Optimal. Leaf size=23 \[ 3-e^{\frac {e^{x^2}}{x}}+\log (4)-\frac {\log (x)}{3} \]
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Rubi [F]
time = 0.31, 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 {-x+e^{\frac {e^{x^2}}{x}+x^2} \left (3-6 x^2\right )}{3 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}{3} \int \frac {-x+e^{\frac {e^{x^2}}{x}+x^2} \left (3-6 x^2\right )}{x^2} \, dx\\ &=\frac {1}{3} \int \left (-\frac {1}{x}-\frac {3 e^{\frac {e^{x^2}}{x}+x^2} \left (-1+2 x^2\right )}{x^2}\right ) \, dx\\ &=-\frac {\log (x)}{3}-\int \frac {e^{\frac {e^{x^2}}{x}+x^2} \left (-1+2 x^2\right )}{x^2} \, dx\\ &=-\frac {\log (x)}{3}-\int \left (2 e^{\frac {e^{x^2}}{x}+x^2}-\frac {e^{\frac {e^{x^2}}{x}+x^2}}{x^2}\right ) \, dx\\ &=-\frac {\log (x)}{3}-2 \int e^{\frac {e^{x^2}}{x}+x^2} \, dx+\int \frac {e^{\frac {e^{x^2}}{x}+x^2}}{x^2} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.05, size = 22, normalized size = 0.96 \begin {gather*} \frac {1}{3} \left (-3 e^{\frac {e^{x^2}}{x}}-\log (x)\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.13, size = 17, normalized size = 0.74
method | result | size |
norman | \(-{\mathrm e}^{\frac {{\mathrm e}^{x^{2}}}{x}}-\frac {\ln \left (x \right )}{3}\) | \(17\) |
risch | \(-{\mathrm e}^{\frac {{\mathrm e}^{x^{2}}}{x}}-\frac {\ln \left (x \right )}{3}\) | \(17\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.32, size = 16, normalized size = 0.70 \begin {gather*} -e^{\left (\frac {e^{\left (x^{2}\right )}}{x}\right )} - \frac {1}{3} \, \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.39, size = 31, normalized size = 1.35 \begin {gather*} -\frac {1}{3} \, {\left (e^{\left (x^{2}\right )} \log \left (x\right ) + 3 \, e^{\left (\frac {x^{3} + e^{\left (x^{2}\right )}}{x}\right )}\right )} e^{\left (-x^{2}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.09, size = 14, normalized size = 0.61 \begin {gather*} - e^{\frac {e^{x^{2}}}{x}} - \frac {\log {\left (x \right )}}{3} \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 = 3.54, size = 16, normalized size = 0.70 \begin {gather*} -{\mathrm {e}}^{\frac {{\mathrm {e}}^{x^2}}{x}}-\frac {\ln \left (x\right )}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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