Optimal. Leaf size=43 \[ \frac {1}{121 (1-2 x)}+\frac {7}{44 (1-2 x)^2}-\frac {5 \log (1-2 x)}{1331}+\frac {5 \log (5 x+3)}{1331} \]
[Out]
________________________________________________________________________________________
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 = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {77} \[ \frac {1}{121 (1-2 x)}+\frac {7}{44 (1-2 x)^2}-\frac {5 \log (1-2 x)}{1331}+\frac {5 \log (5 x+3)}{1331} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 77
Rubi steps
\begin {align*} \int \frac {2+3 x}{(1-2 x)^3 (3+5 x)} \, dx &=\int \left (-\frac {7}{11 (-1+2 x)^3}+\frac {2}{121 (-1+2 x)^2}-\frac {10}{1331 (-1+2 x)}+\frac {25}{1331 (3+5 x)}\right ) \, dx\\ &=\frac {7}{44 (1-2 x)^2}+\frac {1}{121 (1-2 x)}-\frac {5 \log (1-2 x)}{1331}+\frac {5 \log (3+5 x)}{1331}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.03, size = 46, normalized size = 1.07 \[ \frac {-88 x-20 (1-2 x)^2 \log (1-2 x)+20 (1-2 x)^2 \log (10 x+6)+891}{5324 (1-2 x)^2} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.52, size = 55, normalized size = 1.28 \[ \frac {20 \, {\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (5 \, x + 3\right ) - 20 \, {\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (2 \, x - 1\right ) - 88 \, x + 891}{5324 \, {\left (4 \, x^{2} - 4 \, x + 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 1.17, size = 33, normalized size = 0.77 \[ -\frac {8 \, x - 81}{484 \, {\left (2 \, x - 1\right )}^{2}} + \frac {5}{1331} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) - \frac {5}{1331} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.01, size = 36, normalized size = 0.84 \[ -\frac {5 \ln \left (2 x -1\right )}{1331}+\frac {5 \ln \left (5 x +3\right )}{1331}+\frac {7}{44 \left (2 x -1\right )^{2}}-\frac {1}{121 \left (2 x -1\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.50, size = 36, normalized size = 0.84 \[ -\frac {8 \, x - 81}{484 \, {\left (4 \, x^{2} - 4 \, x + 1\right )}} + \frac {5}{1331} \, \log \left (5 \, x + 3\right ) - \frac {5}{1331} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.04, size = 26, normalized size = 0.60 \[ \frac {10\,\mathrm {atanh}\left (\frac {20\,x}{11}+\frac {1}{11}\right )}{1331}-\frac {\frac {x}{242}-\frac {81}{1936}}{x^2-x+\frac {1}{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.14, size = 34, normalized size = 0.79 \[ - \frac {8 x - 81}{1936 x^{2} - 1936 x + 484} - \frac {5 \log {\left (x - \frac {1}{2} \right )}}{1331} + \frac {5 \log {\left (x + \frac {3}{5} \right )}}{1331} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________