Optimal. Leaf size=24 \[ \frac {1}{2} e^{\frac {1+e^3}{4+e^x-x}} \log (4) \]
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Rubi [A]
time = 0.70, antiderivative size = 24, normalized size of antiderivative = 1.00, number of steps
used = 3, number of rules used = 3, integrand size = 69, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.043, Rules used = {6820, 12, 6838}
\begin {gather*} \frac {1}{2} e^{\frac {1+e^3}{-x+e^x+4}} \log (4) \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 6820
Rule 6838
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {e^{\frac {1+e^3}{4+e^x-x}} \left (1+e^3\right ) \left (1-e^x\right ) \log (4)}{2 \left (4+e^x-x\right )^2} \, dx\\ &=\frac {1}{2} \left (\left (1+e^3\right ) \log (4)\right ) \int \frac {e^{\frac {1+e^3}{4+e^x-x}} \left (1-e^x\right )}{\left (4+e^x-x\right )^2} \, dx\\ &=\frac {1}{2} e^{\frac {1+e^3}{4+e^x-x}} \log (4)\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.16, size = 24, normalized size = 1.00 \begin {gather*} \frac {1}{2} e^{\frac {1+e^3}{4+e^x-x}} \log (4) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.47, size = 19, normalized size = 0.79
method | result | size |
risch | \(\ln \left (2\right ) {\mathrm e}^{\frac {{\mathrm e}^{3}+1}{{\mathrm e}^{x}-x +4}}\) | \(19\) |
norman | \(\frac {x \ln \left (2\right ) {\mathrm e}^{\frac {{\mathrm e}^{3}+1}{{\mathrm e}^{x}-x +4}}-4 \ln \left (2\right ) {\mathrm e}^{\frac {{\mathrm e}^{3}+1}{{\mathrm e}^{x}-x +4}}-{\mathrm e}^{x} \ln \left (2\right ) {\mathrm e}^{\frac {{\mathrm e}^{3}+1}{{\mathrm e}^{x}-x +4}}}{x -{\mathrm e}^{x}-4}\) | \(71\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.60, size = 29, normalized size = 1.21 \begin {gather*} e^{\left (-\frac {e^{3}}{x - e^{x} - 4} - \frac {1}{x - e^{x} - 4}\right )} \log \left (2\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.39, size = 19, normalized size = 0.79 \begin {gather*} e^{\left (-\frac {e^{3} + 1}{x - e^{x} - 4}\right )} \log \left (2\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.18, size = 15, normalized size = 0.62 \begin {gather*} e^{\frac {1 + e^{3}}{- x + e^{x} + 4}} \log {\left (2 \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*} \text {could not integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 4.42, size = 18, normalized size = 0.75 \begin {gather*} {\mathrm {e}}^{\frac {{\mathrm {e}}^3+1}{{\mathrm {e}}^x-x+4}}\,\ln \left (2\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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