Optimal. Leaf size=23 \[ e^{-5+\left (e^{16}-\frac {1}{2 (-1+x)}\right )^2}-x \]
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Rubi [F] time = 10.66, 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 (-\frac {19-40 x+20 x^2+e^{16} (-4+4 x)+e^{32} \left (-4+8 x-4 x^2\right )}{4-8 x+4 x^2}\right ) \left (-1+e^{16} (-2+2 x)+\exp \left (\frac {19-40 x+20 x^2+e^{16} (-4+4 x)+e^{32} \left (-4+8 x-4 x^2\right )}{4-8 x+4 x^2}\right ) \left (2-6 x+6 x^2-2 x^3\right )\right )}{-2+6 x-6 x^2+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 {\exp \left (-\frac {19-4 e^{16}-4 e^{32}-4 \left (10-e^{16}-2 e^{32}\right ) x+4 \left (5-e^{32}\right ) x^2}{4-8 x+4 x^2}\right ) \left (1-e^{16} (-2+2 x)-\exp \left (\frac {19-40 x+20 x^2+e^{16} (-4+4 x)+e^{32} \left (-4+8 x-4 x^2\right )}{4-8 x+4 x^2}\right ) \left (2-6 x+6 x^2-2 x^3\right )\right )}{2-6 x+6 x^2-2 x^3} \, dx\\ &=\int \left (-\exp \left (-e^{32}+\frac {19}{4 (-1+x)^2}+\frac {e^{16}}{-1+x}-\frac {10 x}{(-1+x)^2}+\frac {5 x^2}{(-1+x)^2}-\frac {19-4 e^{16}-4 e^{32}-4 \left (10-e^{16}-2 e^{32}\right ) x+4 \left (5-e^{32}\right ) x^2}{4-8 x+4 x^2}\right )+\frac {\exp \left (-\frac {19-4 e^{16}-4 e^{32}-4 \left (10-e^{16}-2 e^{32}\right ) x+4 \left (5-e^{32}\right ) x^2}{4-8 x+4 x^2}\right ) \left (-1-2 e^{16}+2 e^{16} x\right )}{2 (-1+x)^3}\right ) \, dx\\ &=\frac {1}{2} \int \frac {\exp \left (-\frac {19-4 e^{16}-4 e^{32}-4 \left (10-e^{16}-2 e^{32}\right ) x+4 \left (5-e^{32}\right ) x^2}{4-8 x+4 x^2}\right ) \left (-1-2 e^{16}+2 e^{16} x\right )}{(-1+x)^3} \, dx-\int \exp \left (-e^{32}+\frac {19}{4 (-1+x)^2}+\frac {e^{16}}{-1+x}-\frac {10 x}{(-1+x)^2}+\frac {5 x^2}{(-1+x)^2}-\frac {19-4 e^{16}-4 e^{32}-4 \left (10-e^{16}-2 e^{32}\right ) x+4 \left (5-e^{32}\right ) x^2}{4-8 x+4 x^2}\right ) \, dx\\ &=\frac {1}{2} \int \left (-\frac {\exp \left (-\frac {19-4 e^{16}-4 e^{32}-4 \left (10-e^{16}-2 e^{32}\right ) x+4 \left (5-e^{32}\right ) x^2}{4-8 x+4 x^2}\right )}{(-1+x)^3}+\frac {2 \exp \left (16-\frac {19-4 e^{16}-4 e^{32}-4 \left (10-e^{16}-2 e^{32}\right ) x+4 \left (5-e^{32}\right ) x^2}{4-8 x+4 x^2}\right )}{(-1+x)^2}\right ) \, dx-\int 1 \, dx\\ &=-x-\frac {1}{2} \int \frac {\exp \left (-\frac {19-4 e^{16}-4 e^{32}-4 \left (10-e^{16}-2 e^{32}\right ) x+4 \left (5-e^{32}\right ) x^2}{4-8 x+4 x^2}\right )}{(-1+x)^3} \, dx+\int \frac {\exp \left (16-\frac {19-4 e^{16}-4 e^{32}-4 \left (10-e^{16}-2 e^{32}\right ) x+4 \left (5-e^{32}\right ) x^2}{4-8 x+4 x^2}\right )}{(-1+x)^2} \, dx\\ &=-x-\frac {1}{2} \int \frac {\exp \left (-\frac {19-4 e^{16}-4 e^{32}-4 \left (10-e^{16}-2 e^{32}\right ) x+4 \left (5-e^{32}\right ) x^2}{4-8 x+4 x^2}\right )}{(-1+x)^3} \, dx+\int \frac {\exp \left (\frac {45+4 e^{16}+4 e^{32}-4 \left (22+e^{16}+2 e^{32}\right ) x+4 \left (11+e^{32}\right ) x^2}{4 (-1+x)^2}\right )}{(1-x)^2} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 1.30, size = 30, normalized size = 1.30 \begin {gather*} e^{-5+e^{32}+\frac {1}{4 (-1+x)^2}-\frac {e^{16}}{-1+x}}-x \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 0.98, size = 46, normalized size = 2.00 \begin {gather*} -x + e^{\left (-\frac {20 \, x^{2} - 4 \, {\left (x^{2} - 2 \, x + 1\right )} e^{32} + 4 \, {\left (x - 1\right )} e^{16} - 40 \, x + 19}{4 \, {\left (x^{2} - 2 \, x + 1\right )}}\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 {{\left (2 \, {\left (x - 1\right )} e^{16} - 2 \, {\left (x^{3} - 3 \, x^{2} + 3 \, x - 1\right )} e^{\left (\frac {20 \, x^{2} - 4 \, {\left (x^{2} - 2 \, x + 1\right )} e^{32} + 4 \, {\left (x - 1\right )} e^{16} - 40 \, x + 19}{4 \, {\left (x^{2} - 2 \, x + 1\right )}}\right )} - 1\right )} e^{\left (-\frac {20 \, x^{2} - 4 \, {\left (x^{2} - 2 \, x + 1\right )} e^{32} + 4 \, {\left (x - 1\right )} e^{16} - 40 \, x + 19}{4 \, {\left (x^{2} - 2 \, x + 1\right )}}\right )}}{2 \, {\left (x^{3} - 3 \, x^{2} + 3 \, x - 1\right )}}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.11, size = 48, normalized size = 2.09
method | result | size |
risch | \(-x +{\mathrm e}^{-\frac {-4 x^{2} {\mathrm e}^{32}+8 x \,{\mathrm e}^{32}+4 x \,{\mathrm e}^{16}+20 x^{2}-4 \,{\mathrm e}^{32}-4 \,{\mathrm e}^{16}-40 x +19}{4 \left (x -1\right )^{2}}}\) | \(48\) |
derivativedivides | \(-x +1+{\mathrm e}^{{\mathrm e}^{32}-\frac {{\mathrm e}^{16}}{x -1}+\frac {1}{4 \left (x -1\right )^{2}}-5}-i {\mathrm e}^{16} \sqrt {\pi }\, {\mathrm e}^{-5} \erf \left (\frac {i}{2 x -2}-i {\mathrm e}^{16}\right )+i \sqrt {\pi }\, {\mathrm e}^{11} \erf \left (\frac {i}{2 x -2}-i {\mathrm e}^{16}\right )\) | \(93\) |
default | \(-x +1+{\mathrm e}^{{\mathrm e}^{32}-\frac {{\mathrm e}^{16}}{x -1}+\frac {1}{4 \left (x -1\right )^{2}}-5}-i {\mathrm e}^{16} \sqrt {\pi }\, {\mathrm e}^{-5} \erf \left (\frac {i}{2 x -2}-i {\mathrm e}^{16}\right )+i \sqrt {\pi }\, {\mathrm e}^{11} \erf \left (\frac {i}{2 x -2}-i {\mathrm e}^{16}\right )\) | \(93\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 1.01, size = 93, normalized size = 4.04 \begin {gather*} -x + \frac {6 \, x - 5}{2 \, {\left (x^{2} - 2 \, x + 1\right )}} - \frac {3 \, {\left (4 \, x - 3\right )}}{2 \, {\left (x^{2} - 2 \, x + 1\right )}} + \frac {3 \, {\left (2 \, x - 1\right )}}{2 \, {\left (x^{2} - 2 \, x + 1\right )}} - \frac {1}{2 \, {\left (x^{2} - 2 \, x + 1\right )}} + e^{\left (-\frac {e^{16}}{x - 1} + \frac {1}{4 \, {\left (x^{2} - 2 \, x + 1\right )}} + e^{32} - 5\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 5.54, size = 144, normalized size = 6.26 \begin {gather*} {\mathrm {e}}^{\frac {40\,x}{4\,x^2-8\,x+4}}\,{\mathrm {e}}^{-\frac {20\,x^2}{4\,x^2-8\,x+4}}\,{\mathrm {e}}^{-\frac {4\,x\,{\mathrm {e}}^{16}}{4\,x^2-8\,x+4}}\,{\mathrm {e}}^{-\frac {8\,x\,{\mathrm {e}}^{32}}{4\,x^2-8\,x+4}}\,{\mathrm {e}}^{-\frac {19}{4\,x^2-8\,x+4}}\,{\mathrm {e}}^{\frac {4\,x^2\,{\mathrm {e}}^{32}}{4\,x^2-8\,x+4}}\,{\mathrm {e}}^{\frac {4\,{\mathrm {e}}^{16}}{4\,x^2-8\,x+4}}\,{\mathrm {e}}^{\frac {4\,{\mathrm {e}}^{32}}{4\,x^2-8\,x+4}}-x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.41, size = 46, normalized size = 2.00 \begin {gather*} - x + e^{- \frac {20 x^{2} - 40 x + \left (4 x - 4\right ) e^{16} + \left (- 4 x^{2} + 8 x - 4\right ) e^{32} + 19}{4 x^{2} - 8 x + 4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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