Optimal. Leaf size=10 \[ \frac{\log (a x+b)}{a} \]
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Rubi [A] time = 0.0035947, antiderivative size = 10, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154, Rules used = {263, 31} \[ \frac{\log (a x+b)}{a} \]
Antiderivative was successfully verified.
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Rule 263
Rule 31
Rubi steps
\begin{align*} \int \frac{1}{\left (a+\frac{b}{x}\right ) x} \, dx &=\int \frac{1}{b+a x} \, dx\\ &=\frac{\log (b+a x)}{a}\\ \end{align*}
Mathematica [A] time = 0.0009955, size = 10, normalized size = 1. \[ \frac{\log (a x+b)}{a} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 11, normalized size = 1.1 \begin{align*}{\frac{\ln \left ( ax+b \right ) }{a}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.992188, size = 14, normalized size = 1.4 \begin{align*} \frac{\log \left (a x + b\right )}{a} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.4874, size = 22, normalized size = 2.2 \begin{align*} \frac{\log \left (a x + b\right )}{a} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.062468, size = 7, normalized size = 0.7 \begin{align*} \frac{\log{\left (a x + b \right )}}{a} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.13985, size = 15, normalized size = 1.5 \begin{align*} \frac{\log \left ({\left | a x + b \right |}\right )}{a} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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