Optimal. Leaf size=20 \[ e^{3 \left (-5+x-\frac {e^5 x}{\log (3+\log (x))}\right )} \]
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Rubi [F] time = 1.49, 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 {\exp \left (5-\frac {e^5 \left (3 x-\frac {(-15+3 x) \log (3+\log (x))}{e^5}\right )}{\log (3+\log (x))}\right ) \left (-3+(9+3 \log (x)) \log (3+\log (x))-\frac {(9+3 \log (x)) \log ^2(3+\log (x))}{e^5}\right )}{(3+\log (x)) \log ^2(3+\log (x))} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-\int \frac {\exp \left (\frac {-3 e^5 x-10 \log (3+\log (x))+3 x \log (3+\log (x))}{\log (3+\log (x))}\right ) \left (-3+(9+3 \log (x)) \log (3+\log (x))-\frac {(9+3 \log (x)) \log ^2(3+\log (x))}{e^5}\right )}{(3+\log (x)) \log ^2(3+\log (x))} \, dx\\ &=-\int \left (-3 \exp \left (-5+\frac {-3 e^5 x-10 \log (3+\log (x))+3 x \log (3+\log (x))}{\log (3+\log (x))}\right )-\frac {3 \exp \left (\frac {-3 e^5 x-10 \log (3+\log (x))+3 x \log (3+\log (x))}{\log (3+\log (x))}\right )}{(3+\log (x)) \log ^2(3+\log (x))}+\frac {3 \exp \left (\frac {-3 e^5 x-10 \log (3+\log (x))+3 x \log (3+\log (x))}{\log (3+\log (x))}\right )}{\log (3+\log (x))}\right ) \, dx\\ &=3 \int \exp \left (-5+\frac {-3 e^5 x-10 \log (3+\log (x))+3 x \log (3+\log (x))}{\log (3+\log (x))}\right ) \, dx+3 \int \frac {\exp \left (\frac {-3 e^5 x-10 \log (3+\log (x))+3 x \log (3+\log (x))}{\log (3+\log (x))}\right )}{(3+\log (x)) \log ^2(3+\log (x))} \, dx-3 \int \frac {\exp \left (\frac {-3 e^5 x-10 \log (3+\log (x))+3 x \log (3+\log (x))}{\log (3+\log (x))}\right )}{\log (3+\log (x))} \, dx\\ &=3 \int e^{3 \left (-5+x-\frac {e^5 x}{\log (3+\log (x))}\right )} \, dx+3 \int \frac {e^{-10+3 x-\frac {3 e^5 x}{\log (3+\log (x))}}}{(3+\log (x)) \log ^2(3+\log (x))} \, dx-3 \int \frac {e^{-10+3 x-\frac {3 e^5 x}{\log (3+\log (x))}}}{\log (3+\log (x))} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.25, size = 20, normalized size = 1.00 \begin {gather*} e^{-15+3 x-\frac {3 e^5 x}{\log (3+\log (x))}} \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 0.73, size = 51, normalized size = 2.55 \begin {gather*} -e^{\left (-\frac {3 \, x e^{5} - {\left (3 \, x - 10\right )} \log \left (\log \relax (x) + 3\right ) + \log \left (-\log \left (\log \relax (x) + 3\right )\right ) \log \left (\log \relax (x) + 3\right )}{\log \left (\log \relax (x) + 3\right )} - 5\right )} \log \left (\log \relax (x) + 3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [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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maple [A] time = 0.06, size = 35, normalized size = 1.75
method | result | size |
risch | \({\mathrm e}^{\frac {3 \left (\ln \left (3+\ln \relax (x )\right ) {\mathrm e}^{-5} x -5 \ln \left (3+\ln \relax (x )\right ) {\mathrm e}^{-5}-x \right ) {\mathrm e}^{5}}{\ln \left (3+\ln \relax (x )\right )}}\) | \(35\) |
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 = 6.23, size = 20, normalized size = 1.00 \begin {gather*} {\mathrm {e}}^{3\,x}\,{\mathrm {e}}^{-15}\,{\mathrm {e}}^{-\frac {3\,x\,{\mathrm {e}}^5}{\ln \left (\ln \relax (x)+3\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.72, size = 31, normalized size = 1.55 \begin {gather*} e^{- \frac {\left (3 x - \frac {\left (3 x - 15\right ) \log {\left (\log {\relax (x )} + 3 \right )}}{e^{5}}\right ) e^{5}}{\log {\left (\log {\relax (x )} + 3 \right )}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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