3.21.50 \(\int \frac {1}{(1-2 x)^{5/2} (2+3 x)^3 (3+5 x)^2} \, dx\)
Optimal. Leaf size=159 \[ \frac {172105}{65219 \sqrt {1-2 x}}+\frac {24}{7 (1-2 x)^{3/2} (3 x+2) (5 x+3)}-\frac {745}{22 (1-2 x)^{3/2} (5 x+3)}+\frac {3}{14 (1-2 x)^{3/2} (3 x+2)^2 (5 x+3)}+\frac {15185}{2541 (1-2 x)^{3/2}}-\frac {4455}{49} \sqrt {\frac {3}{7}} \tanh ^{-1}\left (\sqrt {\frac {3}{7}} \sqrt {1-2 x}\right )+\frac {117500 \sqrt {\frac {5}{11}} \tanh ^{-1}\left (\sqrt {\frac {5}{11}} \sqrt {1-2 x}\right )}{1331} \]
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Rubi [A] time = 0.07, antiderivative size = 159, 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} \begin {gather*} \frac {172105}{65219 \sqrt {1-2 x}}+\frac {24}{7 (1-2 x)^{3/2} (3 x+2) (5 x+3)}-\frac {745}{22 (1-2 x)^{3/2} (5 x+3)}+\frac {3}{14 (1-2 x)^{3/2} (3 x+2)^2 (5 x+3)}+\frac {15185}{2541 (1-2 x)^{3/2}}-\frac {4455}{49} \sqrt {\frac {3}{7}} \tanh ^{-1}\left (\sqrt {\frac {3}{7}} \sqrt {1-2 x}\right )+\frac {117500 \sqrt {\frac {5}{11}} \tanh ^{-1}\left (\sqrt {\frac {5}{11}} \sqrt {1-2 x}\right )}{1331} \end {gather*}
Antiderivative was successfully verified.
[In]
Int[1/((1 - 2*x)^(5/2)*(2 + 3*x)^3*(3 + 5*x)^2),x]
[Out]
15185/(2541*(1 - 2*x)^(3/2)) + 172105/(65219*Sqrt[1 - 2*x]) - 745/(22*(1 - 2*x)^(3/2)*(3 + 5*x)) + 3/(14*(1 -
2*x)^(3/2)*(2 + 3*x)^2*(3 + 5*x)) + 24/(7*(1 - 2*x)^(3/2)*(2 + 3*x)*(3 + 5*x)) - (4455*Sqrt[3/7]*ArcTanh[Sqrt[
3/7]*Sqrt[1 - 2*x]])/49 + (117500*Sqrt[5/11]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/1331
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)^3 (3+5 x)^2} \, dx &=\frac {3}{14 (1-2 x)^{3/2} (2+3 x)^2 (3+5 x)}+\frac {1}{14} \int \frac {22-135 x}{(1-2 x)^{5/2} (2+3 x)^2 (3+5 x)^2} \, dx\\ &=\frac {3}{14 (1-2 x)^{3/2} (2+3 x)^2 (3+5 x)}+\frac {24}{7 (1-2 x)^{3/2} (2+3 x) (3+5 x)}+\frac {1}{98} \int \frac {245-11760 x}{(1-2 x)^{5/2} (2+3 x) (3+5 x)^2} \, dx\\ &=-\frac {745}{22 (1-2 x)^{3/2} (3+5 x)}+\frac {3}{14 (1-2 x)^{3/2} (2+3 x)^2 (3+5 x)}+\frac {24}{7 (1-2 x)^{3/2} (2+3 x) (3+5 x)}-\frac {\int \frac {-98245-547575 x}{(1-2 x)^{5/2} (2+3 x) (3+5 x)} \, dx}{1078}\\ &=\frac {15185}{2541 (1-2 x)^{3/2}}-\frac {745}{22 (1-2 x)^{3/2} (3+5 x)}+\frac {3}{14 (1-2 x)^{3/2} (2+3 x)^2 (3+5 x)}+\frac {24}{7 (1-2 x)^{3/2} (2+3 x) (3+5 x)}+\frac {\int \frac {-\frac {4091745}{2}+\frac {33482925 x}{2}}{(1-2 x)^{3/2} (2+3 x) (3+5 x)} \, dx}{124509}\\ &=\frac {15185}{2541 (1-2 x)^{3/2}}+\frac {172105}{65219 \sqrt {1-2 x}}-\frac {745}{22 (1-2 x)^{3/2} (3+5 x)}+\frac {3}{14 (1-2 x)^{3/2} (2+3 x)^2 (3+5 x)}+\frac {24}{7 (1-2 x)^{3/2} (2+3 x) (3+5 x)}-\frac {2 \int \frac {\frac {618657585}{4}-\frac {379491525 x}{4}}{\sqrt {1-2 x} (2+3 x) (3+5 x)} \, dx}{9587193}\\ &=\frac {15185}{2541 (1-2 x)^{3/2}}+\frac {172105}{65219 \sqrt {1-2 x}}-\frac {745}{22 (1-2 x)^{3/2} (3+5 x)}+\frac {3}{14 (1-2 x)^{3/2} (2+3 x)^2 (3+5 x)}+\frac {24}{7 (1-2 x)^{3/2} (2+3 x) (3+5 x)}+\frac {13365}{98} \int \frac {1}{\sqrt {1-2 x} (2+3 x)} \, dx-\frac {293750 \int \frac {1}{\sqrt {1-2 x} (3+5 x)} \, dx}{1331}\\ &=\frac {15185}{2541 (1-2 x)^{3/2}}+\frac {172105}{65219 \sqrt {1-2 x}}-\frac {745}{22 (1-2 x)^{3/2} (3+5 x)}+\frac {3}{14 (1-2 x)^{3/2} (2+3 x)^2 (3+5 x)}+\frac {24}{7 (1-2 x)^{3/2} (2+3 x) (3+5 x)}-\frac {13365}{98} \operatorname {Subst}\left (\int \frac {1}{\frac {7}{2}-\frac {3 x^2}{2}} \, dx,x,\sqrt {1-2 x}\right )+\frac {293750 \operatorname {Subst}\left (\int \frac {1}{\frac {11}{2}-\frac {5 x^2}{2}} \, dx,x,\sqrt {1-2 x}\right )}{1331}\\ &=\frac {15185}{2541 (1-2 x)^{3/2}}+\frac {172105}{65219 \sqrt {1-2 x}}-\frac {745}{22 (1-2 x)^{3/2} (3+5 x)}+\frac {3}{14 (1-2 x)^{3/2} (2+3 x)^2 (3+5 x)}+\frac {24}{7 (1-2 x)^{3/2} (2+3 x) (3+5 x)}-\frac {4455}{49} \sqrt {\frac {3}{7}} \tanh ^{-1}\left (\sqrt {\frac {3}{7}} \sqrt {1-2 x}\right )+\frac {117500 \sqrt {\frac {5}{11}} \tanh ^{-1}\left (\sqrt {\frac {5}{11}} \sqrt {1-2 x}\right )}{1331}\\ \end {align*}
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Mathematica [C] time = 0.08, size = 78, normalized size = 0.49 \begin {gather*} \frac {359370 \, _2F_1\left (-\frac {3}{2},1;-\frac {1}{2};\frac {3}{7}-\frac {6 x}{7}\right )-329000 \, _2F_1\left (-\frac {3}{2},1;-\frac {1}{2};-\frac {5}{11} (2 x-1)\right )-\frac {33 \left (46935 x^2+60996 x+19771\right )}{(3 x+2)^2 (5 x+3)}}{5082 (1-2 x)^{3/2}} \end {gather*}
Antiderivative was successfully verified.
[In]
Integrate[1/((1 - 2*x)^(5/2)*(2 + 3*x)^3*(3 + 5*x)^2),x]
[Out]
((-33*(19771 + 60996*x + 46935*x^2))/((2 + 3*x)^2*(3 + 5*x)) + 359370*Hypergeometric2F1[-3/2, 1, -1/2, 3/7 - (
6*x)/7] - 329000*Hypergeometric2F1[-3/2, 1, -1/2, (-5*(-1 + 2*x))/11])/(5082*(1 - 2*x)^(3/2))
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IntegrateAlgebraic [A] time = 0.34, size = 130, normalized size = 0.82 \begin {gather*} \frac {23234175 (1-2 x)^4-106925310 (1-2 x)^3+122999835 (1-2 x)^2-142912 (1-2 x)-27104}{195657 (3 (1-2 x)-7)^2 (5 (1-2 x)-11) (1-2 x)^{3/2}}-\frac {4455}{49} \sqrt {\frac {3}{7}} \tanh ^{-1}\left (\sqrt {\frac {3}{7}} \sqrt {1-2 x}\right )+\frac {117500 \sqrt {\frac {5}{11}} \tanh ^{-1}\left (\sqrt {\frac {5}{11}} \sqrt {1-2 x}\right )}{1331} \end {gather*}
Antiderivative was successfully verified.
