Optimal. Leaf size=19 \[ \frac{1}{3} \log (1-x)-\frac{1}{3} \log (x+2) \]
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Rubi [A] time = 0.0029557, antiderivative size = 19, 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} \[ \frac{1}{3} \log (1-x)-\frac{1}{3} \log (x+2) \]
Antiderivative was successfully verified.
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Rule 36
Rule 31
Rubi steps
\begin{align*} \int \frac{1}{(-1+x) (2+x)} \, dx &=\frac{1}{3} \int \frac{1}{-1+x} \, dx-\frac{1}{3} \int \frac{1}{2+x} \, dx\\ &=\frac{1}{3} \log (1-x)-\frac{1}{3} \log (2+x)\\ \end{align*}
Mathematica [A] time = 0.0024767, size = 19, normalized size = 1. \[ \frac{1}{3} \log (1-x)-\frac{1}{3} \log (x+2) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.004, size = 14, normalized size = 0.7 \begin{align*} -{\frac{\ln \left ( 2+x \right ) }{3}}+{\frac{\ln \left ( -1+x \right ) }{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.924871, size = 18, normalized size = 0.95 \begin{align*} -\frac{1}{3} \, \log \left (x + 2\right ) + \frac{1}{3} \, \log \left (x - 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.75034, size = 46, normalized size = 2.42 \begin{align*} -\frac{1}{3} \, \log \left (x + 2\right ) + \frac{1}{3} \, \log \left (x - 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.090317, size = 12, normalized size = 0.63 \begin{align*} \frac{\log{\left (x - 1 \right )}}{3} - \frac{\log{\left (x + 2 \right )}}{3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.07272, size = 20, normalized size = 1.05 \begin{align*} -\frac{1}{3} \, \log \left ({\left | x + 2 \right |}\right ) + \frac{1}{3} \, \log \left ({\left | x - 1 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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