3.44.39 \(\int \frac {e^{e^x} (5-10 x+e^x (25-5 x+5 x^2)-80 x^2 \log ^3(x^2)+(-30 x^2+10 e^x x^3) \log ^4(x^2)-80 x^3 \log ^7(x^2)+(-20 x^3+5 e^x x^4) \log ^8(x^2))}{25-10 x+11 x^2-2 x^3+x^4+(20 x^3-4 x^4+4 x^5) \log ^4(x^2)+(10 x^4-2 x^5+6 x^6) \log ^8(x^2)+4 x^7 \log ^{12}(x^2)+x^8 \log ^{16}(x^2)} \, dx\)

Optimal. Leaf size=32 \[ \frac {e^{e^x}}{1+\frac {1}{5} \left (-x+\left (x+x^2 \log ^4\left (x^2\right )\right )^2\right )} \]

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Rubi [F]  time = 10.65, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int \frac {e^{e^x} \left (5-10 x+e^x \left (25-5 x+5 x^2\right )-80 x^2 \log ^3\left (x^2\right )+\left (-30 x^2+10 e^x x^3\right ) \log ^4\left (x^2\right )-80 x^3 \log ^7\left (x^2\right )+\left (-20 x^3+5 e^x x^4\right ) \log ^8\left (x^2\right )\right )}{25-10 x+11 x^2-2 x^3+x^4+\left (20 x^3-4 x^4+4 x^5\right ) \log ^4\left (x^2\right )+\left (10 x^4-2 x^5+6 x^6\right ) \log ^8\left (x^2\right )+4 x^7 \log ^{12}\left (x^2\right )+x^8 \log ^{16}\left (x^2\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(E^E^x*(5 - 10*x + E^x*(25 - 5*x + 5*x^2) - 80*x^2*Log[x^2]^3 + (-30*x^2 + 10*E^x*x^3)*Log[x^2]^4 - 80*x^3
*Log[x^2]^7 + (-20*x^3 + 5*E^x*x^4)*Log[x^2]^8))/(25 - 10*x + 11*x^2 - 2*x^3 + x^4 + (20*x^3 - 4*x^4 + 4*x^5)*
Log[x^2]^4 + (10*x^4 - 2*x^5 + 6*x^6)*Log[x^2]^8 + 4*x^7*Log[x^2]^12 + x^8*Log[x^2]^16),x]

[Out]

