Optimal. Leaf size=43 \[ \frac {2}{121 (1-2 x)}-\frac {5}{121 (5 x+3)}-\frac {20 \log (1-2 x)}{1331}+\frac {20 \log (5 x+3)}{1331} \]
________________________________________________________________________________________
Rubi [A] time = 0.02, antiderivative size = 43, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {44} \begin {gather*} \frac {2}{121 (1-2 x)}-\frac {5}{121 (5 x+3)}-\frac {20 \log (1-2 x)}{1331}+\frac {20 \log (5 x+3)}{1331} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 44
Rubi steps
\begin {align*} \int \frac {1}{(1-2 x)^2 (3+5 x)^2} \, dx &=\int \left (\frac {4}{121 (-1+2 x)^2}-\frac {40}{1331 (-1+2 x)}+\frac {25}{121 (3+5 x)^2}+\frac {100}{1331 (3+5 x)}\right ) \, dx\\ &=\frac {2}{121 (1-2 x)}-\frac {5}{121 (3+5 x)}-\frac {20 \log (1-2 x)}{1331}+\frac {20 \log (3+5 x)}{1331}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.02, size = 40, normalized size = 0.93 \begin {gather*} \frac {-20 x-1}{121 \left (10 x^2+x-3\right )}-\frac {20 \log (1-2 x)}{1331}+\frac {20 \log (5 x+3)}{1331} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {1}{(1-2 x)^2 (3+5 x)^2} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 1.56, size = 49, normalized size = 1.14 \begin {gather*} \frac {20 \, {\left (10 \, x^{2} + x - 3\right )} \log \left (5 \, x + 3\right ) - 20 \, {\left (10 \, x^{2} + x - 3\right )} \log \left (2 \, x - 1\right ) - 220 \, x - 11}{1331 \, {\left (10 \, x^{2} + x - 3\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 1.19, size = 40, normalized size = 0.93 \begin {gather*} -\frac {5}{121 \, {\left (5 \, x + 3\right )}} + \frac {20}{1331 \, {\left (\frac {11}{5 \, x + 3} - 2\right )}} - \frac {20}{1331} \, \log \left ({\left | -\frac {11}{5 \, x + 3} + 2 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.01, size = 36, normalized size = 0.84 \begin {gather*} -\frac {20 \ln \left (2 x -1\right )}{1331}+\frac {20 \ln \left (5 x +3\right )}{1331}-\frac {5}{121 \left (5 x +3\right )}-\frac {2}{121 \left (2 x -1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.56, size = 34, normalized size = 0.79 \begin {gather*} -\frac {20 \, x + 1}{121 \, {\left (10 \, x^{2} + x - 3\right )}} + \frac {20}{1331} \, \log \left (5 \, x + 3\right ) - \frac {20}{1331} \, \log \left (2 \, x - 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.05, size = 42, normalized size = 0.98 \begin {gather*} \frac {20\,\ln \left (\frac {5\,x+3}{2\,x-1}\right )}{1331}-\frac {1}{11\,\left (2\,x-1\right )\,\left (5\,x+3\right )}-\frac {10}{121\,\left (5\,x+3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.15, size = 36, normalized size = 0.84 \begin {gather*} \frac {- 20 x - 1}{1210 x^{2} + 121 x - 363} - \frac {20 \log {\left (x - \frac {1}{2} \right )}}{1331} + \frac {20 \log {\left (x + \frac {3}{5} \right )}}{1331} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________