Optimal. Leaf size=27 \[ 4+25 x^2 \log ^2(4)-\frac {\left (-1-x^2+\log (4)\right )^2}{x^2} \]
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Rubi [A] time = 0.02, antiderivative size = 27, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 27, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.037, Rules used = {14} \begin {gather*} -\left (x^2 \left (1-25 \log ^2(4)\right )\right )-\frac {(1-\log (4))^2}{x^2} \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (\frac {2 (-1+\log (4))^2}{x^3}+2 x \left (-1+25 \log ^2(4)\right )\right ) \, dx\\ &=-\frac {(1-\log (4))^2}{x^2}-x^2 \left (1-25 \log ^2(4)\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 26, normalized size = 0.96 \begin {gather*} -x^2-\frac {(-1+\log (4))^2}{x^2}+25 x^2 \log ^2(4) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.68, size = 27, normalized size = 1.00 \begin {gather*} -\frac {x^{4} - 4 \, {\left (25 \, x^{4} - 1\right )} \log \relax (2)^{2} - 4 \, \log \relax (2) + 1}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.14, size = 32, normalized size = 1.19 \begin {gather*} 100 \, x^{2} \log \relax (2)^{2} - x^{2} - \frac {4 \, \log \relax (2)^{2} - 4 \, \log \relax (2) + 1}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.05, size = 29, normalized size = 1.07
method | result | size |
norman | \(\frac {\left (100 \ln \relax (2)^{2}-1\right ) x^{4}-4 \ln \relax (2)^{2}+4 \ln \relax (2)-1}{x^{2}}\) | \(29\) |
gosper | \(\frac {100 x^{4} \ln \relax (2)^{2}-x^{4}-4 \ln \relax (2)^{2}+4 \ln \relax (2)-1}{x^{2}}\) | \(31\) |
default | \(\left (100 \ln \relax (2)^{2}-1\right ) x^{2}-\frac {4 \ln \relax (2)^{2}-4 \ln \relax (2)+1}{x^{2}}\) | \(31\) |
risch | \(100 x^{2} \ln \relax (2)^{2}-x^{2}-\frac {4 \ln \relax (2)^{2}}{x^{2}}+\frac {4 \ln \relax (2)}{x^{2}}-\frac {1}{x^{2}}\) | \(37\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.35, size = 30, normalized size = 1.11 \begin {gather*} {\left (100 \, \log \relax (2)^{2} - 1\right )} x^{2} - \frac {4 \, \log \relax (2)^{2} - 4 \, \log \relax (2) + 1}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.09, size = 30, normalized size = 1.11 \begin {gather*} x^2\,\left (100\,{\ln \relax (2)}^2-1\right )-\frac {4\,{\ln \relax (2)}^2-\ln \left (16\right )+1}{x^2} \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 = 1.07 \begin {gather*} - x^{2} \left (1 - 100 \log {\relax (2 )}^{2}\right ) - \frac {- 4 \log {\relax (2 )} + 1 + 4 \log {\relax (2 )}^{2}}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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