3.19.60 \(\int \frac {e^{\frac {e^9-x \log (\frac {e^{e^2} \log ^2(-4+x)}{x^2})}{\log (\frac {e^{e^2} \log ^2(-4+x)}{x^2})}} (-2 e^9 x+e^9 (-8+2 x) \log (-4+x)+(4 x-x^2) \log (-4+x) \log ^2(\frac {e^{e^2} \log ^2(-4+x)}{x^2}))}{(-4 x+x^2) \log (-4+x) \log ^2(\frac {e^{e^2} \log ^2(-4+x)}{x^2})} \, dx\)

Optimal. Leaf size=28 \[ e^{-x+\frac {e^9}{\log \left (\frac {e^{e^2} \log ^2(-4+x)}{x^2}\right )}} \]

________________________________________________________________________________________

Rubi [F]  time = 14.80, 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 {e^9-x \log \left (\frac {e^{e^2} \log ^2(-4+x)}{x^2}\right )}{\log \left (\frac {e^{e^2} \log ^2(-4+x)}{x^2}\right )}\right ) \left (-2 e^9 x+e^9 (-8+2 x) \log (-4+x)+\left (4 x-x^2\right ) \log (-4+x) \log ^2\left (\frac {e^{e^2} \log ^2(-4+x)}{x^2}\right )\right )}{\left (-4 x+x^2\right ) \log (-4+x) \log ^2\left (\frac {e^{e^2} \log ^2(-4+x)}{x^2}\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(E^((E^9 - x*Log[(E^E^2*Log[-4 + x]^2)/x^2])/Log[(E^E^2*Log[-4 + x]^2)/x^2])*(-2*E^9*x + E^9*(-8 + 2*x)*Lo
g[-4 + x] + (4*x - x^2)*Log[-4 + x]*Log[(E^E^2*Log[-4 + x]^2)/x^2]^2))/((-4*x + x^2)*Log[-4 + x]*Log[(E^E^2*Lo
g[-4 + x]^2)/x^2]^2),x]

[Out]

