3.12.57 \(\int \frac {e^{\frac {\log ^2(\frac {-x^2+2 \log (-20+x)}{\log (-20+x)})}{x^2}} ((2 x^3+(80 x^2-4 x^3) \log (-20+x)) \log (\frac {-x^2+2 \log (-20+x)}{\log (-20+x)})+((-40 x^2+2 x^3) \log (-20+x)+(80-4 x) \log ^2(-20+x)) \log ^2(\frac {-x^2+2 \log (-20+x)}{\log (-20+x)}))}{(20 x^5-x^6) \log (-20+x)+(-40 x^3+2 x^4) \log ^2(-20+x)} \, dx\)

Optimal. Leaf size=22 \[ e^{\frac {\log ^2\left (2-\frac {x^2}{\log (-20+x)}\right )}{x^2}} \]

________________________________________________________________________________________

Rubi [F]  time = 9.56, 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 {\exp \left (\frac {\log ^2\left (\frac {-x^2+2 \log (-20+x)}{\log (-20+x)}\right )}{x^2}\right ) \left (\left (2 x^3+\left (80 x^2-4 x^3\right ) \log (-20+x)\right ) \log \left (\frac {-x^2+2 \log (-20+x)}{\log (-20+x)}\right )+\left (\left (-40 x^2+2 x^3\right ) \log (-20+x)+(80-4 x) \log ^2(-20+x)\right ) \log ^2\left (\frac {-x^2+2 \log (-20+x)}{\log (-20+x)}\right )\right )}{\left (20 x^5-x^6\right ) \log (-20+x)+\left (-40 x^3+2 x^4\right ) \log ^2(-20+x)} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(E^(Log[(-x^2 + 2*Log[-20 + x])/Log[-20 + x]]^2/x^2)*((2*x^3 + (80*x^2 - 4*x^3)*Log[-20 + x])*Log[(-x^2 +
2*Log[-20 + x])/Log[-20 + x]] + ((-40*x^2 + 2*x^3)*Log[-20 + x] + (80 - 4*x)*Log[-20 + x]^2)*Log[(-x^2 + 2*Log
[-20 + x])/Log[-20 + x]]^2))/((20*x^5 - x^6)*Log[-20 + x] + (-40*x^3 + 2*x^4)*Log[-20 + x]^2),x]

[Out]

4*Defer[Int][(E^(Log[(-x^2 + 2*Log[-20 + x])/Log[-20 + x]]^2/x^2)*Log[2 - x^2/Log[-20 + x]])/(x*(x^2 - 2*Log[-
20 + x])), x] - 2*Defer[Int][(E^(Log[(-x^2 + 2*Log[-20 + x])/Log[-20 + x]]^2/x^2)*Log[2 - x^2/Log[-20 + x]])/(
(-20 + x)*(x^2 - 2*Log[-20 + x])*Log[-20 + x]), x] - 2*Defer[Int][(E^(Log[(-x^2 + 2*Log[-20 + x])/Log[-20 + x]
]^2/x^2)*Log[2 - x^2/Log[-20 + x]]^2)/x^3, x]

Rubi steps

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

________________________________________________________________________________________

Mathematica [A]  time = 0.19, size = 22, normalized size = 1.00 \begin {gather*} e^{\frac {\log ^2\left (2-\frac {x^2}{\log (-20+x)}\right )}{x^2}} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^(Log[(-x^2 + 2*Log[-20 + x])/Log[-20 + x]]^2/x^2)*((2*x^3 + (80*x^2 - 4*x^3)*Log[-20 + x])*Log[(-
x^2 + 2*Log[-20 + x])/Log[-20 + x]] + ((-40*x^2 + 2*x^3)*Log[-20 + x] + (80 - 4*x)*Log[-20 + x]^2)*Log[(-x^2 +
2*Log[-20 + x])/Log[-20 + x]]^2))/((20*x^5 - x^6)*Log[-20 + x] + (-40*x^3 + 2*x^4)*Log[-20 + x]^2),x]

[Out]

E^(Log[2 - x^2/Log[-20 + x]]^2/x^2)

