Optimal. Leaf size=11 \[ \log (x+1)-\log (x+2) \]
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Rubi [A] time = 0.0014919, antiderivative size = 11, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.182, Rules used = {36, 31} \[ \log (x+1)-\log (x+2) \]
Antiderivative was successfully verified.
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Rule 36
Rule 31
Rubi steps
\begin{align*} \int \frac{1}{(1+x) (2+x)} \, dx &=\int \frac{1}{1+x} \, dx-\int \frac{1}{2+x} \, dx\\ &=\log (1+x)-\log (2+x)\\ \end{align*}
Mathematica [A] time = 0.0028611, size = 11, normalized size = 1. \[ \log (x+1)-\log (x+2) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.004, size = 12, normalized size = 1.1 \begin{align*} \ln \left ( 1+x \right ) -\ln \left ( 2+x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.92628, size = 15, normalized size = 1.36 \begin{align*} -\log \left (x + 2\right ) + \log \left (x + 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.91272, size = 35, normalized size = 3.18 \begin{align*} -\log \left (x + 2\right ) + \log \left (x + 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.090856, size = 8, normalized size = 0.73 \begin{align*} \log{\left (x + 1 \right )} - \log{\left (x + 2 \right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.06296, size = 18, normalized size = 1.64 \begin{align*} -\log \left ({\left | x + 2 \right |}\right ) + \log \left ({\left | x + 1 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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