Optimal. Leaf size=28 \[ e^{-3 e^{\left .-\frac {3}{2}\right /x}+x}-\frac {10 x^2}{-\frac {3}{4}+x} \]
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Rubi [F]
time = 1.09, 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^{\left .-\frac {3}{2}\right /x} \left (e^{\left .\frac {3}{2}\right /x} \left (480 x^3-320 x^4\right )+e^{e^{\left .-\frac {3}{2}\right /x} \left (-3+e^{\left .\frac {3}{2}\right /x} x\right )} \left (-81+216 x-144 x^2+e^{\left .\frac {3}{2}\right /x} \left (18 x^2-48 x^3+32 x^4\right )\right )\right )}{18 x^2-48 x^3+32 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 \frac {e^{\left .-\frac {3}{2}\right /x} \left (e^{\left .\frac {3}{2}\right /x} \left (480 x^3-320 x^4\right )+e^{e^{\left .-\frac {3}{2}\right /x} \left (-3+e^{\left .\frac {3}{2}\right /x} x\right )} \left (-81+216 x-144 x^2+e^{\left .\frac {3}{2}\right /x} \left (18 x^2-48 x^3+32 x^4\right )\right )\right )}{x^2 \left (18-48 x+32 x^2\right )} \, dx\\ &=\int \frac {e^{\left .-\frac {3}{2}\right /x} \left (e^{\left .\frac {3}{2}\right /x} \left (480 x^3-320 x^4\right )+e^{e^{\left .-\frac {3}{2}\right /x} \left (-3+e^{\left .\frac {3}{2}\right /x} x\right )} \left (-81+216 x-144 x^2+e^{\left .\frac {3}{2}\right /x} \left (18 x^2-48 x^3+32 x^4\right )\right )\right )}{2 x^2 (-3+4 x)^2} \, dx\\ &=\frac {1}{2} \int \frac {e^{\left .-\frac {3}{2}\right /x} \left (e^{\left .\frac {3}{2}\right /x} \left (480 x^3-320 x^4\right )+e^{e^{\left .-\frac {3}{2}\right /x} \left (-3+e^{\left .\frac {3}{2}\right /x} x\right )} \left (-81+216 x-144 x^2+e^{\left .\frac {3}{2}\right /x} \left (18 x^2-48 x^3+32 x^4\right )\right )\right )}{x^2 (-3+4 x)^2} \, dx\\ &=\frac {1}{2} \int \left (2 e^{-3 e^{\left .-\frac {3}{2}\right /x}+x}-\frac {9 e^{-3 e^{\left .-\frac {3}{2}\right /x}-\frac {3}{2 x}+x}}{x^2}+\frac {160 (3-2 x) x}{(3-4 x)^2}\right ) \, dx\\ &=-\left (\frac {9}{2} \int \frac {e^{-3 e^{\left .-\frac {3}{2}\right /x}-\frac {3}{2 x}+x}}{x^2} \, dx\right )+80 \int \frac {(3-2 x) x}{(3-4 x)^2} \, dx+\int e^{-3 e^{\left .-\frac {3}{2}\right /x}+x} \, dx\\ &=\frac {40 x^2}{3-4 x}-\frac {9}{2} \int \frac {e^{-3 e^{\left .-\frac {3}{2}\right /x}-\frac {3}{2 x}+x}}{x^2} \, dx+\int e^{-3 e^{\left .-\frac {3}{2}\right /x}+x} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.09, size = 30, normalized size = 1.07 \begin {gather*} e^{-3 e^{\left .-\frac {3}{2}\right /x}+x}-10 x-\frac {45}{2 (-3+4 x)} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.10, size = 30, normalized size = 1.07
method | result | size |
risch | \(-10 x -\frac {45}{8 \left (x -\frac {3}{4}\right )}+{\mathrm e}^{\left (x \,{\mathrm e}^{\frac {3}{2 x}}-3\right ) {\mathrm e}^{-\frac {3}{2 x}}}\) | \(30\) |
norman | \(\frac {\left (-40 \,{\mathrm e}^{\frac {3}{2 x}} x^{3}+4 x^{2} {\mathrm e}^{\left (x \,{\mathrm e}^{\frac {3}{2 x}}-3\right ) {\mathrm e}^{-\frac {3}{2 x}}} {\mathrm e}^{\frac {3}{2 x}}-3 \,{\mathrm e}^{\frac {3}{2 x}} {\mathrm e}^{\left (x \,{\mathrm e}^{\frac {3}{2 x}}-3\right ) {\mathrm e}^{-\frac {3}{2 x}}} x \right ) {\mathrm e}^{-\frac {3}{2 x}}}{x \left (4 x -3\right )}\) | \(92\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Failed to integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.41, size = 44, normalized size = 1.57 \begin {gather*} -\frac {80 \, x^{2} - 2 \, {\left (4 \, x - 3\right )} e^{\left ({\left (x e^{\left (\frac {3}{2 \, x}\right )} - 3\right )} e^{\left (-\frac {3}{2 \, x}\right )}\right )} - 60 \, x + 45}{2 \, {\left (4 \, x - 3\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.20, size = 27, normalized size = 0.96 \begin {gather*} - 10 x + e^{\left (x e^{\frac {3}{2 x}} - 3\right ) e^{- \frac {3}{2 x}}} - \frac {45}{8 x - 6} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 100 vs.
\(2 (24) = 48\).
time = 0.45, size = 100, normalized size = 3.57 \begin {gather*} -\frac {80 \, x^{2} e^{\left (-\frac {3}{2 \, x}\right )} - 8 \, x e^{\left (\frac {2 \, x^{2} - 6 \, x e^{\left (-\frac {3}{2 \, x}\right )} - 3}{2 \, x}\right )} - 60 \, x e^{\left (-\frac {3}{2 \, x}\right )} + 6 \, e^{\left (\frac {2 \, x^{2} - 6 \, x e^{\left (-\frac {3}{2 \, x}\right )} - 3}{2 \, x}\right )} + 45 \, e^{\left (-\frac {3}{2 \, x}\right )}}{2 \, {\left (4 \, x e^{\left (-\frac {3}{2 \, x}\right )} - 3 \, e^{\left (-\frac {3}{2 \, x}\right )}\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.93, size = 25, normalized size = 0.89 \begin {gather*} {\mathrm {e}}^{-\frac {3}{{\left ({\mathrm {e}}^{1/x}\right )}^{3/2}}}\,{\mathrm {e}}^x-\frac {45}{8\,\left (x-\frac {3}{4}\right )}-10\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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