-15*Defer[Int][E^E^x/(5 - x + x^2 + 2*x^3*Log[x^2]^4 + x^4*Log[x^2]^8)^2, x] + 100*Defer[Int][E^E^x/(x*(5 - x
+ x^2 + 2*x^3*Log[x^2]^4 + x^4*Log[x^2]^8)^2), x] + 10*Defer[Int][(E^E^x*x)/(5 - x + x^2 + 2*x^3*Log[x^2]^4 +
x^4*Log[x^2]^8)^2, x] - 80*Defer[Int][(E^E^x*x^2*Log[x^2]^3)/(5 - x + x^2 + 2*x^3*Log[x^2]^4 + x^4*Log[x^2]^8)
^2, x] + 10*Defer[Int][(E^E^x*x^2*Log[x^2]^4)/(5 - x + x^2 + 2*x^3*Log[x^2]^4 + x^4*Log[x^2]^8)^2, x] - 80*Def
er[Int][(E^E^x*x^3*Log[x^2]^7)/(5 - x + x^2 + 2*x^3*Log[x^2]^4 + x^4*Log[x^2]^8)^2, x] + 5*Defer[Int][E^(E^x +
x)/(5 - x + x^2 + 2*x^3*Log[x^2]^4 + x^4*Log[x^2]^8), x] - 20*Defer[Int][E^E^x/(x*(5 - x + x^2 + 2*x^3*Log[x^
2]^4 + x^4*Log[x^2]^8)), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {5 e^{e^x} \left (1-2 x+e^x \left (5-x+x^2\right )-16 x^2 \log ^3\left (x^2\right )+2 x^2 \left (-3+e^x x\right ) \log ^4\left (x^2\right )-16 x^3 \log ^7\left (x^2\right )+x^3 \left (-4+e^x x\right ) \log ^8\left (x^2\right )\right )}{\left (5-x+x^2+2 x^3 \log ^4\left (x^2\right )+x^4 \log ^8\left (x^2\right )\right )^2} \, dx\\ &=5 \int \frac {e^{e^x} \left (1-2 x+e^x \left (5-x+x^2\right )-16 x^2 \log ^3\left (x^2\right )+2 x^2 \left (-3+e^x x\right ) \log ^4\left (x^2\right )-16 x^3 \log ^7\left (x^2\right )+x^3 \left (-4+e^x x\right ) \log ^8\left (x^2\right )\right )}{\left (5-x+x^2+2 x^3 \log ^4\left (x^2\right )+x^4 \log ^8\left (x^2\right )\right )^2} \, dx\\ &=5 \int \left (\frac {e^{e^x}}{\left (5-x+x^2+2 x^3 \log ^4\left (x^2\right )+x^4 \log ^8\left (x^2\right )\right )^2}-\frac {2 e^{e^x} x}{\left (5-x+x^2+2 x^3 \log ^4\left (x^2\right )+x^4 \log ^8\left (x^2\right )\right )^2}-\frac {16 e^{e^x} x^2 \log ^3\left (x^2\right )}{\left (5-x+x^2+2 x^3 \log ^4\left (x^2\right )+x^4 \log ^8\left (x^2\right )\right )^2}-\frac {6 e^{e^x} x^2 \log ^4\left (x^2\right )}{\left (5-x+x^2+2 x^3 \log ^4\left (x^2\right )+x^4 \log ^8\left (x^2\right )\right )^2}-\frac {16 e^{e^x} x^3 \log ^7\left (x^2\right )}{\left (5-x+x^2+2 x^3 \log ^4\left (x^2\right )+x^4 \log ^8\left (x^2\right )\right )^2}-\frac {4 e^{e^x} x^3 \log ^8\left (x^2\right )}{\left (5-x+x^2+2 x^3 \log ^4\left (x^2\right )+x^4 \log ^8\left (x^2\right )\right )^2}+\frac {e^{e^x+x}}{5-x+x^2+2 x^3 \log ^4\left (x^2\right )+x^4 \log ^8\left (x^2\right )}\right ) \, dx\\ &=5 \int \frac {e^{e^x}}{\left (5-x+x^2+2 x^3 \log ^4\left (x^2\right )+x^4 \log ^8\left (x^2\right )\right )^2} \, dx+5 \int \frac {e^{e^x+x}}{5-x+x^2+2 x^3 \log ^4\left (x^2\right )+x^4 \log ^8\left (x^2\right )} \, dx-10 \int \frac {e^{e^x} x}{\left (5-x+x^2+2 x^3 \log ^4\left (x^2\right )+x^4 \log ^8\left (x^2\right )\right )^2} \, dx-20 \int \frac {e^{e^x} x^3 \log ^8\left (x^2\right )}{\left (5-x+x^2+2 x^3 \log ^4\left (x^2\right )+x^4 \log ^8\left (x^2\right )\right )^2} \, dx-30 \int \frac {e^{e^x} x^2 \log ^4\left (x^2\right )}{\left (5-x+x^2+2 x^3 \log ^4\left (x^2\right )+x^4 \log ^8\left (x^2\right )\right )^2} \, dx-80 \int \frac {e^{e^x} x^2 \log ^3\left (x^2\right )}{\left (5-x+x^2+2 x^3 \log ^4\left (x^2\right )+x^4 \log ^8\left (x^2\right )\right )^2} \, dx-80 \int \frac {e^{e^x} x^3 \log ^7\left (x^2\right )}{\left (5-x+x^2+2 x^3 \log ^4\left (x^2\right )+x^4 \log ^8\left (x^2\right )\right )^2} \, dx\\ &=5 \int \frac {e^{e^x}}{\left (5-x+x^2+2 x^3 \log ^4\left (x^2\right )+x^4 \log ^8\left (x^2\right )\right )^2} \, dx+5 \int \frac {e^{e^x+x}}{5-x+x^2+2 x^3 \log ^4\left (x^2\right )+x^4 \log ^8\left (x^2\right )} \, dx-10 \int \frac {e^{e^x} x}{\left (5-x+x^2+2 x^3 \log ^4\left (x^2\right )+x^4 \log ^8\left (x^2\right )\right )^2} \, dx-20 \int \left (\frac {e^{e^x} \left (-5+x-x^2-2 x^3 \log ^4\left (x^2\right )\right )}{x \left (5-x+x^2+2 x^3 \log ^4\left (x^2\right )+x^4 \log ^8\left (x^2\right )\right )^2}+\frac {e^{e^x}}{x \left (5-x+x^2+2 x^3 \log ^4\left (x^2\right )+x^4 \log ^8\left (x^2\right )\right )}\right ) \, dx-30 \int \frac {e^{e^x} x^2 \log ^4\left (x^2\right )}{\left (5-x+x^2+2 x^3 \log ^4\left (x^2\right )+x^4 \log ^8\left (x^2\right )\right )^2} \, dx-80 \int \frac {e^{e^x} x^2 \log ^3\left (x^2\right )}{\left (5-x+x^2+2 x^3 \log ^4\left (x^2\right )+x^4 \log ^8\left (x^2\right )\right )^2} \, dx-80 \int \frac {e^{e^x} x^3 \log ^7\left (x^2\right )}{\left (5-x+x^2+2 x^3 \log ^4\left (x^2\right )+x^4 \log ^8\left (x^2\right )\right )^2} \, dx\\ &=5 \int \frac {e^{e^x}}{\left (5-x+x^2+2 x^3 \log ^4\left (x^2\right )+x^4 \log ^8\left (x^2\right )\right )^2} \, dx+5 \int \frac {e^{e^x+x}}{5-x+x^2+2 x^3 \log ^4\left (x^2\right )+x^4 \log ^8\left (x^2\right )} \, dx-10 \int \frac {e^{e^x} x}{\left (5-x+x^2+2 x^3 \log ^4\left (x^2\right )+x^4 \log ^8\left (x^2\right )\right )^2} \, dx-20 \int \frac {e^{e^x} \left (-5+x-x^2-2 x^3 \log ^4\left (x^2\right )\right )}{x \left (5-x+x^2+2 x^3 \log ^4\left (x^2\right )+x^4 \log ^8\left (x^2\right )\right )^2} \, dx-20 \int \frac {e^{e^x}}{x \left (5-x+x^2+2 x^3 \log ^4\left (x^2\right )+x^4 \log ^8\left (x^2\right )\right )} \, dx-30 \int \frac {e^{e^x} x^2 \log ^4\left (x^2\right )}{\left (5-x+x^2+2 x^3 \log ^4\left (x^2\right )+x^4 \log ^8\left (x^2\right )\right )^2} \, dx-80 \int \frac {e^{e^x} x^2 \log ^3\left (x^2\right )}{\left (5-x+x^2+2 x^3 \log ^4\left (x^2\right )+x^4 \log ^8\left (x^2\right )\right )^2} \, dx-80 \int \frac {e^{e^x} x^3 \log ^7\left (x^2\right )}{\left (5-x+x^2+2 x^3 \log ^4\left (x^2\right )+x^4 \log ^8\left (x^2\right )\right )^2} \, dx\\ &=5 \int \frac {e^{e^x}}{\left (5-x+x^2+2 x^3 \log ^4\left (x^2\right )+x^4 \log ^8\left (x^2\right )\right )^2} \, dx+5 \int \frac {e^{e^x+x}}{5-x+x^2+2 x^3 \log ^4\left (x^2\right )+x^4 \log ^8\left (x^2\right )} \, dx-10 \int \frac {e^{e^x} x}{\left (5-x+x^2+2 x^3 \log ^4\left (x^2\right )+x^4 \log ^8\left (x^2\right )\right )^2} \, dx-20 \int \frac {e^{e^x}}{x \left (5-x+x^2+2 x^3 \log ^4\left (x^2\right )+x^4 \log ^8\left (x^2\right )\right )} \, dx-20 \int \left (\frac {e^{e^x}}{\left (5-x+x^2+2 x^3 \log ^4\left (x^2\right )+x^4 \log ^8\left (x^2\right )\right )^2}-\frac {5 e^{e^x}}{x \left (5-x+x^2+2 x^3 \log ^4\left (x^2\right )+x^4 \log ^8\left (x^2\right )\right )^2}-\frac {e^{e^x} x}{\left (5-x+x^2+2 x^3 \log ^4\left (x^2\right )+x^4 \log ^8\left (x^2\right )\right )^2}-\frac {2 e^{e^x} x^2 \log ^4\left (x^2\right )}{\left (5-x+x^2+2 x^3 \log ^4\left (x^2\right )+x^4 \log ^8\left (x^2\right )\right )^2}\right ) \, dx-30 \int \frac {e^{e^x} x^2 \log ^4\left (x^2\right )}{\left (5-x+x^2+2 x^3 \log ^4\left (x^2\right )+x^4 \log ^8\left (x^2\right )\right )^2} \, dx-80 \int \frac {e^{e^x} x^2 \log ^3\left (x^2\right )}{\left (5-x+x^2+2 x^3 \log ^4\left (x^2\right )+x^4 \log ^8\left (x^2\right )\right )^2} \, dx-80 \int \frac {e^{e^x} x^3 \log ^7\left (x^2\right )}{\left (5-x+x^2+2 x^3 \log ^4\left (x^2\right )+x^4 \log ^8\left (x^2\right )\right )^2} \, dx\\ &=5 \int \frac {e^{e^x}}{\left (5-x+x^2+2 x^3 \log ^4\left (x^2\right )+x^4 \log ^8\left (x^2\right )\right )^2} \, dx+5 \int \frac {e^{e^x+x}}{5-x+x^2+2 x^3 \log ^4\left (x^2\right )+x^4 \log ^8\left (x^2\right )} \, dx-10 \int \frac {e^{e^x} x}{\left (5-x+x^2+2 x^3 \log ^4\left (x^2\right )+x^4 \log ^8\left (x^2\right )\right )^2} \, dx-20 \int \frac {e^{e^x}}{\left (5-x+x^2+2 x^3 \log ^4\left (x^2\right )+x^4 \log ^8\left (x^2\right )\right )^2} \, dx+20 \int \frac {e^{e^x} x}{\left (5-x+x^2+2 x^3 \log ^4\left (x^2\right )+x^4 \log ^8\left (x^2\right )\right )^2} \, dx-20 \int \frac {e^{e^x}}{x \left (5-x+x^2+2 x^3 \log ^4\left (x^2\right )+x^4 \log ^8\left (x^2\right )\right )} \, dx-30 \int \frac {e^{e^x} x^2 \log ^4\left (x^2\right )}{\left (5-x+x^2+2 x^3 \log ^4\left (x^2\right )+x^4 \log ^8\left (x^2\right )\right )^2} \, dx+40 \int \frac {e^{e^x} x^2 \log ^4\left (x^2\right )}{\left (5-x+x^2+2 x^3 \log ^4\left (x^2\right )+x^4 \log ^8\left (x^2\right )\right )^2} \, dx-80 \int \frac {e^{e^x} x^2 \log ^3\left (x^2\right )}{\left (5-x+x^2+2 x^3 \log ^4\left (x^2\right )+x^4 \log ^8\left (x^2\right )\right )^2} \, dx-80 \int \frac {e^{e^x} x^3 \log ^7\left (x^2\right )}{\left (5-x+x^2+2 x^3 \log ^4\left (x^2\right )+x^4 \log ^8\left (x^2\right )\right )^2} \, dx+100 \int \frac {e^{e^x}}{x \left (5-x+x^2+2 x^3 \log ^4\left (x^2\right )+x^4 \log ^8\left (x^2\right )\right )^2} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.28, size = 38, normalized size = 1.19 \begin {gather*} \frac {5 e^{e^x}}{5-x+x^2+2 x^3 \log ^4\left (x^2\right )+x^4 \log ^8\left (x^2\right )} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^E^x*(5 - 10*x + E^x*(25 - 5*x + 5*x^2) - 80*x^2*Log[x^2]^3 + (-30*x^2 + 10*E^x*x^3)*Log[x^2]^4 -
80*x^3*Log[x^2]^7 + (-20*x^3 + 5*E^x*x^4)*Log[x^2]^8))/(25 - 10*x + 11*x^2 - 2*x^3 + x^4 + (20*x^3 - 4*x^4 + 4
*x^5)*Log[x^2]^4 + (10*x^4 - 2*x^5 + 6*x^6)*Log[x^2]^8 + 4*x^7*Log[x^2]^12 + x^8*Log[x^2]^16),x]

