Optimal. Leaf size=18 \[ \frac {3}{\log ^2\left (5+\frac {25}{x^2}+x+25 x^2\right )} \]
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Rubi [A] time = 0.09, antiderivative size = 24, normalized size of antiderivative = 1.33, number of steps used = 1, number of rules used = 1, integrand size = 54, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.019, Rules used = {6686} \begin {gather*} \frac {3}{\log ^2\left (\frac {25 x^4+x^3+5 x^2+25}{x^2}\right )} \end {gather*}
Antiderivative was successfully verified.
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Rule 6686
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {3}{\log ^2\left (\frac {25+5 x^2+x^3+25 x^4}{x^2}\right )}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.02, size = 18, normalized size = 1.00 \begin {gather*} \frac {3}{\log ^2\left (5+\frac {25}{x^2}+x+25 x^2\right )} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 1.24, size = 24, normalized size = 1.33 \begin {gather*} \frac {3}{\log \left (\frac {25 \, x^{4} + x^{3} + 5 \, x^{2} + 25}{x^{2}}\right )^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.21, size = 92, normalized size = 5.11 \begin {gather*} \frac {3 \, {\left (50 \, x^{4} + x^{3} - 50\right )}}{50 \, x^{4} \log \left (\frac {25 \, x^{4} + x^{3} + 5 \, x^{2} + 25}{x^{2}}\right )^{2} + x^{3} \log \left (\frac {25 \, x^{4} + x^{3} + 5 \, x^{2} + 25}{x^{2}}\right )^{2} - 50 \, \log \left (\frac {25 \, x^{4} + x^{3} + 5 \, x^{2} + 25}{x^{2}}\right )^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.06, size = 25, normalized size = 1.39
method | result | size |
norman | \(\frac {3}{\ln \left (\frac {25 x^{4}+x^{3}+5 x^{2}+25}{x^{2}}\right )^{2}}\) | \(25\) |
risch | \(\frac {3}{\ln \left (\frac {25 x^{4}+x^{3}+5 x^{2}+25}{x^{2}}\right )^{2}}\) | \(25\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.41, size = 49, normalized size = 2.72 \begin {gather*} \frac {3}{\log \left (25 \, x^{4} + x^{3} + 5 \, x^{2} + 25\right )^{2} - 4 \, \log \left (25 \, x^{4} + x^{3} + 5 \, x^{2} + 25\right ) \log \relax (x) + 4 \, \log \relax (x)^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.63, size = 24, normalized size = 1.33 \begin {gather*} \frac {3}{{\ln \left (\frac {25\,x^4+x^3+5\,x^2+25}{x^2}\right )}^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.17, size = 22, normalized size = 1.22 \begin {gather*} \frac {3}{\log {\left (\frac {25 x^{4} + x^{3} + 5 x^{2} + 25}{x^{2}} \right )}^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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