Optimal. Leaf size=51 \[ -\frac {1125 x^6}{4}-\frac {5805 x^5}{4}-\frac {110205 x^4}{32}-\frac {247157 x^3}{48}-\frac {377045 x^2}{64}-\frac {442709 x}{64}-\frac {456533}{128} \log (1-2 x) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.02, antiderivative size = 51, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.045, Rules used = {88} \[ -\frac {1125 x^6}{4}-\frac {5805 x^5}{4}-\frac {110205 x^4}{32}-\frac {247157 x^3}{48}-\frac {377045 x^2}{64}-\frac {442709 x}{64}-\frac {456533}{128} \log (1-2 x) \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 88
Rubi steps
\begin {align*} \int \frac {(2+3 x)^3 (3+5 x)^3}{1-2 x} \, dx &=\int \left (-\frac {442709}{64}-\frac {377045 x}{32}-\frac {247157 x^2}{16}-\frac {110205 x^3}{8}-\frac {29025 x^4}{4}-\frac {3375 x^5}{2}-\frac {456533}{64 (-1+2 x)}\right ) \, dx\\ &=-\frac {442709 x}{64}-\frac {377045 x^2}{64}-\frac {247157 x^3}{48}-\frac {110205 x^4}{32}-\frac {5805 x^5}{4}-\frac {1125 x^6}{4}-\frac {456533}{128} \log (1-2 x)\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.01, size = 42, normalized size = 0.82 \[ \frac {-432000 x^6-2229120 x^5-5289840 x^4-7909024 x^3-9049080 x^2-10625016 x-5478396 \log (1-2 x)+8970431}{1536} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.93, size = 37, normalized size = 0.73 \[ -\frac {1125}{4} \, x^{6} - \frac {5805}{4} \, x^{5} - \frac {110205}{32} \, x^{4} - \frac {247157}{48} \, x^{3} - \frac {377045}{64} \, x^{2} - \frac {442709}{64} \, x - \frac {456533}{128} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.95, size = 38, normalized size = 0.75 \[ -\frac {1125}{4} \, x^{6} - \frac {5805}{4} \, x^{5} - \frac {110205}{32} \, x^{4} - \frac {247157}{48} \, x^{3} - \frac {377045}{64} \, x^{2} - \frac {442709}{64} \, x - \frac {456533}{128} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.00, size = 38, normalized size = 0.75 \[ -\frac {1125 x^{6}}{4}-\frac {5805 x^{5}}{4}-\frac {110205 x^{4}}{32}-\frac {247157 x^{3}}{48}-\frac {377045 x^{2}}{64}-\frac {442709 x}{64}-\frac {456533 \ln \left (2 x -1\right )}{128} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.50, size = 37, normalized size = 0.73 \[ -\frac {1125}{4} \, x^{6} - \frac {5805}{4} \, x^{5} - \frac {110205}{32} \, x^{4} - \frac {247157}{48} \, x^{3} - \frac {377045}{64} \, x^{2} - \frac {442709}{64} \, x - \frac {456533}{128} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.03, size = 35, normalized size = 0.69 \[ -\frac {442709\,x}{64}-\frac {456533\,\ln \left (x-\frac {1}{2}\right )}{128}-\frac {377045\,x^2}{64}-\frac {247157\,x^3}{48}-\frac {110205\,x^4}{32}-\frac {5805\,x^5}{4}-\frac {1125\,x^6}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.11, size = 49, normalized size = 0.96 \[ - \frac {1125 x^{6}}{4} - \frac {5805 x^{5}}{4} - \frac {110205 x^{4}}{32} - \frac {247157 x^{3}}{48} - \frac {377045 x^{2}}{64} - \frac {442709 x}{64} - \frac {456533 \log {\left (2 x - 1 \right )}}{128} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________