3.65.32 \(\int \frac {(-5400+2160 x^3-216 x^6+e^{e^{\frac {x}{-20+4 x^3}}} (200-80 x^3+8 x^6)) \log (\frac {1}{5} (27-e^{e^{\frac {x}{-20+4 x^3}}}))+e^{e^{\frac {x}{-20+4 x^3}}+\frac {x}{-20+4 x^3}} (5 x+2 x^4) \log (x^2)}{(-2700 x+1080 x^4-108 x^7+e^{e^{\frac {x}{-20+4 x^3}}} (100 x-40 x^4+4 x^7)) \log ^2(\frac {1}{5} (27-e^{e^{\frac {x}{-20+4 x^3}}}))} \, dx\)

Optimal. Leaf size=34 \[ \frac {\log \left (x^2\right )}{\log \left (5+\frac {1}{5} \left (2-e^{e^{\frac {x}{4 \left (-5+x^3\right )}}}\right )\right )} \]

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Rubi [F]  time = 29.11, 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 {\left (-5400+2160 x^3-216 x^6+e^{e^{\frac {x}{-20+4 x^3}}} \left (200-80 x^3+8 x^6\right )\right ) \log \left (\frac {1}{5} \left (27-e^{e^{\frac {x}{-20+4 x^3}}}\right )\right )+e^{e^{\frac {x}{-20+4 x^3}}+\frac {x}{-20+4 x^3}} \left (5 x+2 x^4\right ) \log \left (x^2\right )}{\left (-2700 x+1080 x^4-108 x^7+e^{e^{\frac {x}{-20+4 x^3}}} \left (100 x-40 x^4+4 x^7\right )\right ) \log ^2\left (\frac {1}{5} \left (27-e^{e^{\frac {x}{-20+4 x^3}}}\right )\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[((-5400 + 2160*x^3 - 216*x^6 + E^E^(x/(-20 + 4*x^3))*(200 - 80*x^3 + 8*x^6))*Log[(27 - E^E^(x/(-20 + 4*x^3
)))/5] + E^(E^(x/(-20 + 4*x^3)) + x/(-20 + 4*x^3))*(5*x + 2*x^4)*Log[x^2])/((-2700*x + 1080*x^4 - 108*x^7 + E^
E^(x/(-20 + 4*x^3))*(100*x - 40*x^4 + 4*x^7))*Log[(27 - E^E^(x/(-20 + 4*x^3)))/5]^2),x]

[Out]

2*Defer[Int][1/(x*Log[(27 - E^E^(x/(4*(-5 + x^3))))/5]), x] - Defer[Int][(E^(E^(x/(4*(-5 + x^3))) + x/(4*(-5 +
x^3)))*Log[x^2])/((-27 + E^E^(x/(4*(-5 + x^3))))*(5^(1/3) - x)*Log[(27 - E^E^(x/(4*(-5 + x^3))))/5]^2), x]/(6
*5^(2/3)) - Defer[Int][(E^(E^(x/(4*(-5 + x^3))) + x/(4*(-5 + x^3)))*Log[x^2])/((-27 + E^E^(x/(4*(-5 + x^3))))*
(5^(1/3) + (-1)^(1/3)*x)*Log[(27 - E^E^(x/(4*(-5 + x^3))))/5]^2), x]/(6*5^(2/3)) - Defer[Int][(E^(E^(x/(4*(-5
+ x^3))) + x/(4*(-5 + x^3)))*Log[x^2])/((-27 + E^E^(x/(4*(-5 + x^3))))*(5^(1/3) - (-1)^(2/3)*x)*Log[(27 - E^E^
(x/(4*(-5 + x^3))))/5]^2), x]/(6*5^(2/3)) + (15*Defer[Int][(E^(E^(x/(4*(-5 + x^3))) + x/(4*(-5 + x^3)))*Log[x^
2])/((-27 + E^E^(x/(4*(-5 + x^3))))*(-5 + x^3)^2*Log[(27 - E^E^(x/(4*(-5 + x^3))))/5]^2), x])/4

