Optimal. Leaf size=21 \[ -\frac {1}{5} \log (1-3 x)+\frac {1}{5} \log (2-x) \]
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Rubi [A]
time = 0.00, 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 = {630, 31}
\begin {gather*} \frac {1}{5} \log (2-x)-\frac {1}{5} \log (1-3 x) \end {gather*}
Antiderivative was successfully verified.
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Rule 31
Rule 630
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 \begin {gather*} -\frac {1}{5} \log (1-3 x)+\frac {1}{5} \log (2-x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.08, size = 16, normalized size = 0.76
method | result | size |
default | \(\frac {\ln \left (-2+x \right )}{5}-\frac {\ln \left (3 x -1\right )}{5}\) | \(16\) |
norman | \(\frac {\ln \left (-2+x \right )}{5}-\frac {\ln \left (3 x -1\right )}{5}\) | \(16\) |
risch | \(\frac {\ln \left (-2+x \right )}{5}-\frac {\ln \left (3 x -1\right )}{5}\) | \(16\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 2.57, size = 15, normalized size = 0.71 \begin {gather*} -\frac {1}{5} \, \log \left (3 \, x - 1\right ) + \frac {1}{5} \, \log \left (x - 2\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.40, size = 15, normalized size = 0.71 \begin {gather*} -\frac {1}{5} \, \log \left (3 \, x - 1\right ) + \frac {1}{5} \, \log \left (x - 2\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.03, size = 14, normalized size = 0.67 \begin {gather*} \frac {\log {\left (x - 2 \right )}}{5} - \frac {\log {\left (x - \frac {1}{3} \right )}}{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.09, size = 17, normalized size = 0.81 \begin {gather*} -\frac {1}{5} \, \log \left ({\left | 3 \, x - 1 \right |}\right ) + \frac {1}{5} \, \log \left ({\left | x - 2 \right |}\right ) \end {gather*}
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 \begin {gather*} -\frac {2\,\mathrm {atanh}\left (\frac {6\,x}{5}-\frac {7}{5}\right )}{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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