-Defer[Int][E^(-x + E^9/(E^2 + Log[Log[-4 + x]^2/x^2])), x] + 2*Defer[Int][E^(9 - x + E^9/(E^2 + Log[Log[-4 +
x]^2/x^2]))/(x*(E^2 + Log[Log[-4 + x]^2/x^2])^2), x] - 2*Defer[Int][E^(9 - x + E^9/(E^2 + Log[Log[-4 + x]^2/x^
2]))/((-4 + x)*Log[-4 + x]*(E^2 + Log[Log[-4 + x]^2/x^2])^2), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {\exp \left (\frac {e^9-x \log \left (\frac {e^{e^2} \log ^2(-4+x)}{x^2}\right )}{\log \left (\frac {e^{e^2} \log ^2(-4+x)}{x^2}\right )}\right ) \left (-2 e^9 x+e^9 (-8+2 x) \log (-4+x)+\left (4 x-x^2\right ) \log (-4+x) \log ^2\left (\frac {e^{e^2} \log ^2(-4+x)}{x^2}\right )\right )}{(-4+x) x \log (-4+x) \log ^2\left (\frac {e^{e^2} \log ^2(-4+x)}{x^2}\right )} \, dx\\ &=\int \left (-\exp \left (\frac {e^9-x \log \left (\frac {e^{e^2} \log ^2(-4+x)}{x^2}\right )}{\log \left (\frac {e^{e^2} \log ^2(-4+x)}{x^2}\right )}\right )+\frac {2 \exp \left (9+\frac {e^9-x \log \left (\frac {e^{e^2} \log ^2(-4+x)}{x^2}\right )}{\log \left (\frac {e^{e^2} \log ^2(-4+x)}{x^2}\right )}\right ) (-x-4 \log (-4+x)+x \log (-4+x))}{(-4+x) x \log (-4+x) \left (e^2+\log \left (\frac {\log ^2(-4+x)}{x^2}\right )\right )^2}\right ) \, dx\\ &=2 \int \frac {\exp \left (9+\frac {e^9-x \log \left (\frac {e^{e^2} \log ^2(-4+x)}{x^2}\right )}{\log \left (\frac {e^{e^2} \log ^2(-4+x)}{x^2}\right )}\right ) (-x-4 \log (-4+x)+x \log (-4+x))}{(-4+x) x \log (-4+x) \left (e^2+\log \left (\frac {\log ^2(-4+x)}{x^2}\right )\right )^2} \, dx-\int \exp \left (\frac {e^9-x \log \left (\frac {e^{e^2} \log ^2(-4+x)}{x^2}\right )}{\log \left (\frac {e^{e^2} \log ^2(-4+x)}{x^2}\right )}\right ) \, dx\\ &=2 \int \frac {e^{9-x+\frac {e^9}{e^2+\log \left (\frac {\log ^2(-4+x)}{x^2}\right )}} (x-(-4+x) \log (-4+x))}{(4-x) x \log (-4+x) \left (e^2+\log \left (\frac {\log ^2(-4+x)}{x^2}\right )\right )^2} \, dx-\int e^{-x+\frac {e^9}{e^2+\log \left (\frac {\log ^2(-4+x)}{x^2}\right )}} \, dx\\ &=2 \int \left (\frac {e^{9-x+\frac {e^9}{e^2+\log \left (\frac {\log ^2(-4+x)}{x^2}\right )}} (x+4 \log (-4+x)-x \log (-4+x))}{4 x \log (-4+x) \left (e^2+\log \left (\frac {\log ^2(-4+x)}{x^2}\right )\right )^2}+\frac {e^{9-x+\frac {e^9}{e^2+\log \left (\frac {\log ^2(-4+x)}{x^2}\right )}} (-x-4 \log (-4+x)+x \log (-4+x))}{4 (-4+x) \log (-4+x) \left (e^2+\log \left (\frac {\log ^2(-4+x)}{x^2}\right )\right )^2}\right ) \, dx-\int e^{-x+\frac {e^9}{e^2+\log \left (\frac {\log ^2(-4+x)}{x^2}\right )}} \, dx\\ &=\frac {1}{2} \int \frac {e^{9-x+\frac {e^9}{e^2+\log \left (\frac {\log ^2(-4+x)}{x^2}\right )}} (x+4 \log (-4+x)-x \log (-4+x))}{x \log (-4+x) \left (e^2+\log \left (\frac {\log ^2(-4+x)}{x^2}\right )\right )^2} \, dx+\frac {1}{2} \int \frac {e^{9-x+\frac {e^9}{e^2+\log \left (\frac {\log ^2(-4+x)}{x^2}\right )}} (-x-4 \log (-4+x)+x \log (-4+x))}{(-4+x) \log (-4+x) \left (e^2+\log \left (\frac {\log ^2(-4+x)}{x^2}\right )\right )^2} \, dx-\int e^{-x+\frac {e^9}{e^2+\log \left (\frac {\log ^2(-4+x)}{x^2}\right )}} \, dx\\ &=\frac {1}{2} \int \frac {e^{9-x+\frac {e^9}{e^2+\log \left (\frac {\log ^2(-4+x)}{x^2}\right )}} (x-(-4+x) \log (-4+x))}{x \log (-4+x) \left (e^2+\log \left (\frac {\log ^2(-4+x)}{x^2}\right )\right )^2} \, dx+\frac {1}{2} \int \left (-\frac {4 e^{9-x+\frac {e^9}{e^2+\log \left (\frac {\log ^2(-4+x)}{x^2}\right )}}}{(-4+x) \left (e^2+\log \left (\frac {\log ^2(-4+x)}{x^2}\right )\right )^2}+\frac {e^{9-x+\frac {e^9}{e^2+\log \left (\frac {\log ^2(-4+x)}{x^2}\right )}} x}{(-4+x) \left (e^2+\log \left (\frac {\log ^2(-4+x)}{x^2}\right )\right )^2}-\frac {e^{9-x+\frac {e^9}{e^2+\log \left (\frac {\log ^2(-4+x)}{x^2}\right )}} x}{(-4+x) \log (-4+x) \left (e^2+\log \left (\frac {\log ^2(-4+x)}{x^2}\right )\right )^2}\right ) \, dx-\int e^{-x+\frac {e^9}{e^2+\log \left (\frac {\log ^2(-4+x)}{x^2}\right )}} \, dx\\ &=\frac {1}{2} \int \frac {e^{9-x+\frac {e^9}{e^2+\log \left (\frac {\log ^2(-4+x)}{x^2}\right )}} x}{(-4+x) \left (e^2+\log \left (\frac {\log ^2(-4+x)}{x^2}\right )\right )^2} \, dx-\frac {1}{2} \int \frac {e^{9-x+\frac {e^9}{e^2+\log \left (\frac {\log ^2(-4+x)}{x^2}\right )}} x}{(-4+x) \log (-4+x) \left (e^2+\log \left (\frac {\log ^2(-4+x)}{x^2}\right )\right )^2} \, dx+\frac {1}{2} \int \left (-\frac {e^{9-x+\frac {e^9}{e^2+\log \left (\frac {\log ^2(-4+x)}{x^2}\right )}}}{\left (e^2+\log \left (\frac {\log ^2(-4+x)}{x^2}\right )\right )^2}+\frac {4 e^{9-x+\frac {e^9}{e^2+\log \left (\frac {\log ^2(-4+x)}{x^2}\right )}}}{x \left (e^2+\log \left (\frac {\log ^2(-4+x)}{x^2}\right )\right )^2}+\frac {e^{9-x+\frac {e^9}{e^2+\log \left (\frac {\log ^2(-4+x)}{x^2}\right )}}}{\log (-4+x) \left (e^2+\log \left (\frac {\log ^2(-4+x)}{x^2}\right )\right )^2}\right ) \, dx-2 \int \frac {e^{9-x+\frac {e^9}{e^2+\log \left (\frac {\log ^2(-4+x)}{x^2}\right )}}}{(-4+x) \left (e^2+\log \left (\frac {\log ^2(-4+x)}{x^2}\right )\right )^2} \, dx-\int e^{-x+\frac {e^9}{e^2+\log \left (\frac {\log ^2(-4+x)}{x^2}\right )}} \, dx\\ &=-\left (\frac {1}{2} \int \frac {e^{9-x+\frac {e^9}{e^2+\log \left (\frac {\log ^2(-4+x)}{x^2}\right )}}}{\left (e^2+\log \left (\frac {\log ^2(-4+x)}{x^2}\right )\right )^2} \, dx\right )+\frac {1}{2} \int \frac {e^{9-x+\frac {e^9}{e^2+\log \left (\frac {\log ^2(-4+x)}{x^2}\right )}}}{\log (-4+x) \left (e^2+\log \left (\frac {\log ^2(-4+x)}{x^2}\right )\right )^2} \, dx+\frac {1}{2} \int \left (\frac {e^{9-x+\frac {e^9}{e^2+\log \left (\frac {\log ^2(-4+x)}{x^2}\right )}}}{\left (e^2+\log \left (\frac {\log ^2(-4+x)}{x^2}\right )\right )^2}+\frac {4 e^{9-x+\frac {e^9}{e^2+\log \left (\frac {\log ^2(-4+x)}{x^2}\right )}}}{(-4+x) \left (e^2+\log \left (\frac {\log ^2(-4+x)}{x^2}\right )\right )^2}\right ) \, dx-\frac {1}{2} \int \left (\frac {e^{9-x+\frac {e^9}{e^2+\log \left (\frac {\log ^2(-4+x)}{x^2}\right )}}}{\log (-4+x) \left (e^2+\log \left (\frac {\log ^2(-4+x)}{x^2}\right )\right )^2}+\frac {4 e^{9-x+\frac {e^9}{e^2+\log \left (\frac {\log ^2(-4+x)}{x^2}\right )}}}{(-4+x) \log (-4+x) \left (e^2+\log \left (\frac {\log ^2(-4+x)}{x^2}\right )\right )^2}\right ) \, dx-2 \int \frac {e^{9-x+\frac {e^9}{e^2+\log \left (\frac {\log ^2(-4+x)}{x^2}\right )}}}{(-4+x) \left (e^2+\log \left (\frac {\log ^2(-4+x)}{x^2}\right )\right )^2} \, dx+2 \int \frac {e^{9-x+\frac {e^9}{e^2+\log \left (\frac {\log ^2(-4+x)}{x^2}\right )}}}{x \left (e^2+\log \left (\frac {\log ^2(-4+x)}{x^2}\right )\right )^2} \, dx-\int e^{-x+\frac {e^9}{e^2+\log \left (\frac {\log ^2(-4+x)}{x^2}\right )}} \, dx\\ &=2 \int \frac {e^{9-x+\frac {e^9}{e^2+\log \left (\frac {\log ^2(-4+x)}{x^2}\right )}}}{x \left (e^2+\log \left (\frac {\log ^2(-4+x)}{x^2}\right )\right )^2} \, dx-2 \int \frac {e^{9-x+\frac {e^9}{e^2+\log \left (\frac {\log ^2(-4+x)}{x^2}\right )}}}{(-4+x) \log (-4+x) \left (e^2+\log \left (\frac {\log ^2(-4+x)}{x^2}\right )\right )^2} \, dx-\int e^{-x+\frac {e^9}{e^2+\log \left (\frac {\log ^2(-4+x)}{x^2}\right )}} \, dx\\ \end {aligned} \end {gather*}