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {\frac {8 \log \left (\frac {1}{5} \left (27-e^{e^{\frac {x}{4 \left (-5+x^3\right )}}}\right )\right )}{x}+\frac {e^{e^{\frac {x}{4 \left (-5+x^3\right )}}+\frac {x}{4 \left (-5+x^3\right )}} \left (5+2 x^3\right ) \log \left (x^2\right )}{\left (-27+e^{e^{\frac {x}{4 \left (-5+x^3\right )}}}\right ) \left (-5+x^3\right )^2}}{4 \log ^2\left (\frac {1}{5} \left (27-e^{e^{\frac {x}{4 \left (-5+x^3\right )}}}\right )\right )} \, dx\\ &=\frac {1}{4} \int \frac {\frac {8 \log \left (\frac {1}{5} \left (27-e^{e^{\frac {x}{4 \left (-5+x^3\right )}}}\right )\right )}{x}+\frac {e^{e^{\frac {x}{4 \left (-5+x^3\right )}}+\frac {x}{4 \left (-5+x^3\right )}} \left (5+2 x^3\right ) \log \left (x^2\right )}{\left (-27+e^{e^{\frac {x}{4 \left (-5+x^3\right )}}}\right ) \left (-5+x^3\right )^2}}{\log ^2\left (\frac {1}{5} \left (27-e^{e^{\frac {x}{4 \left (-5+x^3\right )}}}\right )\right )} \, dx\\ &=\frac {1}{4} \int \left (\frac {8}{x \log \left (\frac {1}{5} \left (27-e^{e^{\frac {x}{4 \left (-5+x^3\right )}}}\right )\right )}+\frac {e^{e^{\frac {x}{4 \left (-5+x^3\right )}}+\frac {x}{4 \left (-5+x^3\right )}} \left (5+2 x^3\right ) \log \left (x^2\right )}{\left (-27+e^{e^{\frac {x}{4 \left (-5+x^3\right )}}}\right ) \left (-5+x^3\right )^2 \log ^2\left (\frac {1}{5} \left (27-e^{e^{\frac {x}{4 \left (-5+x^3\right )}}}\right )\right )}\right ) \, dx\\ &=\frac {1}{4} \int \frac {e^{e^{\frac {x}{4 \left (-5+x^3\right )}}+\frac {x}{4 \left (-5+x^3\right )}} \left (5+2 x^3\right ) \log \left (x^2\right )}{\left (-27+e^{e^{\frac {x}{4 \left (-5+x^3\right )}}}\right ) \left (-5+x^3\right )^2 \log ^2\left (\frac {1}{5} \left (27-e^{e^{\frac {x}{4 \left (-5+x^3\right )}}}\right )\right )} \, dx+2 \int \frac {1}{x \log \left (\frac {1}{5} \left (27-e^{e^{\frac {x}{4 \left (-5+x^3\right )}}}\right )\right )} \, dx\\ &=\frac {1}{4} \int \left (\frac {15 e^{e^{\frac {x}{4 \left (-5+x^3\right )}}+\frac {x}{4 \left (-5+x^3\right )}} \log \left (x^2\right )}{\left (-27+e^{e^{\frac {x}{4 \left (-5+x^3\right )}}}\right ) \left (-5+x^3\right )^2 \log ^2\left (\frac {1}{5} \left (27-e^{e^{\frac {x}{4 \left (-5+x^3\right )}}}\right )\right )}+\frac {2 e^{e^{\frac {x}{4 \left (-5+x^3\right )}}+\frac {x}{4 \left (-5+x^3\right )}} \log \left (x^2\right )}{\left (-27+e^{e^{\frac {x}{4 \left (-5+x^3\right )}}}\right ) \left (-5+x^3\right ) \log ^2\left (\frac {1}{5} \left (27-e^{e^{\frac {x}{4 \left (-5+x^3\right )}}}\right )\right )}\right ) \, dx+2 \int \frac {1}{x \log \left (\frac {1}{5} \left (27-e^{e^{\frac {x}{4 \left (-5+x^3\right )}}}\right )\right )} \, dx\\ &=\frac {1}{2} \int \frac {e^{e^{\frac {x}{4 \left (-5+x^3\right )}}+\frac {x}{4 \left (-5+x^3\right )}} \log \left (x^2\right )}{\left (-27+e^{e^{\frac {x}{4 \left (-5+x^3\right )}}}\right ) \left (-5+x^3\right ) \log ^2\left (\frac {1}{5} \left (27-e^{e^{\frac {x}{4 \left (-5+x^3\right )}}}\right )\right )} \, dx+2 \int \frac {1}{x \log \left (\frac {1}{5} \left (27-e^{e^{\frac {x}{4 \left (-5+x^3\right )}}}\right )\right )} \, dx+\frac {15}{4} \int \frac {e^{e^{\frac {x}{4 \left (-5+x^3\right )}}+\frac {x}{4 \left (-5+x^3\right )}} \log \left (x^2\right )}{\left (-27+e^{e^{\frac {x}{4 \left (-5+x^3\right )}}}\right ) \left (-5+x^3\right )^2 \log ^2\left (\frac {1}{5} \left (27-e^{e^{\frac {x}{4 \left (-5+x^3\right )}}}\right )\right )} \, dx\\ &=\frac {1}{2} \int \left (-\frac {e^{e^{\frac {x}{4 \left (-5+x^3\right )}}+\frac {x}{4 \left (-5+x^3\right )}} \log \left (x^2\right )}{3\ 5^{2/3} \left (-27+e^{e^{\frac {x}{4 \left (-5+x^3\right )}}}\right ) \left (\sqrt [3]{5}-x\right ) \log ^2\left (\frac {1}{5} \left (27-e^{e^{\frac {x}{4 \left (-5+x^3\right )}}}\right )\right )}-\frac {e^{e^{\frac {x}{4 \left (-5+x^3\right )}}+\frac {x}{4 \left (-5+x^3\right )}} \log \left (x^2\right )}{3\ 5^{2/3} \left (-27+e^{e^{\frac {x}{4 \left (-5+x^3\right )}}}\right ) \left (\sqrt [3]{5}+\sqrt [3]{-1} x\right ) \log ^2\left (\frac {1}{5} \left (27-e^{e^{\frac {x}{4 \left (-5+x^3\right )}}}\right )\right )}-\frac {e^{e^{\frac {x}{4 \left (-5+x^3\right )}}+\frac {x}{4 \left (-5+x^3\right )}} \log \left (x^2\right )}{3\ 5^{2/3} \left (-27+e^{e^{\frac {x}{4 \left (-5+x^3\right )}}}\right ) \left (\sqrt [3]{5}-(-1)^{2/3} x\right ) \log ^2\left (\frac {1}{5} \left (27-e^{e^{\frac {x}{4 \left (-5+x^3\right )}}}\right )\right )}\right ) \, dx+2 \int \frac {1}{x \log \left (\frac {1}{5} \left (27-e^{e^{\frac {x}{4 \left (-5+x^3\right )}}}\right )\right )} \, dx+\frac {15}{4} \int \frac {e^{e^{\frac {x}{4 \left (-5+x^3\right )}}+\frac {x}{4 \left (-5+x^3\right )}} \log \left (x^2\right )}{\left (-27+e^{e^{\frac {x}{4 \left (-5+x^3\right )}}}\right ) \left (-5+x^3\right )^2 \log ^2\left (\frac {1}{5} \left (27-e^{e^{\frac {x}{4 \left (-5+x^3\right )}}}\right )\right )} \, dx\\ &=2 \int \frac {1}{x \log \left (\frac {1}{5} \left (27-e^{e^{\frac {x}{4 \left (-5+x^3\right )}}}\right )\right )} \, dx+\frac {15}{4} \int \frac {e^{e^{\frac {x}{4 \left (-5+x^3\right )}}+\frac {x}{4 \left (-5+x^3\right )}} \log \left (x^2\right )}{\left (-27+e^{e^{\frac {x}{4 \left (-5+x^3\right )}}}\right ) \left (-5+x^3\right )^2 \log ^2\left (\frac {1}{5} \left (27-e^{e^{\frac {x}{4 \left (-5+x^3\right )}}}\right )\right )} \, dx-\frac {\int \frac {e^{e^{\frac {x}{4 \left (-5+x^3\right )}}+\frac {x}{4 \left (-5+x^3\right )}} \log \left (x^2\right )}{\left (-27+e^{e^{\frac {x}{4 \left (-5+x^3\right )}}}\right ) \left (\sqrt [3]{5}-x\right ) \log ^2\left (\frac {1}{5} \left (27-e^{e^{\frac {x}{4 \left (-5+x^3\right )}}}\right )\right )} \, dx}{6\ 5^{2/3}}-\frac {\int \frac {e^{e^{\frac {x}{4 \left (-5+x^3\right )}}+\frac {x}{4 \left (-5+x^3\right )}} \log \left (x^2\right )}{\left (-27+e^{e^{\frac {x}{4 \left (-5+x^3\right )}}}\right ) \left (\sqrt [3]{5}+\sqrt [3]{-1} x\right ) \log ^2\left (\frac {1}{5} \left (27-e^{e^{\frac {x}{4 \left (-5+x^3\right )}}}\right )\right )} \, dx}{6\ 5^{2/3}}-\frac {\int \frac {e^{e^{\frac {x}{4 \left (-5+x^3\right )}}+\frac {x}{4 \left (-5+x^3\right )}} \log \left (x^2\right )}{\left (-27+e^{e^{\frac {x}{4 \left (-5+x^3\right )}}}\right ) \left (\sqrt [3]{5}-(-1)^{2/3} x\right ) \log ^2\left (\frac {1}{5} \left (27-e^{e^{\frac {x}{4 \left (-5+x^3\right )}}}\right )\right )} \, dx}{6\ 5^{2/3}}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.36, size = 32, normalized size = 0.94 \begin {gather*} \frac {\log \left (x^2\right )}{\log \left (\frac {1}{5} \left (27-e^{e^{\frac {x}{4 \left (-5+x^3\right )}}}\right )\right )} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[((-5400 + 2160*x^3 - 216*x^6 + E^E^(x/(-20 + 4*x^3))*(200 - 80*x^3 + 8*x^6))*Log[(27 - E^E^(x/(-20 +
4*x^3)))/5] + E^(E^(x/(-20 + 4*x^3)) + x/(-20 + 4*x^3))*(5*x + 2*x^4)*Log[x^2])/((-2700*x + 1080*x^4 - 108*x^
7 + E^E^(x/(-20 + 4*x^3))*(100*x - 40*x^4 + 4*x^7))*Log[(27 - E^E^(x/(-20 + 4*x^3)))/5]^2),x]

