Optimal. Leaf size=24 \[ -1+e^6-x-5 e^{2 x} x-\log (x \log (\log (x))) \]
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Rubi [A]
time = 0.75, antiderivative size = 37, normalized size of antiderivative = 1.54, number of steps
used = 9, number of rules used = 6, integrand size = 41, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.146, Rules used = {6874, 2207,
2225, 6820, 2339, 29} \begin {gather*} -x+\frac {5 e^{2 x}}{2}-\frac {5}{2} e^{2 x} (2 x+1)-\log (x)-\log (\log (\log (x))) \end {gather*}
Antiderivative was successfully verified.
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Rule 29
Rule 2207
Rule 2225
Rule 2339
Rule 6820
Rule 6874
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-5 e^{2 x} (1+2 x)+\frac {-1-\log (x) \log (\log (x))-x \log (x) \log (\log (x))}{x \log (x) \log (\log (x))}\right ) \, dx\\ &=-\left (5 \int e^{2 x} (1+2 x) \, dx\right )+\int \frac {-1-\log (x) \log (\log (x))-x \log (x) \log (\log (x))}{x \log (x) \log (\log (x))} \, dx\\ &=-\frac {5}{2} e^{2 x} (1+2 x)+5 \int e^{2 x} \, dx+\int \left (-1-\frac {1}{x}-\frac {1}{x \log (x) \log (\log (x))}\right ) \, dx\\ &=\frac {5 e^{2 x}}{2}-x-\frac {5}{2} e^{2 x} (1+2 x)-\log (x)-\int \frac {1}{x \log (x) \log (\log (x))} \, dx\\ &=\frac {5 e^{2 x}}{2}-x-\frac {5}{2} e^{2 x} (1+2 x)-\log (x)-\text {Subst}\left (\int \frac {1}{x \log (x)} \, dx,x,\log (x)\right )\\ &=\frac {5 e^{2 x}}{2}-x-\frac {5}{2} e^{2 x} (1+2 x)-\log (x)-\text {Subst}\left (\int \frac {1}{x} \, dx,x,\log (\log (x))\right )\\ &=\frac {5 e^{2 x}}{2}-x-\frac {5}{2} e^{2 x} (1+2 x)-\log (x)-\log (\log (\log (x)))\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.10, size = 22, normalized size = 0.92 \begin {gather*} -x-5 e^{2 x} x-\log (x)-\log (\log (\log (x))) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.13, size = 22, normalized size = 0.92
method | result | size |
default | \(-5 x \,{\mathrm e}^{2 x}-x -\ln \left (x \right )-\ln \left (\ln \left (\ln \left (x \right )\right )\right )\) | \(22\) |
risch | \(-5 x \,{\mathrm e}^{2 x}-x -\ln \left (x \right )-\ln \left (\ln \left (\ln \left (x \right )\right )\right )\) | \(22\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.26, size = 31, normalized size = 1.29 \begin {gather*} -\frac {5}{2} \, {\left (2 \, x - 1\right )} e^{\left (2 \, x\right )} - x - \frac {5}{2} \, e^{\left (2 \, x\right )} - \log \left (x\right ) - \log \left (\log \left (\log \left (x\right )\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.37, size = 21, normalized size = 0.88 \begin {gather*} -5 \, x e^{\left (2 \, x\right )} - x - \log \left (x\right ) - \log \left (\log \left (\log \left (x\right )\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.13, size = 20, normalized size = 0.83 \begin {gather*} - 5 x e^{2 x} - x - \log {\left (x \right )} - \log {\left (\log {\left (\log {\left (x \right )} \right )} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.42, size = 21, normalized size = 0.88 \begin {gather*} -5 \, x e^{\left (2 \, x\right )} - x - \log \left (x\right ) - \log \left (\log \left (\log \left (x\right )\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 2.28, size = 21, normalized size = 0.88 \begin {gather*} -x-\ln \left (\ln \left (\ln \left (x\right )\right )\right )-\ln \left (x\right )-5\,x\,{\mathrm {e}}^{2\,x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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