Optimal. Leaf size=28 \[ e^{\frac {-5+e^{e^{-4+x}} (5-x)}{4-\frac {e}{3}+x}} \]
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Rubi [F] time = 12.38, 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^{\frac {15+e^{e^{-4+x}} (-15+3 x)}{-12+e-3 x}} \left (45+e^{e^{-4+x}} \left (-81+3 e+e^{-4+x} \left (180+9 x-9 x^2+e (-15+3 x)\right )\right )\right )}{144+e^2+e (-24-6 x)+72 x+9 x^2} \, 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^{\frac {15+e^{e^{-4+x}} (-15+3 x)}{-12+e-3 x}} \left (45+e^{e^{-4+x}} \left (-81+3 e+e^{-4+x} \left (180+9 x-9 x^2+e (-15+3 x)\right )\right )\right )}{(-12+e)^2+6 (12-e) x+9 x^2} \, dx\\ &=\int \frac {e^{\frac {15+e^{e^{-4+x}} (-15+3 x)}{-12+e-3 x}} \left (45+e^{e^{-4+x}} \left (-81+3 e+e^{-4+x} \left (180+9 x-9 x^2+e (-15+3 x)\right )\right )\right )}{(-12+e-3 x)^2} \, dx\\ &=\int \left (\frac {3 \exp \left (-4+e^{-4+x}+x+\frac {15+e^{e^{-4+x}} (-15+3 x)}{-12+e-3 x}\right ) (-5+x)}{-12+e-3 x}+\frac {3 e^{\frac {15+e^{e^{-4+x}} (-15+3 x)}{-12+e-3 x}} \left (15-27 \left (1-\frac {e}{27}\right ) e^{e^{-4+x}}\right )}{(12-e+3 x)^2}\right ) \, dx\\ &=3 \int \frac {\exp \left (-4+e^{-4+x}+x+\frac {15+e^{e^{-4+x}} (-15+3 x)}{-12+e-3 x}\right ) (-5+x)}{-12+e-3 x} \, dx+3 \int \frac {e^{\frac {15+e^{e^{-4+x}} (-15+3 x)}{-12+e-3 x}} \left (15-27 \left (1-\frac {e}{27}\right ) e^{e^{-4+x}}\right )}{(12-e+3 x)^2} \, dx\\ &=3 \int \left (\frac {15 e^{\frac {15+e^{e^{-4+x}} (-15+3 x)}{-12+e-3 x}}}{(-12+e-3 x)^2}+\frac {(-27+e) \exp \left (e^{-4+x}+\frac {15+e^{e^{-4+x}} (-15+3 x)}{-12+e-3 x}\right )}{(-12+e-3 x)^2}\right ) \, dx+3 \int \left (-\frac {1}{3} \exp \left (-4+e^{-4+x}+x+\frac {15+e^{e^{-4+x}} (-15+3 x)}{-12+e-3 x}\right )+\frac {(-27+e) \exp \left (-4+e^{-4+x}+x+\frac {15+e^{e^{-4+x}} (-15+3 x)}{-12+e-3 x}\right )}{3 (-12+e-3 x)}\right ) \, dx\\ &=45 \int \frac {e^{\frac {15+e^{e^{-4+x}} (-15+3 x)}{-12+e-3 x}}}{(-12+e-3 x)^2} \, dx-(3 (27-e)) \int \frac {\exp \left (e^{-4+x}+\frac {15+e^{e^{-4+x}} (-15+3 x)}{-12+e-3 x}\right )}{(-12+e-3 x)^2} \, dx+(-27+e) \int \frac {\exp \left (-4+e^{-4+x}+x+\frac {15+e^{e^{-4+x}} (-15+3 x)}{-12+e-3 x}\right )}{-12+e-3 x} \, dx-\int \exp \left (-4+e^{-4+x}+x+\frac {15+e^{e^{-4+x}} (-15+3 x)}{-12+e-3 x}\right ) \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 3.53, size = 26, normalized size = 0.93 \begin {gather*} e^{\frac {3 \left (5+e^{e^{-4+x}} (-5+x)\right )}{e-3 (4+x)}} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.66, size = 25, normalized size = 0.89 \begin {gather*} e^{\left (-\frac {3 \, {\left ({\left (x - 5\right )} e^{\left (e^{\left (x - 4\right )}\right )} + 5\right )}}{3 \, x - e + 12}\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*} \int -\frac {3 \, {\left ({\left ({\left (3 \, x^{2} - {\left (x - 5\right )} e - 3 \, x - 60\right )} e^{\left (x - 4\right )} - e + 27\right )} e^{\left (e^{\left (x - 4\right )}\right )} - 15\right )} e^{\left (-\frac {3 \, {\left ({\left (x - 5\right )} e^{\left (e^{\left (x - 4\right )}\right )} + 5\right )}}{3 \, x - e + 12}\right )}}{9 \, x^{2} - 6 \, {\left (x + 4\right )} e + 72 \, x + e^{2} + 144}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.46, size = 29, normalized size = 1.04
method | result | size |
risch | \({\mathrm e}^{\frac {3 x \,{\mathrm e}^{{\mathrm e}^{x -4}}-15 \,{\mathrm e}^{{\mathrm e}^{x -4}}+15}{{\mathrm e}-3 x -12}}\) | \(29\) |
norman | \(\frac {\left ({\mathrm e}-12\right ) {\mathrm e}^{\frac {\left (3 x -15\right ) {\mathrm e}^{{\mathrm e}^{x -4}}+15}{{\mathrm e}-3 x -12}}-3 x \,{\mathrm e}^{\frac {\left (3 x -15\right ) {\mathrm e}^{{\mathrm e}^{x -4}}+15}{{\mathrm e}-3 x -12}}}{{\mathrm e}-3 x -12}\) | \(68\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.56, size = 60, normalized size = 2.14 \begin {gather*} e^{\left (-\frac {e^{\left (e^{\left (x - 4\right )} + 1\right )}}{3 \, x - e + 12} + \frac {27 \, e^{\left (e^{\left (x - 4\right )}\right )}}{3 \, x - e + 12} - \frac {15}{3 \, x - e + 12} - e^{\left (e^{\left (x - 4\right )}\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.48, size = 56, normalized size = 2.00 \begin {gather*} {\mathrm {e}}^{-\frac {15}{3\,x-\mathrm {e}+12}}\,{\mathrm {e}}^{\frac {15\,{\mathrm {e}}^{{\mathrm {e}}^{-4}\,{\mathrm {e}}^x}}{3\,x-\mathrm {e}+12}}\,{\mathrm {e}}^{-\frac {3\,x\,{\mathrm {e}}^{{\mathrm {e}}^{-4}\,{\mathrm {e}}^x}}{3\,x-\mathrm {e}+12}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 1.24, size = 22, normalized size = 0.79 \begin {gather*} e^{\frac {\left (3 x - 15\right ) e^{e^{x - 4}} + 15}{- 3 x - 12 + e}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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