Optimal. Leaf size=9 \[ \log (x)-\log (x+1) \]
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Rubi [A] time = 0.0009658, antiderivative size = 9, normalized size of antiderivative = 1., 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 36
Rule 29
Rule 31
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*}
Mathematica [A] time = 0.0020154, size = 9, normalized size = 1. \[ \log (x)-\log (x+1) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 10, normalized size = 1.1 \begin{align*} \ln \left ( x \right ) -\ln \left ( 1+x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.949721, size = 12, normalized size = 1.33 \begin{align*} -\log \left (x + 1\right ) + \log \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.55904, size = 30, normalized size = 3.33 \begin{align*} -\log \left (x + 1\right ) + \log \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.085563, size = 7, normalized size = 0.78 \begin{align*} \log{\left (x \right )} - \log{\left (x + 1 \right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.07695, size = 15, normalized size = 1.67 \begin{align*} -\log \left ({\left | x + 1 \right |}\right ) + \log \left ({\left | x \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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