Optimal. Leaf size=25 \[ e^x-x+2 \left (e^3+\log ^2\left (2-x+\log \left (\frac {5}{2}\right )\right )\right ) \]
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Rubi [A]
time = 0.13, antiderivative size = 21, normalized size of antiderivative = 0.84, number of steps
used = 6, number of rules used = 5, integrand size = 46, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.109, Rules used = {6820, 2225,
2437, 12, 2338} \begin {gather*} e^x-x+2 \log ^2\left (-x+2+\log \left (\frac {5}{2}\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2225
Rule 2338
Rule 2437
Rule 6820
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-1+e^x+\frac {4 \log \left (2-x+\log \left (\frac {5}{2}\right )\right )}{-2+x-\log \left (\frac {5}{2}\right )}\right ) \, dx\\ &=-x+4 \int \frac {\log \left (2-x+\log \left (\frac {5}{2}\right )\right )}{-2+x-\log \left (\frac {5}{2}\right )} \, dx+\int e^x \, dx\\ &=e^x-x-4 \text {Subst}\left (\int \frac {\left (2+\log \left (\frac {5}{2}\right )\right ) \log (x)}{x \left (-2-\log \left (\frac {5}{2}\right )\right )} \, dx,x,2-x+\log \left (\frac {5}{2}\right )\right )\\ &=e^x-x+4 \text {Subst}\left (\int \frac {\log (x)}{x} \, dx,x,2-x+\log \left (\frac {5}{2}\right )\right )\\ &=e^x-x+2 \log ^2\left (2-x+\log \left (\frac {5}{2}\right )\right )\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.02, size = 21, normalized size = 0.84 \begin {gather*} e^x-x+2 \log ^2\left (2-x+\log \left (\frac {5}{2}\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.59, size = 19, normalized size = 0.76
method | result | size |
default | \(-x +2 \ln \left (\ln \left (\frac {5}{2}\right )+2-x \right )^{2}+{\mathrm e}^{x}\) | \(19\) |
norman | \(-x +2 \ln \left (\ln \left (\frac {5}{2}\right )+2-x \right )^{2}+{\mathrm e}^{x}\) | \(19\) |
risch | \(2 \ln \left (\ln \left (5\right )-\ln \left (2\right )+2-x \right )^{2}-x +{\mathrm e}^{x}\) | \(23\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Failed to integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.38, size = 18, normalized size = 0.72 \begin {gather*} 2 \, \log \left (-x + \log \left (\frac {5}{2}\right ) + 2\right )^{2} - x + e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.09, size = 17, normalized size = 0.68 \begin {gather*} - x + e^{x} + 2 \log {\left (- x + \log {\left (\frac {5}{2} \right )} + 2 \right )}^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.41, size = 21, normalized size = 0.84 \begin {gather*} 2 \, \log \left (-x + \log \left (\frac {5}{2}\right ) + 2\right )^{2} - x + e^{x} + \log \left (\frac {5}{2}\right ) + 2 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 3.23, size = 18, normalized size = 0.72 \begin {gather*} 2\,{\ln \left (\ln \left (\frac {5}{2}\right )-x+2\right )}^2-x+{\mathrm {e}}^x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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