
255329384993056*(x - 1/2)**6 - 71627664692496528*(x - 1/2)**5 - 20891402201978154*(x - 1/2)**4 - 2708144729886
057*(x - 1/2)**3) + 544271378466039840*sqrt(21)*I*pi*(x - 1/2)**6/(-676317715831296*(x - 1/2)**12 - 7101336016
228608*(x - 1/2)**11 - 33139568075733504*(x - 1/2)**10 - 90213268650607872*(x - 1/2)**9 - 157873220138563776*(
x - 1/2)**8 - 184185423494991072*(x - 1/2)**7 - 143255329384993056*(x - 1/2)**6 - 71627664692496528*(x - 1/2)*
*5 - 20891402201978154*(x - 1/2)**4 - 2708144729886057*(x - 1/2)**3) + 336343278984300000*sqrt(55)*I*(x - 1/2)
**5*atan(sqrt(110)*sqrt(x - 1/2)/11)/(-676317715831296*(x - 1/2)**12 - 7101336016228608*(x - 1/2)**11 - 331395
68075733504*(x - 1/2)**10 - 90213268650607872*(x - 1/2)**9 - 157873220138563776*(x - 1/2)**8 - 184185423494991
072*(x - 1/2)**7 - 143255329384993056*(x - 1/2)**6 - 71627664692496528*(x - 1/2)**5 - 20891402201978154*(x - 1
/2)**4 - 2708144729886057*(x - 1/2)**3) - 544271378466039840*sqrt(21)*I*(x - 1/2)**5*atan(sqrt(42)*sqrt(x - 1/
2)/7)/(-676317715831296*(x - 1/2)**12 - 7101336016228608*(x - 1/2)**11 - 33139568075733504*(x - 1/2)**10 - 902
13268650607872*(x - 1/2)**9 - 157873220138563776*(x - 1/2)**8 - 184185423494991072*(x - 1/2)**7 - 143255329384
993056*(x - 1/2)**6 - 71627664692496528*(x - 1/2)**5 - 20891402201978154*(x - 1/2)**4 - 2708144729886057*(x -
1/2)**3) - 168171639492150000*sqrt(55)*I*pi*(x - 1/2)**5/(-676317715831296*(x - 1/2)**12 - 7101336016228608*(x
- 1/2)**11 - 33139568075733504*(x - 1/2)**10 - 90213268650607872*(x - 1/2)**9 - 157873220138563776*(x - 1/2)*
*8 - 184185423494991072*(x - 1/2)**7 - 143255329384993056*(x - 1/2)**6 - 71627664692496528*(x - 1/2)**5 - 2089
1402201978154*(x - 1/2)**4 - 2708144729886057*(x - 1/2)**3) + 272135689233019920*sqrt(21)*I*pi*(x - 1/2)**5/(-
676317715831296*(x - 1/2)**12 - 7101336016228608*(x - 1/2)**11 - 33139568075733504*(x - 1/2)**10 - 90213268650
607872*(x - 1/2)**9 - 157873220138563776*(x - 1/2)**8 - 184185423494991072*(x - 1/2)**7 - 143255329384993056*(
x - 1/2)**6 - 71627664692496528*(x - 1/2)**5 - 20891402201978154*(x - 1/2)**4 - 2708144729886057*(x - 1/2)**3)
+ 98100123037087500*sqrt(55)*I*(x - 1/2)**4*atan(sqrt(110)*sqrt(x - 1/2)/11)/(-676317715831296*(x - 1/2)**12
- 7101336016228608*(x - 1/2)**11 - 33139568075733504*(x - 1/2)**10 - 90213268650607872*(x - 1/2)**9 - 15787322
0138563776*(x - 1/2)**8 - 184185423494991072*(x - 1/2)**7 - 143255329384993056*(x - 1/2)**6 - 7162766469249652
8*(x - 1/2)**5 - 20891402201978154*(x - 1/2)**4 - 2708144729886057*(x - 1/2)**3) - 158745818719261620*sqrt(21)
*I*(x - 1/2)**4*atan(sqrt(42)*sqrt(x - 1/2)/7)/(-676317715831296*(x - 1/2)**12 - 7101336016228608*(x - 1/2)**1