[Out]

(5*E^E^x)/(5 - x + x^2 + 2*x^3*Log[x^2]^4 + x^4*Log[x^2]^8)

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fricas [A]  time = 1.03, size = 36, normalized size = 1.12 \begin {gather*} \frac {5 \, e^{\left (e^{x}\right )}}{x^{4} \log \left (x^{2}\right )^{8} + 2 \, x^{3} \log \left (x^{2}\right )^{4} + x^{2} - x + 5} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((5*exp(x)*x^4-20*x^3)*log(x^2)^8-80*x^3*log(x^2)^7+(10*exp(x)*x^3-30*x^2)*log(x^2)^4-80*x^2*log(x^2
)^3+(5*x^2-5*x+25)*exp(x)-10*x+5)*exp(exp(x))/(x^8*log(x^2)^16+4*x^7*log(x^2)^12+(6*x^6-2*x^5+10*x^4)*log(x^2)
^8+(4*x^5-4*x^4+20*x^3)*log(x^2)^4+x^4-2*x^3+11*x^2-10*x+25),x, algorithm="fricas")

[Out]

5*e^(e^x)/(x^4*log(x^2)^8 + 2*x^3*log(x^2)^4 + x^2 - x + 5)

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giac [F(-1)]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((5*exp(x)*x^4-20*x^3)*log(x^2)^8-80*x^3*log(x^2)^7+(10*exp(x)*x^3-30*x^2)*log(x^2)^4-80*x^2*log(x^2
)^3+(5*x^2-5*x+25)*exp(x)-10*x+5)*exp(exp(x))/(x^8*log(x^2)^16+4*x^7*log(x^2)^12+(6*x^6-2*x^5+10*x^4)*log(x^2)
^8+(4*x^5-4*x^4+20*x^3)*log(x^2)^4+x^4-2*x^3+11*x^2-10*x+25),x, algorithm="giac")

[Out]

Timed out

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maple [F]  time = 180.00, size = 0, normalized size = 0.00 \[\int \frac {\left (\left (5 \,{\mathrm e}^{x} x^{4}-20 x^{3}\right ) \ln \left (x^{2}\right )^{8}-80 x^{3} \ln \left (x^{2}\right )^{7}+\left (10 \,{\mathrm e}^{x} x^{3}-30 x^{2}\right ) \ln \left (x^{2}\right )^{4}-80 x^{2} \ln \left (x^{2}\right )^{3}+\left (5 x^{2}-5 x +25\right ) {\mathrm e}^{x}-10 x +5\right ) {\mathrm e}^{{\mathrm e}^{x}}}{x^{8} \ln \left (x^{2}\right )^{16}+4 x^{7} \ln \left (x^{2}\right )^{12}+\left (6 x^{6}-2 x^{5}+10 x^{4}\right ) \ln \left (x^{2}\right )^{8}+\left (4 x^{5}-4 x^{4}+20 x^{3}\right ) \ln \left (x^{2}\right )^{4}+x^{4}-2 x^{3}+11 x^{2}-10 x +25}\, dx\]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((5*exp(x)*x^4-20*x^3)*ln(x^2)^8-80*x^3*ln(x^2)^7+(10*exp(x)*x^3-30*x^2)*ln(x^2)^4-80*x^2*ln(x^2)^3+(5*x^2
-5*x+25)*exp(x)-10*x+5)*exp(exp(x))/(x^8*ln(x^2)^16+4*x^7*ln(x^2)^12+(6*x^6-2*x^5+10*x^4)*ln(x^2)^8+(4*x^5-4*x
^4+20*x^3)*ln(x^2)^4+x^4-2*x^3+11*x^2-10*x+25),x)

