Optimal. Leaf size=34 \[ -e^{\frac {e^{-2+x} x}{(4+x) (i \pi +\log (9-e))^2}}+2 x \]
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Rubi [F] time = 5.44, 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^{-2+x} \left (\exp \left (\frac {e^{-2+x} x}{(4+x) (i \pi +\log (9-e))^2}\right ) \left (-4-4 x-x^2\right )+e^{2-x} \left (32+16 x+2 x^2\right ) (i \pi +\log (9-e))^2\right )}{\left (16+8 x+x^2\right ) (i \pi +\log (9-e))^2} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int \frac {e^{-2+x} \left (\exp \left (\frac {e^{-2+x} x}{(4+x) (i \pi +\log (9-e))^2}\right ) \left (-4-4 x-x^2\right )+e^{2-x} \left (32+16 x+2 x^2\right ) (i \pi +\log (9-e))^2\right )}{16+8 x+x^2} \, dx}{(i \pi +\log (9-e))^2}\\ &=\frac {\int \frac {e^{-2+x} \left (\exp \left (\frac {e^{-2+x} x}{(4+x) (i \pi +\log (9-e))^2}\right ) \left (-4-4 x-x^2\right )+e^{2-x} \left (32+16 x+2 x^2\right ) (i \pi +\log (9-e))^2\right )}{(4+x)^2} \, dx}{(i \pi +\log (9-e))^2}\\ &=\frac {\int \left (-\frac {\exp \left (-2+x+\frac {e^{-2+x} x}{(4+x) (i \pi +\log (9-e))^2}\right ) (2+x)^2}{(4+x)^2}-2 (\pi -i \log (9-e))^2\right ) \, dx}{(i \pi +\log (9-e))^2}\\ &=2 x-\frac {\int \frac {\exp \left (-2+x+\frac {e^{-2+x} x}{(4+x) (i \pi +\log (9-e))^2}\right ) (2+x)^2}{(4+x)^2} \, dx}{(i \pi +\log (9-e))^2}\\ &=2 x-\frac {\int \left (\exp \left (-2+x+\frac {e^{-2+x} x}{(4+x) (i \pi +\log (9-e))^2}\right )+\frac {4 \exp \left (-2+x+\frac {e^{-2+x} x}{(4+x) (i \pi +\log (9-e))^2}\right )}{(4+x)^2}-\frac {4 \exp \left (-2+x+\frac {e^{-2+x} x}{(4+x) (i \pi +\log (9-e))^2}\right )}{4+x}\right ) \, dx}{(i \pi +\log (9-e))^2}\\ &=2 x-\frac {\int \exp \left (-2+x+\frac {e^{-2+x} x}{(4+x) (i \pi +\log (9-e))^2}\right ) \, dx}{(i \pi +\log (9-e))^2}-\frac {4 \int \frac {\exp \left (-2+x+\frac {e^{-2+x} x}{(4+x) (i \pi +\log (9-e))^2}\right )}{(4+x)^2} \, dx}{(i \pi +\log (9-e))^2}+\frac {4 \int \frac {\exp \left (-2+x+\frac {e^{-2+x} x}{(4+x) (i \pi +\log (9-e))^2}\right )}{4+x} \, dx}{(i \pi +\log (9-e))^2}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 1.07, size = 35, normalized size = 1.03 \begin {gather*} -e^{-\frac {e^{-2+x} x}{(4+x) (\pi -i \log (9-e))^2}}+2 x \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.82, size = 25, normalized size = 0.74 \begin {gather*} 2 \, x - e^{\left (\frac {x e^{\left (x - 2\right )}}{{\left (x + 4\right )} \log \left (e - 9\right )^{2}}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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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.
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maple [A] time = 0.34, size = 26, normalized size = 0.76
method | result | size |
risch | \(2 x -{\mathrm e}^{\frac {x \,{\mathrm e}^{x -2}}{\left (4+x \right ) \ln \left ({\mathrm e}-9\right )^{2}}}\) | \(26\) |
norman | \(\frac {\left (-32 \,{\mathrm e}^{2-x} \ln \left ({\mathrm e}-9\right )-4 \,{\mathrm e}^{2-x} \ln \left ({\mathrm e}-9\right ) {\mathrm e}^{\frac {x \,{\mathrm e}^{x -2}}{\left (4+x \right ) \ln \left ({\mathrm e}-9\right )^{2}}}+2 \ln \left ({\mathrm e}-9\right ) x^{2} {\mathrm e}^{2-x}-\ln \left ({\mathrm e}-9\right ) x \,{\mathrm e}^{2-x} {\mathrm e}^{\frac {x \,{\mathrm e}^{x -2}}{\left (4+x \right ) \ln \left ({\mathrm e}-9\right )^{2}}}\right ) {\mathrm e}^{x -2}}{\left (4+x \right ) \ln \left ({\mathrm e}-9\right )}\) | \(125\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.54, size = 120, normalized size = 3.53 \begin {gather*} \frac {2 \, {\left (x - \frac {16}{x + 4} - 8 \, \log \left (x + 4\right )\right )} \log \left (e - 9\right )^{2} + 16 \, {\left (\frac {4}{x + 4} + \log \left (x + 4\right )\right )} \log \left (e - 9\right )^{2} - e^{\left (-\frac {4 \, e^{x}}{x e^{2} \log \left (e - 9\right )^{2} + 4 \, e^{2} \log \left (e - 9\right )^{2}} + \frac {e^{\left (x - 2\right )}}{\log \left (e - 9\right )^{2}}\right )} \log \left (e - 9\right )^{2} - \frac {32 \, \log \left (e - 9\right )^{2}}{x + 4}}{\log \left (e - 9\right )^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 5.89, size = 34, normalized size = 1.00 \begin {gather*} 2\,x-{\mathrm {e}}^{\frac {x\,{\mathrm {e}}^{-2}\,{\mathrm {e}}^x}{x\,{\ln \left (\mathrm {e}-9\right )}^2+4\,{\ln \left (\mathrm {e}-9\right )}^2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 2.36, size = 85, normalized size = 2.50 \begin {gather*} 2 x - e^{\frac {x e^{x}}{- \pi ^{2} x e^{2} + x e^{2} \log {\left (9 - e \right )}^{2} + 2 i \pi x e^{2} \log {\left (9 - e \right )} - 4 \pi ^{2} e^{2} + 4 e^{2} \log {\left (9 - e \right )}^{2} + 8 i \pi e^{2} \log {\left (9 - e \right )}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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