Optimal. Leaf size=13 \[ -2+\frac {\log \left (\log \left (4+x^2\right )\right )}{x^5} \]
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Rubi [F] time = 0.33, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int \frac {2 x^2+\left (-20-5 x^2\right ) \log \left (4+x^2\right ) \log \left (\log \left (4+x^2\right )\right )}{\left (4 x^6+x^8\right ) \log \left (4+x^2\right )} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {2 x^2+\left (-20-5 x^2\right ) \log \left (4+x^2\right ) \log \left (\log \left (4+x^2\right )\right )}{x^6 \left (4+x^2\right ) \log \left (4+x^2\right )} \, dx\\ &=\int \left (\frac {2}{x^4 \left (4+x^2\right ) \log \left (4+x^2\right )}-\frac {5 \log \left (\log \left (4+x^2\right )\right )}{x^6}\right ) \, dx\\ &=2 \int \frac {1}{x^4 \left (4+x^2\right ) \log \left (4+x^2\right )} \, dx-5 \int \frac {\log \left (\log \left (4+x^2\right )\right )}{x^6} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.77, size = 11, normalized size = 0.85 \begin {gather*} \frac {\log \left (\log \left (4+x^2\right )\right )}{x^5} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.63, size = 11, normalized size = 0.85 \begin {gather*} \frac {\log \left (\log \left (x^{2} + 4\right )\right )}{x^{5}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.16, size = 11, normalized size = 0.85 \begin {gather*} \frac {\log \left (\log \left (x^{2} + 4\right )\right )}{x^{5}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.20, size = 12, normalized size = 0.92
method | result | size |
risch | \(\frac {\ln \left (\ln \left (x^{2}+4\right )\right )}{x^{5}}\) | \(12\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.41, size = 11, normalized size = 0.85 \begin {gather*} \frac {\log \left (\log \left (x^{2} + 4\right )\right )}{x^{5}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.81, size = 11, normalized size = 0.85 \begin {gather*} \frac {\ln \left (\ln \left (x^2+4\right )\right )}{x^5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.32, size = 10, normalized size = 0.77 \begin {gather*} \frac {\log {\left (\log {\left (x^{2} + 4 \right )} \right )}}{x^{5}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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