Optimal. Leaf size=12 \[ x \left (-5+\log \left (3-\frac {13 x}{2}\right )\right ) \]
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Rubi [B] time = 0.07, antiderivative size = 31, normalized size of antiderivative = 2.58, number of steps used = 6, number of rules used = 4, integrand size = 29, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.138, Rules used = {6742, 43, 2389, 2295} \begin {gather*} -5 x+\frac {6}{13} \log (6-13 x)-\frac {1}{13} (6-13 x) \log \left (3-\frac {13 x}{2}\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 43
Rule 2295
Rule 2389
Rule 6742
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-\frac {2 (-15+26 x)}{-6+13 x}+\log \left (3-\frac {13 x}{2}\right )\right ) \, dx\\ &=-\left (2 \int \frac {-15+26 x}{-6+13 x} \, dx\right )+\int \log \left (3-\frac {13 x}{2}\right ) \, dx\\ &=-\left (\frac {2}{13} \operatorname {Subst}\left (\int \log (x) \, dx,x,3-\frac {13 x}{2}\right )\right )-2 \int \left (2-\frac {3}{-6+13 x}\right ) \, dx\\ &=-5 x+\frac {6}{13} \log (6-13 x)-\frac {1}{13} (6-13 x) \log \left (3-\frac {13 x}{2}\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.03, size = 22, normalized size = 1.83 \begin {gather*} \frac {6 \log (2)}{13}-x (5+\log (2))+x \log (6-13 x) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.59, size = 12, normalized size = 1.00 \begin {gather*} x \log \left (-\frac {13}{2} \, x + 3\right ) - 5 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.16, size = 12, normalized size = 1.00 \begin {gather*} x \log \left (-\frac {13}{2} \, x + 3\right ) - 5 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.46, size = 13, normalized size = 1.08
method | result | size |
norman | \(\ln \left (-\frac {13 x}{2}+3\right ) x -5 x\) | \(13\) |
risch | \(\ln \left (-\frac {13 x}{2}+3\right ) x -5 x\) | \(13\) |
derivativedivides | \(-\frac {2 \left (-\frac {13 x}{2}+3\right ) \ln \left (-\frac {13 x}{2}+3\right )}{13}-5 x +\frac {30}{13}+\frac {6 \ln \left (-\frac {13 x}{2}+3\right )}{13}\) | \(27\) |
default | \(-\frac {2 \left (-\frac {13 x}{2}+3\right ) \ln \left (-\frac {13 x}{2}+3\right )}{13}-5 x +\frac {30}{13}+\frac {6 \ln \left (-\frac {13 x}{2}+3\right )}{13}\) | \(27\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.48, size = 54, normalized size = 4.50 \begin {gather*} -\frac {3}{13} \, \log \left (13 \, x - 6\right )^{2} + \frac {1}{13} \, {\left (13 \, x + 6 \, \log \left (13 \, x - 6\right )\right )} \log \left (-\frac {13}{2} \, x + 3\right ) + \frac {6}{13} \, \log \relax (2) \log \left (-13 \, x + 6\right ) - \frac {3}{13} \, \log \left (-13 \, x + 6\right )^{2} - 5 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.10, size = 10, normalized size = 0.83 \begin {gather*} x\,\left (\ln \left (3-\frac {13\,x}{2}\right )-5\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.10, size = 12, normalized size = 1.00 \begin {gather*} x \log {\left (3 - \frac {13 x}{2} \right )} - 5 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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