3.55.93 \(\int \frac {-2 e^{6-\frac {2}{-4+e^{6-x}}} x^2+e^x (16 x^2+e^{12-2 x} x^2-8 e^{6-x} x^2)+e^{6-x} (-24-24 x) \log (3)+e^{12-2 x} (3+3 x) \log (3)+(48+48 x) \log (3)}{e^{-\frac {2}{-4+e^{6-x}}+x} (16 x^2+e^{12-2 x} x^2-8 e^{6-x} x^2)+e^x (16 x^3+e^{12-2 x} x^3-8 e^{6-x} x^3)-48 x \log (3)-3 e^{12-2 x} x \log (3)+24 e^{6-x} x \log (3)} \, dx\)
Optimal. Leaf size=36 \[ \log \left (e^{\frac {2}{4-e^{2 (3-x)+x}}}+x-\frac {3 e^{-x} \log (3)}{x}\right ) \]
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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[(-2*E^(6 - 2/(-4 + E^(6 - x)))*x^2 + E^x*(16*x^2 + E^(12 - 2*x)*x^2 - 8*E^(6 - x)*x^2) + E^(6 - x)*(-24 -
24*x)*Log[3] + E^(12 - 2*x)*(3 + 3*x)*Log[3] + (48 + 48*x)*Log[3])/(E^(-2/(-4 + E^(6 - x)) + x)*(16*x^2 + E^(1
2 - 2*x)*x^2 - 8*E^(6 - x)*x^2) + E^x*(16*x^3 + E^(12 - 2*x)*x^3 - 8*E^(6 - x)*x^3) - 48*x*Log[3] - 3*E^(12 -
2*x)*x*Log[3] + 24*E^(6 - x)*x*Log[3]),x]
[Out]
$Aborted
Rubi steps
Aborted
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Mathematica [A] time = 1.37, size = 63, normalized size = 1.75 \begin {gather*} -\frac {2}{-4+e^{6-x}}-\log (x)+\log \left (x+e^{\frac {2}{-4+e^{6-x}}} x^2-3 e^{\frac {2}{-4+e^{6-x}}-x} \log (3)\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
Integrate[(-2*E^(6 - 2/(-4 + E^(6 - x)))*x^2 + E^x*(16*x^2 + E^(12 - 2*x)*x^2 - 8*E^(6 - x)*x^2) + E^(6 - x)*(
-24 - 24*x)*Log[3] + E^(12 - 2*x)*(3 + 3*x)*Log[3] + (48 + 48*x)*Log[3])/(E^(-2/(-4 + E^(6 - x)) + x)*(16*x^2
+ E^(12 - 2*x)*x^2 - 8*E^(6 - x)*x^2) + E^x*(16*x^3 + E^(12 - 2*x)*x^3 - 8*E^(6 - x)*x^3) - 48*x*Log[3] - 3*E^
(12 - 2*x)*x*Log[3] + 24*E^(6 - x)*x*Log[3]),x]
[Out]
-2/(-4 + E^(6 - x)) - Log[x] + Log[x + E^(2/(-4 + E^(6 - x)))*x^2 - 3*E^(2/(-4 + E^(6 - x)) - x)*Log[3]]
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fricas [A] time = 1.46, size = 47, normalized size = 1.31 \begin {gather*} -x + \log \left (\frac {x^{2} e^{x} + x e^{\left (\frac {x e^{6} - 2 \, {\left (2 \, x + 1\right )} e^{x}}{e^{6} - 4 \, e^{x}}\right )} - 3 \, \log \relax (3)}{x}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((-2*x^2*exp(-x+6)*exp(x)*exp(-2/(exp(-x+6)-4))+(x^2*exp(-x+6)^2-8*x^2*exp(-x+6)+16*x^2)*exp(x)+(3*x+
3)*log(3)*exp(-x+6)^2+(-24*x-24)*log(3)*exp(-x+6)+(48*x+48)*log(3))/((x^2*exp(-x+6)^2-8*x^2*exp(-x+6)+16*x^2)*
exp(x)*exp(-2/(exp(-x+6)-4))+(x^3*exp(-x+6)^2-8*x^3*exp(-x+6)+16*x^3)*exp(x)-3*x*log(3)*exp(-x+6)^2+24*x*log(3
)*exp(-x+6)-48*x*log(3)),x, algorithm="fricas")