[In]
IntegrateAlgebraic[1/((1 - 2*x)^(5/2)*(2 + 3*x)^3*(3 + 5*x)^2),x]
[Out]
(-27104 - 142912*(1 - 2*x) + 122999835*(1 - 2*x)^2 - 106925310*(1 - 2*x)^3 + 23234175*(1 - 2*x)^4)/(195657*(-7
+ 3*(1 - 2*x))^2*(-11 + 5*(1 - 2*x))*(1 - 2*x)^(3/2)) - (4455*Sqrt[3/7]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/49
+ (117500*Sqrt[5/11]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/1331
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fricas [A] time = 1.28, size = 182, normalized size = 1.14 \begin {gather*} \frac {120907500 \, \sqrt {11} \sqrt {5} {\left (180 \, x^{5} + 168 \, x^{4} - 79 \, x^{3} - 89 \, x^{2} + 8 \, x + 12\right )} \log \left (-\frac {\sqrt {11} \sqrt {5} \sqrt {-2 \, x + 1} - 5 \, x + 8}{5 \, x + 3}\right ) + 195676965 \, \sqrt {7} \sqrt {3} {\left (180 \, x^{5} + 168 \, x^{4} - 79 \, x^{3} - 89 \, x^{2} + 8 \, x + 12\right )} \log \left (\frac {\sqrt {7} \sqrt {3} \sqrt {-2 \, x + 1} + 3 \, x - 5}{3 \, x + 2}\right ) - 77 \, {\left (92936700 \, x^{4} + 27977220 \, x^{3} - 58371045 \, x^{2} - 9008764 \, x + 9784671\right )} \sqrt {-2 \, x + 1}}{30131178 \, {\left (180 \, x^{5} + 168 \, x^{4} - 79 \, x^{3} - 89 \, x^{2} + 8 \, x + 12\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(1/(1-2*x)^(5/2)/(2+3*x)^3/(3+5*x)^2,x, algorithm="fricas")
[Out]
1/30131178*(120907500*sqrt(11)*sqrt(5)*(180*x^5 + 168*x^4 - 79*x^3 - 89*x^2 + 8*x + 12)*log(-(sqrt(11)*sqrt(5)
*sqrt(-2*x + 1) - 5*x + 8)/(5*x + 3)) + 195676965*sqrt(7)*sqrt(3)*(180*x^5 + 168*x^4 - 79*x^3 - 89*x^2 + 8*x +
12)*log((sqrt(7)*sqrt(3)*sqrt(-2*x + 1) + 3*x - 5)/(3*x + 2)) - 77*(92936700*x^4 + 27977220*x^3 - 58371045*x^
2 - 9008764*x + 9784671)*sqrt(-2*x + 1))/(180*x^5 + 168*x^4 - 79*x^3 - 89*x^2 + 8*x + 12)
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giac [A] time = 1.27, size = 144, normalized size = 0.91 \begin {gather*} -\frac {58750}{14641} \, \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 {4455}{686} \, \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 {64 \, {\left (507 \, x - 292\right )}}{9587193 \, {\left (2 \, x - 1\right )} \sqrt {-2 \, x + 1}} - \frac {3125 \, \sqrt {-2 \, x + 1}}{1331 \, {\left (5 \, x + 3\right )}} + \frac {243 \, {\left (151 \, {\left (-2 \, x + 1\right )}^{\frac {3}{2}} - 357 \, \sqrt {-2 \, x + 1}\right )}}{9604 \, {\left (3 \, x + 2\right )}^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(1/(1-2*x)^(5/2)/(2+3*x)^3/(3+5*x)^2,x, algorithm="giac")
[Out]
-58750/14641*sqrt(55)*log(1/2*abs(-2*sqrt(55) + 10*sqrt(-2*x + 1))/(sqrt(55) + 5*sqrt(-2*x + 1))) + 4455/686*s
qrt(21)*log(1/2*abs(-2*sqrt(21) + 6*sqrt(-2*x + 1))/(sqrt(21) + 3*sqrt(-2*x + 1))) + 64/9587193*(507*x - 292)/
