Optimal. Leaf size=26 \[ \log \left (\frac {\left (-12+x+4 x^2+\left (5+\left (-1+x^2\right )^2\right )^2\right )^2}{x^2}\right ) \]
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Rubi [A] time = 0.11, antiderivative size = 29, normalized size of antiderivative = 1.12, number of steps used = 3, number of rules used = 2, integrand size = 50, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.040, Rules used = {2074, 1587} \begin {gather*} 2 \log \left (x^8-4 x^6+16 x^4-20 x^2+x+24\right )-2 \log (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 1587
Rule 2074
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-\frac {2}{x}+\frac {2 \left (1-40 x+64 x^3-24 x^5+8 x^7\right )}{24+x-20 x^2+16 x^4-4 x^6+x^8}\right ) \, dx\\ &=-2 \log (x)+2 \int \frac {1-40 x+64 x^3-24 x^5+8 x^7}{24+x-20 x^2+16 x^4-4 x^6+x^8} \, dx\\ &=-2 \log (x)+2 \log \left (24+x-20 x^2+16 x^4-4 x^6+x^8\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.02, size = 29, normalized size = 1.12 \begin {gather*} 2 \left (-\log (x)+\log \left (24+x-20 x^2+16 x^4-4 x^6+x^8\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.54, size = 29, normalized size = 1.12 \begin {gather*} 2 \, \log \left (x^{8} - 4 \, x^{6} + 16 \, x^{4} - 20 \, x^{2} + x + 24\right ) - 2 \, \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.45, size = 30, normalized size = 1.15 \begin {gather*} 2 \, \log \left (x^{8} - 4 \, x^{6} + 16 \, x^{4} - 20 \, x^{2} + x + 24\right ) - 2 \, \log \left ({\left | x \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 30, normalized size = 1.15
method | result | size |
default | \(2 \ln \left (x^{8}-4 x^{6}+16 x^{4}-20 x^{2}+x +24\right )-2 \ln \relax (x )\) | \(30\) |
norman | \(2 \ln \left (x^{8}-4 x^{6}+16 x^{4}-20 x^{2}+x +24\right )-2 \ln \relax (x )\) | \(30\) |
risch | \(2 \ln \left (x^{8}-4 x^{6}+16 x^{4}-20 x^{2}+x +24\right )-2 \ln \relax (x )\) | \(30\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.80, size = 29, normalized size = 1.12 \begin {gather*} 2 \, \log \left (x^{8} - 4 \, x^{6} + 16 \, x^{4} - 20 \, x^{2} + x + 24\right ) - 2 \, \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.31, size = 29, normalized size = 1.12 \begin {gather*} 2\,\ln \left (x^8-4\,x^6+16\,x^4-20\,x^2+x+24\right )-2\,\ln \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.13, size = 29, normalized size = 1.12 \begin {gather*} - 2 \log {\relax (x )} + 2 \log {\left (x^{8} - 4 x^{6} + 16 x^{4} - 20 x^{2} + x + 24 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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