Optimal. Leaf size=22 \[ 2 \log \left (2+x+3 \left (-3-x+\frac {x^2}{5}\right )^2\right ) \]
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Rubi [A]
time = 0.02, antiderivative size = 23, normalized size of antiderivative = 1.05, number of steps
used = 1, number of rules used = 1, integrand size = 38, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.026, Rules used = {1601}
\begin {gather*} 2 \log \left (3 x^4-30 x^3-15 x^2+475 x+725\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 1601
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=2 \log \left (725+475 x-15 x^2-30 x^3+3 x^4\right )\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.01, size = 23, normalized size = 1.05 \begin {gather*} 2 \log \left (725+475 x-15 x^2-30 x^3+3 x^4\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.01, size = 24, normalized size = 1.09
method | result | size |
default | \(2 \ln \left (3 x^{4}-30 x^{3}-15 x^{2}+475 x +725\right )\) | \(24\) |
norman | \(2 \ln \left (3 x^{4}-30 x^{3}-15 x^{2}+475 x +725\right )\) | \(24\) |
risch | \(2 \ln \left (3 x^{4}-30 x^{3}-15 x^{2}+475 x +725\right )\) | \(24\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 23, normalized size = 1.05 \begin {gather*} 2 \, \log \left (3 \, x^{4} - 30 \, x^{3} - 15 \, x^{2} + 475 \, x + 725\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.33, size = 23, normalized size = 1.05 \begin {gather*} 2 \, \log \left (3 \, x^{4} - 30 \, x^{3} - 15 \, x^{2} + 475 \, x + 725\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.04, size = 22, normalized size = 1.00 \begin {gather*} 2 \log {\left (3 x^{4} - 30 x^{3} - 15 x^{2} + 475 x + 725 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.39, size = 24, normalized size = 1.09 \begin {gather*} 2 \, \log \left ({\left | 3 \, x^{4} - 30 \, x^{3} - 15 \, x^{2} + 475 \, x + 725 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.10, size = 21, normalized size = 0.95 \begin {gather*} 2\,\ln \left (x^4-10\,x^3-5\,x^2+\frac {475\,x}{3}+\frac {725}{3}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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