3.216 \(\int \frac {1}{(1-x)^{7/2} x^5} \, dx\)

Optimal. Leaf size=118 \[ -\frac {1}{4 (1-x)^{5/2} x^4}-\frac {13}{24 (1-x)^{5/2} x^3}-\frac {143}{96 (1-x)^{5/2} x^2}+\frac {3003}{64 \sqrt {1-x}}-\frac {429}{64 (1-x)^{5/2} x}+\frac {1001}{64 (1-x)^{3/2}}+\frac {3003}{320 (1-x)^{5/2}}-\frac {3003}{64} \tanh ^{-1}\left (\sqrt {1-x}\right ) \]

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Rubi [A]  time = 0.04, antiderivative size = 127, normalized size of antiderivative = 1.08, number of steps used = 9, number of rules used = 3, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.231, Rules used = {51, 63, 206} \[ -\frac {1001 \sqrt {1-x}}{32 x^2}-\frac {1001 \sqrt {1-x}}{40 x^3}-\frac {429 \sqrt {1-x}}{20 x^4}+\frac {286}{15 \sqrt {1-x} x^4}+\frac {26}{15 (1-x)^{3/2} x^4}+\frac {2}{5 (1-x)^{5/2} x^4}-\frac {3003 \sqrt {1-x}}{64 x}-\frac {3003}{64} \tanh ^{-1}\left (\sqrt {1-x}\right ) \]

Antiderivative was successfully verified.

[In]

Int[1/((1 - x)^(7/2)*x^5),x]

[Out]

2/(5*(1 - x)^(5/2)*x^4) + 26/(15*(1 - x)^(3/2)*x^4) + 286/(15*Sqrt[1 - x]*x^4) - (429*Sqrt[1 - x])/(20*x^4) -
(1001*Sqrt[1 - x])/(40*x^3) - (1001*Sqrt[1 - x])/(32*x^2) - (3003*Sqrt[1 - x])/(64*x) - (3003*ArcTanh[Sqrt[1 -
x]])/64

Rule 51

Int[((a_.) + (b_.)*(x_))^(m_)*((c_.) + (d_.)*(x_))^(n_), x_Symbol] :> Simp[((a + b*x)^(m + 1)*(c + d*x)^(n + 1
))/((b*c - a*d)*(m + 1)), x] - Dist[(d*(m + n + 2))/((b*c - a*d)*(m + 1)), Int[(a + b*x)^(m + 1)*(c + d*x)^n,
x], x] /; FreeQ[{a, b, c, d, n}, x] && NeQ[b*c - a*d, 0] && LtQ[m, -1] &&  !(LtQ[n, -1] && (EqQ[a, 0] || (NeQ[
c, 0] && LtQ[m - n, 0] && IntegerQ[n]))) && IntLinearQ[a, b, c, d, m, n, x]

