Optimal. Leaf size=28 \[ -\frac {a x^2}{4}+\frac {1}{2} a x^2 \log (x)-b x+b x \log (x) \]
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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} \[ \frac {1}{2} \log (x) \left (a x^2+2 b x\right )-\frac {a x^2}{4}-b x \]
Antiderivative was successfully verified.
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Rule 2313
Rubi steps
\begin {align*} \int (b+a x) \log (x) \, dx &=\frac {1}{2} \left (2 b x+a x^2\right ) \log (x)-\int \left (b+\frac {a x}{2}\right ) \, dx\\ &=-b x-\frac {a x^2}{4}+\frac {1}{2} \left (2 b x+a x^2\right ) \log (x)\\ \end {align*}
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Mathematica [A] time = 0.00, size = 28, normalized size = 1.00 \[ -\frac {a x^2}{4}+\frac {1}{2} a x^2 \log (x)-b x+b x \log (x) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.44, size = 25, normalized size = 0.89 \[ -\frac {1}{4} \, a x^{2} - b x + \frac {1}{2} \, {\left (a x^{2} + 2 \, b x\right )} \log \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.18, size = 24, normalized size = 0.86 \[ \frac {1}{2} \, a x^{2} \log \relax (x) - \frac {1}{4} \, a x^{2} + b x \log \relax (x) - b x \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 25, normalized size = 0.89 \[ \frac {a \,x^{2} \ln \relax (x )}{2}-\frac {a \,x^{2}}{4}+b x \ln \relax (x )-b x \]
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 \[ -\frac {1}{4} \, a x^{2} - b x + \frac {1}{2} \, {\left (a x^{2} + 2 \, b x\right )} \log \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.14, size = 21, normalized size = 0.75 \[ -\frac {x\,\left (4\,b+a\,x-4\,b\,\ln \relax (x)-2\,a\,x\,\ln \relax (x)\right )}{4} \]
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 \[ - \frac {a x^{2}}{4} - b x + \left (\frac {a x^{2}}{2} + b x\right ) \log {\relax (x )} \]
Verification of antiderivative is not currently implemented for this CAS.
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