Optimal. Leaf size=20 \[ -7-e^{\frac {e}{\log \left (e^{3/x}+x\right )}} \]
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Rubi [A]
time = 0.30, antiderivative size = 18, normalized size of antiderivative = 0.90, number of steps
used = 1, number of rules used = 1, integrand size = 63, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.016, Rules used = {6838}
\begin {gather*} -e^{\frac {e}{\log \left (x+e^{3/x}\right )}} \end {gather*}
Antiderivative was successfully verified.
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Rule 6838
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-e^{\frac {e}{\log \left (e^{3/x}+x\right )}}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.11, size = 18, normalized size = 0.90 \begin {gather*} -e^{\frac {e}{\log \left (e^{3/x}+x\right )}} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.28, size = 18, normalized size = 0.90
method | result | size |
risch | \(-{\mathrm e}^{\frac {{\mathrm e}}{\ln \left ({\mathrm e}^{\frac {3}{x}}+x \right )}}\) | \(18\) |
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. 72 vs.
\(2 (19) = 38\).
time = 0.29, size = 72, normalized size = 3.60 \begin {gather*} -\frac {x^{2} e^{\left (\frac {e}{\log \left (x + e^{\frac {3}{x}}\right )}\right )}}{x^{2} - 3 \, e^{\frac {3}{x}}} + \frac {3 \, e^{\left (\frac {e}{\log \left (x + e^{\frac {3}{x}}\right )} + \frac {3}{x}\right )}}{x^{2} - 3 \, e^{\frac {3}{x}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.35, size = 25, normalized size = 1.25 \begin {gather*} -e^{\left (\frac {e}{\log \left ({\left (x e + e^{\left (\frac {x + 3}{x}\right )}\right )} e^{\left (-1\right )}\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F(-1)] Timed out
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.39, size = 17, normalized size = 0.85 \begin {gather*} -e^{\left (\frac {e}{\log \left (x + e^{\frac {3}{x}}\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 4.40, size = 17, normalized size = 0.85 \begin {gather*} -{\mathrm {e}}^{\frac {\mathrm {e}}{\ln \left (x+{\mathrm {e}}^{3/x}\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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