Optimal. Leaf size=22 \[ e^{e^{\frac {-6-e^5+7 x}{(-4+2 x)^2}}} \]
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Rubi [F] time = 3.29, 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 {\exp \left (e^{\frac {-6-e^5+7 x}{16-16 x+4 x^2}}+\frac {-6-e^5+7 x}{16-16 x+4 x^2}\right ) \left (-2+2 e^5-7 x\right )}{-32+48 x-24 x^2+4 x^3} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (\frac {\exp \left (e^{\frac {-6-e^5+7 x}{16-16 x+4 x^2}}+\frac {-6-e^5+7 x}{16-16 x+4 x^2}\right ) \left (-8+e^5\right )}{2 (-2+x)^3}-\frac {7 \exp \left (e^{\frac {-6-e^5+7 x}{16-16 x+4 x^2}}+\frac {-6-e^5+7 x}{16-16 x+4 x^2}\right )}{4 (-2+x)^2}\right ) \, dx\\ &=-\left (\frac {7}{4} \int \frac {\exp \left (e^{\frac {-6-e^5+7 x}{16-16 x+4 x^2}}+\frac {-6-e^5+7 x}{16-16 x+4 x^2}\right )}{(-2+x)^2} \, dx\right )+\frac {1}{2} \left (-8+e^5\right ) \int \frac {\exp \left (e^{\frac {-6-e^5+7 x}{16-16 x+4 x^2}}+\frac {-6-e^5+7 x}{16-16 x+4 x^2}\right )}{(-2+x)^3} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 2.08, size = 21, normalized size = 0.95 \begin {gather*} e^{e^{-\frac {6+e^5-7 x}{4 (-2+x)^2}}} \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 0.64, size = 76, normalized size = 3.45 \begin {gather*} e^{\left (\frac {4 \, {\left (x^{2} - 4 \, x + 4\right )} e^{\left (\frac {7 \, x - e^{5} - 6}{4 \, {\left (x^{2} - 4 \, x + 4\right )}}\right )} + 7 \, x - e^{5} - 6}{4 \, {\left (x^{2} - 4 \, x + 4\right )}} - \frac {7 \, x - e^{5} - 6}{4 \, {\left (x^{2} - 4 \, x + 4\right )}}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 2.70, size = 136, normalized size = 6.18 \begin {gather*} e^{\left (\frac {x^{2} e^{5} + 16 \, x^{2} e^{\left (\frac {7 \, x - e^{5} - 6}{4 \, {\left (x^{2} - 4 \, x + 4\right )}}\right )} + 6 \, x^{2} - 4 \, x e^{5} - 64 \, x e^{\left (\frac {7 \, x - e^{5} - 6}{4 \, {\left (x^{2} - 4 \, x + 4\right )}}\right )} + 4 \, x + 64 \, e^{\left (\frac {7 \, x - e^{5} - 6}{4 \, {\left (x^{2} - 4 \, x + 4\right )}}\right )}}{16 \, {\left (x^{2} - 4 \, x + 4\right )}} - \frac {7 \, x - e^{5} - 6}{4 \, {\left (x^{2} - 4 \, x + 4\right )}} - \frac {1}{16} \, e^{5} - \frac {3}{8}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.26, size = 17, normalized size = 0.77
method | result | size |
risch | \({\mathrm e}^{{\mathrm e}^{-\frac {{\mathrm e}^{5}-7 x +6}{4 \left (x -2\right )^{2}}}}\) | \(17\) |
norman | \(\frac {x^{2} {\mathrm e}^{{\mathrm e}^{\frac {-{\mathrm e}^{5}+7 x -6}{4 x^{2}-16 x +16}}}-4 x \,{\mathrm e}^{{\mathrm e}^{\frac {-{\mathrm e}^{5}+7 x -6}{4 x^{2}-16 x +16}}}+4 \,{\mathrm e}^{{\mathrm e}^{\frac {-{\mathrm e}^{5}+7 x -6}{4 x^{2}-16 x +16}}}}{\left (x -2\right )^{2}}\) | \(89\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.75, size = 36, normalized size = 1.64 \begin {gather*} e^{\left (e^{\left (-\frac {e^{5}}{4 \, {\left (x^{2} - 4 \, x + 4\right )}} + \frac {2}{x^{2} - 4 \, x + 4} + \frac {7}{4 \, {\left (x - 2\right )}}\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.49, size = 50, normalized size = 2.27 \begin {gather*} {\mathrm {e}}^{{\mathrm {e}}^{\frac {7\,x}{4\,x^2-16\,x+16}}\,{\mathrm {e}}^{-\frac {3}{2\,x^2-8\,x+8}}\,{\mathrm {e}}^{-\frac {{\mathrm {e}}^5}{4\,x^2-16\,x+16}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.65, size = 20, normalized size = 0.91 \begin {gather*} e^{e^{\frac {7 x - e^{5} - 6}{4 x^{2} - 16 x + 16}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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