Optimal. Leaf size=14 \[ \frac {5}{\frac {1}{2}+\log ^2\left (x^2\right )} \]
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Rubi [A]
time = 0.05, antiderivative size = 14, normalized size of antiderivative = 1.00, number of steps
used = 3, number of rules used = 4, integrand size = 28, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.143, Rules used = {12, 205, 209,
267} \begin {gather*} \frac {10}{2 \log ^2\left (x^2\right )+1} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 205
Rule 209
Rule 267
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-\left (80 \int \frac {\log \left (x^2\right )}{x+4 x \log ^2\left (x^2\right )+4 x \log ^4\left (x^2\right )} \, dx\right )\\ &=-\left (40 \text {Subst}\left (\int \frac {x}{\left (1+2 x^2\right )^2} \, dx,x,\log \left (x^2\right )\right )\right )\\ &=\frac {10}{1+2 \log ^2\left (x^2\right )}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.01, size = 14, normalized size = 1.00 \begin {gather*} \frac {10}{1+2 \log ^2\left (x^2\right )} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.18, size = 15, normalized size = 1.07
method | result | size |
default | \(\frac {10}{2 \ln \left (x^{2}\right )^{2}+1}\) | \(15\) |
norman | \(\frac {10}{2 \ln \left (x^{2}\right )^{2}+1}\) | \(15\) |
risch | \(\frac {10}{2 \ln \left (x^{2}\right )^{2}+1}\) | \(15\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.30, size = 12, normalized size = 0.86 \begin {gather*} \frac {10}{8 \, \log \left (x\right )^{2} + 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.36, size = 14, normalized size = 1.00 \begin {gather*} \frac {10}{2 \, \log \left (x^{2}\right )^{2} + 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.03, size = 10, normalized size = 0.71 \begin {gather*} \frac {10}{2 \log {\left (x^{2} \right )}^{2} + 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.42, size = 14, normalized size = 1.00 \begin {gather*} \frac {10}{2 \, \log \left (x^{2}\right )^{2} + 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 3.30, size = 14, normalized size = 1.00 \begin {gather*} \frac {10}{2\,{\ln \left (x^2\right )}^2+1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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