Optimal. Leaf size=27 \[ e^{e^x}+e^{6+2 e^4+2 (1-\log (5 x))^2} \]
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Rubi [A] time = 0.10, antiderivative size = 28, normalized size of antiderivative = 1.04, number of steps used = 5, number of rules used = 4, integrand size = 60, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {14, 2282, 2194, 2288} \begin {gather*} \frac {e^{2 \left (\log ^2(5 x)+e^4+4\right )}}{625 x^4}+e^{e^x} \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rule 2194
Rule 2282
Rule 2288
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (e^{e^x+x}+\frac {4 e^{2 \left (4 \left (1+\frac {e^4}{4}\right )+\log ^2(5 x)\right )} (-1+\log (5 x))}{625 x^5}\right ) \, dx\\ &=\frac {4}{625} \int \frac {e^{2 \left (4 \left (1+\frac {e^4}{4}\right )+\log ^2(5 x)\right )} (-1+\log (5 x))}{x^5} \, dx+\int e^{e^x+x} \, dx\\ &=\frac {e^{2 \left (4+e^4+\log ^2(5 x)\right )}}{625 x^4}+\operatorname {Subst}\left (\int e^x \, dx,x,e^x\right )\\ &=e^{e^x}+\frac {e^{2 \left (4+e^4+\log ^2(5 x)\right )}}{625 x^4}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.09, size = 31, normalized size = 1.15 \begin {gather*} \frac {1}{625} \left (625 e^{e^x}+\frac {e^{2 \left (4+e^4+\log ^2(5 x)\right )}}{x^4}\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.88, size = 33, normalized size = 1.22 \begin {gather*} {\left (e^{\left (2 \, \log \left (5 \, x\right )^{2} + x + 2 \, e^{4} - 4 \, \log \left (5 \, x\right ) + 8\right )} + e^{\left (x + e^{x}\right )}\right )} e^{\left (-x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.28, size = 36, normalized size = 1.33 \begin {gather*} \frac {{\left (625 \, x^{4} e^{\left (x + e^{x}\right )} + e^{\left (2 \, \log \left (5 \, x\right )^{2} + x + 2 \, e^{4} + 8\right )}\right )} e^{\left (-x\right )}}{625 \, x^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.14, size = 25, normalized size = 0.93
method | result | size |
risch | \(\frac {{\mathrm e}^{2 \,{\mathrm e}^{4}+8+2 \ln \left (5 x \right )^{2}}}{625 x^{4}}+{\mathrm e}^{{\mathrm e}^{x}}\) | \(25\) |
default | \(\frac {{\mathrm e}^{6} {\mathrm e}^{2 \,{\mathrm e}^{4}} {\mathrm e}^{2 \ln \left (5 x \right )^{2}+2}}{625 x^{4}}+{\mathrm e}^{{\mathrm e}^{x}}\) | \(32\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [C] time = 0.52, size = 119, normalized size = 4.41 \begin {gather*} i \, \sqrt {2} \sqrt {\pi } \operatorname {erf}\left (i \, \sqrt {2} \log \left (5 \, x\right ) - i \, \sqrt {2}\right ) e^{\left (2 \, e^{4} + 6\right )} + \frac {1}{2} \, \sqrt {2} {\left (\frac {2 \, \sqrt {\pi } {\left (\operatorname {erf}\left (\sqrt {2} \sqrt {-{\left (\log \left (5 \, x\right ) - 1\right )}^{2}}\right ) - 1\right )} {\left (\log \left (5 \, x\right ) - 1\right )}}{\sqrt {-{\left (\log \left (5 \, x\right ) - 1\right )}^{2}}} + \sqrt {2} e^{\left (2 \, {\left (\log \left (5 \, x\right ) - 1\right )}^{2}\right )}\right )} e^{\left (2 \, {\left (e^{2} + 2 \, e + 2\right )} {\left (e^{2} - 2 \, e + 2\right )} - 2\right )} + e^{\left (e^{x}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 7.66, size = 36, normalized size = 1.33 \begin {gather*} {\mathrm {e}}^{{\mathrm {e}}^x}+\frac {x^{4\,\ln \relax (5)}\,{\mathrm {e}}^{2\,{\ln \relax (x)}^2}\,{\mathrm {e}}^{2\,{\mathrm {e}}^4}\,{\mathrm {e}}^8\,{\mathrm {e}}^{2\,{\ln \relax (5)}^2}}{625\,x^4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.64, size = 31, normalized size = 1.15 \begin {gather*} e^{e^{x}} + \frac {e^{6} e^{2 \log {\left (5 x \right )}^{2} + 2} e^{2 e^{4}}}{625 x^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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