Optimal. Leaf size=8 \[ \frac{\log (x)}{a+b} \]
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Rubi [A] time = 0.0031854, antiderivative size = 8, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 3, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.333, Rules used = {6, 12, 29} \[ \frac{\log (x)}{a+b} \]
Antiderivative was successfully verified.
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Rule 6
Rule 12
Rule 29
Rubi steps
\begin{align*} \int \frac{1}{a x+b x} \, dx &=\int \frac{1}{(a+b) x} \, dx\\ &=\frac{\int \frac{1}{x} \, dx}{a+b}\\ &=\frac{\log (x)}{a+b}\\ \end{align*}
Mathematica [A] time = 0.0025627, size = 14, normalized size = 1.75 \[ \frac{\log (a x+b x)}{a+b} \]
Antiderivative was successfully verified.
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Maple [A] time = 0., size = 9, normalized size = 1.1 \begin{align*}{\frac{\ln \left ( x \right ) }{a+b}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.02556, size = 19, normalized size = 2.38 \begin{align*} \frac{\log \left (a x + b x\right )}{a + b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 0.84249, size = 22, normalized size = 2.75 \begin{align*} \frac{\log \left (x\right )}{a + b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.093372, size = 5, normalized size = 0.62 \begin{align*} \frac{\log{\left (x \right )}}{a + b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.18924, size = 20, normalized size = 2.5 \begin{align*} \frac{\log \left ({\left | a x + b x \right |}\right )}{a + b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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