1 - 33139568075733504*(x - 1/2)**10 - 90213268650607872*(x - 1/2)**9 - 157873220138563776*(x - 1/2)**8 - 18418
5423494991072*(x - 1/2)**7 - 143255329384993056*(x - 1/2)**6 - 71627664692496528*(x - 1/2)**5 - 20891402201978
154*(x - 1/2)**4 - 2708144729886057*(x - 1/2)**3) - 49050061518543750*sqrt(55)*I*pi*(x - 1/2)**4/(-67631771583
1296*(x - 1/2)**12 - 7101336016228608*(x - 1/2)**11 - 33139568075733504*(x - 1/2)**10 - 90213268650607872*(x -
1/2)**9 - 157873220138563776*(x - 1/2)**8 - 184185423494991072*(x - 1/2)**7 - 143255329384993056*(x - 1/2)**6
- 71627664692496528*(x - 1/2)**5 - 20891402201978154*(x - 1/2)**4 - 2708144729886057*(x - 1/2)**3) + 79372909
359630810*sqrt(21)*I*pi*(x - 1/2)**4/(-676317715831296*(x - 1/2)**12 - 7101336016228608*(x - 1/2)**11 - 331395
68075733504*(x - 1/2)**10 - 90213268650607872*(x - 1/2)**9 - 157873220138563776*(x - 1/2)**8 - 184185423494991
072*(x - 1/2)**7 - 143255329384993056*(x - 1/2)**6 - 71627664692496528*(x - 1/2)**5 - 20891402201978154*(x - 1
/2)**4 - 2708144729886057*(x - 1/2)**3) + 12716682615918750*sqrt(55)*I*(x - 1/2)**3*atan(sqrt(110)*sqrt(x - 1/
2)/11)/(-676317715831296*(x - 1/2)**12 - 7101336016228608*(x - 1/2)**11 - 33139568075733504*(x - 1/2)**10 - 90
213268650607872*(x - 1/2)**9 - 157873220138563776*(x - 1/2)**8 - 184185423494991072*(x - 1/2)**7 - 14325532938
4993056*(x - 1/2)**6 - 71627664692496528*(x - 1/2)**5 - 20891402201978154*(x - 1/2)**4 - 2708144729886057*(x -
1/2)**3) - 20578161685830210*sqrt(21)*I*(x - 1/2)**3*atan(sqrt(42)*sqrt(x - 1/2)/7)/(-676317715831296*(x - 1/
2)**12 - 7101336016228608*(x - 1/2)**11 - 33139568075733504*(x - 1/2)**10 - 90213268650607872*(x - 1/2)**9 - 1
57873220138563776*(x - 1/2)**8 - 184185423494991072*(x - 1/2)**7 - 143255329384993056*(x - 1/2)**6 - 716276646
92496528*(x - 1/2)**5 - 20891402201978154*(x - 1/2)**4 - 2708144729886057*(x - 1/2)**3) - 6358341307959375*sqr
t(55)*I*pi*(x - 1/2)**3/(-676317715831296*(x - 1/2)**12 - 7101336016228608*(x - 1/2)**11 - 33139568075733504*(
x - 1/2)**10 - 90213268650607872*(x - 1/2)**9 - 157873220138563776*(x - 1/2)**8 - 184185423494991072*(x - 1/2)
**7 - 143255329384993056*(x - 1/2)**6 - 71627664692496528*(x - 1/2)**5 - 20891402201978154*(x - 1/2)**4 - 2708
144729886057*(x - 1/2)**3) + 10289080842915105*sqrt(21)*I*pi*(x - 1/2)**3/(-676317715831296*(x - 1/2)**12 - 71
01336016228608*(x - 1/2)**11 - 33139568075733504*(x - 1/2)**10 - 90213268650607872*(x - 1/2)**9 - 157873220138
563776*(x - 1/2)**8 - 184185423494991072*(x - 1/2)**7 - 143255329384993056*(x - 1/2)**6 - 71627664692496528*(x
- 1/2)**5 - 20891402201978154*(x - 1/2)**4 - 2708144729886057*(x - 1/2)**3)
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