3.71.76 \(\int \frac {e^{-2 x+e^{-2 x} (x^5+2 x^4 \log (5)+x^3 \log ^2(5)+e^x (-2 x^3-2 x^2 \log (5)) \log (x)+e^{2 x} x \log ^2(x)+(e^x (-2 x^3-2 x^2 \log (5))+2 e^{2 x} x \log (x)) \log (-\frac {\log (x)}{-2+x})+e^{2 x} x \log ^2(-\frac {\log (x)}{-2+x}))} (e^x (4 x^2-2 x^3+(4 x-2 x^2) \log (5))+(-10 x^4+9 x^5-2 x^6+e^{2 x} (-4+2 x)+(-16 x^3+16 x^4-4 x^5) \log (5)+(-6 x^2+7 x^3-2 x^4) \log ^2(5)+e^x (4 x^2+4 x \log (5))) \log (x)+(-4 e^{2 x}+e^x (12 x^2-10 x^3+2 x^4+(8 x-8 x^2+2 x^3) \log (5))) \log ^2(x)+e^{2 x} (-2+x) \log ^3(x)+(e^{2 x} (-4+2 x)+(-4 e^{2 x}+e^x (12 x^2-10 x^3+2 x^4+(8 x-8 x^2+2 x^3) \log (5))) \log (x)+e^{2 x} (-4+2 x) \log ^2(x)) \log (-\frac {\log (x)}{-2+x})+e^{2 x} (-2+x) \log (x) \log ^2(-\frac {\log (x)}{-2+x}))}{(-2+x) \log (x)} \, dx\)

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

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Rubi [F]  time = 180.00, 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*} \text {\$Aborted} \end {gather*}

Verification is not applicable to the result.

[In]

Int[(E^(-2*x + (x^5 + 2*x^4*Log[5] + x^3*Log[5]^2 + E^x*(-2*x^3 - 2*x^2*Log[5])*Log[x] + E^(2*x)*x*Log[x]^2 +
(E^x*(-2*x^3 - 2*x^2*Log[5]) + 2*E^(2*x)*x*Log[x])*Log[-(Log[x]/(-2 + x))] + E^(2*x)*x*Log[-(Log[x]/(-2 + x))]
^2)/E^(2*x))*(E^x*(4*x^2 - 2*x^3 + (4*x - 2*x^2)*Log[5]) + (-10*x^4 + 9*x^5 - 2*x^6 + E^(2*x)*(-4 + 2*x) + (-1
6*x^3 + 16*x^4 - 4*x^5)*Log[5] + (-6*x^2 + 7*x^3 - 2*x^4)*Log[5]^2 + E^x*(4*x^2 + 4*x*Log[5]))*Log[x] + (-4*E^
(2*x) + E^x*(12*x^2 - 10*x^3 + 2*x^4 + (8*x - 8*x^2 + 2*x^3)*Log[5]))*Log[x]^2 + E^(2*x)*(-2 + x)*Log[x]^3 + (
E^(2*x)*(-4 + 2*x) + (-4*E^(2*x) + E^x*(12*x^2 - 10*x^3 + 2*x^4 + (8*x - 8*x^2 + 2*x^3)*Log[5]))*Log[x] + E^(2
*x)*(-4 + 2*x)*Log[x]^2)*Log[-(Log[x]/(-2 + x))] + E^(2*x)*(-2 + x)*Log[x]*Log[-(Log[x]/(-2 + x))]^2))/((-2 +
x)*Log[x]),x]

[Out]

