Optimal. Leaf size=15 \[ 2 \log (1-x)-\log (x+2) \]
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Rubi [A] time = 0.00, antiderivative size = 15, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, integrand size = 12, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.167, Rules used = {632, 31} \[ 2 \log (1-x)-\log (x+2) \]
Antiderivative was successfully verified.
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Rule 31
Rule 632
Rubi steps
\begin {align*} \int \frac {5+x}{-2+x+x^2} \, dx &=2 \int \frac {1}{-1+x} \, dx-\int \frac {1}{2+x} \, dx\\ &=2 \log (1-x)-\log (2+x)\\ \end {align*}
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Mathematica [A] time = 0.00, size = 15, normalized size = 1.00 \[ 2 \log (1-x)-\log (x+2) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.38, size = 13, normalized size = 0.87 \[ -\log \left (x + 2\right ) + 2 \, \log \left (x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.78, size = 15, normalized size = 1.00 \[ -\log \left ({\left | x + 2 \right |}\right ) + 2 \, \log \left ({\left | x - 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 14, normalized size = 0.93 \[ 2 \ln \left (x -1\right )-\ln \left (x +2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.43, size = 13, normalized size = 0.87 \[ -\log \left (x + 2\right ) + 2 \, \log \left (x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.18, size = 13, normalized size = 0.87 \[ 2\,\ln \left (x-1\right )-\ln \left (x+2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.10, size = 10, normalized size = 0.67 \[ 2 \log {\left (x - 1 \right )} - \log {\left (x + 2 \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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