[Out]
-x + log((x^2*e^x + x*e^((x*e^6 - 2*(2*x + 1)*e^x)/(e^6 - 4*e^x)) - 3*log(3))/x)
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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((-2*x^2*exp(-x+6)*exp(x)*exp(-2/(exp(-x+6)-4))+(x^2*exp(-x+6)^2-8*x^2*exp(-x+6)+16*x^2)*exp(x)+(3*x+
3)*log(3)*exp(-x+6)^2+(-24*x-24)*log(3)*exp(-x+6)+(48*x+48)*log(3))/((x^2*exp(-x+6)^2-8*x^2*exp(-x+6)+16*x^2)*
exp(x)*exp(-2/(exp(-x+6)-4))+(x^3*exp(-x+6)^2-8*x^3*exp(-x+6)+16*x^3)*exp(x)-3*x*log(3)*exp(-x+6)^2+24*x*log(3
)*exp(-x+6)-48*x*log(3)),x, algorithm="giac")
[Out]
Timed out
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maple [B] time = 0.11, size = 63, normalized size = 1.75
|
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result |
size |
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| risch |
\(-\frac {{\mathrm e}^{6}}{2 \left ({\mathrm e}^{6}-4 \,{\mathrm e}^{x}\right )}+\frac {2}{{\mathrm e}^{-x +6}-4}+\ln \left ({\mathrm e}^{-\frac {2}{{\mathrm e}^{-x +6}-4}}-\frac {\left (-{\mathrm e}^{x} x^{2}+3 \ln \relax (3)\right ) {\mathrm e}^{-x}}{x}\right )\) |
\(63\) |
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Verification of antiderivative is not currently implemented for this CAS.
[In]
int((-2*x^2*exp(-x+6)*exp(x)*exp(-2/(exp(-x+6)-4))+(x^2*exp(-x+6)^2-8*x^2*exp(-x+6)+16*x^2)*exp(x)+(3*x+3)*ln(
3)*exp(-x+6)^2+(-24*x-24)*ln(3)*exp(-x+6)+(48*x+48)*ln(3))/((x^2*exp(-x+6)^2-8*x^2*exp(-x+6)+16*x^2)*exp(x)*ex
p(-2/(exp(-x+6)-4))+(x^3*exp(-x+6)^2-8*x^3*exp(-x+6)+16*x^3)*exp(x)-3*x*ln(3)*exp(-x+6)^2+24*x*ln(3)*exp(-x+6)
-48*x*ln(3)),x,method=_RETURNVERBOSE)
[Out]
-1/2*exp(6)/(exp(6)-4*exp(x))+2/(exp(-x+6)-4)+ln(exp(-2/(exp(-x+6)-4))-(-exp(x)*x^2+3*ln(3))/x*exp(-x))
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maxima [A] time = 0.59, size = 38, normalized size = 1.06 \begin {gather*} \log \left (\frac {{\left (x^{2} e^{x} + x e^{\left (x - \frac {2 \, e^{x}}{e^{6} - 4 \, e^{x}}\right )} - 3 \, \log \relax (3)\right )} e^{\left (-x\right )}}{x}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((-2*x^2*exp(-x+6)*exp(x)*exp(-2/(exp(-x+6)-4))+(x^2*exp(-x+6)^2-8*x^2*exp(-x+6)+16*x^2)*exp(x)+(3*x+
3)*log(3)*exp(-x+6)^2+(-24*x-24)*log(3)*exp(-x+6)+(48*x+48)*log(3))/((x^2*exp(-x+6)^2-8*x^2*exp(-x+6)+16*x^2)*
exp(x)*exp(-2/(exp(-x+6)-4))+(x^3*exp(-x+6)^2-8*x^3*exp(-x+6)+16*x^3)*exp(x)-3*x*log(3)*exp(-x+6)^2+24*x*log(3
)*exp(-x+6)-48*x*log(3)),x, algorithm="maxima")
[Out]
log((x^2*e^x + x*e^(x - 2*e^x/(e^6 - 4*e^x)) - 3*log(3))*e^(-x)/x)
