Optimal. Leaf size=9 \[ \log (x)-\log (x+1) \]
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Rubi [A] time = 0.00, antiderivative size = 9, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 3, integrand size = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.333, Rules used = {36, 29, 31} \[ \log (x)-\log (x+1) \]
Antiderivative was successfully verified.
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Rule 29
Rule 31
Rule 36
Rubi steps
\begin {align*} \int \frac {1}{x (1+x)} \, dx &=\int \frac {1}{x} \, dx-\int \frac {1}{1+x} \, dx\\ &=\log (x)-\log (1+x)\\ \end {align*}
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Mathematica [A] time = 0.00, size = 9, normalized size = 1.00 \[ \log (x)-\log (x+1) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.41, size = 9, normalized size = 1.00 \[ -\log \left (x + 1\right ) + \log \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.16, size = 11, normalized size = 1.22 \[ -\log \left ({\left | x + 1 \right |}\right ) + \log \left ({\left | x \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 10, normalized size = 1.11 \[ \ln \relax (x )-\ln \left (x +1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.42, size = 9, normalized size = 1.00 \[ -\log \left (x + 1\right ) + \log \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.20, size = 8, normalized size = 0.89 \[ -\ln \left (\frac {1}{x}+1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.09, size = 7, normalized size = 0.78 \[ \log {\relax (x )} - \log {\left (x + 1 \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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