Optimal. Leaf size=31 \[ e^{\frac {16 \left (-\frac {1}{e}-e^{2/x}+22 e^{-x}\right )^2}{x^2}} \]
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Rubi [F]
time = 17.88, 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 (-2+\frac {e^{-2-2 x} \left (7744 e^2+e^x \left (-704 e-704 e^{2+\frac {2}{x}}\right )+e^{2 x} \left (16+32 e^{1+\frac {2}{x}}+16 e^{2+\frac {4}{x}}\right )\right )}{x^2}-2 x\right ) \left (e^{2 x} \left (e^{1+\frac {2}{x}} (-64-64 x)+e^{2+\frac {4}{x}} (-64-32 x)-32 x\right )+e^2 \left (-15488 x-15488 x^2\right )+e^x \left (e \left (1408 x+704 x^2\right )+e^{2+\frac {2}{x}} \left (1408+1408 x+704 x^2\right )\right )\right )}{x^4} \, 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 {15488 \exp \left (\frac {e^{-2-2 x} \left (7744 e^2+e^x \left (-704 e-704 e^{2+\frac {2}{x}}\right )+e^{2 x} \left (16+32 e^{1+\frac {2}{x}}+16 e^{2+\frac {4}{x}}\right )\right )}{x^2}-2 x\right ) (1+x)}{x^3}-\frac {32 \exp \left (-2+\frac {e^{-2-2 x} \left (7744 e^2+e^x \left (-704 e-704 e^{2+\frac {2}{x}}\right )+e^{2 x} \left (16+32 e^{1+\frac {2}{x}}+16 e^{2+\frac {4}{x}}\right )\right )}{x^2}\right ) \left (1+e^{1+\frac {2}{x}}\right ) \left (2 e^{1+\frac {2}{x}}+x+e^{1+\frac {2}{x}} x\right )}{x^4}+\frac {704 \exp \left (-1+\frac {e^{-2-2 x} \left (7744 e^2+e^x \left (-704 e-704 e^{2+\frac {2}{x}}\right )+e^{2 x} \left (16+32 e^{1+\frac {2}{x}}+16 e^{2+\frac {4}{x}}\right )\right )}{x^2}-x\right ) \left (2 e^{1+\frac {2}{x}}+2 x+2 e^{1+\frac {2}{x}} x+x^2+e^{1+\frac {2}{x}} x^2\right )}{x^4}\right ) \, dx\\ &=-\left (32 \int \frac {\exp \left (-2+\frac {e^{-2-2 x} \left (7744 e^2+e^x \left (-704 e-704 e^{2+\frac {2}{x}}\right )+e^{2 x} \left (16+32 e^{1+\frac {2}{x}}+16 e^{2+\frac {4}{x}}\right )\right )}{x^2}\right ) \left (1+e^{1+\frac {2}{x}}\right ) \left (2 e^{1+\frac {2}{x}}+x+e^{1+\frac {2}{x}} x\right )}{x^4} \, dx\right )+704 \int \frac {\exp \left (-1+\frac {e^{-2-2 x} \left (7744 e^2+e^x \left (-704 e-704 e^{2+\frac {2}{x}}\right )+e^{2 x} \left (16+32 e^{1+\frac {2}{x}}+16 e^{2+\frac {4}{x}}\right )\right )}{x^2}-x\right ) \left (2 e^{1+\frac {2}{x}}+2 x+2 e^{1+\frac {2}{x}} x+x^2+e^{1+\frac {2}{x}} x^2\right )}{x^4} \, dx-15488 \int \frac {\exp \left (\frac {e^{-2-2 x} \left (7744 e^2+e^x \left (-704 e-704 e^{2+\frac {2}{x}}\right )+e^{2 x} \left (16+32 e^{1+\frac {2}{x}}+16 e^{2+\frac {4}{x}}\right )\right )}{x^2}-2 x\right ) (1+x)}{x^3} \, dx\\ &=-\left (32 \int \left (\frac {\exp \left (-2+\frac {e^{-2-2 x} \left (7744 e^2+e^x \left (-704 e-704 e^{2+\frac {2}{x}}\right )+e^{2 x} \left (16+32 e^{1+\frac {2}{x}}+16 e^{2+\frac {4}{x}}\right )\right )}{x^2}\right )}{x^3}+\frac {2 \exp \left (-1+\frac {e^{-2-2 x} \left (7744 e^2+e^x \left (-704 e-704 e^{2+\frac {2}{x}}\right )+e^{2 x} \left (16+32 e^{1+\frac {2}{x}}+16 e^{2+\frac {4}{x}}\right )\right )}{x^2}+\frac {2}{x}\right ) (1+x)}{x^4}+\frac {\exp \left (\frac {e^{-2-2 x} \left (7744 e^2+e^x \left (-704 e-704 e^{2+\frac {2}{x}}\right )+e^{2 x} \left (16+32 e^{1+\frac {2}{x}}+16 e^{2+\frac {4}{x}}\right )\right )}{x^2}+\frac {4}{x}\right ) (2+x)}{x^4}\right ) \, dx\right )+704 \int \left (\frac {\exp \left (-1+\frac {e^{-2-2 x} \left (7744 e^2+e^x \left (-704 e-704 e^{2+\frac {2}{x}}\right )+e^{2 x} \left (16+32 e^{1+\frac {2}{x}}+16 e^{2+\frac {4}{x}}\right )\right )}{x^2}-x\right ) (2+x)}{x^3}+\frac {\exp \left (\frac {e^{-2-2 x} \left (7744 e^2+e^x \left (-704 e-704 e^{2+\frac {2}{x}}\right )+e^{2 x} \left (16+32 e^{1+\frac {2}{x}}+16 e^{2+\frac {4}{x}}\right )\right )}{x^2}+\frac {2}{x}-x\right ) \left (2+2 x+x^2\right )}{x^4}\right ) \, dx-15488 \int \left (\frac {\exp \left (\frac {e^{-2-2 x} \left (7744 e^2+e^x \left (-704 e-704 e^{2+\frac {2}{x}}\right )+e^{2 x} \left (16+32 e^{1+\frac {2}{x}}+16 e^{2+\frac {4}{x}}\right )\right )}{x^2}-2 x\right )}{x^3}+\frac {\exp \left (\frac {e^{-2-2 x} \left (7744 e^2+e^x \left (-704 e-704 e^{2+\frac {2}{x}}\right )+e^{2 x} \left (16+32 e^{1+\frac {2}{x}}+16 e^{2+\frac {4}{x}}\right )\right )}{x^2}-2 x\right )}{x^2}\right ) \, dx\\ &=-\left (32 \int \frac {\exp \left (-2+\frac {e^{-2-2 x} \left (7744 e^2+e^x \left (-704 e-704 e^{2+\frac {2}{x}}\right )+e^{2 x} \left (16+32 e^{1+\frac {2}{x}}+16 e^{2+\frac {4}{x}}\right )\right )}{x^2}\right )}{x^3} \, dx\right )-32 \int \frac {\exp \left (\frac {e^{-2-2 x} \left (7744 e^2+e^x \left (-704 e-704 e^{2+\frac {2}{x}}\right )+e^{2 x} \left (16+32 e^{1+\frac {2}{x}}+16 e^{2+\frac {4}{x}}\right )\right )}{x^2}+\frac {4}{x}\right ) (2+x)}{x^4} \, dx-64 \int \frac {\exp \left (-1+\frac {e^{-2-2 x} \left (7744 e^2+e^x \left (-704 e-704 e^{2+\frac {2}{x}}\right )+e^{2 x} \left (16+32 e^{1+\frac {2}{x}}+16 e^{2+\frac {4}{x}}\right )\right )}{x^2}+\frac {2}{x}\right ) (1+x)}{x^4} \, dx+704 \int \frac {\exp \left (-1+\frac {e^{-2-2 x} \left (7744 e^2+e^x \left (-704 e-704 e^{2+\frac {2}{x}}\right )+e^{2 x} \left (16+32 e^{1+\frac {2}{x}}+16 e^{2+\frac {4}{x}}\right )\right )}{x^2}-x\right ) (2+x)}{x^3} \, dx+704 \int \frac {\exp \left (\frac {e^{-2-2 x} \left (7744 e^2+e^x \left (-704 e-704 e^{2+\frac {2}{x}}\right )+e^{2 x} \left (16+32 e^{1+\frac {2}{x}}+16 e^{2+\frac {4}{x}}\right )\right )}{x^2}+\frac {2}{x}-x\right ) \left (2+2 x+x^2\right )}{x^4} \, dx-15488 \int \frac {\exp \left (\frac {e^{-2-2 x} \left (7744 e^2+e^x \left (-704 e-704 e^{2+\frac {2}{x}}\right )+e^{2 x} \left (16+32 e^{1+\frac {2}{x}}+16 e^{2+\frac {4}{x}}\right )\right )}{x^2}-2 x\right )}{x^3} \, dx-15488 \int \frac {\exp \left (\frac {e^{-2-2 x} \left (7744 e^2+e^x \left (-704 e-704 e^{2+\frac {2}{x}}\right )+e^{2 x} \left (16+32 e^{1+\frac {2}{x}}+16 e^{2+\frac {4}{x}}\right )\right )}{x^2}-2 x\right )}{x^2} \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}
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Mathematica [F]