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 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-x)^{7/2} x^5} \, dx &=\frac {2}{5 (1-x)^{5/2} x^4}+\frac {13}{5} \int \frac {1}{(1-x)^{5/2} x^5} \, dx\\ &=\frac {2}{5 (1-x)^{5/2} x^4}+\frac {26}{15 (1-x)^{3/2} x^4}+\frac {143}{15} \int \frac {1}{(1-x)^{3/2} x^5} \, dx\\ &=\frac {2}{5 (1-x)^{5/2} x^4}+\frac {26}{15 (1-x)^{3/2} x^4}+\frac {286}{15 \sqrt {1-x} x^4}+\frac {429}{5} \int \frac {1}{\sqrt {1-x} x^5} \, dx\\ &=\frac {2}{5 (1-x)^{5/2} x^4}+\frac {26}{15 (1-x)^{3/2} x^4}+\frac {286}{15 \sqrt {1-x} x^4}-\frac {429 \sqrt {1-x}}{20 x^4}+\frac {3003}{40} \int \frac {1}{\sqrt {1-x} x^4} \, dx\\ &=\frac {2}{5 (1-x)^{5/2} x^4}+\frac {26}{15 (1-x)^{3/2} x^4}+\frac {286}{15 \sqrt {1-x} x^4}-\frac {429 \sqrt {1-x}}{20 x^4}-\frac {1001 \sqrt {1-x}}{40 x^3}+\frac {1001}{16} \int \frac {1}{\sqrt {1-x} x^3} \, dx\\ &=\frac {2}{5 (1-x)^{5/2} x^4}+\frac {26}{15 (1-x)^{3/2} x^4}+\frac {286}{15 \sqrt {1-x} x^4}-\frac {429 \sqrt {1-x}}{20 x^4}-\frac {1001 \sqrt {1-x}}{40 x^3}-\frac {1001 \sqrt {1-x}}{32 x^2}+\frac {3003}{64} \int \frac {1}{\sqrt {1-x} x^2} \, dx\\ &=\frac {2}{5 (1-x)^{5/2} x^4}+\frac {26}{15 (1-x)^{3/2} x^4}+\frac {286}{15 \sqrt {1-x} x^4}-\frac {429 \sqrt {1-x}}{20 x^4}-\frac {1001 \sqrt {1-x}}{40 x^3}-\frac {1001 \sqrt {1-x}}{32 x^2}-\frac {3003 \sqrt {1-x}}{64 x}+\frac {3003}{128} \int \frac {1}{\sqrt {1-x} x} \, dx\\ &=\frac {2}{5 (1-x)^{5/2} x^4}+\frac {26}{15 (1-x)^{3/2} x^4}+\frac {286}{15 \sqrt {1-x} x^4}-\frac {429 \sqrt {1-x}}{20 x^4}-\frac {1001 \sqrt {1-x}}{40 x^3}-\frac {1001 \sqrt {1-x}}{32 x^2}-\frac {3003 \sqrt {1-x}}{64 x}-\frac {3003}{64} \operatorname {Subst}\left (\int \frac {1}{1-x^2} \, dx,x,\sqrt {1-x}\right )\\ &=\frac {2}{5 (1-x)^{5/2} x^4}+\frac {26}{15 (1-x)^{3/2} x^4}+\frac {286}{15 \sqrt {1-x} x^4}-\frac {429 \sqrt {1-x}}{20 x^4}-\frac {1001 \sqrt {1-x}}{40 x^3}-\frac {1001 \sqrt {1-x}}{32 x^2}-\frac {3003 \sqrt {1-x}}{64 x}-\frac {3003}{64} \tanh ^{-1}\left (\sqrt {1-x}\right )\\ \end {align*}

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Mathematica [C]  time = 0.01, size = 26, normalized size = 0.22 \[ \frac {2 \, _2F_1\left (-\frac {5}{2},5;-\frac {3}{2};1-x\right )}{5 (1-x)^{5/2}} \]

Antiderivative was successfully verified.

[In]

Integrate[1/((1 - x)^(7/2)*x^5),x]

[Out]

(2*Hypergeometric2F1[-5/2, 5, -3/2, 1 - x])/(5*(1 - x)^(5/2))

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IntegrateAlgebraic [A]  time = 0.07, size = 66, normalized size = 0.56 \[ \frac {\sqrt {1-x} \left (-45045 x^6+105105 x^5-69069 x^4+6435 x^3+1430 x^2+520 x+240\right )}{960 (x-1)^3 x^4}-\frac {3003}{64} \tanh ^{-1}\left (\sqrt {1-x}\right ) \]

Antiderivative was successfully verified.

