Optimal. Leaf size=21 \[ \frac {1}{5} \log (2-x)-\frac {1}{5} \log (1-3 x) \]
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Rubi [A] time = 0.01, antiderivative size = 21, 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 = {616, 31} \[ \frac {1}{5} \log (2-x)-\frac {1}{5} \log (1-3 x) \]
Antiderivative was successfully verified.
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Rule 31
Rule 616
Rubi steps
\begin {align*} \int \frac {1}{2-7 x+3 x^2} \, dx &=\frac {3}{5} \int \frac {1}{-6+3 x} \, dx-\frac {3}{5} \int \frac {1}{-1+3 x} \, dx\\ &=-\frac {1}{5} \log (1-3 x)+\frac {1}{5} \log (2-x)\\ \end {align*}
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Mathematica [A] time = 0.00, size = 21, normalized size = 1.00 \[ \frac {1}{5} \log (2-x)-\frac {1}{5} \log (1-3 x) \]
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 0.01, size = 19, normalized size = 0.90 \[ \frac {1}{5} \log (x-2)-\frac {1}{5} \log (3 x-1) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.78, size = 15, normalized size = 0.71 \[ -\frac {1}{5} \, \log \left (3 \, x - 1\right ) + \frac {1}{5} \, \log \left (x - 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.82, size = 17, normalized size = 0.81 \[ -\frac {1}{5} \, \log \left ({\left | 3 \, x - 1 \right |}\right ) + \frac {1}{5} \, \log \left ({\left | x - 2 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.28, size = 16, normalized size = 0.76
method | result | size |
default | \(-\frac {\ln \left (-1+3 x \right )}{5}+\frac {\ln \left (-2+x \right )}{5}\) | \(16\) |
norman | \(-\frac {\ln \left (-1+3 x \right )}{5}+\frac {\ln \left (-2+x \right )}{5}\) | \(16\) |
risch | \(-\frac {\ln \left (-1+3 x \right )}{5}+\frac {\ln \left (-2+x \right )}{5}\) | \(16\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.43, size = 15, normalized size = 0.71 \[ -\frac {1}{5} \, \log \left (3 \, x - 1\right ) + \frac {1}{5} \, \log \left (x - 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.09, size = 8, normalized size = 0.38 \[ -\frac {2\,\mathrm {atanh}\left (\frac {6\,x}{5}-\frac {7}{5}\right )}{5} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.11, size = 14, normalized size = 0.67 \[ \frac {\log {\left (x - 2 \right )}}{5} - \frac {\log {\left (x - \frac {1}{3} \right )}}{5} \]
Verification of antiderivative is not currently implemented for this CAS.
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