________________________________________________________________________________________

fricas [A]  time = 0.89, size = 26, normalized size = 1.18 \begin {gather*} e^{\left (\frac {\log \left (-\frac {x^{2} - 2 \, \log \left (x - 20\right )}{\log \left (x - 20\right )}\right )^{2}}{x^{2}}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-4*x+80)*log(x-20)^2+(2*x^3-40*x^2)*log(x-20))*log((2*log(x-20)-x^2)/log(x-20))^2+((-4*x^3+80*x^2
)*log(x-20)+2*x^3)*log((2*log(x-20)-x^2)/log(x-20)))*exp(log((2*log(x-20)-x^2)/log(x-20))^2/x^2)/((2*x^4-40*x^
3)*log(x-20)^2+(-x^6+20*x^5)*log(x-20)),x, algorithm="fricas")

[Out]

e^(log(-(x^2 - 2*log(x - 20))/log(x - 20))^2/x^2)

________________________________________________________________________________________

giac [A]  time = 27.58, size = 21, normalized size = 0.95 \begin {gather*} e^{\left (\frac {\log \left (-\frac {x^{2}}{\log \left (x - 20\right )} + 2\right )^{2}}{x^{2}}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-4*x+80)*log(x-20)^2+(2*x^3-40*x^2)*log(x-20))*log((2*log(x-20)-x^2)/log(x-20))^2+((-4*x^3+80*x^2
)*log(x-20)+2*x^3)*log((2*log(x-20)-x^2)/log(x-20)))*exp(log((2*log(x-20)-x^2)/log(x-20))^2/x^2)/((2*x^4-40*x^
3)*log(x-20)^2+(-x^6+20*x^5)*log(x-20)),x, algorithm="giac")

[Out]

e^(log(-x^2/log(x - 20) + 2)^2/x^2)

________________________________________________________________________________________

maple [C]  time = 0.28, size = 210, normalized size = 9.55

method	result	size
risch	\({\mathrm e}^{\frac {\left (-i \pi \mathrm {csgn}\left (\frac {i \left (-2 \ln \left (x -20\right )+x^{2}\right )}{\ln \left (x -20\right )}\right )^{3}-i \pi \mathrm {csgn}\left (\frac {i \left (-2 \ln \left (x -20\right )+x^{2}\right )}{\ln \left (x -20\right )}\right )^{2} \mathrm {csgn}\left (\frac {i}{\ln \left (x -20\right )}\right )-i \pi \mathrm {csgn}\left (\frac {i \left (-2 \ln \left (x -20\right )+x^{2}\right )}{\ln \left (x -20\right )}\right )^{2} \mathrm {csgn}\left (i \left (-2 \ln \left (x -20\right )+x^{2}\right )\right )+i \pi \,\mathrm {csgn}\left (\frac {i \left (-2 \ln \left (x -20\right )+x^{2}\right )}{\ln \left (x -20\right )}\right ) \mathrm {csgn}\left (\frac {i}{\ln \left (x -20\right )}\right ) \mathrm {csgn}\left (i \left (-2 \ln \left (x -20\right )+x^{2}\right )\right )+2 i \pi \mathrm {csgn}\left (\frac {i \left (-2 \ln \left (x -20\right )+x^{2}\right )}{\ln \left (x -20\right )}\right )^{2}-2 i \pi +2 \ln \left (\ln \left (x -20\right )\right )-2 \ln \left (-2 \ln \left (x -20\right )+x^{2}\right )\right )^{2}}{4 x^{2}}}\)	\(210\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((-4*x+80)*ln(x-20)^2+(2*x^3-40*x^2)*ln(x-20))*ln((2*ln(x-20)-x^2)/ln(x-20))^2+((-4*x^3+80*x^2)*ln(x-20)+
2*x^3)*ln((2*ln(x-20)-x^2)/ln(x-20)))*exp(ln((2*ln(x-20)-x^2)/ln(x-20))^2/x^2)/((2*x^4-40*x^3)*ln(x-20)^2+(-x^
6+20*x^5)*ln(x-20)),x,method=_RETURNVERBOSE)

