Optimal. Leaf size=10 \[ \log \left (b x+c x^2\right ) \]
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Rubi [A] time = 0.00, antiderivative size = 10, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 18, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.056, Rules used = {628} \[ \log \left (b x+c x^2\right ) \]
Antiderivative was successfully verified.
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Rule 628
Rubi steps
\begin {align*} \int \frac {b+2 c x}{b x+c x^2} \, dx &=\log \left (b x+c x^2\right )\\ \end {align*}
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Mathematica [A] time = 0.00, size = 9, normalized size = 0.90 \[ \log (b+c x)+\log (x) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.78, size = 10, normalized size = 1.00 \[ \log \left (c x^{2} + b x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.23, size = 11, normalized size = 1.10 \[ \log \left ({\left | c x^{2} + b x \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 9, normalized size = 0.90 \[ \ln \left (\left (c x +b \right ) x \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.55, size = 10, normalized size = 1.00 \[ \log \left (c x^{2} + b x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.05, size = 8, normalized size = 0.80 \[ \ln \left (x\,\left (b+c\,x\right )\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.13, size = 8, normalized size = 0.80 \[ \log {\left (b x + c x^{2} \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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