Optimal. Leaf size=22 \[ 5+e^{\frac {(3-x) (-7+x)}{(-2+x)^2}-x} \]
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Rubi [F] time = 0.97, 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 {-21+6 x+3 x^2-x^3}{4-4 x+x^2}} \left (30-18 x+6 x^2-x^3\right )}{-8+12 x-6 x^2+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 \frac {e^{\frac {-21+6 x+3 x^2-x^3}{(-2+x)^2}} \left (-30+18 x-6 x^2+x^3\right )}{(2-x)^3} \, dx\\ &=\int \left (-e^{\frac {-21+6 x+3 x^2-x^3}{(-2+x)^2}}+\frac {10 e^{\frac {-21+6 x+3 x^2-x^3}{(-2+x)^2}}}{(-2+x)^3}-\frac {6 e^{\frac {-21+6 x+3 x^2-x^3}{(-2+x)^2}}}{(-2+x)^2}\right ) \, dx\\ &=-\left (6 \int \frac {e^{\frac {-21+6 x+3 x^2-x^3}{(-2+x)^2}}}{(-2+x)^2} \, dx\right )+10 \int \frac {e^{\frac {-21+6 x+3 x^2-x^3}{(-2+x)^2}}}{(-2+x)^3} \, dx-\int e^{\frac {-21+6 x+3 x^2-x^3}{(-2+x)^2}} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.18, size = 21, normalized size = 0.95 \begin {gather*} e^{-1-\frac {5}{(-2+x)^2}+\frac {6}{-2+x}-x} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.68, size = 26, normalized size = 1.18 \begin {gather*} e^{\left (-\frac {x^{3} - 3 \, x^{2} - 6 \, x + 21}{x^{2} - 4 \, x + 4}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.17, size = 57, normalized size = 2.59 \begin {gather*} e^{\left (-\frac {x^{3}}{x^{2} - 4 \, x + 4} + \frac {3 \, x^{2}}{x^{2} - 4 \, x + 4} + \frac {6 \, x}{x^{2} - 4 \, x + 4} - \frac {21}{x^{2} - 4 \, x + 4}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.11, size = 22, normalized size = 1.00
method | result | size |
risch | \({\mathrm e}^{-\frac {x^{3}-3 x^{2}-6 x +21}{\left (x -2\right )^{2}}}\) | \(22\) |
gosper | \({\mathrm e}^{-\frac {x^{3}-3 x^{2}-6 x +21}{x^{2}-4 x +4}}\) | \(27\) |
norman | \(\frac {x^{2} {\mathrm e}^{\frac {-x^{3}+3 x^{2}+6 x -21}{x^{2}-4 x +4}}-4 x \,{\mathrm e}^{\frac {-x^{3}+3 x^{2}+6 x -21}{x^{2}-4 x +4}}+4 \,{\mathrm e}^{\frac {-x^{3}+3 x^{2}+6 x -21}{x^{2}-4 x +4}}}{\left (x -2\right )^{2}}\) | \(98\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.70, size = 25, normalized size = 1.14 \begin {gather*} e^{\left (-x - \frac {5}{x^{2} - 4 \, x + 4} + \frac {6}{x - 2} - 1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.16, size = 60, normalized size = 2.73 \begin {gather*} {\mathrm {e}}^{-\frac {x^3}{x^2-4\,x+4}}\,{\mathrm {e}}^{\frac {3\,x^2}{x^2-4\,x+4}}\,{\mathrm {e}}^{-\frac {21}{x^2-4\,x+4}}\,{\mathrm {e}}^{\frac {6\,x}{x^2-4\,x+4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.20, size = 22, normalized size = 1.00 \begin {gather*} e^{\frac {- x^{3} + 3 x^{2} + 6 x - 21}{x^{2} - 4 x + 4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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