Optimal. Leaf size=19 \[ -9+x-\left (2-x^2\right )^2-x \log (x) \]
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Rubi [A]
time = 0.00, antiderivative size = 17, normalized size of antiderivative = 0.89, number of steps
used = 2, number of rules used = 1, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {2332}
\begin {gather*} -x^4+4 x^2+x-x \log (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 2332
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=4 x^2-x^4-\int \log (x) \, dx\\ &=x+4 x^2-x^4-x \log (x)\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.00, size = 17, normalized size = 0.89 \begin {gather*} x+4 x^2-x^4-x \log (x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.01, size = 18, normalized size = 0.95
method | result | size |
default | \(-x^{4}+4 x^{2}+x -x \ln \left (x \right )\) | \(18\) |
norman | \(-x^{4}+4 x^{2}+x -x \ln \left (x \right )\) | \(18\) |
risch | \(-x^{4}+4 x^{2}+x -x \ln \left (x \right )\) | \(18\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.25, size = 17, normalized size = 0.89 \begin {gather*} -x^{4} + 4 \, x^{2} - x \log \left (x\right ) + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.33, size = 17, normalized size = 0.89 \begin {gather*} -x^{4} + 4 \, x^{2} - x \log \left (x\right ) + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.04, size = 14, normalized size = 0.74 \begin {gather*} - x^{4} + 4 x^{2} - x \log {\left (x \right )} + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.41, size = 17, normalized size = 0.89 \begin {gather*} -x^{4} + 4 \, x^{2} - x \log \left (x\right ) + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 6.33, size = 16, normalized size = 0.84 \begin {gather*} x\,\left (4\,x-\ln \left (x\right )-x^3+1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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