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 = {642}
\begin {gather*} \log \left (b x+c x^2\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 642
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 \begin {gather*} \log (x)+\log (b+c x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.19, size = 9, normalized size = 0.90
method | result | size |
default | \(\ln \left (x \left (c x +b \right )\right )\) | \(9\) |
norman | \(\ln \left (x \right )+\ln \left (c x +b \right )\) | \(10\) |
derivativedivides | \(\ln \left (c \,x^{2}+b x \right )\) | \(11\) |
risch | \(\ln \left (c \,x^{2}+b x \right )\) | \(11\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 10, normalized size = 1.00 \begin {gather*} \log \left (c x^{2} + b x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.37, size = 10, normalized size = 1.00 \begin {gather*} \log \left (c x^{2} + b x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.04, size = 8, normalized size = 0.80 \begin {gather*} \log {\left (b x + c x^{2} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 4.37, size = 11, normalized size = 1.10 \begin {gather*} \log \left ({\left | c x^{2} + b x \right |}\right ) \end {gather*}
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 \begin {gather*} \ln \left (x\,\left (b+c\,x\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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