[In]

IntegrateAlgebraic[1/((1 - x)^(7/2)*x^5),x]

[Out]

(Sqrt[1 - x]*(240 + 520*x + 1430*x^2 + 6435*x^3 - 69069*x^4 + 105105*x^5 - 45045*x^6))/(960*(-1 + x)^3*x^4) -
(3003*ArcTanh[Sqrt[1 - x]])/64

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fricas [A]  time = 0.98, size = 125, normalized size = 1.06 \[ -\frac {45045 \, {\left (x^{7} - 3 \, x^{6} + 3 \, x^{5} - x^{4}\right )} \log \left (\sqrt {-x + 1} + 1\right ) - 45045 \, {\left (x^{7} - 3 \, x^{6} + 3 \, x^{5} - x^{4}\right )} \log \left (\sqrt {-x + 1} - 1\right ) + 2 \, {\left (45045 \, x^{6} - 105105 \, x^{5} + 69069 \, x^{4} - 6435 \, x^{3} - 1430 \, x^{2} - 520 \, x - 240\right )} \sqrt {-x + 1}}{1920 \, {\left (x^{7} - 3 \, x^{6} + 3 \, x^{5} - x^{4}\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(1-x)^(7/2)/x^5,x, algorithm="fricas")

[Out]

-1/1920*(45045*(x^7 - 3*x^6 + 3*x^5 - x^4)*log(sqrt(-x + 1) + 1) - 45045*(x^7 - 3*x^6 + 3*x^5 - x^4)*log(sqrt(
-x + 1) - 1) + 2*(45045*x^6 - 105105*x^5 + 69069*x^4 - 6435*x^3 - 1430*x^2 - 520*x - 240)*sqrt(-x + 1))/(x^7 -
3*x^6 + 3*x^5 - x^4)

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giac [A]  time = 0.92, size = 104, normalized size = 0.88 \[ \frac {2 \, {\left (225 \, {\left (x - 1\right )}^{2} - 25 \, x + 28\right )}}{15 \, {\left (x - 1\right )}^{2} \sqrt {-x + 1}} - \frac {3249 \, {\left (x - 1\right )}^{3} \sqrt {-x + 1} + 10633 \, {\left (x - 1\right )}^{2} \sqrt {-x + 1} - 11767 \, {\left (-x + 1\right )}^{\frac {3}{2}} + 4431 \, \sqrt {-x + 1}}{192 \, x^{4}} - \frac {3003}{128} \, \log \left (\sqrt {-x + 1} + 1\right ) + \frac {3003}{128} \, \log \left ({\left | \sqrt {-x + 1} - 1 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(1-x)^(7/2)/x^5,x, algorithm="giac")

[Out]

2/15*(225*(x - 1)^2 - 25*x + 28)/((x - 1)^2*sqrt(-x + 1)) - 1/192*(3249*(x - 1)^3*sqrt(-x + 1) + 10633*(x - 1)
^2*sqrt(-x + 1) - 11767*(-x + 1)^(3/2) + 4431*sqrt(-x + 1))/x^4 - 3003/128*log(sqrt(-x + 1) + 1) + 3003/128*lo
g(abs(sqrt(-x + 1) - 1))

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maple [A]  time = 0.33, size = 59, normalized size = 0.50