[Out]

int(((5*exp(x)*x^4-20*x^3)*ln(x^2)^8-80*x^3*ln(x^2)^7+(10*exp(x)*x^3-30*x^2)*ln(x^2)^4-80*x^2*ln(x^2)^3+(5*x^2
-5*x+25)*exp(x)-10*x+5)*exp(exp(x))/(x^8*ln(x^2)^16+4*x^7*ln(x^2)^12+(6*x^6-2*x^5+10*x^4)*ln(x^2)^8+(4*x^5-4*x
^4+20*x^3)*ln(x^2)^4+x^4-2*x^3+11*x^2-10*x+25),x)

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maxima [A]  time = 0.41, size = 33, normalized size = 1.03 \begin {gather*} \frac {5 \, e^{\left (e^{x}\right )}}{256 \, x^{4} \log \relax (x)^{8} + 32 \, x^{3} \log \relax (x)^{4} + x^{2} - x + 5} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((5*exp(x)*x^4-20*x^3)*log(x^2)^8-80*x^3*log(x^2)^7+(10*exp(x)*x^3-30*x^2)*log(x^2)^4-80*x^2*log(x^2
)^3+(5*x^2-5*x+25)*exp(x)-10*x+5)*exp(exp(x))/(x^8*log(x^2)^16+4*x^7*log(x^2)^12+(6*x^6-2*x^5+10*x^4)*log(x^2)
^8+(4*x^5-4*x^4+20*x^3)*log(x^2)^4+x^4-2*x^3+11*x^2-10*x+25),x, algorithm="maxima")

[Out]

5*e^(e^x)/(256*x^4*log(x)^8 + 32*x^3*log(x)^4 + x^2 - x + 5)

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mupad [B]  time = 3.61, size = 36, normalized size = 1.12 \begin {gather*} \frac {5\,{\mathrm {e}}^{{\mathrm {e}}^x}}{x^4\,{\ln \left (x^2\right )}^8+2\,x^3\,{\ln \left (x^2\right )}^4+x^2-x+5} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(exp(x))*(exp(x)*(5*x^2 - 5*x + 25) - 10*x + log(x^2)^8*(5*x^4*exp(x) - 20*x^3) + log(x^2)^4*(10*x^3*e
xp(x) - 30*x^2) - 80*x^2*log(x^2)^3 - 80*x^3*log(x^2)^7 + 5))/(log(x^2)^8*(10*x^4 - 2*x^5 + 6*x^6) - 10*x + lo
g(x^2)^4*(20*x^3 - 4*x^4 + 4*x^5) + 11*x^2 - 2*x^3 + x^4 + 4*x^7*log(x^2)^12 + x^8*log(x^2)^16 + 25),x)

[Out]

(5*exp(exp(x)))/(x^2 - x + 2*x^3*log(x^2)^4 + x^4*log(x^2)^8 + 5)

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sympy [A]  time = 0.48, size = 34, normalized size = 1.06 \begin {gather*} \frac {5 e^{e^{x}}}{x^{4} \log {\left (x^{2} \right )}^{8} + 2 x^{3} \log {\left (x^{2} \right )}^{4} + x^{2} - x + 5} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((5*exp(x)*x**4-20*x**3)*ln(x**2)**8-80*x**3*ln(x**2)**7+(10*exp(x)*x**3-30*x**2)*ln(x**2)**4-80*x**
2*ln(x**2)**3+(5*x**2-5*x+25)*exp(x)-10*x+5)*exp(exp(x))/(x**8*ln(x**2)**16+4*x**7*ln(x**2)**12+(6*x**6-2*x**5
+10*x**4)*ln(x**2)**8+(4*x**5-4*x**4+20*x**3)*ln(x**2)**4+x**4-2*x**3+11*x**2-10*x+25),x)

[Out]

5*exp(exp(x))/(x**4*log(x**2)**8 + 2*x**3*log(x**2)**4 + x**2 - x + 5)

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