[Out]

exp(1/4*(-I*Pi*csgn(I/ln(x-20)*(-2*ln(x-20)+x^2))^3-I*Pi*csgn(I/ln(x-20)*(-2*ln(x-20)+x^2))^2*csgn(I/ln(x-20))
-I*Pi*csgn(I/ln(x-20)*(-2*ln(x-20)+x^2))^2*csgn(I*(-2*ln(x-20)+x^2))+I*Pi*csgn(I/ln(x-20)*(-2*ln(x-20)+x^2))*c
sgn(I/ln(x-20))*csgn(I*(-2*ln(x-20)+x^2))+2*I*Pi*csgn(I/ln(x-20)*(-2*ln(x-20)+x^2))^2-2*I*Pi+2*ln(ln(x-20))-2*
ln(-2*ln(x-20)+x^2))^2/x^2)

________________________________________________________________________________________

maxima [B]  time = 0.81, size = 55, normalized size = 2.50 \begin {gather*} e^{\left (\frac {\log \left (-x^{2} + 2 \, \log \left (x - 20\right )\right )^{2}}{x^{2}} - \frac {2 \, \log \left (-x^{2} + 2 \, \log \left (x - 20\right )\right ) \log \left (\log \left (x - 20\right )\right )}{x^{2}} + \frac {\log \left (\log \left (x - 20\right )\right )^{2}}{x^{2}}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-4*x+80)*log(x-20)^2+(2*x^3-40*x^2)*log(x-20))*log((2*log(x-20)-x^2)/log(x-20))^2+((-4*x^3+80*x^2
)*log(x-20)+2*x^3)*log((2*log(x-20)-x^2)/log(x-20)))*exp(log((2*log(x-20)-x^2)/log(x-20))^2/x^2)/((2*x^4-40*x^
3)*log(x-20)^2+(-x^6+20*x^5)*log(x-20)),x, algorithm="maxima")

[Out]

e^(log(-x^2 + 2*log(x - 20))^2/x^2 - 2*log(-x^2 + 2*log(x - 20))*log(log(x - 20))/x^2 + log(log(x - 20))^2/x^2
)

________________________________________________________________________________________

mupad [B]  time = 1.46, size = 27, normalized size = 1.23 \begin {gather*} {\mathrm {e}}^{\frac {{\ln \left (\frac {2\,\ln \left (x-20\right )-x^2}{\ln \left (x-20\right )}\right )}^2}{x^2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(log((2*log(x - 20) - x^2)/log(x - 20))^2/x^2)*(log((2*log(x - 20) - x^2)/log(x - 20))*(log(x - 20)*(8
0*x^2 - 4*x^3) + 2*x^3) - log((2*log(x - 20) - x^2)/log(x - 20))^2*(log(x - 20)^2*(4*x - 80) + log(x - 20)*(40
*x^2 - 2*x^3))))/(log(x - 20)*(20*x^5 - x^6) - log(x - 20)^2*(40*x^3 - 2*x^4)),x)

[Out]

exp(log((2*log(x - 20) - x^2)/log(x - 20))^2/x^2)

________________________________________________________________________________________

sympy [A]  time = 4.77, size = 22, normalized size = 1.00 \begin {gather*} e^{\frac {\log {\left (\frac {- x^{2} + 2 \log {\left (x - 20 \right )}}{\log {\left (x - 20 \right )}} \right )}^{2}}{x^{2}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-4*x+80)*ln(x-20)**2+(2*x**3-40*x**2)*ln(x-20))*ln((2*ln(x-20)-x**2)/ln(x-20))**2+((-4*x**3+80*x*
*2)*ln(x-20)+2*x**3)*ln((2*ln(x-20)-x**2)/ln(x-20)))*exp(ln((2*ln(x-20)-x**2)/ln(x-20))**2/x**2)/((2*x**4-40*x
**3)*ln(x-20)**2+(-x**6+20*x**5)*ln(x-20)),x)

[Out]

exp(log((-x**2 + 2*log(x - 20))/log(x - 20))**2/x**2)

________________________________________________________________________________________