Optimal. Leaf size=19 \[ 5+x+\log (2) \log \left (5^{1+\frac {4 x}{e^4}}+x\right ) \]
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Rubi [F] time = 0.48, 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 {e^4 x+e^4 \log (2)+625^{\frac {x}{e^4}} \left (5 e^4+5 \log (2) \log (625)\right )}{5^{1+\frac {4 x}{e^4}} e^4+e^4 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 {e^4 x+e^4 \log (2)+625^{\frac {x}{e^4}} \left (5 e^4+5 \log (2) \log (625)\right )}{e^4 \left (5^{1+\frac {4 x}{e^4}}+x\right )} \, dx\\ &=\frac {\int \frac {e^4 x+e^4 \log (2)+625^{\frac {x}{e^4}} \left (5 e^4+5 \log (2) \log (625)\right )}{5^{1+\frac {4 x}{e^4}}+x} \, dx}{e^4}\\ &=\frac {\int \left (-\frac {\log (2) \left (-e^4+x \log (625)\right )}{5^{1+\frac {4 x}{e^4}}+x}+e^4 \left (1+\frac {\log (2) \log (625)}{e^4}\right )\right ) \, dx}{e^4}\\ &=x \left (1+\frac {\log (2) \log (625)}{e^4}\right )-\frac {\log (2) \int \frac {-e^4+x \log (625)}{5^{1+\frac {4 x}{e^4}}+x} \, dx}{e^4}\\ &=x \left (1+\frac {\log (2) \log (625)}{e^4}\right )-\frac {\log (2) \int \left (-\frac {e^4}{5^{1+\frac {4 x}{e^4}}+x}+\frac {x \log (625)}{5^{1+\frac {4 x}{e^4}}+x}\right ) \, dx}{e^4}\\ &=x \left (1+\frac {\log (2) \log (625)}{e^4}\right )+\log (2) \int \frac {1}{5^{1+\frac {4 x}{e^4}}+x} \, dx-\frac {(\log (2) \log (625)) \int \frac {x}{5^{1+\frac {4 x}{e^4}}+x} \, dx}{e^4}\\ \end {aligned} \end {gather*}
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Mathematica [F] time = 0.61, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {e^4 x+e^4 \log (2)+625^{\frac {x}{e^4}} \left (5 e^4+5 \log (2) \log (625)\right )}{5^{1+\frac {4 x}{e^4}} e^4+e^4 x} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 0.78, size = 17, normalized size = 0.89 \begin {gather*} \log \relax (2) \log \left (5 \cdot 5^{4 \, x e^{\left (-4\right )}} + x\right ) + x \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*} \int \frac {5 \, {\left (4 \, \log \relax (5) \log \relax (2) + e^{4}\right )} 5^{4 \, x e^{\left (-4\right )}} + x e^{4} + e^{4} \log \relax (2)}{5 \cdot 5^{4 \, x e^{\left (-4\right )}} e^{4} + x e^{4}}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.30, size = 21, normalized size = 1.11
method | result | size |
norman | \(x +\ln \relax (2) \ln \left (x +5 \,{\mathrm e}^{4 x \ln \relax (5) {\mathrm e}^{-4}}\right )\) | \(21\) |
risch | \({\mathrm e}^{4} {\mathrm e}^{-4} x +\ln \relax (2) \ln \left (\frac {x}{5}+625^{x \,{\mathrm e}^{-4}}\right )\) | \(22\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.57, size = 17, normalized size = 0.89 \begin {gather*} \log \relax (2) \log \left (5^{4 \, x e^{\left (-4\right )}} + \frac {1}{5} \, x\right ) + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.56, size = 17, normalized size = 0.89 \begin {gather*} x+\ln \left (x+5\,5^{4\,x\,{\mathrm {e}}^{-4}}\right )\,\ln \relax (2) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.16, size = 20, normalized size = 1.05 \begin {gather*} x + \log {\relax (2 )} \log {\left (\frac {x}{5} + e^{\frac {4 x \log {\relax (5 )}}{e^{4}}} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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