method	result	size
risch	\(\frac {45045 x^{6}-105105 x^{5}+69069 x^{4}-6435 x^{3}-1430 x^{2}-520 x -240}{960 x^{4} \sqrt {1-x}\, \left (-1+x \right )^{2}}-\frac {3003 \arctanh \left (\sqrt {1-x}\right )}{64}\)	\(59\)
trager	\(-\frac {\left (45045 x^{6}-105105 x^{5}+69069 x^{4}-6435 x^{3}-1430 x^{2}-520 x -240\right ) \sqrt {1-x}}{960 \left (-1+x \right )^{3} x^{4}}+\frac {3003 \ln \left (\frac {-2+x +2 \sqrt {1-x}}{x}\right )}{128}\)	\(68\)
meijerg	\(\frac {\frac {\sqrt {\pi }\, \left (-329177 x^{4}+110880 x^{3}+30240 x^{2}+8960 x +1920\right )}{7680 x^{4}}-\frac {\sqrt {\pi }\, \left (-180180 x^{6}+420420 x^{5}-276276 x^{4}+25740 x^{3}+5720 x^{2}+2080 x +960\right )}{3840 x^{4} \left (1-x \right )^{\frac {5}{2}}}-\frac {3003 \sqrt {\pi }\, \ln \left (\frac {1}{2}+\frac {\sqrt {1-x}}{2}\right )}{64}+\frac {3003 \left (\frac {329177}{180180}-2 \ln \relax (2)+\ln \relax (x )+i \pi \right ) \sqrt {\pi }}{128}-\frac {\sqrt {\pi }}{4 x^{4}}-\frac {7 \sqrt {\pi }}{6 x^{3}}-\frac {63 \sqrt {\pi }}{16 x^{2}}-\frac {231 \sqrt {\pi }}{16 x}}{\sqrt {\pi }}\)	\(146\)
derivativedivides	\(-\frac {1}{64 \left (\sqrt {1-x}-1\right )^{4}}+\frac {17}{96 \left (\sqrt {1-x}-1\right )^{3}}-\frac {159}{128 \left (\sqrt {1-x}-1\right )^{2}}+\frac {1083}{128 \left (\sqrt {1-x}-1\right )}+\frac {3003 \ln \left (\sqrt {1-x}-1\right )}{128}+\frac {2}{5 \left (1-x \right )^{\frac {5}{2}}}+\frac {10}{3 \left (1-x \right )^{\frac {3}{2}}}+\frac {30}{\sqrt {1-x}}+\frac {1}{64 \left (\sqrt {1-x}+1\right )^{4}}+\frac {17}{96 \left (\sqrt {1-x}+1\right )^{3}}+\frac {159}{128 \left (\sqrt {1-x}+1\right )^{2}}+\frac {1083}{128 \left (\sqrt {1-x}+1\right )}-\frac {3003 \ln \left (\sqrt {1-x}+1\right )}{128}\)	\(157\)
default	\(-\frac {1}{64 \left (\sqrt {1-x}-1\right )^{4}}+\frac {17}{96 \left (\sqrt {1-x}-1\right )^{3}}-\frac {159}{128 \left (\sqrt {1-x}-1\right )^{2}}+\frac {1083}{128 \left (\sqrt {1-x}-1\right )}+\frac {3003 \ln \left (\sqrt {1-x}-1\right )}{128}+\frac {2}{5 \left (1-x \right )^{\frac {5}{2}}}+\frac {10}{3 \left (1-x \right )^{\frac {3}{2}}}+\frac {30}{\sqrt {1-x}}+\frac {1}{64 \left (\sqrt {1-x}+1\right )^{4}}+\frac {17}{96 \left (\sqrt {1-x}+1\right )^{3}}+\frac {159}{128 \left (\sqrt {1-x}+1\right )^{2}}+\frac {1083}{128 \left (\sqrt {1-x}+1\right )}-\frac {3003 \ln \left (\sqrt {1-x}+1\right )}{128}\)	\(157\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/(1-x)^(7/2)/x^5,x,method=_RETURNVERBOSE)

[Out]

1/960*(45045*x^6-105105*x^5+69069*x^4-6435*x^3-1430*x^2-520*x-240)/x^4/(1-x)^(1/2)/(-1+x)^2-3003/64*arctanh((1
-x)^(1/2))

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maxima [A]  time = 0.52, size = 111, normalized size = 0.94 \[ \frac {45045 \, {\left (x - 1\right )}^{6} + 165165 \, {\left (x - 1\right )}^{5} + 219219 \, {\left (x - 1\right )}^{4} + 119691 \, {\left (x - 1\right )}^{3} + 18304 \, {\left (x - 1\right )}^{2} - 1664 \, x + 2048}{960 \, {\left ({\left (-x + 1\right )}^{\frac {13}{2}} - 4 \, {\left (-x + 1\right )}^{\frac {11}{2}} + 6 \, {\left (-x + 1\right )}^{\frac {9}{2}} - 4 \, {\left (-x + 1\right )}^{\frac {7}{2}} + {\left (-x + 1\right )}^{\frac {5}{2}}\right )}} - \frac {3003}{128} \, \log \left (\sqrt {-x + 1} + 1\right ) + \frac {3003}{128} \, \log \left (\sqrt {-x + 1} - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(1-x)^(7/2)/x^5,x, algorithm="maxima")