((2*x - 1)*sqrt(-2*x + 1)) - 3125/1331*sqrt(-2*x + 1)/(5*x + 3) + 243/9604*(151*(-2*x + 1)^(3/2) - 357*sqrt(-2
*x + 1))/(3*x + 2)^2
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maple [A] time = 0.02, size = 100, normalized size = 0.63 \begin {gather*} -\frac {4455 \sqrt {21}\, \arctanh \left (\frac {\sqrt {21}\, \sqrt {-2 x +1}}{7}\right )}{343}+\frac {117500 \sqrt {55}\, \arctanh \left (\frac {\sqrt {55}\, \sqrt {-2 x +1}}{11}\right )}{14641}+\frac {32}{124509 \left (-2 x +1\right )^{\frac {3}{2}}}+\frac {5408}{3195731 \sqrt {-2 x +1}}+\frac {1250 \sqrt {-2 x +1}}{1331 \left (-2 x -\frac {6}{5}\right )}+\frac {\frac {36693 \left (-2 x +1\right )^{\frac {3}{2}}}{2401}-\frac {12393 \sqrt {-2 x +1}}{343}}{\left (-6 x -4\right )^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
int(1/(-2*x+1)^(5/2)/(3*x+2)^3/(5*x+3)^2,x)
[Out]
32/124509/(-2*x+1)^(3/2)+5408/3195731/(-2*x+1)^(1/2)+1250/1331*(-2*x+1)^(1/2)/(-2*x-6/5)+117500/14641*arctanh(
1/11*55^(1/2)*(-2*x+1)^(1/2))*55^(1/2)+4374/2401*(151/18*(-2*x+1)^(3/2)-119/6*(-2*x+1)^(1/2))/(-6*x-4)^2-4455/
343*arctanh(1/7*21^(1/2)*(-2*x+1)^(1/2))*21^(1/2)
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maxima [A] time = 1.18, size = 146, normalized size = 0.92 \begin {gather*} -\frac {58750}{14641} \, \sqrt {55} \log \left (-\frac {\sqrt {55} - 5 \, \sqrt {-2 \, x + 1}}{\sqrt {55} + 5 \, \sqrt {-2 \, x + 1}}\right ) + \frac {4455}{686} \, \sqrt {21} \log \left (-\frac {\sqrt {21} - 3 \, \sqrt {-2 \, x + 1}}{\sqrt {21} + 3 \, \sqrt {-2 \, x + 1}}\right ) + \frac {23234175 \, {\left (2 \, x - 1\right )}^{4} + 106925310 \, {\left (2 \, x - 1\right )}^{3} + 122999835 \, {\left (2 \, x - 1\right )}^{2} + 285824 \, x - 170016}{195657 \, {\left (45 \, {\left (-2 \, x + 1\right )}^{\frac {9}{2}} - 309 \, {\left (-2 \, x + 1\right )}^{\frac {7}{2}} + 707 \, {\left (-2 \, x + 1\right )}^{\frac {5}{2}} - 539 \, {\left (-2 \, x + 1\right )}^{\frac {3}{2}}\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(1/(1-2*x)^(5/2)/(2+3*x)^3/(3+5*x)^2,x, algorithm="maxima")
[Out]
-58750/14641*sqrt(55)*log(-(sqrt(55) - 5*sqrt(-2*x + 1))/(sqrt(55) + 5*sqrt(-2*x + 1))) + 4455/686*sqrt(21)*lo
g(-(sqrt(21) - 3*sqrt(-2*x + 1))/(sqrt(21) + 3*sqrt(-2*x + 1))) + 1/195657*(23234175*(2*x - 1)^4 + 106925310*(
2*x - 1)^3 + 122999835*(2*x - 1)^2 + 285824*x - 170016)/(45*(-2*x + 1)^(9/2) - 309*(-2*x + 1)^(7/2) + 707*(-2*
x + 1)^(5/2) - 539*(-2*x + 1)^(3/2))
