Optimal. Leaf size=28 \[ -1+x-\frac {e^{e^{-2+x+\frac {1+3 x}{3+\log (2)}}}}{\log (6)} \]
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Rubi [A] time = 0.18, antiderivative size = 41, normalized size of antiderivative = 1.46, number of steps used = 4, number of rules used = 3, integrand size = 67, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.045, Rules used = {12, 2282, 2194} \begin {gather*} x-\frac {e^{2^{-\frac {2-x}{3+\log (2)}} e^{-\frac {5-6 x}{3+\log (2)}}}}{\log (6)} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2194
Rule 2282
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int \left (\exp \left (e^{\frac {-5+6 x+(-2+x) \log (2)}{3+\log (2)}}+\frac {-5+6 x+(-2+x) \log (2)}{3+\log (2)}\right ) (-6-\log (2))+(3+\log (2)) \log (6)\right ) \, dx}{(3+\log (2)) \log (6)}\\ &=x-\frac {(6+\log (2)) \int \exp \left (e^{\frac {-5+6 x+(-2+x) \log (2)}{3+\log (2)}}+\frac {-5+6 x+(-2+x) \log (2)}{3+\log (2)}\right ) \, dx}{(3+\log (2)) \log (6)}\\ &=x-\frac {\operatorname {Subst}\left (\int e^x \, dx,x,e^{\frac {-5+6 x+(-2+x) \log (2)}{3+\log (2)}}\right )}{\log (6)}\\ &=x-\frac {e^{2^{-\frac {2-x}{3+\log (2)}} e^{-\frac {5-6 x}{3+\log (2)}}}}{\log (6)}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.26, size = 41, normalized size = 1.46 \begin {gather*} x+\frac {e^{e^{\frac {-5+6 x+(-2+x) \log (2)}{3+\log (2)}}} (-6-\log (2))}{(6+\log (2)) \log (6)} \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 0.98, size = 94, normalized size = 3.36 \begin {gather*} \frac {{\left (x e^{\left (\frac {{\left (x - 2\right )} \log \relax (2) + 6 \, x - 5}{\log \relax (2) + 3}\right )} \log \relax (6) - e^{\left (\frac {{\left (\log \relax (2) + 3\right )} e^{\left (\frac {{\left (x - 2\right )} \log \relax (2) + 6 \, x - 5}{\log \relax (2) + 3}\right )} + {\left (x - 2\right )} \log \relax (2) + 6 \, x - 5}{\log \relax (2) + 3}\right )}\right )} e^{\left (-\frac {{\left (x - 2\right )} \log \relax (2) + 6 \, x - 5}{\log \relax (2) + 3}\right )}}{\log \relax (6)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.37, size = 254, normalized size = 9.07 \begin {gather*} \frac {2 \, x {\left (\log \relax (2) + 3\right )} \log \relax (6) - \frac {{\left (2^{\frac {8}{9}} e^{\left (\frac {x \log \relax (2) + e^{\left (\frac {x \log \relax (2) + 6 \, x - 2 \, \log \relax (2) - 5}{\log \relax (2) + 3}\right )} \log \relax (2) + 6 \, x + 3 \, e^{\left (\frac {x \log \relax (2) + 6 \, x - 2 \, \log \relax (2) - 5}{\log \relax (2) + 3}\right )}}{\log \relax (2) + 3} + \frac {\log \relax (2)^{2} - 15 \, \log \relax (2) - 45}{9 \, {\left (\log \relax (2) + 3\right )}}\right )} \log \relax (2) + 3 \cdot 2^{\frac {8}{9}} e^{\left (\frac {x \log \relax (2) + e^{\left (\frac {x \log \relax (2) + 6 \, x - 2 \, \log \relax (2) - 5}{\log \relax (2) + 3}\right )} \log \relax (2) + 6 \, x + 3 \, e^{\left (\frac {x \log \relax (2) + 6 \, x - 2 \, \log \relax (2) - 5}{\log \relax (2) + 3}\right )}}{\log \relax (2) + 3} + \frac {\log \relax (2)^{2} - 15 \, \log \relax (2) - 45}{9 \, {\left (\log \relax (2) + 3\right )}}\right )}\right )} {\left (\log \relax (2) + 6\right )}}{e^{\left (\frac {x \log \relax (2) + 6 \, x - 2 \, \log \relax (2) - 5}{\log \relax (2) + 3}\right )} \log \relax (2) + 6 \, e^{\left (\frac {x \log \relax (2) + 6 \, x - 2 \, \log \relax (2) - 5}{\log \relax (2) + 3}\right )}}}{2 \, {\left (\log \relax (2) + 3\right )} \log \relax (6)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.12, size = 29, normalized size = 1.04