$Aborted

Rubi steps

Aborted

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Mathematica [F]  time = 26.87, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {e^{-2 x+e^{-2 x} \left (x^5+2 x^4 \log (5)+x^3 \log ^2(5)+e^x \left (-2 x^3-2 x^2 \log (5)\right ) \log (x)+e^{2 x} x \log ^2(x)+\left (e^x \left (-2 x^3-2 x^2 \log (5)\right )+2 e^{2 x} x \log (x)\right ) \log \left (-\frac {\log (x)}{-2+x}\right )+e^{2 x} x \log ^2\left (-\frac {\log (x)}{-2+x}\right )\right )} \left (e^x \left (4 x^2-2 x^3+\left (4 x-2 x^2\right ) \log (5)\right )+\left (-10 x^4+9 x^5-2 x^6+e^{2 x} (-4+2 x)+\left (-16 x^3+16 x^4-4 x^5\right ) \log (5)+\left (-6 x^2+7 x^3-2 x^4\right ) \log ^2(5)+e^x \left (4 x^2+4 x \log (5)\right )\right ) \log (x)+\left (-4 e^{2 x}+e^x \left (12 x^2-10 x^3+2 x^4+\left (8 x-8 x^2+2 x^3\right ) \log (5)\right )\right ) \log ^2(x)+e^{2 x} (-2+x) \log ^3(x)+\left (e^{2 x} (-4+2 x)+\left (-4 e^{2 x}+e^x \left (12 x^2-10 x^3+2 x^4+\left (8 x-8 x^2+2 x^3\right ) \log (5)\right )\right ) \log (x)+e^{2 x} (-4+2 x) \log ^2(x)\right ) \log \left (-\frac {\log (x)}{-2+x}\right )+e^{2 x} (-2+x) \log (x) \log ^2\left (-\frac {\log (x)}{-2+x}\right )\right )}{(-2+x) \log (x)} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Integrate[(E^(-2*x + (x^5 + 2*x^4*Log[5] + x^3*Log[5]^2 + E^x*(-2*x^3 - 2*x^2*Log[5])*Log[x] + E^(2*x)*x*Log[x
]^2 + (E^x*(-2*x^3 - 2*x^2*Log[5]) + 2*E^(2*x)*x*Log[x])*Log[-(Log[x]/(-2 + x))] + E^(2*x)*x*Log[-(Log[x]/(-2
+ x))]^2)/E^(2*x))*(E^x*(4*x^2 - 2*x^3 + (4*x - 2*x^2)*Log[5]) + (-10*x^4 + 9*x^5 - 2*x^6 + E^(2*x)*(-4 + 2*x)
+ (-16*x^3 + 16*x^4 - 4*x^5)*Log[5] + (-6*x^2 + 7*x^3 - 2*x^4)*Log[5]^2 + E^x*(4*x^2 + 4*x*Log[5]))*Log[x] +
(-4*E^(2*x) + E^x*(12*x^2 - 10*x^3 + 2*x^4 + (8*x - 8*x^2 + 2*x^3)*Log[5]))*Log[x]^2 + E^(2*x)*(-2 + x)*Log[x]
^3 + (E^(2*x)*(-4 + 2*x) + (-4*E^(2*x) + E^x*(12*x^2 - 10*x^3 + 2*x^4 + (8*x - 8*x^2 + 2*x^3)*Log[5]))*Log[x]
+ E^(2*x)*(-4 + 2*x)*Log[x]^2)*Log[-(Log[x]/(-2 + x))] + E^(2*x)*(-2 + x)*Log[x]*Log[-(Log[x]/(-2 + x))]^2))/(
(-2 + x)*Log[x]),x]

[Out]

Integrate[(E^(-2*x + (x^5 + 2*x^4*Log[5] + x^3*Log[5]^2 + E^x*(-2*x^3 - 2*x^2*Log[5])*Log[x] + E^(2*x)*x*Log[x
]^2 + (E^x*(-2*x^3 - 2*x^2*Log[5]) + 2*E^(2*x)*x*Log[x])*Log[-(Log[x]/(-2 + x))] + E^(2*x)*x*Log[-(Log[x]/(-2
+ x))]^2)/E^(2*x))*(E^x*(4*x^2 - 2*x^3 + (4*x - 2*x^2)*Log[5]) + (-10*x^4 + 9*x^5 - 2*x^6 + E^(2*x)*(-4 + 2*x)
+ (-16*x^3 + 16*x^4 - 4*x^5)*Log[5] + (-6*x^2 + 7*x^3 - 2*x^4)*Log[5]^2 + E^x*(4*x^2 + 4*x*Log[5]))*Log[x] +
(-4*E^(2*x) + E^x*(12*x^2 - 10*x^3 + 2*x^4 + (8*x - 8*x^2 + 2*x^3)*Log[5]))*Log[x]^2 + E^(2*x)*(-2 + x)*Log[x]
^3 + (E^(2*x)*(-4 + 2*x) + (-4*E^(2*x) + E^x*(12*x^2 - 10*x^3 + 2*x^4 + (8*x - 8*x^2 + 2*x^3)*Log[5]))*Log[x]
+ E^(2*x)*(-4 + 2*x)*Log[x]^2)*Log[-(Log[x]/(-2 + x))] + E^(2*x)*(-2 + x)*Log[x]*Log[-(Log[x]/(-2 + x))]^2))/(
(-2 + x)*Log[x]), x]

