Optimal. Leaf size=18 \[ -41+e^5+e^{\frac {2 x^2}{\log (\log (x))}}+x \]
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Rubi [A] time = 0.61, antiderivative size = 14, normalized size of antiderivative = 0.78, number of steps used = 3, number of rules used = 2, integrand size = 44, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.045, Rules used = {6742, 6706} \begin {gather*} e^{\frac {2 x^2}{\log (\log (x))}}+x \end {gather*}
Antiderivative was successfully verified.
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Rule 6706
Rule 6742
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (1+\frac {2 e^{\frac {2 x^2}{\log (\log (x))}} x (-1+2 \log (x) \log (\log (x)))}{\log (x) \log ^2(\log (x))}\right ) \, dx\\ &=x+2 \int \frac {e^{\frac {2 x^2}{\log (\log (x))}} x (-1+2 \log (x) \log (\log (x)))}{\log (x) \log ^2(\log (x))} \, dx\\ &=e^{\frac {2 x^2}{\log (\log (x))}}+x\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.11, size = 14, normalized size = 0.78 \begin {gather*} e^{\frac {2 x^2}{\log (\log (x))}}+x \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.76, size = 13, normalized size = 0.72 \begin {gather*} x + e^{\left (\frac {2 \, x^{2}}{\log \left (\log \relax (x)\right )}\right )} \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*} \mathit {undef} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 14, normalized size = 0.78
method | result | size |
risch | \(x +{\mathrm e}^{\frac {2 x^{2}}{\ln \left (\ln \relax (x )\right )}}\) | \(14\) |
default | \(x +{\mathrm e}^{\frac {2 x^{2}}{\ln \left (\ln \relax (x )\right )}}\) | \(15\) |
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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mupad [B] time = 1.20, size = 13, normalized size = 0.72 \begin {gather*} x+{\mathrm {e}}^{\frac {2\,x^2}{\ln \left (\ln \relax (x)\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.51, size = 12, normalized size = 0.67 \begin {gather*} x + e^{\frac {2 x^{2}}{\log {\left (\log {\relax (x )} \right )}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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