Optimal. Leaf size=17 \[ e^{2 x} \log (\log (5)+e (11+x+\log (x))) \]
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Rubi [A]
time = 0.13, antiderivative size = 19, normalized size of antiderivative = 1.12, number of steps
used = 2, number of rules used = 2, integrand size = 84, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.024, Rules used = {6820, 2326}
\begin {gather*} e^{2 x} \log (e (x+11)+e \log (x)+\log (5)) \end {gather*}
Antiderivative was successfully verified.
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Rule 2326
Rule 6820
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int e^{2 x} \left (\frac {e (1+x)}{x (e (11+x)+\log (5)+e \log (x))}+2 \log (e (11+x)+\log (5)+e \log (x))\right ) \, dx\\ &=e^{2 x} \log (e (11+x)+\log (5)+e \log (x))\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.04, size = 19, normalized size = 1.12 \begin {gather*} e^{2 x} \log (e (11+x)+\log (5)+e \log (x)) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.74, size = 21, normalized size = 1.24
method | result | size |
risch | \(\ln \left ({\mathrm e} \ln \left (x \right )+\ln \left (5\right )+\left (11+x \right ) {\mathrm e}\right ) {\mathrm e}^{2 x}\) | \(21\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.53, size = 22, normalized size = 1.29 \begin {gather*} e^{\left (2 \, x\right )} \log \left (x e + e \log \left (x\right ) + 11 \, e + \log \left (5\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.37, size = 20, normalized size = 1.18 \begin {gather*} e^{\left (2 \, x\right )} \log \left ({\left (x + 11\right )} e + e \log \left (x\right ) + \log \left (5\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 2.65, size = 22, normalized size = 1.29 \begin {gather*} e^{2 x} \log {\left (e \left (x + 11\right ) + e \log {\left (x \right )} + \log {\left (5 \right )} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.42, size = 22, normalized size = 1.29 \begin {gather*} e^{\left (2 \, x\right )} \log \left (x e + e \log \left (x\right ) + 11 \, e + \log \left (5\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [F]
time = 0.00, size = -1, normalized size = -0.06 \begin {gather*} \int \frac {\ln \left (\ln \left (5\right )+\mathrm {e}\,\left (x+11\right )+\mathrm {e}\,\ln \left (x\right )\right )\,\left ({\mathrm {e}}^{2\,x}\,\left (\mathrm {e}\,\left (2\,x^2+22\,x\right )+2\,x\,\ln \left (5\right )\right )+2\,x\,{\mathrm {e}}^{2\,x+1}\,\ln \left (x\right )\right )+{\mathrm {e}}^{2\,x+1}\,\left (x+1\right )}{x\,\ln \left (5\right )+\mathrm {e}\,\left (x^2+11\,x\right )+x\,\mathrm {e}\,\ln \left (x\right )} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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