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fricas [B]  time = 0.68, size = 115, normalized size = 3.59 \begin {gather*} e^{\left ({\left (x^{5} + 2 \, x^{4} \log \relax (5) + x^{3} \log \relax (5)^{2} + x e^{\left (2 \, x\right )} \log \relax (x)^{2} + x e^{\left (2 \, x\right )} \log \left (-\frac {\log \relax (x)}{x - 2}\right )^{2} - 2 \, {\left (x^{3} + x^{2} \log \relax (5)\right )} e^{x} \log \relax (x) - 2 \, x e^{\left (2 \, x\right )} + 2 \, {\left (x e^{\left (2 \, x\right )} \log \relax (x) - {\left (x^{3} + x^{2} \log \relax (5)\right )} e^{x}\right )} \log \left (-\frac {\log \relax (x)}{x - 2}\right )\right )} e^{\left (-2 \, x\right )} + 2 \, x\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((x-2)*exp(x)^2*log(x)*log(-log(x)/(x-2))^2+((2*x-4)*exp(x)^2*log(x)^2+(-4*exp(x)^2+((2*x^3-8*x^2+8*
x)*log(5)+2*x^4-10*x^3+12*x^2)*exp(x))*log(x)+(2*x-4)*exp(x)^2)*log(-log(x)/(x-2))+(x-2)*exp(x)^2*log(x)^3+(-4
*exp(x)^2+((2*x^3-8*x^2+8*x)*log(5)+2*x^4-10*x^3+12*x^2)*exp(x))*log(x)^2+((2*x-4)*exp(x)^2+(4*x*log(5)+4*x^2)
*exp(x)+(-2*x^4+7*x^3-6*x^2)*log(5)^2+(-4*x^5+16*x^4-16*x^3)*log(5)-2*x^6+9*x^5-10*x^4)*log(x)+((-2*x^2+4*x)*l
og(5)-2*x^3+4*x^2)*exp(x))*exp((x*exp(x)^2*log(-log(x)/(x-2))^2+(2*x*exp(x)^2*log(x)+(-2*x^2*log(5)-2*x^3)*exp
(x))*log(-log(x)/(x-2))+x*exp(x)^2*log(x)^2+(-2*x^2*log(5)-2*x^3)*exp(x)*log(x)+x^3*log(5)^2+2*x^4*log(5)+x^5)
/exp(x)^2)/(x-2)/exp(x)^2/log(x),x, algorithm="fricas")

[Out]

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

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giac [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \mathit {undef} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((x-2)*exp(x)^2*log(x)*log(-log(x)/(x-2))^2+((2*x-4)*exp(x)^2*log(x)^2+(-4*exp(x)^2+((2*x^3-8*x^2+8*
x)*log(5)+2*x^4-10*x^3+12*x^2)*exp(x))*log(x)+(2*x-4)*exp(x)^2)*log(-log(x)/(x-2))+(x-2)*exp(x)^2*log(x)^3+(-4
*exp(x)^2+((2*x^3-8*x^2+8*x)*log(5)+2*x^4-10*x^3+12*x^2)*exp(x))*log(x)^2+((2*x-4)*exp(x)^2+(4*x*log(5)+4*x^2)
*exp(x)+(-2*x^4+7*x^3-6*x^2)*log(5)^2+(-4*x^5+16*x^4-16*x^3)*log(5)-2*x^6+9*x^5-10*x^4)*log(x)+((-2*x^2+4*x)*l
og(5)-2*x^3+4*x^2)*exp(x))*exp((x*exp(x)^2*log(-log(x)/(x-2))^2+(2*x*exp(x)^2*log(x)+(-2*x^2*log(5)-2*x^3)*exp
(x))*log(-log(x)/(x-2))+x*exp(x)^2*log(x)^2+(-2*x^2*log(5)-2*x^3)*exp(x)*log(x)+x^3*log(5)^2+2*x^4*log(5)+x^5)
/exp(x)^2)/(x-2)/exp(x)^2/log(x),x, algorithm="giac")