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mupad [B] time = 1.26, size = 110, normalized size = 0.69 \begin {gather*} \frac {117500\,\sqrt {55}\,\mathrm {atanh}\left (\frac {\sqrt {55}\,\sqrt {1-2\,x}}{11}\right )}{14641}-\frac {4455\,\sqrt {21}\,\mathrm {atanh}\left (\frac {\sqrt {21}\,\sqrt {1-2\,x}}{7}\right )}{343}-\frac {\frac {3712\,x}{114345}+\frac {1171427\,{\left (2\,x-1\right )}^2}{83853}+\frac {2376118\,{\left (2\,x-1\right )}^3}{195657}+\frac {172105\,{\left (2\,x-1\right )}^4}{65219}-\frac {736}{38115}}{\frac {539\,{\left (1-2\,x\right )}^{3/2}}{45}-\frac {707\,{\left (1-2\,x\right )}^{5/2}}{45}+\frac {103\,{\left (1-2\,x\right )}^{7/2}}{15}-{\left (1-2\,x\right )}^{9/2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
int(1/((1 - 2*x)^(5/2)*(3*x + 2)^3*(5*x + 3)^2),x)
[Out]
(117500*55^(1/2)*atanh((55^(1/2)*(1 - 2*x)^(1/2))/11))/14641 - (4455*21^(1/2)*atanh((21^(1/2)*(1 - 2*x)^(1/2))
/7))/343 - ((3712*x)/114345 + (1171427*(2*x - 1)^2)/83853 + (2376118*(2*x - 1)^3)/195657 + (172105*(2*x - 1)^4
)/65219 - 736/38115)/((539*(1 - 2*x)^(3/2))/45 - (707*(1 - 2*x)^(5/2))/45 + (103*(1 - 2*x)^(7/2))/15 - (1 - 2*
x)^(9/2))
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sympy [C] time = 25.32, size = 3028, normalized size = 19.04
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)**3/(3+5*x)**2,x)
[Out]
8587351080000*sqrt(2)*I*(x - 1/2)**(17/2)/(-6508334448000*(x - 1/2)**9 - 44256674246400*(x - 1/2)**8 - 1253722
15916640*(x - 1/2)**7 - 189385783052928*(x - 1/2)**6 - 160894343759688*(x - 1/2)**5 - 72888283779696*(x - 1/2)
**4 - 13755877085874*(x - 1/2)**3) + 48670545924000*sqrt(2)*I*(x - 1/2)**(15/2)/(-6508334448000*(x - 1/2)**9 -
44256674246400*(x - 1/2)**8 - 125372215916640*(x - 1/2)**7 - 189385783052928*(x - 1/2)**6 - 160894343759688*(
x - 1/2)**5 - 72888283779696*(x - 1/2)**4 - 13755877085874*(x - 1/2)**3) + 110321398202400*sqrt(2)*I*(x - 1/2)
**(13/2)/(-6508334448000*(x - 1/2)**9 - 44256674246400*(x - 1/2)**8 - 125372215916640*(x - 1/2)**7 - 189385783
052928*(x - 1/2)**6 - 160894343759688*(x - 1/2)**5 - 72888283779696*(x - 1/2)**4 - 13755877085874*(x - 1/2)**3
) + 125018036238480*sqrt(2)*I*(x - 1/2)**(11/2)/(-6508334448000*(x - 1/2)**9 - 44256674246400*(x - 1/2)**8 - 1
25372215916640*(x - 1/2)**7 - 189385783052928*(x - 1/2)**6 - 160894343759688*(x - 1/2)**5 - 72888283779696*(x
- 1/2)**4 - 13755877085874*(x - 1/2)**3) + 70838364022580*sqrt(2)*I*(x - 1/2)**(9/2)/(-6508334448000*(x - 1/2)
**9 - 44256674246400*(x - 1/2)**8 - 125372215916640*(x - 1/2)**7 - 189385783052928*(x - 1/2)**6 - 160894343759
688*(x - 1/2)**5 - 72888283779696*(x - 1/2)**4 - 13755877085874*(x - 1/2)**3) + 16066680171234*sqrt(2)*I*(x -
1/2)**(7/2)/(-6508334448000*(x - 1/2)**9 - 44256674246400*(x - 1/2)**8 - 125372215916640*(x - 1/2)**7 - 189385
783052928*(x - 1/2)**6 - 160894343759688*(x - 1/2)**5 - 72888283779696*(x - 1/2)**4 - 13755877085874*(x - 1/2)
**3) + 6955997664*sqrt(2)*I*(x - 1/2)**(5/2)/(-6508334448000*(x - 1/2)**9 - 44256674246400*(x - 1/2)**8 - 1253
72215916640*(x - 1/2)**7 - 189385783052928*(x - 1/2)**6 - 160894343759688*(x - 1/2)**5 - 72888283779696*(x - 1