[Out]

Log[x^2]/Log[(27 - E^E^(x/(4*(-5 + x^3))))/5]

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fricas [B]  time = 0.63, size = 65, normalized size = 1.91 \begin {gather*} \frac {\log \left (x^{2}\right )}{\log \left (-\frac {1}{5} \, {\left (e^{\left (\frac {4 \, {\left (x^{3} - 5\right )} e^{\left (\frac {x}{4 \, {\left (x^{3} - 5\right )}}\right )} + x}{4 \, {\left (x^{3} - 5\right )}}\right )} - 27 \, e^{\left (\frac {x}{4 \, {\left (x^{3} - 5\right )}}\right )}\right )} e^{\left (-\frac {x}{4 \, {\left (x^{3} - 5\right )}}\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((8*x^6-80*x^3+200)*exp(exp(x/(4*x^3-20)))-216*x^6+2160*x^3-5400)*log(-1/5*exp(exp(x/(4*x^3-20)))+2
7/5)+(2*x^4+5*x)*exp(x/(4*x^3-20))*log(x^2)*exp(exp(x/(4*x^3-20))))/((4*x^7-40*x^4+100*x)*exp(exp(x/(4*x^3-20)
))-108*x^7+1080*x^4-2700*x)/log(-1/5*exp(exp(x/(4*x^3-20)))+27/5)^2,x, algorithm="fricas")

[Out]

log(x^2)/log(-1/5*(e^(1/4*(4*(x^3 - 5)*e^(1/4*x/(x^3 - 5)) + x)/(x^3 - 5)) - 27*e^(1/4*x/(x^3 - 5)))*e^(-1/4*x
/(x^3 - 5)))

