Optimal. Leaf size=28 \[ -a x-\frac {b x^2}{4}+a x \log (x)+\frac {1}{2} b x^2 \log (x) \]
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Rubi [A]
time = 0.01, antiderivative size = 28, normalized size of antiderivative = 1.00, 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 = {2350}
\begin {gather*} -a x+a x \log (x)-\frac {b x^2}{4}+\frac {1}{2} b x^2 \log (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 2350
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 \begin {gather*} -a x-\frac {b x^2}{4}+a x \log (x)+\frac {1}{2} b x^2 \log (x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.01, size = 27, normalized size = 0.96
method | result | size |
norman | \(-a x -\frac {x^{2} b}{4}+a x \ln \left (x \right )+\frac {b \,x^{2} \ln \left (x \right )}{2}\) | \(25\) |
risch | \(\left (\frac {1}{2} x^{2} b +a x \right ) \ln \left (x \right )-\frac {x^{2} b}{4}-a x\) | \(25\) |
default | \(b \left (-\frac {x^{2}}{4}+\frac {x^{2} \ln \left (x \right )}{2}\right )+a \left (-x +x \ln \left (x \right )\right )\) | \(27\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 1.46, size = 25, normalized size = 0.89 \begin {gather*} -\frac {1}{4} \, b x^{2} - a x + \frac {1}{2} \, {\left (b x^{2} + 2 \, a x\right )} \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.63, size = 25, normalized size = 0.89 \begin {gather*} -\frac {1}{4} \, b x^{2} - a x + \frac {1}{2} \, {\left (b x^{2} + 2 \, a x\right )} \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.04, size = 22, normalized size = 0.79 \begin {gather*} - a x - \frac {b x^{2}}{4} + \left (a x + \frac {b x^{2}}{2}\right ) \log {\left (x \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.93, size = 24, normalized size = 0.86 \begin {gather*} \frac {1}{2} \, b x^{2} \log \left (x\right ) - \frac {1}{4} \, b x^{2} + a x \log \left (x\right ) - a x \end {gather*}
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 \begin {gather*} -\frac {x\,\left (4\,a+b\,x-4\,a\,\ln \left (x\right )-2\,b\,x\,\ln \left (x\right )\right )}{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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