/2)**4 - 13755877085874*(x - 1/2)**3) - 883847888*sqrt(2)*I*(x - 1/2)**(3/2)/(-6508334448000*(x - 1/2)**9 - 44
256674246400*(x - 1/2)**8 - 125372215916640*(x - 1/2)**7 - 189385783052928*(x - 1/2)**6 - 160894343759688*(x -
1/2)**5 - 72888283779696*(x - 1/2)**4 - 13755877085874*(x - 1/2)**3) - 52232040000000*sqrt(55)*I*(x - 1/2)**9
*atan(sqrt(110)*sqrt(x - 1/2)/11)/(-6508334448000*(x - 1/2)**9 - 44256674246400*(x - 1/2)**8 - 125372215916640
*(x - 1/2)**7 - 189385783052928*(x - 1/2)**6 - 160894343759688*(x - 1/2)**5 - 72888283779696*(x - 1/2)**4 - 13
755877085874*(x - 1/2)**3) + 84532448880000*sqrt(21)*I*(x - 1/2)**9*atan(sqrt(42)*sqrt(x - 1/2)/7)/(-650833444
8000*(x - 1/2)**9 - 44256674246400*(x - 1/2)**8 - 125372215916640*(x - 1/2)**7 - 189385783052928*(x - 1/2)**6
- 160894343759688*(x - 1/2)**5 - 72888283779696*(x - 1/2)**4 - 13755877085874*(x - 1/2)**3) - 42266224440000*s
qrt(21)*I*pi*(x - 1/2)**9/(-6508334448000*(x - 1/2)**9 - 44256674246400*(x - 1/2)**8 - 125372215916640*(x - 1/
2)**7 - 189385783052928*(x - 1/2)**6 - 160894343759688*(x - 1/2)**5 - 72888283779696*(x - 1/2)**4 - 1375587708
5874*(x - 1/2)**3) + 26116020000000*sqrt(55)*I*pi*(x - 1/2)**9/(-6508334448000*(x - 1/2)**9 - 44256674246400*(
x - 1/2)**8 - 125372215916640*(x - 1/2)**7 - 189385783052928*(x - 1/2)**6 - 160894343759688*(x - 1/2)**5 - 728
88283779696*(x - 1/2)**4 - 13755877085874*(x - 1/2)**3) - 355177872000000*sqrt(55)*I*(x - 1/2)**8*atan(sqrt(11
0)*sqrt(x - 1/2)/11)/(-6508334448000*(x - 1/2)**9 - 44256674246400*(x - 1/2)**8 - 125372215916640*(x - 1/2)**7
- 189385783052928*(x - 1/2)**6 - 160894343759688*(x - 1/2)**5 - 72888283779696*(x - 1/2)**4 - 13755877085874*
(x - 1/2)**3) + 574820652384000*sqrt(21)*I*(x - 1/2)**8*atan(sqrt(42)*sqrt(x - 1/2)/7)/(-6508334448000*(x - 1/
2)**9 - 44256674246400*(x - 1/2)**8 - 125372215916640*(x - 1/2)**7 - 189385783052928*(x - 1/2)**6 - 1608943437
59688*(x - 1/2)**5 - 72888283779696*(x - 1/2)**4 - 13755877085874*(x - 1/2)**3) - 287410326192000*sqrt(21)*I*p
i*(x - 1/2)**8/(-6508334448000*(x - 1/2)**9 - 44256674246400*(x - 1/2)**8 - 125372215916640*(x - 1/2)**7 - 189
385783052928*(x - 1/2)**6 - 160894343759688*(x - 1/2)**5 - 72888283779696*(x - 1/2)**4 - 13755877085874*(x - 1
/2)**3) + 177588936000000*sqrt(55)*I*pi*(x - 1/2)**8/(-6508334448000*(x - 1/2)**9 - 44256674246400*(x - 1/2)**
8 - 125372215916640*(x - 1/2)**7 - 189385783052928*(x - 1/2)**6 - 160894343759688*(x - 1/2)**5 - 7288828377969
6*(x - 1/2)**4 - 13755877085874*(x - 1/2)**3) - 1006163197200000*sqrt(55)*I*(x - 1/2)**7*atan(sqrt(110)*sqrt(x
- 1/2)/11)/(-6508334448000*(x - 1/2)**9 - 44256674246400*(x - 1/2)**8 - 125372215916640*(x - 1/2)**7 - 189385