________________________________________________________________________________________

Mathematica [A]  time = 0.28, size = 27, normalized size = 0.96 \begin {gather*} e^{-x+\frac {e^9}{e^2+\log \left (\frac {\log ^2(-4+x)}{x^2}\right )}} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^((E^9 - x*Log[(E^E^2*Log[-4 + x]^2)/x^2])/Log[(E^E^2*Log[-4 + x]^2)/x^2])*(-2*E^9*x + E^9*(-8 + 2
*x)*Log[-4 + x] + (4*x - x^2)*Log[-4 + x]*Log[(E^E^2*Log[-4 + x]^2)/x^2]^2))/((-4*x + x^2)*Log[-4 + x]*Log[(E^
E^2*Log[-4 + x]^2)/x^2]^2),x]

[Out]

E^(-x + E^9/(E^2 + Log[Log[-4 + x]^2/x^2]))

________________________________________________________________________________________

fricas [A]  time = 0.61, size = 40, normalized size = 1.43 \begin {gather*} e^{\left (-\frac {x \log \left (\frac {e^{\left (e^{2}\right )} \log \left (x - 4\right )^{2}}{x^{2}}\right ) - e^{9}}{\log \left (\frac {e^{\left (e^{2}\right )} \log \left (x - 4\right )^{2}}{x^{2}}\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-x^2+4*x)*log(x-4)*log(exp(exp(2))*log(x-4)^2/x^2)^2+(2*x-8)*exp(9)*log(x-4)-2*x*exp(9))*exp((-x*l
og(exp(exp(2))*log(x-4)^2/x^2)+exp(9))/log(exp(exp(2))*log(x-4)^2/x^2))/(x^2-4*x)/log(x-4)/log(exp(exp(2))*log
(x-4)^2/x^2)^2,x, algorithm="fricas")

[Out]

e^(-(x*log(e^(e^2)*log(x - 4)^2/x^2) - e^9)/log(e^(e^2)*log(x - 4)^2/x^2))

