Optimal. Leaf size=13 \[ d \log \left (a+b x+c x^2\right ) \]
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Rubi [A] time = 0.00, antiderivative size = 13, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.045, Rules used = {628} \[ d \log \left (a+b x+c x^2\right ) \]
Antiderivative was successfully verified.
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Rule 628
Rubi steps
\begin {align*} \int \frac {b d+2 c d x}{a+b x+c x^2} \, dx &=d \log \left (a+b x+c x^2\right )\\ \end {align*}
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Mathematica [A] time = 0.00, size = 12, normalized size = 0.92 \[ d \log (a+x (b+c x)) \]
Antiderivative was successfully verified.
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fricas [A] time = 1.01, size = 13, normalized size = 1.00 \[ d \log \left (c x^{2} + b x + a\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.16, size = 21, normalized size = 1.62 \[ d \log \left ({\left | a + \frac {c d x^{2} + b d x}{d} \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 14, normalized size = 1.08 \[ d \ln \left (c \,x^{2}+b x +a \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.30, size = 13, normalized size = 1.00 \[ d \log \left (c x^{2} + b x + a\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 13, normalized size = 1.00 \[ d\,\ln \left (c\,x^2+b\,x+a\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.20, size = 12, normalized size = 0.92 \[ d \log {\left (a + b x + c x^{2} \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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