783052928*(x - 1/2)**6 - 160894343759688*(x - 1/2)**5 - 72888283779696*(x - 1/2)**4 - 13755877085874*(x - 1/2)
**3) + 1628376740258400*sqrt(21)*I*(x - 1/2)**7*atan(sqrt(42)*sqrt(x - 1/2)/7)/(-6508334448000*(x - 1/2)**9 -
44256674246400*(x - 1/2)**8 - 125372215916640*(x - 1/2)**7 - 189385783052928*(x - 1/2)**6 - 160894343759688*(x
- 1/2)**5 - 72888283779696*(x - 1/2)**4 - 13755877085874*(x - 1/2)**3) - 814188370129200*sqrt(21)*I*pi*(x - 1
/2)**7/(-6508334448000*(x - 1/2)**9 - 44256674246400*(x - 1/2)**8 - 125372215916640*(x - 1/2)**7 - 18938578305
2928*(x - 1/2)**6 - 160894343759688*(x - 1/2)**5 - 72888283779696*(x - 1/2)**4 - 13755877085874*(x - 1/2)**3)
+ 503081598600000*sqrt(55)*I*pi*(x - 1/2)**7/(-6508334448000*(x - 1/2)**9 - 44256674246400*(x - 1/2)**8 - 1253
72215916640*(x - 1/2)**7 - 189385783052928*(x - 1/2)**6 - 160894343759688*(x - 1/2)**5 - 72888283779696*(x - 1
/2)**4 - 13755877085874*(x - 1/2)**3) - 1519898197440000*sqrt(55)*I*(x - 1/2)**6*atan(sqrt(110)*sqrt(x - 1/2)/
11)/(-6508334448000*(x - 1/2)**9 - 44256674246400*(x - 1/2)**8 - 125372215916640*(x - 1/2)**7 - 18938578305292
8*(x - 1/2)**6 - 160894343759688*(x - 1/2)**5 - 72888283779696*(x - 1/2)**4 - 13755877085874*(x - 1/2)**3) + 2
459806599127680*sqrt(21)*I*(x - 1/2)**6*atan(sqrt(42)*sqrt(x - 1/2)/7)/(-6508334448000*(x - 1/2)**9 - 44256674
246400*(x - 1/2)**8 - 125372215916640*(x - 1/2)**7 - 189385783052928*(x - 1/2)**6 - 160894343759688*(x - 1/2)*
*5 - 72888283779696*(x - 1/2)**4 - 13755877085874*(x - 1/2)**3) - 1229903299563840*sqrt(21)*I*pi*(x - 1/2)**6/
(-6508334448000*(x - 1/2)**9 - 44256674246400*(x - 1/2)**8 - 125372215916640*(x - 1/2)**7 - 189385783052928*(x
- 1/2)**6 - 160894343759688*(x - 1/2)**5 - 72888283779696*(x - 1/2)**4 - 13755877085874*(x - 1/2)**3) + 75994
9098720000*sqrt(55)*I*pi*(x - 1/2)**6/(-6508334448000*(x - 1/2)**9 - 44256674246400*(x - 1/2)**8 - 12537221591
6640*(x - 1/2)**7 - 189385783052928*(x - 1/2)**6 - 160894343759688*(x - 1/2)**5 - 72888283779696*(x - 1/2)**4
- 13755877085874*(x - 1/2)**3) - 1291242769740000*sqrt(55)*I*(x - 1/2)**5*atan(sqrt(110)*sqrt(x - 1/2)/11)/(-6
508334448000*(x - 1/2)**9 - 44256674246400*(x - 1/2)**8 - 125372215916640*(x - 1/2)**7 - 189385783052928*(x -
1/2)**6 - 160894343759688*(x - 1/2)**5 - 72888283779696*(x - 1/2)**4 - 13755877085874*(x - 1/2)**3) + 20897501
49998280*sqrt(21)*I*(x - 1/2)**5*atan(sqrt(42)*sqrt(x - 1/2)/7)/(-6508334448000*(x - 1/2)**9 - 44256674246400*
(x - 1/2)**8 - 125372215916640*(x - 1/2)**7 - 189385783052928*(x - 1/2)**6 - 160894343759688*(x - 1/2)**5 - 72
888283779696*(x - 1/2)**4 - 13755877085874*(x - 1/2)**3) - 1044875074999140*sqrt(21)*I*pi*(x - 1/2)**5/(-65083
