Optimal. Leaf size=18 \[ \frac {\log (x)}{b}-\frac {\log (b+c x)}{b} \]
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Rubi [A] time = 0.00, antiderivative size = 18, normalized size of antiderivative = 1.00, 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*}
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Mathematica [A] time = 0.00, size = 18, normalized size = 1.00 \[ \frac {\log (x)}{b}-\frac {\log (b+c x)}{b} \]
Antiderivative was successfully verified.
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fricas [A] time = 1.03, size = 16, normalized size = 0.89 \[ -\frac {\log \left (c x + b\right ) - \log \relax (x)}{b} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 20, normalized size = 1.11 \[ -\frac {\log \left ({\left | c x + b \right |}\right )}{b} + \frac {\log \left ({\left | x \right |}\right )}{b} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.05, size = 19, normalized size = 1.06 \[ \frac {\ln \relax (x )}{b}-\frac {\ln \left (c x +b \right )}{b} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.31, size = 18, normalized size = 1.00 \[ -\frac {\log \left (c x + b\right )}{b} + \frac {\log \relax (x)}{b} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.16, size = 15, normalized size = 0.83 \[ -\frac {2\,\mathrm {atanh}\left (\frac {2\,c\,x}{b}+1\right )}{b} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.15, size = 10, normalized size = 0.56 \[ \frac {\log {\relax (x )} - \log {\left (\frac {b}{c} + x \right )}}{b} \]
Verification of antiderivative is not currently implemented for this CAS.
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