Optimal. Leaf size=22 \[ \log \left (\left (x+\frac {2 x}{3 \left (3+x^2\right )}\right ) \log (22-x)\right ) \]
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Rubi [A] time = 0.77, antiderivative size = 26, normalized size of antiderivative = 1.18, number of steps used = 9, number of rules used = 7, integrand size = 86, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.081, Rules used = {6741, 6742, 1663, 1628, 2390, 2302, 29} \begin {gather*} -\log \left (x^2+3\right )+\log \left (3 x^2+11\right )+\log (x)+\log (\log (22-x)) \end {gather*}
Antiderivative was successfully verified.
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Rule 29
Rule 1628
Rule 1663
Rule 2302
Rule 2390
Rule 6741
Rule 6742
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-33 x-20 x^3-3 x^5-\left (-726+33 x-352 x^2+16 x^3-66 x^4+3 x^5\right ) \log (22-x)}{x \left (726-33 x+440 x^2-20 x^3+66 x^4-3 x^5\right ) \log (22-x)} \, dx\\ &=\int \left (\frac {33+16 x^2+3 x^4}{x \left (33+20 x^2+3 x^4\right )}+\frac {1}{(-22+x) \log (22-x)}\right ) \, dx\\ &=\int \frac {33+16 x^2+3 x^4}{x \left (33+20 x^2+3 x^4\right )} \, dx+\int \frac {1}{(-22+x) \log (22-x)} \, dx\\ &=\frac {1}{2} \operatorname {Subst}\left (\int \frac {33+16 x+3 x^2}{x \left (33+20 x+3 x^2\right )} \, dx,x,x^2\right )+\operatorname {Subst}\left (\int \frac {1}{x \log (x)} \, dx,x,22-x\right )\\ &=\frac {1}{2} \operatorname {Subst}\left (\int \left (\frac {1}{x}-\frac {2}{3+x}+\frac {6}{11+3 x}\right ) \, dx,x,x^2\right )+\operatorname {Subst}\left (\int \frac {1}{x} \, dx,x,\log (22-x)\right )\\ &=\log (x)-\log \left (3+x^2\right )+\log \left (11+3 x^2\right )+\log (\log (22-x))\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.04, size = 26, normalized size = 1.18 \begin {gather*} \log (x)-\log \left (3+x^2\right )+\log \left (11+3 x^2\right )+\log (\log (22-x)) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.54, size = 26, normalized size = 1.18 \begin {gather*} \log \left (3 \, x^{3} + 11 \, x\right ) - \log \left (x^{2} + 3\right ) + \log \left (\log \left (-x + 22\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.16, size = 26, normalized size = 1.18 \begin {gather*} \log \left (3 \, x^{2} + 11\right ) - \log \left (x^{2} + 3\right ) + \log \relax (x) + \log \left (\log \left (-x + 22\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.11, size = 27, normalized size = 1.23
method | result | size |
norman | \(-\ln \left (x^{2}+3\right )+\ln \relax (x )+\ln \left (\ln \left (22-x \right )\right )+\ln \left (3 x^{2}+11\right )\) | \(27\) |
risch | \(-\ln \left (x^{2}+3\right )+\ln \left (3 x^{3}+11 x \right )+\ln \left (\ln \left (22-x \right )\right )\) | \(27\) |
derivativedivides | \(\ln \left (\ln \left (22-x \right )\right )-\ln \left (\left (22-x \right )^{2}-481+44 x \right )+\ln \left (3 \left (22-x \right )^{2}-1441+132 x \right )+\ln \left (-x \right )\) | \(43\) |
default | \(\ln \left (\ln \left (22-x \right )\right )-\ln \left (\left (22-x \right )^{2}-481+44 x \right )+\ln \left (3 \left (22-x \right )^{2}-1441+132 x \right )+\ln \left (-x \right )\) | \(43\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.50, size = 26, normalized size = 1.18 \begin {gather*} \log \left (3 \, x^{2} + 11\right ) - \log \left (x^{2} + 3\right ) + \log \relax (x) + \log \left (\log \left (-x + 22\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 5.47, size = 24, normalized size = 1.09 \begin {gather*} \ln \left (\ln \left (22-x\right )\right )+\ln \left (x^3+\frac {11\,x}{3}\right )-\ln \left (x^2+3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.19, size = 22, normalized size = 1.00 \begin {gather*} - \log {\left (x^{2} + 3 \right )} + \log {\left (3 x^{3} + 11 x \right )} + \log {\left (\log {\left (22 - x \right )} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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