Optimal. Leaf size=34 \[ x+\frac {1}{3} \left (-x+\left (2+e^{x \left (-e^{3/x}+x\right )}\right ) x-x \log (x)\right ) \]
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Rubi [B] Leaf count is larger than twice the leaf count of optimal. \(77\) vs. \(2(34)=68\).
time = 0.07, antiderivative size = 77, normalized size of antiderivative = 2.26, number of steps
used = 4, number of rules used = 3, integrand size = 47, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.064, Rules used = {12, 2326, 2332}
\begin {gather*} -\frac {e^{x^2-e^{3/x} x} \left (2 x^2+e^{3/x} (3-x)\right )}{3 \left (-2 x+e^{3/x}-\frac {3 e^{3/x}}{x}\right )}+\frac {4 x}{3}-\frac {1}{3} x \log (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2326
Rule 2332
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{3} \int \left (3+e^{-e^{3/x} x+x^2} \left (1+e^{3/x} (3-x)+2 x^2\right )-\log (x)\right ) \, dx\\ &=x+\frac {1}{3} \int e^{-e^{3/x} x+x^2} \left (1+e^{3/x} (3-x)+2 x^2\right ) \, dx-\frac {1}{3} \int \log (x) \, dx\\ &=\frac {4 x}{3}-\frac {e^{-e^{3/x} x+x^2} \left (e^{3/x} (3-x)+2 x^2\right )}{3 \left (e^{3/x}-\frac {3 e^{3/x}}{x}-2 x\right )}-\frac {1}{3} x \log (x)\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.13, size = 26, normalized size = 0.76 \begin {gather*} \frac {1}{3} x \left (4+e^{x \left (-e^{3/x}+x\right )}-\log (x)\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.31, size = 27, normalized size = 0.79
method | result | size |
risch | \(\frac {4 x}{3}+\frac {x \,{\mathrm e}^{\left (x -{\mathrm e}^{\frac {3}{x}}\right ) x}}{3}-\frac {x \ln \left (x \right )}{3}\) | \(26\) |
default | \(\frac {4 x}{3}+\frac {x \,{\mathrm e}^{-x \,{\mathrm e}^{\frac {3}{x}}+x^{2}}}{3}-\frac {x \ln \left (x \right )}{3}\) | \(27\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.30, size = 26, normalized size = 0.76 \begin {gather*} \frac {1}{3} \, x e^{\left (x^{2} - x e^{\frac {3}{x}}\right )} - \frac {1}{3} \, x \log \left (x\right ) + \frac {4}{3} \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.40, size = 26, normalized size = 0.76 \begin {gather*} \frac {1}{3} \, x e^{\left (x^{2} - x e^{\frac {3}{x}}\right )} - \frac {1}{3} \, x \log \left (x\right ) + \frac {4}{3} \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 1.29, size = 26, normalized size = 0.76 \begin {gather*} \frac {x e^{x^{2} - x e^{\frac {3}{x}}}}{3} - \frac {x \log {\left (x \right )}}{3} + \frac {4 x}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.44, size = 39, normalized size = 1.15 \begin {gather*} \frac {1}{3} \, x e^{\left (\frac {x^{3} - x^{2} e^{\frac {3}{x}} + 3}{x} - \frac {3}{x}\right )} - \frac {1}{3} \, x \log \left (x\right ) + \frac {4}{3} \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 5.61, size = 23, normalized size = 0.68 \begin {gather*} \frac {x\,\left ({\mathrm {e}}^{x^2-x\,{\mathrm {e}}^{3/x}}-\ln \left (x\right )+4\right )}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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