Optimal. Leaf size=24 \[ e^{\frac {e^{5-x-\frac {5}{4} x (4+\log (x))}}{x}}+x \]
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Rubi [F]
time = 0.79, 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 {4 x^2+\exp \left (\frac {e^{\frac {1}{4} (20-24 x-5 x \log (x))}}{x}+\frac {1}{4} (20-24 x-5 x \log (x))\right ) (-4-29 x-5 x \log (x))}{4 x^2} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{4} \int \frac {4 x^2+\exp \left (\frac {e^{\frac {1}{4} (20-24 x-5 x \log (x))}}{x}+\frac {1}{4} (20-24 x-5 x \log (x))\right ) (-4-29 x-5 x \log (x))}{x^2} \, dx\\ &=\frac {1}{4} \int \left (4-e^{5-6 x+e^{5-6 x} x^{-1-\frac {5 x}{4}}} x^{-2-\frac {5 x}{4}} (4+29 x+5 x \log (x))\right ) \, dx\\ &=x-\frac {1}{4} \int e^{5-6 x+e^{5-6 x} x^{-1-\frac {5 x}{4}}} x^{-2-\frac {5 x}{4}} (4+29 x+5 x \log (x)) \, dx\\ &=x-\frac {1}{4} \int \left (4 e^{5-6 x+e^{5-6 x} x^{-1-\frac {5 x}{4}}} x^{-2-\frac {5 x}{4}}+29 e^{5-6 x+e^{5-6 x} x^{-1-\frac {5 x}{4}}} x^{-1-\frac {5 x}{4}}+5 e^{5-6 x+e^{5-6 x} x^{-1-\frac {5 x}{4}}} x^{-1-\frac {5 x}{4}} \log (x)\right ) \, dx\\ &=x-\frac {5}{4} \int e^{5-6 x+e^{5-6 x} x^{-1-\frac {5 x}{4}}} x^{-1-\frac {5 x}{4}} \log (x) \, dx-\frac {29}{4} \int e^{5-6 x+e^{5-6 x} x^{-1-\frac {5 x}{4}}} x^{-1-\frac {5 x}{4}} \, dx-\int e^{5-6 x+e^{5-6 x} x^{-1-\frac {5 x}{4}}} x^{-2-\frac {5 x}{4}} \, dx\\ &=x+\frac {5}{4} \int \frac {\int e^{5-6 x+e^{5-6 x} x^{-1-\frac {5 x}{4}}} x^{-1-\frac {5 x}{4}} \, dx}{x} \, dx-\frac {29}{4} \int e^{5-6 x+e^{5-6 x} x^{-1-\frac {5 x}{4}}} x^{-1-\frac {5 x}{4}} \, dx-\frac {1}{4} (5 \log (x)) \int e^{5-6 x+e^{5-6 x} x^{-1-\frac {5 x}{4}}} x^{-1-\frac {5 x}{4}} \, dx-\int e^{5-6 x+e^{5-6 x} x^{-1-\frac {5 x}{4}}} x^{-2-\frac {5 x}{4}} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.40, size = 21, normalized size = 0.88 \begin {gather*} e^{e^{5-6 x} x^{-1-\frac {5 x}{4}}}+x \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.22, size = 19, normalized size = 0.79
method | result | size |
risch | \(x +{\mathrm e}^{\frac {x^{-\frac {5 x}{4}} {\mathrm e}^{5-6 x}}{x}}\) | \(19\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.45, size = 18, normalized size = 0.75 \begin {gather*} x + e^{\left (\frac {e^{\left (-\frac {5}{4} \, x \log \left (x\right ) - 6 \, x + 5\right )}}{x}\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. 61 vs.
\(2 (20) = 40\).
time = 0.37, size = 61, normalized size = 2.54 \begin {gather*} {\left (x e^{\left (-\frac {5}{4} \, x \log \left (x\right ) - 6 \, x + 5\right )} + e^{\left (-\frac {5 \, x^{2} \log \left (x\right ) + 24 \, x^{2} - 20 \, x - 4 \, e^{\left (-\frac {5}{4} \, x \log \left (x\right ) - 6 \, x + 5\right )}}{4 \, x}\right )}\right )} e^{\left (\frac {5}{4} \, x \log \left (x\right ) + 6 \, x - 5\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.34, size = 19, normalized size = 0.79 \begin {gather*} x + e^{\frac {e^{- \frac {5 x \log {\left (x \right )}}{4} - 6 x + 5}}{x}} \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 = 7.61, size = 20, normalized size = 0.83 \begin {gather*} x+{\mathrm {e}}^{\frac {{\mathrm {e}}^{-6\,x}\,{\mathrm {e}}^5}{x^{\frac {5\,x}{4}}\,x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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