[Out]

1/960*(45045*(x - 1)^6 + 165165*(x - 1)^5 + 219219*(x - 1)^4 + 119691*(x - 1)^3 + 18304*(x - 1)^2 - 1664*x + 2
048)/((-x + 1)^(13/2) - 4*(-x + 1)^(11/2) + 6*(-x + 1)^(9/2) - 4*(-x + 1)^(7/2) + (-x + 1)^(5/2)) - 3003/128*l
og(sqrt(-x + 1) + 1) + 3003/128*log(sqrt(-x + 1) - 1)

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mupad [B]  time = 0.21, size = 96, normalized size = 0.81 \[ \frac {\frac {286\,{\left (x-1\right )}^2}{15}-\frac {26\,x}{15}+\frac {39897\,{\left (x-1\right )}^3}{320}+\frac {73073\,{\left (x-1\right )}^4}{320}+\frac {11011\,{\left (x-1\right )}^5}{64}+\frac {3003\,{\left (x-1\right )}^6}{64}+\frac {32}{15}}{{\left (1-x\right )}^{5/2}-4\,{\left (1-x\right )}^{7/2}+6\,{\left (1-x\right )}^{9/2}-4\,{\left (1-x\right )}^{11/2}+{\left (1-x\right )}^{13/2}}-\frac {3003\,\mathrm {atanh}\left (\sqrt {1-x}\right )}{64} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/(x^5*(1 - x)^(7/2)),x)

[Out]

((286*(x - 1)^2)/15 - (26*x)/15 + (39897*(x - 1)^3)/320 + (73073*(x - 1)^4)/320 + (11011*(x - 1)^5)/64 + (3003
*(x - 1)^6)/64 + 32/15)/((1 - x)^(5/2) - 4*(1 - x)^(7/2) + 6*(1 - x)^(9/2) - 4*(1 - x)^(11/2) + (1 - x)^(13/2)
) - (3003*atanh((1 - x)^(1/2)))/64

