Optimal. Leaf size=20 \[ 3+\log \left (3 e^{-e^4} x \left (\frac {3}{x}+x\right )\right ) \]
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Rubi [A] time = 0.00, antiderivative size = 6, normalized size of antiderivative = 0.30, number of steps used = 2, number of rules used = 2, integrand size = 10, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.200, Rules used = {12, 260} \begin {gather*} \log \left (x^2+3\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 260
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=2 \int \frac {x}{3+x^2} \, dx\\ &=\log \left (3+x^2\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 6, normalized size = 0.30 \begin {gather*} \log \left (3+x^2\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.66, size = 6, normalized size = 0.30 \begin {gather*} \log \left (x^{2} + 3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.25, size = 6, normalized size = 0.30 \begin {gather*} \log \left (x^{2} + 3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.40, size = 7, normalized size = 0.35
method | result | size |
derivativedivides | \(\ln \left (x^{2}+3\right )\) | \(7\) |
default | \(\ln \left (x^{2}+3\right )\) | \(7\) |
norman | \(\ln \left (x^{2}+3\right )\) | \(7\) |
risch | \(\ln \left (x^{2}+3\right )\) | \(7\) |
meijerg | \(\ln \left (1+\frac {x^{2}}{3}\right )\) | \(9\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.37, size = 6, normalized size = 0.30 \begin {gather*} \log \left (x^{2} + 3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.05, size = 6, normalized size = 0.30 \begin {gather*} \ln \left (x^2+3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.07, size = 5, normalized size = 0.25 \begin {gather*} \log {\left (x^{2} + 3 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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