Optimal. Leaf size=27 \[ e^{\frac {3 \left (x+\left (\frac {1}{10}+x\right ) (3+x)\right )}{\log \left (\frac {2}{x}+x\right )}} x \]
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Rubi [B] Leaf count is larger than twice the leaf count of optimal. \(164\) vs. \(2(27)=54\).
time = 1.26, antiderivative size = 164, normalized size of antiderivative = 6.07, number of steps
used = 1, number of rules used = 1, integrand size = 120, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.008, Rules used = {2326}
\begin {gather*} -\frac {e^{\frac {3 \left (10 x^2+41 x+3\right )}{10 \log \left (\frac {x^2+2}{x}\right )}} \left (-10 x^4-41 x^3+17 x^2+\left (20 x^4+41 x^3+40 x^2+82 x\right ) \log \left (\frac {x^2+2}{x}\right )+82 x+6\right )}{\left (x^2+2\right ) \left (\frac {x \left (10 x^2+41 x+3\right ) \left (2-\frac {x^2+2}{x^2}\right )}{\left (x^2+2\right ) \log ^2\left (\frac {x^2+2}{x}\right )}-\frac {20 x+41}{\log \left (\frac {x^2+2}{x}\right )}\right ) \log ^2\left (\frac {x^2+2}{x}\right )} \end {gather*}
Antiderivative was successfully verified.
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Rule 2326
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-\frac {e^{\frac {3 \left (3+41 x+10 x^2\right )}{10 \log \left (\frac {2+x^2}{x}\right )}} \left (6+82 x+17 x^2-41 x^3-10 x^4+\left (82 x+40 x^2+41 x^3+20 x^4\right ) \log \left (\frac {2+x^2}{x}\right )\right )}{\left (2+x^2\right ) \left (\frac {x \left (3+41 x+10 x^2\right ) \left (2-\frac {2+x^2}{x^2}\right )}{\left (2+x^2\right ) \log ^2\left (\frac {2+x^2}{x}\right )}-\frac {41+20 x}{\log \left (\frac {2+x^2}{x}\right )}\right ) \log ^2\left (\frac {2+x^2}{x}\right )}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.08, size = 28, normalized size = 1.04 \begin {gather*} e^{\frac {3 \left (3+41 x+10 x^2\right )}{10 \log \left (\frac {2}{x}+x\right )}} x \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.98, size = 28, normalized size = 1.04
method | result | size |
risch | \(x \,{\mathrm e}^{\frac {3 x^{2}+\frac {123}{10} x +\frac {9}{10}}{\ln \left (\frac {x^{2}+2}{x}\right )}}\) | \(28\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F(-2)]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: RuntimeError} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.42, size = 27, normalized size = 1.00 \begin {gather*} x e^{\left (\frac {3 \, {\left (10 \, x^{2} + 41 \, x + 3\right )}}{10 \, \log \left (\frac {x^{2} + 2}{x}\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F(-2)]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: TypeError} \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 = 8.82, size = 62, normalized size = 2.30 \begin {gather*} x\,{\mathrm {e}}^{\frac {3\,x^2}{\ln \left (\frac {1}{x}\right )+\ln \left (x^2+2\right )}}\,{\mathrm {e}}^{\frac {9}{10\,\left (\ln \left (\frac {1}{x}\right )+\ln \left (x^2+2\right )\right )}}\,{\mathrm {e}}^{\frac {123\,x}{10\,\left (\ln \left (\frac {1}{x}\right )+\ln \left (x^2+2\right )\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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