method | result | size |
norman | \(x -\frac {{\mathrm e}^{{\mathrm e}^{\frac {\left (x -2\right ) \ln \relax (2)+6 x -5}{3+\ln \relax (2)}}}}{\ln \relax (6)}\) | \(29\) |
derivativedivides | \(\frac {\ln \relax (6) \ln \relax (2) \ln \left ({\mathrm e}^{\frac {\left (x -2\right ) \ln \relax (2)+6 x -5}{3+\ln \relax (2)}}\right )+3 \ln \relax (6) \ln \left ({\mathrm e}^{\frac {\left (x -2\right ) \ln \relax (2)+6 x -5}{3+\ln \relax (2)}}\right )-{\mathrm e}^{{\mathrm e}^{\frac {\left (x -2\right ) \ln \relax (2)+6 x -5}{3+\ln \relax (2)}}} \ln \relax (2)-6 \,{\mathrm e}^{{\mathrm e}^{\frac {\left (x -2\right ) \ln \relax (2)+6 x -5}{3+\ln \relax (2)}}}}{\ln \relax (6) \left (\ln \relax (2)+6\right )}\) | \(108\) |
default | \(\frac {\ln \relax (6) x \ln \relax (2)+3 x \ln \relax (6)-\frac {{\mathrm e}^{{\mathrm e}^{\frac {\left (x -2\right ) \ln \relax (2)+6 x -5}{3+\ln \relax (2)}}} \ln \relax (2)^{2}}{\ln \relax (2)+6}-\frac {9 \,{\mathrm e}^{{\mathrm e}^{\frac {\left (x -2\right ) \ln \relax (2)+6 x -5}{3+\ln \relax (2)}}} \ln \relax (2)}{\ln \relax (2)+6}-\frac {18 \,{\mathrm e}^{{\mathrm e}^{\frac {\left (x -2\right ) \ln \relax (2)+6 x -5}{3+\ln \relax (2)}}}}{\ln \relax (2)+6}}{\left (3+\ln \relax (2)\right ) \ln \relax (6)}\) | \(114\) |
risch | \(\frac {x \ln \relax (2)^{2}}{\left (3+\ln \relax (2)\right ) \left (\ln \relax (2)+\ln \relax (3)\right )}+\frac {x \ln \relax (2) \ln \relax (3)}{\left (3+\ln \relax (2)\right ) \left (\ln \relax (2)+\ln \relax (3)\right )}+\frac {3 x \ln \relax (2)}{\left (3+\ln \relax (2)\right ) \left (\ln \relax (2)+\ln \relax (3)\right )}+\frac {3 x \ln \relax (3)}{\left (3+\ln \relax (2)\right ) \left (\ln \relax (2)+\ln \relax (3)\right )}-\frac {{\mathrm e}^{{\mathrm e}^{\frac {x \ln \relax (2)-2 \ln \relax (2)+6 x -5}{3+\ln \relax (2)}}} \ln \relax (2)}{\left (3+\ln \relax (2)\right ) \left (\ln \relax (2)+\ln \relax (3)\right )}-\frac {3 \,{\mathrm e}^{{\mathrm e}^{\frac {x \ln \relax (2)-2 \ln \relax (2)+6 x -5}{3+\ln \relax (2)}}}}{\left (3+\ln \relax (2)\right ) \left (\ln \relax (2)+\ln \relax (3)\right )}\) | \(152\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.45, size = 69, normalized size = 2.46 \begin {gather*} \frac {x {\left (\log \relax (2) + 3\right )} \log \relax (6) - {\left (\log \relax (2) + 3\right )} e^{\left (\frac {e^{\left (\frac {x \log \relax (2)}{\log \relax (2) + 3} + \frac {6 \, x}{\log \relax (2) + 3} - \frac {5}{\log \relax (2) + 3}\right )}}{2^{\frac {2}{\log \relax (2) + 3}}}\right )}}{{\left (\log \relax (2) + 3\right )} \log \relax (6)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.31, size = 61, normalized size = 2.18 \begin {gather*} x-\frac {{\mathrm {e}}^{\frac {2^{\frac {x}{\ln \relax (2)+3}}\,{\mathrm {e}}^{\frac {6\,x}{\ln \relax (2)+3}}\,{\mathrm {e}}^{-\frac {5}{\ln \relax (2)+3}}}{2^{\frac {2}{\ln \relax (2)+3}}}}\,\left (\ln \relax (2)+3\right )}{\ln \left (216\right )+\ln \relax (2)\,\ln \relax (6)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.27, size = 24, normalized size = 0.86 \begin {gather*} x - \frac {e^{e^{\frac {6 x + \left (x - 2\right ) \log {\relax (2 )} - 5}{\log {\relax (2 )} + 3}}}}{\log {\relax (6 )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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