Optimal. Leaf size=19 \[ \frac {1}{4} \log (1-x)-\frac {1}{4} \log (x+3) \]
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Rubi [A] time = 0.00, antiderivative size = 19, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, integrand size = 10, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.200, Rules used = {616, 31} \[ \frac {1}{4} \log (1-x)-\frac {1}{4} \log (x+3) \]
Antiderivative was successfully verified.
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Rule 31
Rule 616
Rubi steps
\begin {align*} \int \frac {1}{-3+2 x+x^2} \, dx &=\frac {1}{4} \int \frac {1}{-1+x} \, dx-\frac {1}{4} \int \frac {1}{3+x} \, dx\\ &=\frac {1}{4} \log (1-x)-\frac {1}{4} \log (3+x)\\ \end {align*}
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Mathematica [A] time = 0.00, size = 19, normalized size = 1.00 \[ \frac {1}{4} \log (1-x)-\frac {1}{4} \log (x+3) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.40, size = 13, normalized size = 0.68 \[ -\frac {1}{4} \, \log \left (x + 3\right ) + \frac {1}{4} \, \log \left (x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.84, size = 15, normalized size = 0.79 \[ -\frac {1}{4} \, \log \left ({\left | x + 3 \right |}\right ) + \frac {1}{4} \, \log \left ({\left | x - 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 14, normalized size = 0.74 \[ \frac {\ln \left (x -1\right )}{4}-\frac {\ln \left (x +3\right )}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.57, size = 13, normalized size = 0.68 \[ -\frac {1}{4} \, \log \left (x + 3\right ) + \frac {1}{4} \, \log \left (x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.08, size = 8, normalized size = 0.42 \[ -\frac {\mathrm {atanh}\left (\frac {x}{2}+\frac {1}{2}\right )}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.11, size = 12, normalized size = 0.63 \[ \frac {\log {\left (x - 1 \right )}}{4} - \frac {\log {\left (x + 3 \right )}}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
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