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sympy [C]  time = 20.37, size = 971, normalized size = 8.23 \[ \begin {cases} - \frac {45045 i x^{7} \operatorname {asin}{\left (\frac {1}{\sqrt {x}} \right )}}{- 960 x^{7} + 2880 x^{6} - 2880 x^{5} + 960 x^{4}} + \frac {45045 i x^{6} \sqrt {x - 1}}{- 960 x^{7} + 2880 x^{6} - 2880 x^{5} + 960 x^{4}} + \frac {135135 i x^{6} \operatorname {asin}{\left (\frac {1}{\sqrt {x}} \right )}}{- 960 x^{7} + 2880 x^{6} - 2880 x^{5} + 960 x^{4}} - \frac {105105 i x^{5} \sqrt {x - 1}}{- 960 x^{7} + 2880 x^{6} - 2880 x^{5} + 960 x^{4}} - \frac {135135 i x^{5} \operatorname {asin}{\left (\frac {1}{\sqrt {x}} \right )}}{- 960 x^{7} + 2880 x^{6} - 2880 x^{5} + 960 x^{4}} + \frac {69069 i x^{4} \sqrt {x - 1}}{- 960 x^{7} + 2880 x^{6} - 2880 x^{5} + 960 x^{4}} + \frac {45045 i x^{4} \operatorname {asin}{\left (\frac {1}{\sqrt {x}} \right )}}{- 960 x^{7} + 2880 x^{6} - 2880 x^{5} + 960 x^{4}} - \frac {6435 i x^{3} \sqrt {x - 1}}{- 960 x^{7} + 2880 x^{6} - 2880 x^{5} + 960 x^{4}} - \frac {1430 i x^{2} \sqrt {x - 1}}{- 960 x^{7} + 2880 x^{6} - 2880 x^{5} + 960 x^{4}} - \frac {520 i x \sqrt {x - 1}}{- 960 x^{7} + 2880 x^{6} - 2880 x^{5} + 960 x^{4}} - \frac {240 i \sqrt {x - 1}}{- 960 x^{7} + 2880 x^{6} - 2880 x^{5} + 960 x^{4}} & \text {for}\: \left |{x}\right | > 1 \\- \frac {45045 x^{7} \log {\relax (x )}}{- 1920 x^{7} + 5760 x^{6} - 5760 x^{5} + 1920 x^{4}} + \frac {90090 x^{7} \log {\left (\sqrt {1 - x} + 1 \right )}}{- 1920 x^{7} + 5760 x^{6} - 5760 x^{5} + 1920 x^{4}} - \frac {45045 i \pi x^{7}}{- 1920 x^{7} + 5760 x^{6} - 5760 x^{5} + 1920 x^{4}} + \frac {90090 x^{6} \sqrt {1 - x}}{- 1920 x^{7} + 5760 x^{6} - 5760 x^{5} + 1920 x^{4}} + \frac {135135 x^{6} \log {\relax (x )}}{- 1920 x^{7} + 5760 x^{6} - 5760 x^{5} + 1920 x^{4}} - \frac {270270 x^{6} \log {\left (\sqrt {1 - x} + 1 \right )}}{- 1920 x^{7} + 5760 x^{6} - 5760 x^{5} + 1920 x^{4}} + \frac {135135 i \pi x^{6}}{- 1920 x^{7} + 5760 x^{6} - 5760 x^{5} + 1920 x^{4}} - \frac {210210 x^{5} \sqrt {1 - x}}{- 1920 x^{7} + 5760 x^{6} - 5760 x^{5} + 1920 x^{4}} - \frac {135135 x^{5} \log {\relax (x )}}{- 1920 x^{7} + 5760 x^{6} - 5760 x^{5} + 1920 x^{4}} + \frac {270270 x^{5} \log {\left (\sqrt {1 - x} + 1 \right )}}{- 1920 x^{7} + 5760 x^{6} - 5760 x^{5} + 1920 x^{4}} - \frac {135135 i \pi x^{5}}{- 1920 x^{7} + 5760 x^{6} - 5760 x^{5} + 1920 x^{4}} + \frac {138138 x^{4} \sqrt {1 - x}}{- 1920 x^{7} + 5760 x^{6} - 5760 x^{5} + 1920 x^{4}} + \frac {45045 x^{4} \log {\relax (x )}}{- 1920 x^{7} + 5760 x^{6} - 5760 x^{5} + 1920 x^{4}} - \frac {90090 x^{4} \log {\left (\sqrt {1 - x} + 1 \right )}}{- 1920 x^{7} + 5760 x^{6} - 5760 x^{5} + 1920 x^{4}} + \frac {45045 i \pi x^{4}}{- 1920 x^{7} + 5760 x^{6} - 5760 x^{5} + 1920 x^{4}} - \frac {12870 x^{3} \sqrt {1 - x}}{- 1920 x^{7} + 5760 x^{6} - 5760 x^{5} + 1920 x^{4}} - \frac {2860 x^{2} \sqrt {1 - x}}{- 1920 x^{7} + 5760 x^{6} - 5760 x^{5} + 1920 x^{4}} - \frac {1040 x \sqrt {1 - x}}{- 1920 x^{7} + 5760 x^{6} - 5760 x^{5} + 1920 x^{4}} - \frac {480 \sqrt {1 - x}}{- 1920 x^{7} + 5760 x^{6} - 5760 x^{5} + 1920 x^{4}} & \text {otherwise} \end {cases} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(1-x)**(7/2)/x**5,x)

[Out]