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giac [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int -\frac {{\left (2 \, x^{4} + 5 \, x\right )} e^{\left (\frac {x}{4 \, {\left (x^{3} - 5\right )}} + e^{\left (\frac {x}{4 \, {\left (x^{3} - 5\right )}}\right )}\right )} \log \left (x^{2}\right ) - 8 \, {\left (27 \, x^{6} - 270 \, x^{3} - {\left (x^{6} - 10 \, x^{3} + 25\right )} e^{\left (e^{\left (\frac {x}{4 \, {\left (x^{3} - 5\right )}}\right )}\right )} + 675\right )} \log \left (-\frac {1}{5} \, e^{\left (e^{\left (\frac {x}{4 \, {\left (x^{3} - 5\right )}}\right )}\right )} + \frac {27}{5}\right )}{4 \, {\left (27 \, x^{7} - 270 \, x^{4} - {\left (x^{7} - 10 \, x^{4} + 25 \, x\right )} e^{\left (e^{\left (\frac {x}{4 \, {\left (x^{3} - 5\right )}}\right )}\right )} + 675 \, x\right )} \log \left (-\frac {1}{5} \, e^{\left (e^{\left (\frac {x}{4 \, {\left (x^{3} - 5\right )}}\right )}\right )} + \frac {27}{5}\right )^{2}}\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((8*x^6-80*x^3+200)*exp(exp(x/(4*x^3-20)))-216*x^6+2160*x^3-5400)*log(-1/5*exp(exp(x/(4*x^3-20)))+2
7/5)+(2*x^4+5*x)*exp(x/(4*x^3-20))*log(x^2)*exp(exp(x/(4*x^3-20))))/((4*x^7-40*x^4+100*x)*exp(exp(x/(4*x^3-20)
))-108*x^7+1080*x^4-2700*x)/log(-1/5*exp(exp(x/(4*x^3-20)))+27/5)^2,x, algorithm="giac")

[Out]

integrate(-1/4*((2*x^4 + 5*x)*e^(1/4*x/(x^3 - 5) + e^(1/4*x/(x^3 - 5)))*log(x^2) - 8*(27*x^6 - 270*x^3 - (x^6
- 10*x^3 + 25)*e^(e^(1/4*x/(x^3 - 5))) + 675)*log(-1/5*e^(e^(1/4*x/(x^3 - 5))) + 27/5))/((27*x^7 - 270*x^4 - (
x^7 - 10*x^4 + 25*x)*e^(e^(1/4*x/(x^3 - 5))) + 675*x)*log(-1/5*e^(e^(1/4*x/(x^3 - 5))) + 27/5)^2), x)

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maple [C]  time = 0.31, size = 76, normalized size = 2.24

method	result	size
risch	\(\frac {4 \ln \relax (x )-i \pi \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )+2 i \pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2}-i \pi \mathrm {csgn}\left (i x^{2}\right )^{3}}{2 \ln \left (-\frac {{\mathrm e}^{{\mathrm e}^{\frac {x}{4 x^{3}-20}}}}{5}+\frac {27}{5}\right )}\)	\(76\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((8*x^6-80*x^3+200)*exp(exp(x/(4*x^3-20)))-216*x^6+2160*x^3-5400)*ln(-1/5*exp(exp(x/(4*x^3-20)))+27/5)+(2
*x^4+5*x)*exp(x/(4*x^3-20))*ln(x^2)*exp(exp(x/(4*x^3-20))))/((4*x^7-40*x^4+100*x)*exp(exp(x/(4*x^3-20)))-108*x
^7+1080*x^4-2700*x)/ln(-1/5*exp(exp(x/(4*x^3-20)))+27/5)^2,x,method=_RETURNVERBOSE)

[Out]

1/2*(4*ln(x)-I*Pi*csgn(I*x)^2*csgn(I*x^2)+2*I*Pi*csgn(I*x)*csgn(I*x^2)^2-I*Pi*csgn(I*x^2)^3)/ln(-1/5*exp(exp(1
/4*x/(x^3-5)))+27/5)

