Optimal. Leaf size=27 \[ \frac {e^{-e^{e^3+x}+x (-2+x \log (x))}}{x}+\log (5) \]
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Rubi [B] Leaf count is larger than twice the leaf count of optimal. \(67\) vs. \(2(27)=54\).
time = 1.05, antiderivative size = 67, normalized size of antiderivative = 2.48, number of steps
used = 1, number of rules used = 1, integrand size = 50, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.020, Rules used = {2326}
\begin {gather*} \frac {e^{-2 x-e^{x+e^3}} x^{x^2-2} \left (-x^2-2 x^2 \log (x)+e^{x+e^3} x+2 x\right )}{-x+e^{x+e^3}-2 x \log (x)+2} \end {gather*}
Antiderivative was successfully verified.
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Rule 2326
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {e^{-e^{e^3+x}-2 x} x^{-2+x^2} \left (2 x+e^{e^3+x} x-x^2-2 x^2 \log (x)\right )}{2+e^{e^3+x}-x-2 x \log (x)}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.04, size = 23, normalized size = 0.85 \begin {gather*} e^{-e^{e^3+x}-2 x} x^{-1+x^2} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.13, size = 22, normalized size = 0.81
method | result | size |
risch | \(\frac {x^{x^{2}} {\mathrm e}^{-{\mathrm e}^{{\mathrm e}^{3}+x}-2 x}}{x}\) | \(22\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.37, size = 22, normalized size = 0.81 \begin {gather*} \frac {e^{\left (x^{2} \log \left (x\right ) - 2 \, x - e^{\left (x + e^{3}\right )}\right )}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.45, size = 22, normalized size = 0.81 \begin {gather*} \frac {e^{\left (x^{2} \log \left (x\right ) - 2 \, x - e^{\left (x + e^{3}\right )}\right )}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.10, size = 19, normalized size = 0.70 \begin {gather*} \frac {e^{x^{2} \log {\left (x \right )} - 2 x - e^{x + e^{3}}}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.42, size = 22, normalized size = 0.81 \begin {gather*} \frac {e^{\left (x^{2} \log \left (x\right ) - 2 \, x - e^{\left (x + e^{3}\right )}\right )}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 3.26, size = 20, normalized size = 0.74 \begin {gather*} x^{x^2-1}\,{\mathrm {e}}^{-2\,x}\,{\mathrm {e}}^{-{\mathrm {e}}^{{\mathrm {e}}^3}\,{\mathrm {e}}^x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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