[Out]

undef

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maple [C]  time = 0.77, size = 1224, normalized size = 38.25

method	result	size
risch	\(\left (x -2\right )^{2 i \pi x} \ln \relax (x )^{-2 i \pi x} \left (x -2\right )^{-i x \,\mathrm {csgn}\left (\frac {i}{x -2}\right ) \pi } 5^{-2 i x^{2} \pi \,{\mathrm e}^{-x}} x^{-i x \,\mathrm {csgn}\left (\frac {i}{x -2}\right ) \mathrm {csgn}\left (i \ln \relax (x )\right ) \mathrm {csgn}\left (\frac {i \ln \relax (x )}{x -2}\right ) \pi } 5^{-i x^{2} \mathrm {csgn}\left (\frac {i \ln \relax (x )}{x -2}\right ) \pi \,{\mathrm e}^{-x}} \left (x -2\right )^{-2 i \pi x} 5^{i x^{2} \mathrm {csgn}\left (\frac {i}{x -2}\right ) \mathrm {csgn}\left (i \ln \relax (x )\right ) \mathrm {csgn}\left (\frac {i \ln \relax (x )}{x -2}\right ) \pi \,{\mathrm e}^{-x}} \ln \relax (x )^{i x \,\mathrm {csgn}\left (i \ln \relax (x )\right ) \pi } \left (x -2\right )^{2 x^{2} \ln \relax (5) {\mathrm e}^{-x}} x^{i x \,\mathrm {csgn}\left (i \ln \relax (x )\right ) \pi } \left (x -2\right )^{2 x^{3} {\mathrm e}^{-x}} \ln \relax (x )^{i x \,\mathrm {csgn}\left (\frac {i}{x -2}\right ) \pi } \ln \relax (x )^{-2 x^{3} {\mathrm e}^{-x}} x^{2 i \pi x} \left (x -2\right )^{-2 x \ln \relax (x )} \left (x -2\right )^{-i x \,\mathrm {csgn}\left (\frac {i \ln \relax (x )}{x -2}\right ) \pi } \ln \relax (x )^{-i x \,\mathrm {csgn}\left (\frac {i}{x -2}\right ) \mathrm {csgn}\left (i \ln \relax (x )\right ) \mathrm {csgn}\left (\frac {i \ln \relax (x )}{x -2}\right ) \pi } \ln \relax (x )^{-2 x^{2} \ln \relax (5) {\mathrm e}^{-x}} 5^{-i x^{2} \mathrm {csgn}\left (\frac {i}{x -2}\right ) \pi \,{\mathrm e}^{-x}} \ln \relax (x )^{2 i \pi x} x^{-2 i \pi x} 25^{{\mathrm e}^{-2 x} x^{4}} \ln \relax (x )^{i x \,\mathrm {csgn}\left (\frac {i \ln \relax (x )}{x -2}\right ) \pi } \left (x -2\right )^{-i x \,\mathrm {csgn}\left (i \ln \relax (x )\right ) \pi } x^{-2 x^{2} \ln \relax (5) {\mathrm e}^{-x}} 5^{2 i x^{2} \pi \,{\mathrm e}^{-x}} x^{i x \,\mathrm {csgn}\left (\frac {i}{x -2}\right ) \pi } 5^{-i x^{2} \mathrm {csgn}\left (i \ln \relax (x )\right ) \pi \,{\mathrm e}^{-x}} x^{i x \,\mathrm {csgn}\left (\frac {i \ln \relax (x )}{x -2}\right ) \pi } \left (x -2\right )^{i x \,\mathrm {csgn}\left (\frac {i}{x -2}\right ) \mathrm {csgn}\left (i \ln \relax (x )\right ) \mathrm {csgn}\left (\frac {i \ln \relax (x )}{x -2}\right ) \pi } \ln \relax (x )^{-2 x \ln \left (x -2\right )} \ln \relax (x )^{2 x \ln \relax (x )} x^{-2 x^{3} {\mathrm e}^{-x}} {\mathrm e}^{-\frac {x \left (4 \pi ^{2}-4 \ln \left (x -2\right )^{2}-4 \ln \left (\ln \relax (x )\right )^{2}-4 \ln \relax (x )^{2}+4 \,\mathrm {csgn}\left (i \ln \relax (x )\right ) \mathrm {csgn}\left (\frac {i \ln \relax (x )}{x -2}\right )^{2} \pi ^{2}+4 \,\mathrm {csgn}\left (\frac {i}{x -2}\right ) \mathrm {csgn}\left (\frac {i \ln \relax (x )}{x -2}\right )^{2} \pi ^{2}+2 \,\mathrm {csgn}\left (\frac {i}{x -2}\right ) \mathrm {csgn}\left (\frac {i \ln \relax (x )}{x -2}\right )^{5} \pi ^{2}+\mathrm {csgn}\left (i \ln \relax (x )\right )^{2} \mathrm {csgn}\left (\frac {i \ln \relax (x )}{x -2}\right )^{4} \pi ^{2}+\mathrm {csgn}\left (\frac {i}{x -2}\right )^{2} \mathrm {csgn}\left (\frac {i \ln \relax (x )}{x -2}\right )^{4} \pi ^{2}-4 \,\mathrm {csgn}\left (i \ln \relax (x )\right ) \mathrm {csgn}\left (\frac {i \ln \relax (x )}{x -2}\right )^{4} \pi ^{2}-4 \,\mathrm {csgn}\left (\frac {i}{x -2}\right ) \mathrm {csgn}\left (\frac {i \ln \relax (x )}{x -2}\right )^{4} \pi ^{2}+2 \,\mathrm {csgn}\left (i \ln \relax (x )\right ) \mathrm {csgn}\left (\frac {i \ln \relax (x )}{x -2}\right )^{5} \pi ^{2}-4 \,{\mathrm e}^{-2 x} x^{4}+4 i x^{2} \mathrm {csgn}\left (\frac {i \ln \relax (x )}{x -2}\right )^{3} \pi \,{\mathrm e}^{-x}-8 i x^{2} \mathrm {csgn}\left (\frac {i \ln \relax (x )}{x -2}\right )^{2} \pi \,{\mathrm e}^{-x}-4 i x^{2} \mathrm {csgn}\left (\frac {i}{x -2}\right ) \mathrm {csgn}\left (i \ln \relax (x )\right ) \mathrm {csgn}\left (\frac {i \ln \relax (x )}{x -2}\right ) \pi \,{\mathrm e}^{-x}+8 i x^{2} \pi \,{\mathrm e}^{-x}-4 \ln \relax (5)^{2} {\mathrm e}^{-2 x} x^{2}+\mathrm {csgn}\left (\frac {i \ln \relax (x )}{x -2}\right )^{6} \pi ^{2}+4 \mathrm {csgn}\left (\frac {i \ln \relax (x )}{x -2}\right )^{3} \pi ^{2}-8 \mathrm {csgn}\left (\frac {i \ln \relax (x )}{x -2}\right )^{2} \pi ^{2}-4 \mathrm {csgn}\left (\frac {i \ln \relax (x )}{x -2}\right )^{5} \pi ^{2}+4 \mathrm {csgn}\left (\frac {i \ln \relax (x )}{x -2}\right )^{4} \pi ^{2}+4 i x^{2} \mathrm {csgn}\left (\frac {i}{x -2}\right ) \mathrm {csgn}\left (\frac {i \ln \relax (x )}{x -2}\right )^{2} \pi \,{\mathrm e}^{-x}+4 i x^{2} \mathrm {csgn}\left (i \ln \relax (x )\right ) \mathrm {csgn}\left (\frac {i \ln \relax (x )}{x -2}\right )^{2} \pi \,{\mathrm e}^{-x}-2 \,\mathrm {csgn}\left (i \ln \relax (x )\right ) \mathrm {csgn}\left (\frac {i}{x -2}\right )^{2} \mathrm {csgn}\left (\frac {i \ln \relax (x )}{x -2}\right )^{3} \pi ^{2}+\mathrm {csgn}\left (\frac {i}{x -2}\right )^{2} \mathrm {csgn}\left (i \ln \relax (x )\right )^{2} \mathrm {csgn}\left (\frac {i \ln \relax (x )}{x -2}\right )^{2} \pi ^{2}+4 \,\mathrm {csgn}\left (\frac {i}{x -2}\right ) \mathrm {csgn}\left (i \ln \relax (x )\right ) \mathrm {csgn}\left (\frac {i \ln \relax (x )}{x -2}\right )^{3} \pi ^{2}-2 \,\mathrm {csgn}\left (\frac {i}{x -2}\right ) \mathrm {csgn}\left (i \ln \relax (x )\right )^{2} \mathrm {csgn}\left (\frac {i \ln \relax (x )}{x -2}\right )^{3} \pi ^{2}-4 \,\mathrm {csgn}\left (\frac {i}{x -2}\right ) \mathrm {csgn}\left (i \ln \relax (x )\right ) \mathrm {csgn}\left (\frac {i \ln \relax (x )}{x -2}\right ) \pi ^{2}\right )}{4}}\)	\(1224\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((x-2)*exp(x)^2*ln(x)*ln(-ln(x)/(x-2))^2+((2*x-4)*exp(x)^2*ln(x)^2+(-4*exp(x)^2+((2*x^3-8*x^2+8*x)*ln(5)+2
*x^4-10*x^3+12*x^2)*exp(x))*ln(x)+(2*x-4)*exp(x)^2)*ln(-ln(x)/(x-2))+(x-2)*exp(x)^2*ln(x)^3+(-4*exp(x)^2+((2*x
^3-8*x^2+8*x)*ln(5)+2*x^4-10*x^3+12*x^2)*exp(x))*ln(x)^2+((2*x-4)*exp(x)^2+(4*x*ln(5)+4*x^2)*exp(x)+(-2*x^4+7*
x^3-6*x^2)*ln(5)^2+(-4*x^5+16*x^4-16*x^3)*ln(5)-2*x^6+9*x^5-10*x^4)*ln(x)+((-2*x^2+4*x)*ln(5)-2*x^3+4*x^2)*exp
(x))*exp((x*exp(x)^2*ln(-ln(x)/(x-2))^2+(2*x*exp(x)^2*ln(x)+(-2*x^2*ln(5)-2*x^3)*exp(x))*ln(-ln(x)/(x-2))+x*ex
p(x)^2*ln(x)^2+(-2*x^2*ln(5)-2*x^3)*exp(x)*ln(x)+x^3*ln(5)^2+2*x^4*ln(5)+x^5)/exp(x)^2)/(x-2)/exp(x)^2/ln(x),x
,method=_RETURNVERBOSE)