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maxima [A]  time = 0.76, size = 28, normalized size = 0.82 \begin {gather*} -\frac {2 \, \log \relax (x)}{\log \relax (5) - \log \left (-e^{\left (e^{\left (\frac {x}{4 \, {\left (x^{3} - 5\right )}}\right )}\right )} + 27\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((8*x^6-80*x^3+200)*exp(exp(x/(4*x^3-20)))-216*x^6+2160*x^3-5400)*log(-1/5*exp(exp(x/(4*x^3-20)))+2
7/5)+(2*x^4+5*x)*exp(x/(4*x^3-20))*log(x^2)*exp(exp(x/(4*x^3-20))))/((4*x^7-40*x^4+100*x)*exp(exp(x/(4*x^3-20)
))-108*x^7+1080*x^4-2700*x)/log(-1/5*exp(exp(x/(4*x^3-20)))+27/5)^2,x, algorithm="maxima")

[Out]

-2*log(x)/(log(5) - log(-e^(e^(1/4*x/(x^3 - 5))) + 27))

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mupad [F]  time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} \int -\frac {\ln \left (\frac {27}{5}-\frac {{\mathrm {e}}^{{\mathrm {e}}^{\frac {x}{4\,x^3-20}}}}{5}\right )\,\left ({\mathrm {e}}^{{\mathrm {e}}^{\frac {x}{4\,x^3-20}}}\,\left (8\,x^6-80\,x^3+200\right )+2160\,x^3-216\,x^6-5400\right )+\ln \left (x^2\right )\,{\mathrm {e}}^{\frac {x}{4\,x^3-20}}\,{\mathrm {e}}^{{\mathrm {e}}^{\frac {x}{4\,x^3-20}}}\,\left (2\,x^4+5\,x\right )}{{\ln \left (\frac {27}{5}-\frac {{\mathrm {e}}^{{\mathrm {e}}^{\frac {x}{4\,x^3-20}}}}{5}\right )}^2\,\left (2700\,x-{\mathrm {e}}^{{\mathrm {e}}^{\frac {x}{4\,x^3-20}}}\,\left (4\,x^7-40\,x^4+100\,x\right )-1080\,x^4+108\,x^7\right )} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(log(27/5 - exp(exp(x/(4*x^3 - 20)))/5)*(exp(exp(x/(4*x^3 - 20)))*(8*x^6 - 80*x^3 + 200) + 2160*x^3 - 216
*x^6 - 5400) + log(x^2)*exp(x/(4*x^3 - 20))*exp(exp(x/(4*x^3 - 20)))*(5*x + 2*x^4))/(log(27/5 - exp(exp(x/(4*x
^3 - 20)))/5)^2*(2700*x - exp(exp(x/(4*x^3 - 20)))*(100*x - 40*x^4 + 4*x^7) - 1080*x^4 + 108*x^7)),x)

[Out]

int(-(log(27/5 - exp(exp(x/(4*x^3 - 20)))/5)*(exp(exp(x/(4*x^3 - 20)))*(8*x^6 - 80*x^3 + 200) + 2160*x^3 - 216
*x^6 - 5400) + log(x^2)*exp(x/(4*x^3 - 20))*exp(exp(x/(4*x^3 - 20)))*(5*x + 2*x^4))/(log(27/5 - exp(exp(x/(4*x
^3 - 20)))/5)^2*(2700*x - exp(exp(x/(4*x^3 - 20)))*(100*x - 40*x^4 + 4*x^7) - 1080*x^4 + 108*x^7)), x)

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sympy [A]  time = 23.29, size = 22, normalized size = 0.65 \begin {gather*} \frac {\log {\left (x^{2} \right )}}{\log {\left (\frac {27}{5} - \frac {e^{e^{\frac {x}{4 x^{3} - 20}}}}{5} \right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((8*x**6-80*x**3+200)*exp(exp(x/(4*x**3-20)))-216*x**6+2160*x**3-5400)*ln(-1/5*exp(exp(x/(4*x**3-20
)))+27/5)+(2*x**4+5*x)*exp(x/(4*x**3-20))*ln(x**2)*exp(exp(x/(4*x**3-20))))/((4*x**7-40*x**4+100*x)*exp(exp(x/
(4*x**3-20)))-108*x**7+1080*x**4-2700*x)/ln(-1/5*exp(exp(x/(4*x**3-20)))+27/5)**2,x)

[Out]

log(x**2)/log(27/5 - exp(exp(x/(4*x**3 - 20)))/5)

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