Optimal. Leaf size=11 \[ \log \left (a+b x+c x^2\right ) \]
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Rubi [A]
time = 0.00, antiderivative size = 11, normalized size of antiderivative = 1.00, number of steps
used = 1, number of rules used = 1, integrand size = 19, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.053, Rules used = {642}
\begin {gather*} \log \left (a+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}{a+b x+c x^2} \, dx &=\log \left (a+b x+c x^2\right )\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 10, normalized size = 0.91 \begin {gather*} \log (a+x (b+c x)) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.34, size = 12, normalized size = 1.09
method | result | size |
derivativedivides | \(\ln \left (c \,x^{2}+b x +a \right )\) | \(12\) |
default | \(\ln \left (c \,x^{2}+b x +a \right )\) | \(12\) |
norman | \(\ln \left (c \,x^{2}+b x +a \right )\) | \(12\) |
risch | \(\ln \left (c \,x^{2}+b x +a \right )\) | \(12\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 11, normalized size = 1.00 \begin {gather*} \log \left (c x^{2} + b x + a\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.35, size = 11, normalized size = 1.00 \begin {gather*} \log \left (c x^{2} + b x + a\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.06, size = 10, normalized size = 0.91 \begin {gather*} \log {\left (a + 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 = 4.39, size = 12, normalized size = 1.09 \begin {gather*} \log \left ({\left | c x^{2} + b x + a \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.96, size = 11, normalized size = 1.00 \begin {gather*} \ln \left (c\,x^2+b\,x+a\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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