34448000*(x - 1/2)**9 - 44256674246400*(x - 1/2)**8 - 125372215916640*(x - 1/2)**7 - 189385783052928*(x - 1/2)
**6 - 160894343759688*(x - 1/2)**5 - 72888283779696*(x - 1/2)**4 - 13755877085874*(x - 1/2)**3) + 645621384870
000*sqrt(55)*I*pi*(x - 1/2)**5/(-6508334448000*(x - 1/2)**9 - 44256674246400*(x - 1/2)**8 - 125372215916640*(x
- 1/2)**7 - 189385783052928*(x - 1/2)**6 - 160894343759688*(x - 1/2)**5 - 72888283779696*(x - 1/2)**4 - 13755
877085874*(x - 1/2)**3) - 584958223080000*sqrt(55)*I*(x - 1/2)**4*atan(sqrt(110)*sqrt(x - 1/2)/11)/(-650833444
8000*(x - 1/2)**9 - 44256674246400*(x - 1/2)**8 - 125372215916640*(x - 1/2)**7 - 189385783052928*(x - 1/2)**6
- 160894343759688*(x - 1/2)**5 - 72888283779696*(x - 1/2)**4 - 13755877085874*(x - 1/2)**3) + 946697679995760*
sqrt(21)*I*(x - 1/2)**4*atan(sqrt(42)*sqrt(x - 1/2)/7)/(-6508334448000*(x - 1/2)**9 - 44256674246400*(x - 1/2)
**8 - 125372215916640*(x - 1/2)**7 - 189385783052928*(x - 1/2)**6 - 160894343759688*(x - 1/2)**5 - 72888283779
696*(x - 1/2)**4 - 13755877085874*(x - 1/2)**3) - 473348839997880*sqrt(21)*I*pi*(x - 1/2)**4/(-6508334448000*(
x - 1/2)**9 - 44256674246400*(x - 1/2)**8 - 125372215916640*(x - 1/2)**7 - 189385783052928*(x - 1/2)**6 - 1608
94343759688*(x - 1/2)**5 - 72888283779696*(x - 1/2)**4 - 13755877085874*(x - 1/2)**3) + 292479111540000*sqrt(5
5)*I*pi*(x - 1/2)**4/(-6508334448000*(x - 1/2)**9 - 44256674246400*(x - 1/2)**8 - 125372215916640*(x - 1/2)**7
- 189385783052928*(x - 1/2)**6 - 160894343759688*(x - 1/2)**5 - 72888283779696*(x - 1/2)**4 - 13755877085874*
(x - 1/2)**3) - 110396527395000*sqrt(55)*I*(x - 1/2)**3*atan(sqrt(110)*sqrt(x - 1/2)/11)/(-6508334448000*(x -
1/2)**9 - 44256674246400*(x - 1/2)**8 - 125372215916640*(x - 1/2)**7 - 189385783052928*(x - 1/2)**6 - 16089434
3759688*(x - 1/2)**5 - 72888283779696*(x - 1/2)**4 - 13755877085874*(x - 1/2)**3) + 178665983724690*sqrt(21)*I
*(x - 1/2)**3*atan(sqrt(42)*sqrt(x - 1/2)/7)/(-6508334448000*(x - 1/2)**9 - 44256674246400*(x - 1/2)**8 - 1253
72215916640*(x - 1/2)**7 - 189385783052928*(x - 1/2)**6 - 160894343759688*(x - 1/2)**5 - 72888283779696*(x - 1
/2)**4 - 13755877085874*(x - 1/2)**3) - 89332991862345*sqrt(21)*I*pi*(x - 1/2)**3/(-6508334448000*(x - 1/2)**9
- 44256674246400*(x - 1/2)**8 - 125372215916640*(x - 1/2)**7 - 189385783052928*(x - 1/2)**6 - 160894343759688
*(x - 1/2)**5 - 72888283779696*(x - 1/2)**4 - 13755877085874*(x - 1/2)**3) + 55198263697500*sqrt(55)*I*pi*(x -
1/2)**3/(-6508334448000*(x - 1/2)**9 - 44256674246400*(x - 1/2)**8 - 125372215916640*(x - 1/2)**7 - 189385783
052928*(x - 1/2)**6 - 160894343759688*(x - 1/2)**5 - 72888283779696*(x - 1/2)**4 - 13755877085874*(x - 1/2)**3
)
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