Optimal. Leaf size=16 \[ \log \left (\frac {93}{7}\right )+\log (2-\log (5 (e+x))) \]
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Rubi [A]
time = 0.07, antiderivative size = 11, normalized size of antiderivative = 0.69, number of steps
used = 4, number of rules used = 4, integrand size = 21, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.190, Rules used = {6873, 2437,
2339, 29} \begin {gather*} \log (2-\log (5 (x+e))) \end {gather*}
Antiderivative was successfully verified.
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Rule 29
Rule 2339
Rule 2437
Rule 6873
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {1}{(-e-x) (2-\log (5 (e+x)))} \, dx\\ &=-\text {Subst}\left (\int \frac {1}{x (2-\log (5 x))} \, dx,x,e+x\right )\\ &=\text {Subst}\left (\int \frac {1}{x} \, dx,x,2-\log (5 (e+x))\right )\\ &=\log (2-\log (5 (e+x)))\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.02, size = 9, normalized size = 0.56 \begin {gather*} \log (-2+\log (5 (e+x))) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.03, size = 13, normalized size = 0.81
method | result | size |
derivativedivides | \(\ln \left (\ln \left (5 \,{\mathrm e}+5 x \right )-2\right )\) | \(13\) |
default | \(\ln \left (\ln \left (5 \,{\mathrm e}+5 x \right )-2\right )\) | \(13\) |
norman | \(\ln \left (\ln \left (5 \,{\mathrm e}+5 x \right )-2\right )\) | \(13\) |
risch | \(\ln \left (\ln \left (5 \,{\mathrm e}+5 x \right )-2\right )\) | \(13\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.46, size = 10, normalized size = 0.62 \begin {gather*} \log \left (\log \left (5\right ) + \log \left (x + e\right ) - 2\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.35, size = 12, normalized size = 0.75 \begin {gather*} \log \left (\log \left (5 \, x + 5 \, e\right ) - 2\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.05, size = 12, normalized size = 0.75 \begin {gather*} \log {\left (\log {\left (5 x + 5 e \right )} - 2 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.41, size = 12, normalized size = 0.75 \begin {gather*} \log \left (\log \left (5 \, x + 5 \, e\right ) - 2\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.51, size = 12, normalized size = 0.75 \begin {gather*} \ln \left (\ln \left (5\,x+5\,\mathrm {e}\right )-2\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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