Optimal. Leaf size=17 \[ \frac {(a+b \log (e x))^2}{2 b} \]
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Rubi [A] time = 0.01, antiderivative size = 17, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 12, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.083, Rules used = {2301} \[ \frac {(a+b \log (e x))^2}{2 b} \]
Antiderivative was successfully verified.
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Rule 2301
Rubi steps
\begin {align*} \int \frac {a+b \log (e x)}{x} \, dx &=\frac {(a+b \log (e x))^2}{2 b}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 16, normalized size = 0.94 \[ a \log (x)+\frac {1}{2} b \log ^2(e x) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.49, size = 16, normalized size = 0.94 \[ \frac {1}{2} \, b \log \left (e x\right )^{2} + a \log \left (e x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.17, size = 14, normalized size = 0.82 \[ \frac {1}{2} \, b \log \relax (x)^{2} + {\left (a + b\right )} \log \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 17, normalized size = 1.00 \[ \frac {b \ln \left (e x \right )^{2}}{2}+a \ln \left (e x \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.72, size = 15, normalized size = 0.88 \[ \frac {{\left (b \log \left (e x\right ) + a\right )}^{2}}{2 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.15, size = 14, normalized size = 0.82 \[ \frac {b\,{\ln \left (e\,x\right )}^2}{2}+a\,\ln \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.24, size = 14, normalized size = 0.82 \[ a \log {\relax (x )} + \frac {b \log {\left (e x \right )}^{2}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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