[Out]

(x-2)^(2*I*Pi*x)*ln(x)^(-2*I*Pi*x)*(x-2)^(-I*x*csgn(I/(x-2))*Pi)*5^(-2*I*x^2*Pi*exp(-x))*x^(-I*x*csgn(I/(x-2))
*csgn(I*ln(x))*csgn(I*ln(x)/(x-2))*Pi)*5^(-I*x^2*csgn(I*ln(x)/(x-2))*Pi*exp(-x))*(x-2)^(-2*I*Pi*x)*5^(I*x^2*cs
gn(I/(x-2))*csgn(I*ln(x))*csgn(I*ln(x)/(x-2))*Pi*exp(-x))*ln(x)^(I*x*csgn(I*ln(x))*Pi)*(x-2)^(2*x^2*ln(5)*exp(
-x))*x^(I*x*csgn(I*ln(x))*Pi)*(x-2)^(2*x^3*exp(-x))*ln(x)^(I*x*csgn(I/(x-2))*Pi)*ln(x)^(-2*x^3*exp(-x))*x^(2*I
*Pi*x)*(x-2)^(-2*x*ln(x))*(x-2)^(-I*x*csgn(I*ln(x)/(x-2))*Pi)*ln(x)^(-I*x*csgn(I/(x-2))*csgn(I*ln(x))*csgn(I*l
n(x)/(x-2))*Pi)*ln(x)^(-2*x^2*ln(5)*exp(-x))*5^(-I*x^2*csgn(I/(x-2))*Pi*exp(-x))*ln(x)^(2*I*Pi*x)*x^(-2*I*Pi*x
)*25^(exp(-2*x)*x^4)*ln(x)^(I*x*csgn(I*ln(x)/(x-2))*Pi)*(x-2)^(-I*x*csgn(I*ln(x))*Pi)*x^(-2*x^2*ln(5)*exp(-x))
*5^(2*I*x^2*Pi*exp(-x))*x^(I*x*csgn(I/(x-2))*Pi)*5^(-I*x^2*csgn(I*ln(x))*Pi*exp(-x))*x^(I*x*csgn(I*ln(x)/(x-2)
)*Pi)*(x-2)^(I*x*csgn(I/(x-2))*csgn(I*ln(x))*csgn(I*ln(x)/(x-2))*Pi)*ln(x)^(-2*x*ln(x-2))*ln(x)^(2*x*ln(x))*x^
(-2*x^3*exp(-x))*exp(-1/4*x*(4*Pi^2-4*ln(x-2)^2-4*ln(ln(x))^2-4*ln(x)^2+4*I*x^2*csgn(I/(x-2))*csgn(I*ln(x)/(x-
2))^2*Pi*exp(-x)+4*I*x^2*csgn(I*ln(x))*csgn(I*ln(x)/(x-2))^2*Pi*exp(-x)-2*csgn(I*ln(x))*csgn(I/(x-2))^2*csgn(I
*ln(x)/(x-2))^3*Pi^2+csgn(I/(x-2))^2*csgn(I*ln(x))^2*csgn(I*ln(x)/(x-2))^2*Pi^2+4*csgn(I/(x-2))*csgn(I*ln(x))*
csgn(I*ln(x)/(x-2))^3*Pi^2-2*csgn(I/(x-2))*csgn(I*ln(x))^2*csgn(I*ln(x)/(x-2))^3*Pi^2-4*csgn(I/(x-2))*csgn(I*l
n(x))*csgn(I*ln(x)/(x-2))*Pi^2+4*csgn(I*ln(x))*csgn(I*ln(x)/(x-2))^2*Pi^2+4*csgn(I/(x-2))*csgn(I*ln(x)/(x-2))^
2*Pi^2-4*exp(-2*x)*x^4+csgn(I*ln(x)/(x-2))^6*Pi^2+4*csgn(I*ln(x)/(x-2))^3*Pi^2-8*csgn(I*ln(x)/(x-2))^2*Pi^2-4*
csgn(I*ln(x)/(x-2))^5*Pi^2+4*csgn(I*ln(x)/(x-2))^4*Pi^2+8*I*x^2*Pi*exp(-x)-4*I*x^2*csgn(I/(x-2))*csgn(I*ln(x))
*csgn(I*ln(x)/(x-2))*Pi*exp(-x)+2*csgn(I/(x-2))*csgn(I*ln(x)/(x-2))^5*Pi^2+csgn(I*ln(x))^2*csgn(I*ln(x)/(x-2))
^4*Pi^2+csgn(I/(x-2))^2*csgn(I*ln(x)/(x-2))^4*Pi^2-4*csgn(I*ln(x))*csgn(I*ln(x)/(x-2))^4*Pi^2+4*I*x^2*csgn(I*l
n(x)/(x-2))^3*Pi*exp(-x)-8*I*x^2*csgn(I*ln(x)/(x-2))^2*Pi*exp(-x)-4*ln(5)^2*exp(-2*x)*x^2-4*csgn(I/(x-2))*csgn
(I*ln(x)/(x-2))^4*Pi^2+2*csgn(I*ln(x))*csgn(I*ln(x)/(x-2))^5*Pi^2))

