Optimal. Leaf size=25 \[ \frac {e^{10 (-6+x)^2 x^2} x}{\log (2+\log (2-x))} \]
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Rubi [F] time = 3.09, 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 {-e^{360 x^2-120 x^3+10 x^4} x+\left (e^{360 x^2-120 x^3+10 x^4} \left (-4+2 x-2880 x^2+2880 x^3-880 x^4+80 x^5\right )+e^{360 x^2-120 x^3+10 x^4} \left (-2+x-1440 x^2+1440 x^3-440 x^4+40 x^5\right ) \log (2-x)\right ) \log (2+\log (2-x))}{(-4+2 x+(-2+x) \log (2-x)) \log ^2(2+\log (2-x))} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {e^{10 (-6+x)^2 x^2} \left (x-\left (-2+x-1440 x^2+1440 x^3-440 x^4+40 x^5\right ) (2+\log (2-x)) \log (2+\log (2-x))\right )}{(2-x) (2+\log (2-x)) \log ^2(2+\log (2-x))} \, dx\\ &=\int \left (-\frac {e^{10 (-6+x)^2 x^2} x}{(-2+x) (2+\log (2-x)) \log ^2(2+\log (2-x))}+\frac {e^{10 (-6+x)^2 x^2} \left (1+720 x^2-360 x^3+40 x^4\right )}{\log (2+\log (2-x))}\right ) \, dx\\ &=-\int \frac {e^{10 (-6+x)^2 x^2} x}{(-2+x) (2+\log (2-x)) \log ^2(2+\log (2-x))} \, dx+\int \frac {e^{10 (-6+x)^2 x^2} \left (1+720 x^2-360 x^3+40 x^4\right )}{\log (2+\log (2-x))} \, dx\\ &=-\int \left (\frac {e^{10 (-6+x)^2 x^2}}{(2+\log (2-x)) \log ^2(2+\log (2-x))}+\frac {2 e^{10 (-6+x)^2 x^2}}{(-2+x) (2+\log (2-x)) \log ^2(2+\log (2-x))}\right ) \, dx+\int \left (\frac {e^{10 (-6+x)^2 x^2}}{\log (2+\log (2-x))}+\frac {720 e^{10 (-6+x)^2 x^2} x^2}{\log (2+\log (2-x))}-\frac {360 e^{10 (-6+x)^2 x^2} x^3}{\log (2+\log (2-x))}+\frac {40 e^{10 (-6+x)^2 x^2} x^4}{\log (2+\log (2-x))}\right ) \, dx\\ &=-\left (2 \int \frac {e^{10 (-6+x)^2 x^2}}{(-2+x) (2+\log (2-x)) \log ^2(2+\log (2-x))} \, dx\right )+40 \int \frac {e^{10 (-6+x)^2 x^2} x^4}{\log (2+\log (2-x))} \, dx-360 \int \frac {e^{10 (-6+x)^2 x^2} x^3}{\log (2+\log (2-x))} \, dx+720 \int \frac {e^{10 (-6+x)^2 x^2} x^2}{\log (2+\log (2-x))} \, dx-\int \frac {e^{10 (-6+x)^2 x^2}}{(2+\log (2-x)) \log ^2(2+\log (2-x))} \, dx+\int \frac {e^{10 (-6+x)^2 x^2}}{\log (2+\log (2-x))} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.11, size = 25, normalized size = 1.00 \begin {gather*} \frac {e^{10 (-6+x)^2 x^2} x}{\log (2+\log (2-x))} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.46, size = 30, normalized size = 1.20 \begin {gather*} \frac {x e^{\left (10 \, x^{4} - 120 \, x^{3} + 360 \, x^{2}\right )}}{\log \left (\log \left (-x + 2\right ) + 2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.32, size = 30, normalized size = 1.20 \begin {gather*} \frac {x e^{\left (10 \, x^{4} - 120 \, x^{3} + 360 \, x^{2}\right )}}{\log \left (\log \left (-x + 2\right ) + 2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 25, normalized size = 1.00
method | result | size |
risch | \(\frac {{\mathrm e}^{10 x^{2} \left (x -6\right )^{2}} x}{\ln \left (\ln \left (2-x \right )+2\right )}\) | \(25\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.60, size = 30, normalized size = 1.20 \begin {gather*} \frac {x e^{\left (10 \, x^{4} - 120 \, x^{3} + 360 \, x^{2}\right )}}{\log \left (\log \left (-x + 2\right ) + 2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.38, size = 31, normalized size = 1.24 \begin {gather*} \frac {x\,{\mathrm {e}}^{10\,x^4}\,{\mathrm {e}}^{-120\,x^3}\,{\mathrm {e}}^{360\,x^2}}{\ln \left (\ln \left (2-x\right )+2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.58, size = 26, normalized size = 1.04 \begin {gather*} \frac {x e^{10 x^{4} - 120 x^{3} + 360 x^{2}}}{\log {\left (\log {\left (2 - x \right )} + 2 \right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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