Optimal. Leaf size=12 \[ x+(x+13) \log \left (\frac {1}{x+13}\right ) \]
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Rubi [A] time = 0.00, antiderivative size = 12, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 6, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.333, Rules used = {2389, 2295} \[ x+(x+13) \log \left (\frac {1}{x+13}\right ) \]
Antiderivative was successfully verified.
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Rule 2295
Rule 2389
Rubi steps
\begin {align*} \int \log \left (\frac {1}{13+x}\right ) \, dx &=\operatorname {Subst}\left (\int \log \left (\frac {1}{x}\right ) \, dx,x,13+x\right )\\ &=x+(13+x) \log \left (\frac {1}{13+x}\right )\\ \end {align*}
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Mathematica [A] time = 0.00, size = 12, normalized size = 1.00 \[ x+(x+13) \log \left (\frac {1}{x+13}\right ) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.43, size = 12, normalized size = 1.00 \[ {\left (x + 13\right )} \log \left (\frac {1}{x + 13}\right ) + x \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.17, size = 12, normalized size = 1.00 \[ -{\left (x + 13\right )} \log \left (x + 13\right ) + x + 13 \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.07, size = 14, normalized size = 1.17 \[ x +\left (x +13\right ) \ln \left (\frac {1}{x +13}\right )+13 \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.61, size = 12, normalized size = 1.00 \[ -{\left (x + 13\right )} \log \left (x + 13\right ) + x + 13 \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.05, size = 12, normalized size = 1.00 \[ \left (\ln \left (\frac {1}{x+13}\right )+1\right )\,\left (x+13\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.11, size = 15, normalized size = 1.25 \[ x \log {\left (\frac {1}{x + 13} \right )} + x - 13 \log {\left (x + 13 \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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