Optimal. Leaf size=13 \[ -\frac{\log \left (a+\frac{b}{x}\right )}{b} \]
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Rubi [A] time = 0.0038023, antiderivative size = 13, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077, Rules used = {260} \[ -\frac{\log \left (a+\frac{b}{x}\right )}{b} \]
Antiderivative was successfully verified.
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Rule 260
Rubi steps
\begin{align*} \int \frac{1}{\left (a+\frac{b}{x}\right ) x^2} \, dx &=-\frac{\log \left (a+\frac{b}{x}\right )}{b}\\ \end{align*}
Mathematica [A] time = 0.0034102, size = 18, normalized size = 1.38 \[ \frac{\log (x)}{b}-\frac{\log (a x+b)}{b} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 19, normalized size = 1.5 \begin{align*}{\frac{\ln \left ( x \right ) }{b}}-{\frac{\ln \left ( ax+b \right ) }{b}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.03593, size = 18, normalized size = 1.38 \begin{align*} -\frac{\log \left (a + \frac{b}{x}\right )}{b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.45474, size = 38, normalized size = 2.92 \begin{align*} -\frac{\log \left (a x + b\right ) - \log \left (x\right )}{b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.129191, size = 10, normalized size = 0.77 \begin{align*} \frac{\log{\left (x \right )} - \log{\left (x + \frac{b}{a} \right )}}{b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.10156, size = 19, normalized size = 1.46 \begin{align*} -\frac{\log \left ({\left | a + \frac{b}{x} \right |}\right )}{b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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