Optimal. Leaf size=24 \[ 2+\frac {(3+x) \log (6)}{8 \left (-x+\frac {x^2}{5}\right )^4} \]
________________________________________________________________________________________
Rubi [B] time = 0.11, antiderivative size = 86, normalized size of antiderivative = 3.58, number of steps used = 3, number of rules used = 2, integrand size = 46, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.043, Rules used = {12, 2074} \begin {gather*} \frac {3 \log (6)}{8 x^4}+\frac {17 \log (6)}{40 x^3}+\frac {\log (6)}{4 x^2}+\frac {11 \log (6)}{100 x}+\frac {11 \log (6)}{100 (5-x)}+\frac {3 \log (6)}{10 (5-x)^2}+\frac {27 \log (6)}{40 (5-x)^3}+\frac {\log (6)}{(5-x)^4} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 12
Rule 2074
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\log (6) \int \frac {37500-5625 x-4375 x^2}{-25000 x^5+25000 x^6-10000 x^7+2000 x^8-200 x^9+8 x^{10}} \, dx\\ &=\log (6) \int \left (-\frac {4}{(-5+x)^5}+\frac {81}{40 (-5+x)^4}-\frac {3}{5 (-5+x)^3}+\frac {11}{100 (-5+x)^2}-\frac {3}{2 x^5}-\frac {51}{40 x^4}-\frac {1}{2 x^3}-\frac {11}{100 x^2}\right ) \, dx\\ &=\frac {\log (6)}{(5-x)^4}+\frac {27 \log (6)}{40 (5-x)^3}+\frac {3 \log (6)}{10 (5-x)^2}+\frac {11 \log (6)}{100 (5-x)}+\frac {3 \log (6)}{8 x^4}+\frac {17 \log (6)}{40 x^3}+\frac {\log (6)}{4 x^2}+\frac {11 \log (6)}{100 x}\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.01, size = 17, normalized size = 0.71 \begin {gather*} \frac {625 (3+x) \log (6)}{8 (-5+x)^4 x^4} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.86, size = 33, normalized size = 1.38 \begin {gather*} \frac {625 \, {\left (x + 3\right )} \log \relax (6)}{8 \, {\left (x^{8} - 20 \, x^{7} + 150 \, x^{6} - 500 \, x^{5} + 625 \, x^{4}\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.34, size = 16, normalized size = 0.67 \begin {gather*} \frac {625 \, {\left (x + 3\right )} \log \relax (6)}{8 \, {\left (x^{2} - 5 \, x\right )}^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.05, size = 20, normalized size = 0.83
method | result | size |
norman | \(\frac {\frac {625 x \ln \relax (6)}{8}+\frac {1875 \ln \relax (6)}{8}}{x^{4} \left (x -5\right )^{4}}\) | \(20\) |
gosper | \(\frac {625 \left (3+x \right ) \ln \relax (6)}{8 x^{4} \left (x^{4}-20 x^{3}+150 x^{2}-500 x +625\right )}\) | \(31\) |
risch | \(\frac {\left (\ln \relax (2)+\ln \relax (3)\right ) \left (\frac {625 x}{8}+\frac {1875}{8}\right )}{x^{4} \left (x^{4}-20 x^{3}+150 x^{2}-500 x +625\right )}\) | \(35\) |
default | \(\frac {625 \ln \relax (6) \left (\frac {3}{625 x^{4}}+\frac {17}{3125 x^{3}}+\frac {2}{625 x^{2}}+\frac {22}{15625 x}+\frac {8}{625 \left (x -5\right )^{4}}-\frac {27}{3125 \left (x -5\right )^{3}}+\frac {12}{3125 \left (x -5\right )^{2}}-\frac {22}{15625 \left (x -5\right )}\right )}{8}\) | \(54\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.45, size = 33, normalized size = 1.38 \begin {gather*} \frac {625 \, {\left (x + 3\right )} \log \relax (6)}{8 \, {\left (x^{8} - 20 \, x^{7} + 150 \, x^{6} - 500 \, x^{5} + 625 \, x^{4}\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 1.14, size = 39, normalized size = 1.62 \begin {gather*} \frac {1875\,\ln \relax (6)+625\,x\,\ln \relax (6)}{8\,x^8-160\,x^7+1200\,x^6-4000\,x^5+5000\,x^4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [B] time = 0.29, size = 39, normalized size = 1.62 \begin {gather*} - \frac {- 625 x \log {\relax (6 )} - 1875 \log {\relax (6 )}}{8 x^{8} - 160 x^{7} + 1200 x^{6} - 4000 x^{5} + 5000 x^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________