Optimal. Leaf size=28 \[ -a x+a x \log (x)-\frac {b x^2}{4}+\frac {1}{2} b x^2 \log (x) \]
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Rubi [A] time = 0.01, antiderivative size = 29, normalized size of antiderivative = 1.04, number of steps used = 2, number of rules used = 1, integrand size = 8, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.125, Rules used = {2313} \[ \frac {1}{2} \log (x) \left (2 a x+b x^2\right )-a x-\frac {b x^2}{4} \]
Antiderivative was successfully verified.
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Rule 2313
Rubi steps
\begin {align*} \int (a+b x) \log (x) \, dx &=\frac {1}{2} \left (2 a x+b x^2\right ) \log (x)-\int \left (a+\frac {b x}{2}\right ) \, dx\\ &=-a x-\frac {b x^2}{4}+\frac {1}{2} \left (2 a x+b x^2\right ) \log (x)\\ \end {align*}
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Mathematica [A] time = 0.00, size = 28, normalized size = 1.00 \[ -a x+a x \log (x)-\frac {b x^2}{4}+\frac {1}{2} b x^2 \log (x) \]
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int (a+b x) \log (x) \, dx \]
Verification is Not applicable to the result.
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fricas [A] time = 1.05, size = 25, normalized size = 0.89 \[ -\frac {1}{4} \, b x^{2} - a x + \frac {1}{2} \, {\left (b x^{2} + 2 \, a x\right )} \log \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.58, size = 24, normalized size = 0.86 \[ \frac {1}{2} \, b x^{2} \log \relax (x) - \frac {1}{4} \, b x^{2} + a x \log \relax (x) - a x \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 25, normalized size = 0.89
method | result | size |
norman | \(-a x -\frac {b \,x^{2}}{4}+a x \ln \relax (x )+\frac {b \,x^{2} \ln \relax (x )}{2}\) | \(25\) |
risch | \(\left (\frac {1}{2} b \,x^{2}+a x \right ) \ln \relax (x )-\frac {b \,x^{2}}{4}-a x\) | \(25\) |
default | \(b \left (\frac {x^{2} \ln \relax (x )}{2}-\frac {x^{2}}{4}\right )+a \left (x \ln \relax (x )-x \right )\) | \(27\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.42, size = 25, normalized size = 0.89 \[ -\frac {1}{4} \, b x^{2} - a x + \frac {1}{2} \, {\left (b x^{2} + 2 \, a x\right )} \log \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.33, size = 21, normalized size = 0.75 \[ -\frac {x\,\left (4\,a+b\,x-4\,a\,\ln \relax (x)-2\,b\,x\,\ln \relax (x)\right )}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.11, size = 22, normalized size = 0.79 \[ - a x - \frac {b x^{2}}{4} + \left (a x + \frac {b x^{2}}{2}\right ) \log {\relax (x )} \]
Verification of antiderivative is not currently implemented for this CAS.
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