Optimal. Leaf size=20 \[ 8+x+x^2 \log \left (\frac {3 x}{-5+\frac {6 x}{5}}\right ) \]
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Rubi [A] time = 0.08, antiderivative size = 17, normalized size of antiderivative = 0.85, number of steps used = 7, number of rules used = 3, integrand size = 34, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.088, Rules used = {6742, 43, 2492} \begin {gather*} x^2 \log \left (-\frac {15 x}{25-6 x}\right )+x \end {gather*}
Antiderivative was successfully verified.
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Rule 43
Rule 2492
Rule 6742
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (\frac {-25-19 x}{-25+6 x}+2 x \log \left (\frac {15 x}{-25+6 x}\right )\right ) \, dx\\ &=2 \int x \log \left (\frac {15 x}{-25+6 x}\right ) \, dx+\int \frac {-25-19 x}{-25+6 x} \, dx\\ &=x^2 \log \left (-\frac {15 x}{25-6 x}\right )+25 \int \frac {x}{-25+6 x} \, dx+\int \left (-\frac {19}{6}-\frac {625}{6 (-25+6 x)}\right ) \, dx\\ &=-\frac {19 x}{6}-\frac {625}{36} \log (25-6 x)+x^2 \log \left (-\frac {15 x}{25-6 x}\right )+25 \int \left (\frac {1}{6}+\frac {25}{6 (-25+6 x)}\right ) \, dx\\ &=x+x^2 \log \left (-\frac {15 x}{25-6 x}\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.04, size = 17, normalized size = 0.85 \begin {gather*} x+x^2 \log \left (-\frac {15 x}{25-6 x}\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.68, size = 17, normalized size = 0.85 \begin {gather*} x^{2} \log \left (\frac {15 \, x}{6 \, x - 25}\right ) + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.17, size = 17, normalized size = 0.85 \begin {gather*} x^{2} \log \left (\frac {15 \, x}{6 \, x - 25}\right ) + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.24, size = 18, normalized size = 0.90
method | result | size |
norman | \(x +\ln \left (\frac {15 x}{6 x -25}\right ) x^{2}\) | \(18\) |
risch | \(x +\ln \left (\frac {15 x}{6 x -25}\right ) x^{2}\) | \(18\) |
derivativedivides | \(x -\frac {25}{6}-\frac {\ln \left (\frac {5}{2}+\frac {125}{2 \left (6 x -25\right )}\right ) \left (\frac {5}{2}+\frac {125}{2 \left (6 x -25\right )}\right ) \left (-\frac {5}{2}+\frac {125}{2 \left (6 x -25\right )}\right ) \left (6 x -25\right )^{2}}{225}+\frac {5 \ln \left (\frac {5}{2}+\frac {125}{2 \left (6 x -25\right )}\right ) \left (\frac {5}{2}+\frac {125}{2 \left (6 x -25\right )}\right ) \left (6 x -25\right )}{9}\) | \(77\) |
default | \(x -\frac {25}{6}-\frac {\ln \left (\frac {5}{2}+\frac {125}{2 \left (6 x -25\right )}\right ) \left (\frac {5}{2}+\frac {125}{2 \left (6 x -25\right )}\right ) \left (-\frac {5}{2}+\frac {125}{2 \left (6 x -25\right )}\right ) \left (6 x -25\right )^{2}}{225}+\frac {5 \ln \left (\frac {5}{2}+\frac {125}{2 \left (6 x -25\right )}\right ) \left (\frac {5}{2}+\frac {125}{2 \left (6 x -25\right )}\right ) \left (6 x -25\right )}{9}\) | \(77\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.51, size = 40, normalized size = 2.00 \begin {gather*} x^{2} {\left (\log \relax (5) + \log \relax (3)\right )} + x^{2} \log \relax (x) - \frac {1}{36} \, {\left (36 \, x^{2} - 625\right )} \log \left (6 \, x - 25\right ) + x - \frac {625}{36} \, \log \left (6 \, x - 25\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.54, size = 17, normalized size = 0.85 \begin {gather*} x+x^2\,\ln \left (\frac {15\,x}{6\,x-25}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.17, size = 14, normalized size = 0.70 \begin {gather*} x^{2} \log {\left (\frac {15 x}{6 x - 25} \right )} + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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