________________________________________________________________________________________

giac [A]  time = 13.81, size = 24, normalized size = 0.86 \begin {gather*} e^{\left (-x + \frac {e^{9}}{\log \left (\frac {e^{\left (e^{2}\right )} \log \left (x - 4\right )^{2}}{x^{2}}\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-x^2+4*x)*log(x-4)*log(exp(exp(2))*log(x-4)^2/x^2)^2+(2*x-8)*exp(9)*log(x-4)-2*x*exp(9))*exp((-x*l
og(exp(exp(2))*log(x-4)^2/x^2)+exp(9))/log(exp(exp(2))*log(x-4)^2/x^2))/(x^2-4*x)/log(x-4)/log(exp(exp(2))*log
(x-4)^2/x^2)^2,x, algorithm="giac")

[Out]

e^(-x + e^9/log(e^(e^2)*log(x - 4)^2/x^2))

________________________________________________________________________________________

maple [C]  time = 417.42, size = 497, normalized size = 17.75

method	result	size
risch	\({\mathrm e}^{-\frac {-i x \pi \mathrm {csgn}\left (i \ln \left (x -4\right )^{2}\right )^{3}+2 i x \pi \mathrm {csgn}\left (i \ln \left (x -4\right )^{2}\right )^{2} \mathrm {csgn}\left (i \ln \left (x -4\right )\right )-i x \pi \,\mathrm {csgn}\left (i \ln \left (x -4\right )^{2}\right ) \mathrm {csgn}\left (i \ln \left (x -4\right )\right )^{2}+i x \pi \,\mathrm {csgn}\left (i \ln \left (x -4\right )^{2}\right ) \mathrm {csgn}\left (\frac {i \ln \left (x -4\right )^{2}}{x^{2}}\right )^{2}-i x \pi \,\mathrm {csgn}\left (i \ln \left (x -4\right )^{2}\right ) \mathrm {csgn}\left (\frac {i \ln \left (x -4\right )^{2}}{x^{2}}\right ) \mathrm {csgn}\left (\frac {i}{x^{2}}\right )+i \pi x \mathrm {csgn}\left (i x^{2}\right )^{3}-2 i \pi x \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2}+i \pi x \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )-i x \pi \mathrm {csgn}\left (\frac {i \ln \left (x -4\right )^{2}}{x^{2}}\right )^{3}+i x \pi \mathrm {csgn}\left (\frac {i \ln \left (x -4\right )^{2}}{x^{2}}\right )^{2} \mathrm {csgn}\left (\frac {i}{x^{2}}\right )+2 \,{\mathrm e}^{2} x -4 x \ln \relax (x )+4 x \ln \left (\ln \left (x -4\right )\right )-2 \,{\mathrm e}^{9}}{-i \pi \mathrm {csgn}\left (i \ln \left (x -4\right )^{2}\right )^{3}+2 i \pi \mathrm {csgn}\left (i \ln \left (x -4\right )^{2}\right )^{2} \mathrm {csgn}\left (i \ln \left (x -4\right )\right )-i \pi \,\mathrm {csgn}\left (i \ln \left (x -4\right )^{2}\right ) \mathrm {csgn}\left (i \ln \left (x -4\right )\right )^{2}+i \pi \,\mathrm {csgn}\left (i \ln \left (x -4\right )^{2}\right ) \mathrm {csgn}\left (\frac {i \ln \left (x -4\right )^{2}}{x^{2}}\right )^{2}-i \pi \,\mathrm {csgn}\left (i \ln \left (x -4\right )^{2}\right ) \mathrm {csgn}\left (\frac {i \ln \left (x -4\right )^{2}}{x^{2}}\right ) \mathrm {csgn}\left (\frac {i}{x^{2}}\right )+i \pi \mathrm {csgn}\left (i x^{2}\right )^{3}-2 i \pi \mathrm {csgn}\left (i x^{2}\right )^{2} \mathrm {csgn}\left (i x \right )+i \pi \,\mathrm {csgn}\left (i x^{2}\right ) \mathrm {csgn}\left (i x \right )^{2}-i \pi \mathrm {csgn}\left (\frac {i \ln \left (x -4\right )^{2}}{x^{2}}\right )^{3}+i \pi \mathrm {csgn}\left (\frac {i \ln \left (x -4\right )^{2}}{x^{2}}\right )^{2} \mathrm {csgn}\left (\frac {i}{x^{2}}\right )+2 \,{\mathrm e}^{2}-4 \ln \relax (x )+4 \ln \left (\ln \left (x -4\right )\right )}}\)	\(497\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((-x^2+4*x)*ln(x-4)*ln(exp(exp(2))*ln(x-4)^2/x^2)^2+(2*x-8)*exp(9)*ln(x-4)-2*x*exp(9))*exp((-x*ln(exp(exp(
2))*ln(x-4)^2/x^2)+exp(9))/ln(exp(exp(2))*ln(x-4)^2/x^2))/(x^2-4*x)/ln(x-4)/ln(exp(exp(2))*ln(x-4)^2/x^2)^2,x,
method=_RETURNVERBOSE)

