Optimal. Leaf size=17 \[ \log \left (-5-\frac {73}{60 x (-5+x+\log (9))}\right ) \]
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Rubi [A] time = 0.11, antiderivative size = 28, normalized size of antiderivative = 1.65, number of steps used = 7, number of rules used = 6, integrand size = 57, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.105, Rules used = {6, 1680, 12, 1107, 616, 31} \begin {gather*} \log \left (300 x^2-300 x (5-\log (9))+73\right )-\log (x (x-5+\log (9))) \end {gather*}
Antiderivative was successfully verified.
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Rule 6
Rule 12
Rule 31
Rule 616
Rule 1107
Rule 1680
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {365-146 x-73 \log (9)}{-365 x-3000 x^3+300 x^4+\left (73 x-3000 x^2+600 x^3\right ) \log (9)+x^2 \left (7573+300 \log ^2(9)\right )} \, dx\\ &=\operatorname {Subst}\left (\int \frac {584 x}{-1200 x^4-(-5+\log (9))^2 \left (1802-750 \log (9)+75 \log ^2(9)\right )+4 x^2 \left (3677-1500 \log (9)+150 \log ^2(9)\right )} \, dx,x,x+\frac {-3000+600 \log (9)}{1200}\right )\\ &=584 \operatorname {Subst}\left (\int \frac {x}{-1200 x^4-(-5+\log (9))^2 \left (1802-750 \log (9)+75 \log ^2(9)\right )+4 x^2 \left (3677-1500 \log (9)+150 \log ^2(9)\right )} \, dx,x,x+\frac {-3000+600 \log (9)}{1200}\right )\\ &=292 \operatorname {Subst}\left (\int \frac {1}{-1200 x^2-(-5+\log (9))^2 \left (1802-750 \log (9)+75 \log ^2(9)\right )+4 x \left (3677-1500 \log (9)+150 \log ^2(9)\right )} \, dx,x,\left (x+\frac {-3000+600 \log (9)}{1200}\right )^2\right )\\ &=1200 \operatorname {Subst}\left (\int \frac {1}{-1200 x+300 (5-\log (9))^2} \, dx,x,\left (x+\frac {-3000+600 \log (9)}{1200}\right )^2\right )-1200 \operatorname {Subst}\left (\int \frac {1}{-1200 x+4 \left (1802-750 \log (9)+75 \log ^2(9)\right )} \, dx,x,\left (x+\frac {-3000+600 \log (9)}{1200}\right )^2\right )\\ &=\log \left (73+300 x^2-300 x (5-\log (9))\right )-\log (-x (5-x-\log (9)))\\ \end {aligned} \end {gather*}
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Mathematica [B] time = 0.02, size = 43, normalized size = 2.53 \begin {gather*} -73 \left (\frac {\log (x)}{73}+\frac {1}{73} \log (5-x-\log (9))-\frac {1}{73} \log \left (73-1500 x+300 x^2+300 x \log (9)\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.64, size = 32, normalized size = 1.88 \begin {gather*} \log \left (300 \, x^{2} + 600 \, x \log \relax (3) - 1500 \, x + 73\right ) - \log \left (x^{2} + 2 \, x \log \relax (3) - 5 \, x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 34, normalized size = 2.00 \begin {gather*} \log \left ({\left | 300 \, x^{2} + 600 \, x \log \relax (3) - 1500 \, x + 73 \right |}\right ) - \log \left ({\left | x^{2} + 2 \, x \log \relax (3) - 5 \, x \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.07, size = 32, normalized size = 1.88
method | result | size |
default | \(-\ln \relax (x )+\ln \left (600 x \ln \relax (3)+300 x^{2}-1500 x +73\right )-\ln \left (2 \ln \relax (3)+x -5\right )\) | \(32\) |
norman | \(-\ln \relax (x )+\ln \left (600 x \ln \relax (3)+300 x^{2}-1500 x +73\right )-\ln \left (2 \ln \relax (3)+x -5\right )\) | \(32\) |
risch | \(-\ln \left (x^{2}+\left (2 \ln \relax (3)-5\right ) x \right )+\ln \left (-300 x^{2}+\left (-600 \ln \relax (3)+1500\right ) x -73\right )\) | \(33\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.36, size = 32, normalized size = 1.88 \begin {gather*} \log \left (300 \, x^{2} + 300 \, x {\left (2 \, \log \relax (3) - 5\right )} + 73\right ) - \log \left (x + 2 \, \log \relax (3) - 5\right ) - \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.34, size = 88, normalized size = 5.18 \begin {gather*} -\mathrm {atan}\left (\frac {-\ln \relax (3)\,525600000{}\mathrm {i}+x\,\left (105120000\,\ln \relax (3)-262800000\right )\,2{}\mathrm {i}+{\ln \relax (3)}^2\,105120000{}\mathrm {i}+x^2\,105120000{}\mathrm {i}+657000000{}\mathrm {i}}{2\,x^2\,\left (432000000\,{\ln \relax (3)}^2-2160000000\,\ln \relax (3)+2647440000\right )-525600000\,\ln \relax (3)+105120000\,{\ln \relax (3)}^2+2\,x\,\left (16094880000\,\ln \relax (3)-6480000000\,{\ln \relax (3)}^2+864000000\,{\ln \relax (3)}^3-13237200000\right )+657000000}\right )\,2{}\mathrm {i} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.84, size = 29, normalized size = 1.71 \begin {gather*} - \log {\left (x^{2} + x \left (-5 + 2 \log {\relax (3 )}\right ) \right )} + \log {\left (x^{2} + x \left (-5 + 2 \log {\relax (3 )}\right ) + \frac {73}{300} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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