Optimal. Leaf size=19 \[ \log \left (x \left (2-x-9 \left (4-x^2\right )^2\right )\right ) \]
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Rubi [A]
time = 0.02, antiderivative size = 18, normalized size of antiderivative = 0.95, number of steps
used = 1, number of rules used = 1, integrand size = 35, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.029, Rules used = {1601}
\begin {gather*} \log \left (9 x^5-72 x^3+x^2+142 x\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 1601
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\log \left (142 x+x^2-72 x^3+9 x^5\right )\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.01, size = 17, normalized size = 0.89 \begin {gather*} \log (x)+\log \left (142+x-72 x^2+9 x^4\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.16, size = 17, normalized size = 0.89
method | result | size |
default | \(\ln \left (x \left (9 x^{4}-72 x^{2}+x +142\right )\right )\) | \(17\) |
derivativedivides | \(\ln \left (9 x^{5}-72 x^{3}+x^{2}+142 x \right )\) | \(19\) |
risch | \(\ln \left (9 x^{5}-72 x^{3}+x^{2}+142 x \right )\) | \(19\) |
norman | \(\ln \left (x \right )+\ln \left (x -2\right )+\ln \left (9 x^{3}+18 x^{2}-36 x -71\right )\) | \(24\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 18, normalized size = 0.95 \begin {gather*} \log \left (9 \, x^{5} - 72 \, x^{3} + x^{2} + 142 \, x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.40, size = 18, normalized size = 0.95 \begin {gather*} \log \left (9 \, x^{5} - 72 \, x^{3} + x^{2} + 142 \, x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.03, size = 17, normalized size = 0.89 \begin {gather*} \log {\left (9 x^{5} - 72 x^{3} + x^{2} + 142 x \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.40, size = 19, normalized size = 1.00 \begin {gather*} \log \left ({\left | 9 \, x^{5} - 72 \, x^{3} + x^{2} + 142 \, x \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.18, size = 16, normalized size = 0.84 \begin {gather*} \ln \left (x\,\left (9\,x^4-72\,x^2+x+142\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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