[Out]

exp(-(-I*x*Pi*csgn(I*ln(x-4)^2)^3+2*I*x*Pi*csgn(I*ln(x-4)^2)^2*csgn(I*ln(x-4))-I*x*Pi*csgn(I*ln(x-4)^2)*csgn(I
*ln(x-4))^2+I*x*Pi*csgn(I*ln(x-4)^2)*csgn(I/x^2*ln(x-4)^2)^2-I*x*Pi*csgn(I*ln(x-4)^2)*csgn(I/x^2*ln(x-4)^2)*cs
gn(I/x^2)+I*x*Pi*csgn(I*x^2)^3-2*I*x*Pi*csgn(I*x)*csgn(I*x^2)^2+I*x*Pi*csgn(I*x^2)*csgn(I*x)^2-I*x*Pi*csgn(I/x
^2*ln(x-4)^2)^3+I*x*Pi*csgn(I/x^2*ln(x-4)^2)^2*csgn(I/x^2)+2*exp(2)*x-4*x*ln(x)+4*x*ln(ln(x-4))-2*exp(9))/(-I*
Pi*csgn(I*ln(x-4)^2)^3+2*I*Pi*csgn(I*ln(x-4)^2)^2*csgn(I*ln(x-4))-I*Pi*csgn(I*ln(x-4)^2)*csgn(I*ln(x-4))^2+I*P
i*csgn(I*ln(x-4)^2)*csgn(I/x^2*ln(x-4)^2)^2-I*Pi*csgn(I*ln(x-4)^2)*csgn(I/x^2*ln(x-4)^2)*csgn(I/x^2)+I*Pi*csgn
(I*x^2)^3-2*I*Pi*csgn(I*x^2)^2*csgn(I*x)+I*Pi*csgn(I*x^2)*csgn(I*x)^2-I*Pi*csgn(I/x^2*ln(x-4)^2)^3+I*Pi*csgn(I
/x^2*ln(x-4)^2)^2*csgn(I/x^2)+2*exp(2)-4*ln(x)+4*ln(ln(x-4))))

________________________________________________________________________________________

maxima [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} -\int \frac {{\left ({\left (x^{2} - 4 \, x\right )} \log \left (x - 4\right ) \log \left (\frac {e^{\left (e^{2}\right )} \log \left (x - 4\right )^{2}}{x^{2}}\right )^{2} - 2 \, {\left (x - 4\right )} e^{9} \log \left (x - 4\right ) + 2 \, x e^{9}\right )} e^{\left (-\frac {x \log \left (\frac {e^{\left (e^{2}\right )} \log \left (x - 4\right )^{2}}{x^{2}}\right ) - e^{9}}{\log \left (\frac {e^{\left (e^{2}\right )} \log \left (x - 4\right )^{2}}{x^{2}}\right )}\right )}}{{\left (x^{2} - 4 \, x\right )} \log \left (x - 4\right ) \log \left (\frac {e^{\left (e^{2}\right )} \log \left (x - 4\right )^{2}}{x^{2}}\right )^{2}}\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-x^2+4*x)*log(x-4)*log(exp(exp(2))*log(x-4)^2/x^2)^2+(2*x-8)*exp(9)*log(x-4)-2*x*exp(9))*exp((-x*l
og(exp(exp(2))*log(x-4)^2/x^2)+exp(9))/log(exp(exp(2))*log(x-4)^2/x^2))/(x^2-4*x)/log(x-4)/log(exp(exp(2))*log
(x-4)^2/x^2)^2,x, algorithm="maxima")

