Optimal. Leaf size=47 \[ -\frac {1}{6} \left (9-5 \sqrt {6}\right ) \log \left (x-\sqrt {6}+1\right )-\frac {1}{6} \left (9+5 \sqrt {6}\right ) \log \left (x+\sqrt {6}+1\right ) \]
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Rubi [A] time = 0.03, antiderivative size = 47, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, integrand size = 16, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.125, Rules used = {632, 31} \[ -\frac {1}{6} \left (9-5 \sqrt {6}\right ) \log \left (x-\sqrt {6}+1\right )-\frac {1}{6} \left (9+5 \sqrt {6}\right ) \log \left (x+\sqrt {6}+1\right ) \]
Antiderivative was successfully verified.
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Rule 31
Rule 632
Rubi steps
\begin {align*} \int \frac {7-3 x}{-5+2 x+x^2} \, dx &=\frac {1}{6} \left (-9+5 \sqrt {6}\right ) \int \frac {1}{1-\sqrt {6}+x} \, dx-\frac {1}{6} \left (9+5 \sqrt {6}\right ) \int \frac {1}{1+\sqrt {6}+x} \, dx\\ &=-\frac {1}{6} \left (9-5 \sqrt {6}\right ) \log \left (1-\sqrt {6}+x\right )-\frac {1}{6} \left (9+5 \sqrt {6}\right ) \log \left (1+\sqrt {6}+x\right )\\ \end {align*}
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Mathematica [A] time = 0.04, size = 47, normalized size = 1.00 \[ \frac {1}{6} \left (5 \sqrt {6}-9\right ) \log \left (-x+\sqrt {6}-1\right )+\frac {1}{6} \left (-9-5 \sqrt {6}\right ) \log \left (x+\sqrt {6}+1\right ) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.84, size = 54, normalized size = 1.15 \[ \frac {5}{6} \, \sqrt {3} \sqrt {2} \log \left (-\frac {2 \, \sqrt {3} \sqrt {2} {\left (x + 1\right )} - x^{2} - 2 \, x - 7}{x^{2} + 2 \, x - 5}\right ) - \frac {3}{2} \, \log \left (x^{2} + 2 \, x - 5\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.18, size = 44, normalized size = 0.94 \[ \frac {5}{6} \, \sqrt {6} \log \left (\frac {{\left | 2 \, x - 2 \, \sqrt {6} + 2 \right |}}{{\left | 2 \, x + 2 \, \sqrt {6} + 2 \right |}}\right ) - \frac {3}{2} \, \log \left ({\left | x^{2} + 2 \, x - 5 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.05, size = 29, normalized size = 0.62 \[ -\frac {5 \sqrt {6}\, \arctanh \left (\frac {\left (2 x +2\right ) \sqrt {6}}{12}\right )}{3}-\frac {3 \ln \left (x^{2}+2 x -5\right )}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.96, size = 35, normalized size = 0.74 \[ \frac {5}{6} \, \sqrt {6} \log \left (\frac {x - \sqrt {6} + 1}{x + \sqrt {6} + 1}\right ) - \frac {3}{2} \, \log \left (x^{2} + 2 \, x - 5\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.13, size = 34, normalized size = 0.72 \[ \ln \left (x-\sqrt {6}+1\right )\,\left (\frac {5\,\sqrt {6}}{6}-\frac {3}{2}\right )-\ln \left (x+\sqrt {6}+1\right )\,\left (\frac {5\,\sqrt {6}}{6}+\frac {3}{2}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.12, size = 44, normalized size = 0.94 \[ - \left (\frac {3}{2} + \frac {5 \sqrt {6}}{6}\right ) \log {\left (x + 1 + \sqrt {6} \right )} - \left (\frac {3}{2} - \frac {5 \sqrt {6}}{6}\right ) \log {\left (x - \sqrt {6} + 1 \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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