Optimal. Leaf size=15 \[ \log \left (\log (x) \left (x^2+\log \left ((-50+\log (3))^2\right )\right )\right ) \]
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Rubi [A]
time = 0.22, antiderivative size = 16, normalized size of antiderivative = 1.07, number of steps
used = 6, number of rules used = 5, integrand size = 47, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.106, Rules used = {6873, 6857,
2339, 29, 266} \begin {gather*} \log \left (x^2+\log \left ((\log (3)-50)^2\right )\right )+\log (\log (x)) \end {gather*}
Antiderivative was successfully verified.
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Rule 29
Rule 266
Rule 2339
Rule 6857
Rule 6873
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {x^2+2 x^2 \log (x)+\log \left (2500-100 \log (3)+\log ^2(3)\right )}{x \log (x) \left (x^2+\log \left ((-50+\log (3))^2\right )\right )} \, dx\\ &=\int \left (\frac {1}{x \log (x)}+\frac {2 x}{x^2+\log \left ((-50+\log (3))^2\right )}\right ) \, dx\\ &=2 \int \frac {x}{x^2+\log \left ((-50+\log (3))^2\right )} \, dx+\int \frac {1}{x \log (x)} \, dx\\ &=\log \left (x^2+\log \left ((-50+\log (3))^2\right )\right )+\text {Subst}\left (\int \frac {1}{x} \, dx,x,\log (x)\right )\\ &=\log (\log (x))+\log \left (x^2+\log \left ((-50+\log (3))^2\right )\right )\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.03, size = 16, normalized size = 1.07 \begin {gather*} \log (\log (x))+\log \left (x^2+\log \left ((-50+\log (3))^2\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.08, size = 21, normalized size = 1.40
method | result | size |
risch | \(\ln \left (x^{2}+2 \ln \left (-\ln \left (3\right )+50\right )\right )+\ln \left (\ln \left (x \right )\right )\) | \(19\) |
default | \(\ln \left (\ln \left (x \right )\right )+\ln \left (x^{2}+\ln \left (\ln \left (3\right )^{2}-100 \ln \left (3\right )+2500\right )\right )\) | \(21\) |
norman | \(\ln \left (\ln \left (x \right )\right )+\ln \left (x^{2}+\ln \left (\ln \left (3\right )^{2}-100 \ln \left (3\right )+2500\right )\right )\) | \(21\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.50, size = 16, normalized size = 1.07 \begin {gather*} \log \left (x^{2} + 2 \, \log \left (\log \left (3\right ) - 50\right )\right ) + \log \left (\log \left (x\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.37, size = 20, normalized size = 1.33 \begin {gather*} \log \left (x^{2} + \log \left (\log \left (3\right )^{2} - 100 \, \log \left (3\right ) + 2500\right )\right ) + \log \left (\log \left (x\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.07, size = 22, normalized size = 1.47 \begin {gather*} \log {\left (x^{2} + \log {\left (- 100 \log {\left (3 \right )} + \log {\left (3 \right )}^{2} + 2500 \right )} \right )} + \log {\left (\log {\left (x \right )} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.40, size = 20, normalized size = 1.33 \begin {gather*} \log \left (x^{2} + \log \left (\log \left (3\right )^{2} - 100 \, \log \left (3\right ) + 2500\right )\right ) + \log \left (\log \left (x\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.06, size = 16, normalized size = 1.07 \begin {gather*} \ln \left (x^2+\ln \left ({\left (\ln \left (3\right )-50\right )}^2\right )\right )+\ln \left (\ln \left (x\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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