Optimal. Leaf size=18 \[ \frac{\log (x)}{b}-\frac{\log (b+c x)}{b} \]
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Rubi [A] time = 0.0030771, antiderivative size = 18, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091, Rules used = {615} \[ \frac{\log (x)}{b}-\frac{\log (b+c x)}{b} \]
Antiderivative was successfully verified.
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Rule 615
Rubi steps
\begin{align*} \int \frac{1}{b x+c x^2} \, dx &=\frac{\log (x)}{b}-\frac{\log (b+c x)}{b}\\ \end{align*}
Mathematica [A] time = 0.0032633, size = 18, normalized size = 1. \[ \frac{\log (x)}{b}-\frac{\log (b+c x)}{b} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.045, size = 19, normalized size = 1.1 \begin{align*}{\frac{\ln \left ( x \right ) }{b}}-{\frac{\ln \left ( cx+b \right ) }{b}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.11035, size = 24, normalized size = 1.33 \begin{align*} -\frac{\log \left (c x + b\right )}{b} + \frac{\log \left (x\right )}{b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.65764, size = 38, normalized size = 2.11 \begin{align*} -\frac{\log \left (c 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 = 0.589893, size = 10, normalized size = 0.56 \begin{align*} \frac{\log{\left (x \right )} - \log{\left (\frac{b}{c} + x \right )}}{b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.26521, size = 27, normalized size = 1.5 \begin{align*} -\frac{\log \left ({\left | c x + b \right |}\right )}{b} + \frac{\log \left ({\left | x \right |}\right )}{b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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