Piecewise((-45045*I*x**7*asin(1/sqrt(x))/(-960*x**7 + 2880*x**6 - 2880*x**5 + 960*x**4) + 45045*I*x**6*sqrt(x
- 1)/(-960*x**7 + 2880*x**6 - 2880*x**5 + 960*x**4) + 135135*I*x**6*asin(1/sqrt(x))/(-960*x**7 + 2880*x**6 - 2
880*x**5 + 960*x**4) - 105105*I*x**5*sqrt(x - 1)/(-960*x**7 + 2880*x**6 - 2880*x**5 + 960*x**4) - 135135*I*x**
5*asin(1/sqrt(x))/(-960*x**7 + 2880*x**6 - 2880*x**5 + 960*x**4) + 69069*I*x**4*sqrt(x - 1)/(-960*x**7 + 2880*
x**6 - 2880*x**5 + 960*x**4) + 45045*I*x**4*asin(1/sqrt(x))/(-960*x**7 + 2880*x**6 - 2880*x**5 + 960*x**4) - 6
435*I*x**3*sqrt(x - 1)/(-960*x**7 + 2880*x**6 - 2880*x**5 + 960*x**4) - 1430*I*x**2*sqrt(x - 1)/(-960*x**7 + 2
880*x**6 - 2880*x**5 + 960*x**4) - 520*I*x*sqrt(x - 1)/(-960*x**7 + 2880*x**6 - 2880*x**5 + 960*x**4) - 240*I*
sqrt(x - 1)/(-960*x**7 + 2880*x**6 - 2880*x**5 + 960*x**4), Abs(x) > 1), (-45045*x**7*log(x)/(-1920*x**7 + 576
0*x**6 - 5760*x**5 + 1920*x**4) + 90090*x**7*log(sqrt(1 - x) + 1)/(-1920*x**7 + 5760*x**6 - 5760*x**5 + 1920*x
**4) - 45045*I*pi*x**7/(-1920*x**7 + 5760*x**6 - 5760*x**5 + 1920*x**4) + 90090*x**6*sqrt(1 - x)/(-1920*x**7 +
5760*x**6 - 5760*x**5 + 1920*x**4) + 135135*x**6*log(x)/(-1920*x**7 + 5760*x**6 - 5760*x**5 + 1920*x**4) - 27
0270*x**6*log(sqrt(1 - x) + 1)/(-1920*x**7 + 5760*x**6 - 5760*x**5 + 1920*x**4) + 135135*I*pi*x**6/(-1920*x**7
+ 5760*x**6 - 5760*x**5 + 1920*x**4) - 210210*x**5*sqrt(1 - x)/(-1920*x**7 + 5760*x**6 - 5760*x**5 + 1920*x**
4) - 135135*x**5*log(x)/(-1920*x**7 + 5760*x**6 - 5760*x**5 + 1920*x**4) + 270270*x**5*log(sqrt(1 - x) + 1)/(-
1920*x**7 + 5760*x**6 - 5760*x**5 + 1920*x**4) - 135135*I*pi*x**5/(-1920*x**7 + 5760*x**6 - 5760*x**5 + 1920*x
**4) + 138138*x**4*sqrt(1 - x)/(-1920*x**7 + 5760*x**6 - 5760*x**5 + 1920*x**4) + 45045*x**4*log(x)/(-1920*x**
7 + 5760*x**6 - 5760*x**5 + 1920*x**4) - 90090*x**4*log(sqrt(1 - x) + 1)/(-1920*x**7 + 5760*x**6 - 5760*x**5 +
1920*x**4) + 45045*I*pi*x**4/(-1920*x**7 + 5760*x**6 - 5760*x**5 + 1920*x**4) - 12870*x**3*sqrt(1 - x)/(-1920
*x**7 + 5760*x**6 - 5760*x**5 + 1920*x**4) - 2860*x**2*sqrt(1 - x)/(-1920*x**7 + 5760*x**6 - 5760*x**5 + 1920*
x**4) - 1040*x*sqrt(1 - x)/(-1920*x**7 + 5760*x**6 - 5760*x**5 + 1920*x**4) - 480*sqrt(1 - x)/(-1920*x**7 + 57
60*x**6 - 5760*x**5 + 1920*x**4), True))

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