Optimal. Leaf size=27 \[ -e^x-x (4+x)+3 \left (1+e^{2 x}+x-\log (\log (x))\right ) \]
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Rubi [A] time = 0.21, antiderivative size = 26, normalized size of antiderivative = 0.96, number of steps used = 6, number of rules used = 4, integrand size = 36, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {6688, 2194, 2302, 29} \begin {gather*} -x^2-x-e^x+3 e^{2 x}-3 \log (\log (x)) \end {gather*}
Antiderivative was successfully verified.
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Rule 29
Rule 2194
Rule 2302
Rule 6688
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-1-e^x+6 e^{2 x}-2 x-\frac {3}{x \log (x)}\right ) \, dx\\ &=-x-x^2-3 \int \frac {1}{x \log (x)} \, dx+6 \int e^{2 x} \, dx-\int e^x \, dx\\ &=-e^x+3 e^{2 x}-x-x^2-3 \operatorname {Subst}\left (\int \frac {1}{x} \, dx,x,\log (x)\right )\\ &=-e^x+3 e^{2 x}-x-x^2-3 \log (\log (x))\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.02, size = 26, normalized size = 0.96 \begin {gather*} -e^x+3 e^{2 x}-x-x^2-3 \log (\log (x)) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.72, size = 24, normalized size = 0.89 \begin {gather*} -x^{2} - x + 3 \, e^{\left (2 \, x\right )} - e^{x} - 3 \, \log \left (\log \relax (x)\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.14, size = 24, normalized size = 0.89 \begin {gather*} -x^{2} - x + 3 \, e^{\left (2 \, x\right )} - e^{x} - 3 \, \log \left (\log \relax (x)\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 25, normalized size = 0.93
method | result | size |
default | \(-x^{2}-x +3 \,{\mathrm e}^{2 x}-3 \ln \left (\ln \relax (x )\right )-{\mathrm e}^{x}\) | \(25\) |
norman | \(-x^{2}-x +3 \,{\mathrm e}^{2 x}-3 \ln \left (\ln \relax (x )\right )-{\mathrm e}^{x}\) | \(25\) |
risch | \(-x^{2}-x +3 \,{\mathrm e}^{2 x}-3 \ln \left (\ln \relax (x )\right )-{\mathrm e}^{x}\) | \(25\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.36, size = 24, normalized size = 0.89 \begin {gather*} -x^{2} - x + 3 \, e^{\left (2 \, x\right )} - e^{x} - 3 \, \log \left (\log \relax (x)\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 5.94, size = 24, normalized size = 0.89 \begin {gather*} 3\,{\mathrm {e}}^{2\,x}-x-3\,\ln \left (\ln \relax (x)\right )-{\mathrm {e}}^x-x^2 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.29, size = 20, normalized size = 0.74 \begin {gather*} - x^{2} - x + 3 e^{2 x} - e^{x} - 3 \log {\left (\log {\relax (x )} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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