[Out]

-integrate(((x^2 - 4*x)*log(x - 4)*log(e^(e^2)*log(x - 4)^2/x^2)^2 - 2*(x - 4)*e^9*log(x - 4) + 2*x*e^9)*e^(-(
x*log(e^(e^2)*log(x - 4)^2/x^2) - e^9)/log(e^(e^2)*log(x - 4)^2/x^2))/((x^2 - 4*x)*log(x - 4)*log(e^(e^2)*log(
x - 4)^2/x^2)^2), x)

________________________________________________________________________________________

mupad [B]  time = 1.71, size = 92, normalized size = 3.29 \begin {gather*} \frac {{\mathrm {e}}^{-\frac {x\,{\mathrm {e}}^2}{\ln \left ({\ln \left (x-4\right )}^2\right )+\ln \left (\frac {1}{x^2}\right )+{\mathrm {e}}^2}}\,{\mathrm {e}}^{\frac {{\mathrm {e}}^9}{\ln \left ({\ln \left (x-4\right )}^2\right )+\ln \left (\frac {1}{x^2}\right )+{\mathrm {e}}^2}}\,{\left (x^2\right )}^{\frac {x}{\ln \left ({\ln \left (x-4\right )}^2\right )+\ln \left (\frac {1}{x^2}\right )+{\mathrm {e}}^2}}}{{\left ({\ln \left (x-4\right )}^2\right )}^{\frac {x}{\ln \left ({\ln \left (x-4\right )}^2\right )+\ln \left (\frac {1}{x^2}\right )+{\mathrm {e}}^2}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(exp((exp(9) - x*log((log(x - 4)^2*exp(exp(2)))/x^2))/log((log(x - 4)^2*exp(exp(2)))/x^2))*(log(x - 4)*ex
p(9)*(2*x - 8) - 2*x*exp(9) + log((log(x - 4)^2*exp(exp(2)))/x^2)^2*log(x - 4)*(4*x - x^2)))/(log((log(x - 4)^
2*exp(exp(2)))/x^2)^2*log(x - 4)*(4*x - x^2)),x)

[Out]

(exp(-(x*exp(2))/(log(log(x - 4)^2) + log(1/x^2) + exp(2)))*exp(exp(9)/(log(log(x - 4)^2) + log(1/x^2) + exp(2
)))*(x^2)^(x/(log(log(x - 4)^2) + log(1/x^2) + exp(2))))/(log(x - 4)^2)^(x/(log(log(x - 4)^2) + log(1/x^2) + e
xp(2)))

________________________________________________________________________________________

sympy [A]  time = 1.52, size = 39, normalized size = 1.39 \begin {gather*} e^{\frac {- x \log {\left (\frac {e^{e^{2}} \log {\left (x - 4 \right )}^{2}}{x^{2}} \right )} + e^{9}}{\log {\left (\frac {e^{e^{2}} \log {\left (x - 4 \right )}^{2}}{x^{2}} \right )}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-x**2+4*x)*ln(x-4)*ln(exp(exp(2))*ln(x-4)**2/x**2)**2+(2*x-8)*exp(9)*ln(x-4)-2*x*exp(9))*exp((-x*l
n(exp(exp(2))*ln(x-4)**2/x**2)+exp(9))/ln(exp(exp(2))*ln(x-4)**2/x**2))/(x**2-4*x)/ln(x-4)/ln(exp(exp(2))*ln(x
-4)**2/x**2)**2,x)

[Out]

exp((-x*log(exp(exp(2))*log(x - 4)**2/x**2) + exp(9))/log(exp(exp(2))*log(x - 4)**2/x**2))

________________________________________________________________________________________