Optimal. Leaf size=23 \[ -x+\log \left (-2+\log \left (\left (-x+\frac {x}{\frac {25}{324}+x}\right )^2\right )\right ) \]
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Rubi [A] time = 0.67, antiderivative size = 28, normalized size of antiderivative = 1.22, number of steps used = 4, number of rules used = 3, integrand size = 122, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.025, Rules used = {6688, 6728, 6684} \begin {gather*} \log \left (2-\log \left (\frac {(299-324 x)^2 x^2}{(324 x+25)^2}\right )\right )-x \end {gather*}
Antiderivative was successfully verified.
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Rule 6684
Rule 6688
Rule 6728
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {2 \left (-7475+8725 x+16200 x^2+104976 x^3\right )+x \left (7475+88776 x-104976 x^2\right ) \log \left (\frac {x^2 (-299+324 x)^2}{(25+324 x)^2}\right )}{x \left (7475+88776 x-104976 x^2\right ) \left (2-\log \left (\frac {x^2 (-299+324 x)^2}{(25+324 x)^2}\right )\right )} \, dx\\ &=\int \left (-1+\frac {2 \left (-7475+16200 x+104976 x^2\right )}{x (-299+324 x) (25+324 x) \left (-2+\log \left (\frac {x^2 (-299+324 x)^2}{(25+324 x)^2}\right )\right )}\right ) \, dx\\ &=-x+2 \int \frac {-7475+16200 x+104976 x^2}{x (-299+324 x) (25+324 x) \left (-2+\log \left (\frac {x^2 (-299+324 x)^2}{(25+324 x)^2}\right )\right )} \, dx\\ &=-x+\log \left (2-\log \left (\frac {(299-324 x)^2 x^2}{(25+324 x)^2}\right )\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.09, size = 28, normalized size = 1.22 \begin {gather*} -x+\log \left (2-\log \left (\frac {x^2 (-299+324 x)^2}{(25+324 x)^2}\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.67, size = 37, normalized size = 1.61 \begin {gather*} -x + \log \left (\log \left (\frac {104976 \, x^{4} - 193752 \, x^{3} + 89401 \, x^{2}}{104976 \, x^{2} + 16200 \, x + 625}\right ) - 2\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.73, size = 37, normalized size = 1.61 \begin {gather*} -x + \log \left (\log \left (\frac {104976 \, x^{4} - 193752 \, x^{3} + 89401 \, x^{2}}{104976 \, x^{2} + 16200 \, x + 625}\right ) - 2\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.06, size = 38, normalized size = 1.65
method | result | size |
norman | \(-x +\ln \left (\ln \left (\frac {104976 x^{4}-193752 x^{3}+89401 x^{2}}{104976 x^{2}+16200 x +625}\right )-2\right )\) | \(38\) |
risch | \(-x +\ln \left (\ln \left (\frac {104976 x^{4}-193752 x^{3}+89401 x^{2}}{104976 x^{2}+16200 x +625}\right )-2\right )\) | \(38\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.44, size = 25, normalized size = 1.09 \begin {gather*} -x + \log \left (\log \left (324 \, x + 25\right ) - \log \left (324 \, x - 299\right ) - \log \relax (x) + 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.34, size = 37, normalized size = 1.61 \begin {gather*} \ln \left (\ln \left (\frac {104976\,x^4-193752\,x^3+89401\,x^2}{104976\,x^2+16200\,x+625}\right )-2\right )-x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.33, size = 31, normalized size = 1.35 \begin {gather*} - x + \log {\left (\log {\left (\frac {104976 x^{4} - 193752 x^{3} + 89401 x^{2}}{104976 x^{2} + 16200 x + 625} \right )} - 2 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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