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maxima [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(((x-2)*exp(x)^2*log(x)*log(-log(x)/(x-2))^2+((2*x-4)*exp(x)^2*log(x)^2+(-4*exp(x)^2+((2*x^3-8*x^2+8*
x)*log(5)+2*x^4-10*x^3+12*x^2)*exp(x))*log(x)+(2*x-4)*exp(x)^2)*log(-log(x)/(x-2))+(x-2)*exp(x)^2*log(x)^3+(-4
*exp(x)^2+((2*x^3-8*x^2+8*x)*log(5)+2*x^4-10*x^3+12*x^2)*exp(x))*log(x)^2+((2*x-4)*exp(x)^2+(4*x*log(5)+4*x^2)
*exp(x)+(-2*x^4+7*x^3-6*x^2)*log(5)^2+(-4*x^5+16*x^4-16*x^3)*log(5)-2*x^6+9*x^5-10*x^4)*log(x)+((-2*x^2+4*x)*l
og(5)-2*x^3+4*x^2)*exp(x))*exp((x*exp(x)^2*log(-log(x)/(x-2))^2+(2*x*exp(x)^2*log(x)+(-2*x^2*log(5)-2*x^3)*exp
(x))*log(-log(x)/(x-2))+x*exp(x)^2*log(x)^2+(-2*x^2*log(5)-2*x^3)*exp(x)*log(x)+x^3*log(5)^2+2*x^4*log(5)+x^5)
/exp(x)^2)/(x-2)/exp(x)^2/log(x),x, algorithm="maxima")

[Out]