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mupad [F] time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} \int \frac {\ln \relax (3)\,\left (48\,x+48\right )+{\mathrm {e}}^x\,\left (x^2\,{\mathrm {e}}^{12-2\,x}-8\,x^2\,{\mathrm {e}}^{6-x}+16\,x^2\right )-2\,x^2\,{\mathrm {e}}^{6-\frac {2}{{\mathrm {e}}^{6-x}-4}}+{\mathrm {e}}^{12-2\,x}\,\ln \relax (3)\,\left (3\,x+3\right )-{\mathrm {e}}^{6-x}\,\ln \relax (3)\,\left (24\,x+24\right )}{{\mathrm {e}}^x\,\left (x^3\,{\mathrm {e}}^{12-2\,x}-8\,x^3\,{\mathrm {e}}^{6-x}+16\,x^3\right )-48\,x\,\ln \relax (3)+{\mathrm {e}}^{x-\frac {2}{{\mathrm {e}}^{6-x}-4}}\,\left (x^2\,{\mathrm {e}}^{12-2\,x}-8\,x^2\,{\mathrm {e}}^{6-x}+16\,x^2\right )+24\,x\,{\mathrm {e}}^{6-x}\,\ln \relax (3)-3\,x\,{\mathrm {e}}^{12-2\,x}\,\ln \relax (3)} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
int((log(3)*(48*x + 48) + exp(x)*(x^2*exp(12 - 2*x) - 8*x^2*exp(6 - x) + 16*x^2) + exp(12 - 2*x)*log(3)*(3*x +
3) - exp(6 - x)*log(3)*(24*x + 24) - 2*x^2*exp(-2/(exp(6 - x) - 4))*exp(6 - x)*exp(x))/(exp(x)*(x^3*exp(12 -
2*x) - 8*x^3*exp(6 - x) + 16*x^3) - 48*x*log(3) + exp(-2/(exp(6 - x) - 4))*exp(x)*(x^2*exp(12 - 2*x) - 8*x^2*e
xp(6 - x) + 16*x^2) + 24*x*exp(6 - x)*log(3) - 3*x*exp(12 - 2*x)*log(3)),x)
[Out]
int((log(3)*(48*x + 48) + exp(x)*(x^2*exp(12 - 2*x) - 8*x^2*exp(6 - x) + 16*x^2) - 2*x^2*exp(6 - 2/(exp(6 - x)
- 4)) + exp(12 - 2*x)*log(3)*(3*x + 3) - exp(6 - x)*log(3)*(24*x + 24))/(exp(x)*(x^3*exp(12 - 2*x) - 8*x^3*ex
p(6 - x) + 16*x^3) - 48*x*log(3) + exp(x - 2/(exp(6 - x) - 4))*(x^2*exp(12 - 2*x) - 8*x^2*exp(6 - x) + 16*x^2)
+ 24*x*exp(6 - x)*log(3) - 3*x*exp(12 - 2*x)*log(3)), x)
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sympy [A] time = 1.06, size = 31, normalized size = 0.86 \begin {gather*} \log {\left (e^{- \frac {2}{-4 + e^{6} e^{- x}}} + \frac {\left (x^{2} e^{x} - 3 \log {\relax (3 )}\right ) e^{- x}}{x} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((-2*x**2*exp(-x+6)*exp(x)*exp(-2/(exp(-x+6)-4))+(x**2*exp(-x+6)**2-8*x**2*exp(-x+6)+16*x**2)*exp(x)+
(3*x+3)*ln(3)*exp(-x+6)**2+(-24*x-24)*ln(3)*exp(-x+6)+(48*x+48)*ln(3))/((x**2*exp(-x+6)**2-8*x**2*exp(-x+6)+16
*x**2)*exp(x)*exp(-2/(exp(-x+6)-4))+(x**3*exp(-x+6)**2-8*x**3*exp(-x+6)+16*x**3)*exp(x)-3*x*ln(3)*exp(-x+6)**2
+24*x*ln(3)*exp(-x+6)-48*x*ln(3)),x)
[Out]
log(exp(-2/(-4 + exp(6)*exp(-x))) + (x**2*exp(x) - 3*log(3))*exp(-x)/x)
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