Optimal. Leaf size=13 \[ 2 \log \left (\frac {1}{5+x^2+x^3}\right ) \]
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Rubi [A]
time = 0.01, antiderivative size = 11, normalized size of antiderivative = 0.85, number of steps
used = 1, number of rules used = 1, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {1601}
\begin {gather*} -2 \log \left (x^3+x^2+5\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 1601
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-2 \log \left (5+x^2+x^3\right )\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.00, size = 11, normalized size = 0.85 \begin {gather*} -2 \log \left (5+x^2+x^3\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.08, size = 12, normalized size = 0.92
method | result | size |
default | \(-2 \ln \left (x^{3}+x^{2}+5\right )\) | \(12\) |
norman | \(-2 \ln \left (x^{3}+x^{2}+5\right )\) | \(12\) |
risch | \(-2 \ln \left (x^{3}+x^{2}+5\right )\) | \(12\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.26, size = 11, normalized size = 0.85 \begin {gather*} -2 \, \log \left (x^{3} + x^{2} + 5\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.38, size = 11, normalized size = 0.85 \begin {gather*} -2 \, \log \left (x^{3} + x^{2} + 5\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.02, size = 12, normalized size = 0.92 \begin {gather*} - 2 \log {\left (x^{3} + x^{2} + 5 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.40, size = 12, normalized size = 0.92 \begin {gather*} -2 \, \log \left ({\left | x^{3} + x^{2} + 5 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.05, size = 11, normalized size = 0.85 \begin {gather*} -2\,\ln \left (x^3+x^2+5\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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