Optimal. Leaf size=21 \[ \frac {5-\frac {4 x}{3}}{5+\frac {2 x}{509}-\log (3)} \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.02, antiderivative size = 24, normalized size of antiderivative = 1.14, number of steps
used = 5, number of rules used = 4, integrand size = 33, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.121, Rules used = {12, 2006, 27,
32} \begin {gather*} \frac {509 (5105-1018 \log (3))}{3 (2 x+509 (5-\log (3)))} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 12
Rule 27
Rule 32
Rule 2006
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-\left ((1018 (5105-1018 \log (3))) \int \frac {1}{19431075+30540 x+12 x^2+(-7772430-6108 x) \log (3)+777243 \log ^2(3)} \, dx\right )\\ &=-\left ((1018 (5105-1018 \log (3))) \int \frac {1}{12 x^2+6108 x (5-\log (3))+777243 (5-\log (3))^2} \, dx\right )\\ &=-\left ((1018 (5105-1018 \log (3))) \int \frac {1}{3 (2545+2 x-509 \log (3))^2} \, dx\right )\\ &=-\left (\frac {1}{3} (1018 (5105-1018 \log (3))) \int \frac {1}{(2545+2 x-509 \log (3))^2} \, dx\right )\\ &=\frac {509 (5105-1018 \log (3))}{3 (2 x+509 (5-\log (3)))}\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A]
time = 0.01, size = 22, normalized size = 1.05 \begin {gather*} -\frac {509 (-5105+1018 \log (3))}{3 (2 x-509 (-5+\log (3)))} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 3.03, size = 20, normalized size = 0.95
method | result | size |
norman | \(\frac {-\frac {2598445}{3}+\frac {518162 \ln \left (3\right )}{3}}{509 \ln \left (3\right )-2 x -2545}\) | \(19\) |
gosper | \(\frac {-\frac {2598445}{3}+\frac {518162 \ln \left (3\right )}{3}}{509 \ln \left (3\right )-2 x -2545}\) | \(20\) |
default | \(-\frac {1036324 \ln \left (3\right )-5196890}{6 \left (-509 \ln \left (3\right )+2 x +2545\right )}\) | \(20\) |
risch | \(\frac {1018 \ln \left (3\right )}{3 \left (\ln \left (3\right )-\frac {2 x}{509}-5\right )}-\frac {5105}{3 \left (\ln \left (3\right )-\frac {2 x}{509}-5\right )}\) | \(26\) |
meijerg | \(-\frac {5105 x}{3 \left (-\frac {509 \ln \left (3\right )}{2}+\frac {2545}{2}\right ) \left (5-\ln \left (3\right )\right ) \left (1+\frac {2 x}{509 \left (5-\ln \left (3\right )\right )}\right )}+\frac {1018 \ln \left (3\right ) x}{3 \left (-\frac {509 \ln \left (3\right )}{2}+\frac {2545}{2}\right ) \left (5-\ln \left (3\right )\right ) \left (1+\frac {2 x}{509 \left (5-\ln \left (3\right )\right )}\right )}\) | \(72\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.26, size = 19, normalized size = 0.90 \begin {gather*} -\frac {509 \, {\left (1018 \, \log \left (3\right ) - 5105\right )}}{3 \, {\left (2 \, x - 509 \, \log \left (3\right ) + 2545\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.35, size = 19, normalized size = 0.90 \begin {gather*} -\frac {509 \, {\left (1018 \, \log \left (3\right ) - 5105\right )}}{3 \, {\left (2 \, x - 509 \, \log \left (3\right ) + 2545\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.08, size = 17, normalized size = 0.81 \begin {gather*} - \frac {-5196890 + 1036324 \log {\left (3 \right )}}{12 x - 3054 \log {\left (3 \right )} + 15270} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 0.40, size = 19, normalized size = 0.90 \begin {gather*} -\frac {509 \, {\left (1018 \, \log \left (3\right ) - 5105\right )}}{3 \, {\left (2 \, x - 509 \, \log \left (3\right ) + 2545\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 7.58, size = 19, normalized size = 0.90 \begin {gather*} -\frac {\frac {518162\,\ln \left (3\right )}{3}-\frac {2598445}{3}}{2\,x-509\,\ln \left (3\right )+2545} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________