time = 3.96, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {e^{-2+\frac {e^{-2-2 x} \left (7744 e^2+e^x \left (-704 e-704 e^{2+\frac {2}{x}}\right )+e^{2 x} \left (16+32 e^{1+\frac {2}{x}}+16 e^{2+\frac {4}{x}}\right )\right )}{x^2}-2 x} \left (e^{2 x} \left (e^{1+\frac {2}{x}} (-64-64 x)+e^{2+\frac {4}{x}} (-64-32 x)-32 x\right )+e^2 \left (-15488 x-15488 x^2\right )+e^x \left (e \left (1408 x+704 x^2\right )+e^{2+\frac {2}{x}} \left (1408+1408 x+704 x^2\right )\right )\right )}{x^4} \, dx \end {gather*}
Verification is not applicable to the result.
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Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(69\) vs.
\(2(29)=58\).
time = 1.89, size = 70, normalized size = 2.26
method | result | size |
risch | \({\mathrm e}^{\frac {16 \left (-44 \,{\mathrm e}^{x +1}-44 \,{\mathrm e}^{\frac {x^{2}+2 x +2}{x}}+{\mathrm e}^{\frac {2 x^{2}+2 x +4}{x}}+2 \,{\mathrm e}^{\frac {2 x^{2}+x +2}{x}}+484 \,{\mathrm e}^{2}+{\mathrm e}^{2 x}\right ) {\mathrm e}^{-2 x -2}}{x^{2}}}\) | \(70\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 68 vs.
\(2 (23) = 46\).
time = 1.54, size = 68, normalized size = 2.19 \begin {gather*} e^{\left (\frac {16 \, e^{\left (-2\right )}}{x^{2}} + \frac {7744 \, e^{\left (-2 \, x\right )}}{x^{2}} - \frac {704 \, e^{\left (-x + \frac {2}{x}\right )}}{x^{2}} - \frac {704 \, e^{\left (-x - 1\right )}}{x^{2}} + \frac {16 \, e^{\frac {4}{x}}}{x^{2}} + \frac {32 \, e^{\left (\frac {2}{x} - 1\right )}}{x^{2}}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 84 vs.
\(2 (23) = 46\).
time = 0.37, size = 84, normalized size = 2.71 \begin {gather*} e^{\left (2 \, x - \frac {2 \, {\left ({\left ({\left (x^{3} + x^{2}\right )} e^{4} - 8 \, e^{2} - 8 \, e^{\left (\frac {4 \, {\left (x + 1\right )}}{x}\right )} - 16 \, e^{\left (\frac {2 \, {\left (x + 1\right )}}{x} + 1\right )}\right )} e^{\left (2 \, x\right )} + 352 \, {\left (e^{3} + e^{\left (\frac {2 \, {\left (x + 1\right )}}{x} + 2\right )}\right )} e^{x} - 3872 \, e^{4}\right )} e^{\left (-2 \, x - 4\right )}}{x^{2}} + 2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F(-2)]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: SystemError} \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*} \text {could not integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 3.01, size = 73, normalized size = 2.35 \begin {gather*} {\mathrm {e}}^{\frac {16\,{\mathrm {e}}^{-2}}{x^2}}\,{\mathrm {e}}^{\frac {16\,{\mathrm {e}}^{4/x}}{x^2}}\,{\mathrm {e}}^{-\frac {704\,{\mathrm {e}}^{-x}\,{\mathrm {e}}^{-1}}{x^2}}\,{\mathrm {e}}^{-\frac {704\,{\mathrm {e}}^{-x}\,{\mathrm {e}}^{2/x}}{x^2}}\,{\mathrm {e}}^{\frac {32\,{\mathrm {e}}^{-1}\,{\mathrm {e}}^{2/x}}{x^2}}\,{\mathrm {e}}^{\frac {7744\,{\mathrm {e}}^{-2\,x}}{x^2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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