Timed out

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mupad [B]  time = 6.68, size = 143, normalized size = 4.47 \begin {gather*} \frac {5^{2\,x^4\,{\mathrm {e}}^{-2\,x}}\,x^{2\,x\,\ln \left (-\frac {\ln \relax (x)}{x-2}\right )}\,{\mathrm {e}}^{x\,{\ln \relax (x)}^2}\,{\mathrm {e}}^{x\,{\ln \left (-\frac {\ln \relax (x)}{x-2}\right )}^2}\,{\mathrm {e}}^{x^3\,{\mathrm {e}}^{-2\,x}\,{\ln \relax (5)}^2}\,{\mathrm {e}}^{x^5\,{\mathrm {e}}^{-2\,x}}}{x^{2\,x^3\,{\mathrm {e}}^{-x}}\,x^{2\,x^2\,{\mathrm {e}}^{-x}\,\ln \relax (5)}\,{\left (-\frac {\ln \relax (x)}{x-2}\right )}^{2\,x^3\,{\mathrm {e}}^{-x}}\,{\left (-\frac {\ln \relax (x)}{x-2}\right )}^{2\,x^2\,{\mathrm {e}}^{-x}\,\ln \relax (5)}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(exp(-2*x)*(x^3*log(5)^2 - log(-log(x)/(x - 2))*(exp(x)*(2*x^2*log(5) + 2*x^3) - 2*x*exp(2*x)*log(x))
+ 2*x^4*log(5) + x^5 + x*exp(2*x)*log(x)^2 + x*exp(2*x)*log(-log(x)/(x - 2))^2 - exp(x)*log(x)*(2*x^2*log(5) +
2*x^3)))*exp(-2*x)*(exp(x)*(log(5)*(4*x - 2*x^2) + 4*x^2 - 2*x^3) - log(x)*(log(5)^2*(6*x^2 - 7*x^3 + 2*x^4)
- exp(x)*(4*x*log(5) + 4*x^2) + log(5)*(16*x^3 - 16*x^4 + 4*x^5) - exp(2*x)*(2*x - 4) + 10*x^4 - 9*x^5 + 2*x^6
) - log(x)^2*(4*exp(2*x) - exp(x)*(log(5)*(8*x - 8*x^2 + 2*x^3) + 12*x^2 - 10*x^3 + 2*x^4)) + log(-log(x)/(x -
2))*(exp(2*x)*(2*x - 4) - log(x)*(4*exp(2*x) - exp(x)*(log(5)*(8*x - 8*x^2 + 2*x^3) + 12*x^2 - 10*x^3 + 2*x^4
)) + exp(2*x)*log(x)^2*(2*x - 4)) + exp(2*x)*log(x)^3*(x - 2) + exp(2*x)*log(x)*log(-log(x)/(x - 2))^2*(x - 2)
))/(log(x)*(x - 2)),x)

[Out]

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

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sympy [B]  time = 139.27, size = 119, normalized size = 3.72 \begin {gather*} e^{\left (x^{5} + 2 x^{4} \log {\relax (5 )} + x^{3} \log {\relax (5 )}^{2} + x e^{2 x} \log {\relax (x )}^{2} + x e^{2 x} \log {\left (- \frac {\log {\relax (x )}}{x - 2} \right )}^{2} + \left (- 2 x^{3} - 2 x^{2} \log {\relax (5 )}\right ) e^{x} \log {\relax (x )} + \left (2 x e^{2 x} \log {\relax (x )} + \left (- 2 x^{3} - 2 x^{2} \log {\relax (5 )}\right ) e^{x}\right ) \log {\left (- \frac {\log {\relax (x )}}{x - 2} \right )}\right ) e^{- 2 x}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((x-2)*exp(x)**2*ln(x)*ln(-ln(x)/(x-2))**2+((2*x-4)*exp(x)**2*ln(x)**2+(-4*exp(x)**2+((2*x**3-8*x**2
+8*x)*ln(5)+2*x**4-10*x**3+12*x**2)*exp(x))*ln(x)+(2*x-4)*exp(x)**2)*ln(-ln(x)/(x-2))+(x-2)*exp(x)**2*ln(x)**3
+(-4*exp(x)**2+((2*x**3-8*x**2+8*x)*ln(5)+2*x**4-10*x**3+12*x**2)*exp(x))*ln(x)**2+((2*x-4)*exp(x)**2+(4*x*ln(
5)+4*x**2)*exp(x)+(-2*x**4+7*x**3-6*x**2)*ln(5)**2+(-4*x**5+16*x**4-16*x**3)*ln(5)-2*x**6+9*x**5-10*x**4)*ln(x
)+((-2*x**2+4*x)*ln(5)-2*x**3+4*x**2)*exp(x))*exp((x*exp(x)**2*ln(-ln(x)/(x-2))**2+(2*x*exp(x)**2*ln(x)+(-2*x*
*2*ln(5)-2*x**3)*exp(x))*ln(-ln(x)/(x-2))+x*exp(x)**2*ln(x)**2+(-2*x**2*ln(5)-2*x**3)*exp(x)*ln(x)+x**3*ln(5)*
*2+2*x**4*ln(5)+x**5)/exp(x)**2)/(x-2)/exp(x)**2/ln(x),x)

[Out]

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

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