Optimal. Leaf size=72 \[ -\frac{3645 x^9}{2}-\frac{422091 x^8}{32}-\frac{353565 x^7}{8}-\frac{2929689 x^6}{32}-\frac{21272139 x^5}{160}-\frac{37722699 x^4}{256}-\frac{17391129 x^3}{128}-\frac{60332619 x^2}{512}-\frac{63019595 x}{512}-\frac{63412811 \log (1-2 x)}{1024} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0277745, antiderivative size = 72, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05, Rules used = {77} \[ -\frac{3645 x^9}{2}-\frac{422091 x^8}{32}-\frac{353565 x^7}{8}-\frac{2929689 x^6}{32}-\frac{21272139 x^5}{160}-\frac{37722699 x^4}{256}-\frac{17391129 x^3}{128}-\frac{60332619 x^2}{512}-\frac{63019595 x}{512}-\frac{63412811 \log (1-2 x)}{1024} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 77
Rubi steps
\begin{align*} \int \frac{(2+3 x)^8 (3+5 x)}{1-2 x} \, dx &=\int \left (-\frac{63019595}{512}-\frac{60332619 x}{256}-\frac{52173387 x^2}{128}-\frac{37722699 x^3}{64}-\frac{21272139 x^4}{32}-\frac{8789067 x^5}{16}-\frac{2474955 x^6}{8}-\frac{422091 x^7}{4}-\frac{32805 x^8}{2}-\frac{63412811}{512 (-1+2 x)}\right ) \, dx\\ &=-\frac{63019595 x}{512}-\frac{60332619 x^2}{512}-\frac{17391129 x^3}{128}-\frac{37722699 x^4}{256}-\frac{21272139 x^5}{160}-\frac{2929689 x^6}{32}-\frac{353565 x^7}{8}-\frac{422091 x^8}{32}-\frac{3645 x^9}{2}-\frac{63412811 \log (1-2 x)}{1024}\\ \end{align*}
Mathematica [A] time = 0.0167705, size = 57, normalized size = 0.79 \[ \frac{-74649600 x^9-540276480 x^8-1810252800 x^7-3750001920 x^6-5445667584 x^5-6035631840 x^4-5565161280 x^3-4826609520 x^2-5041567600 x-2536512440 \log (1-2 x)+5045478077}{40960} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.003, size = 53, normalized size = 0.7 \begin{align*} -{\frac{3645\,{x}^{9}}{2}}-{\frac{422091\,{x}^{8}}{32}}-{\frac{353565\,{x}^{7}}{8}}-{\frac{2929689\,{x}^{6}}{32}}-{\frac{21272139\,{x}^{5}}{160}}-{\frac{37722699\,{x}^{4}}{256}}-{\frac{17391129\,{x}^{3}}{128}}-{\frac{60332619\,{x}^{2}}{512}}-{\frac{63019595\,x}{512}}-{\frac{63412811\,\ln \left ( 2\,x-1 \right ) }{1024}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 1.06692, size = 70, normalized size = 0.97 \begin{align*} -\frac{3645}{2} \, x^{9} - \frac{422091}{32} \, x^{8} - \frac{353565}{8} \, x^{7} - \frac{2929689}{32} \, x^{6} - \frac{21272139}{160} \, x^{5} - \frac{37722699}{256} \, x^{4} - \frac{17391129}{128} \, x^{3} - \frac{60332619}{512} \, x^{2} - \frac{63019595}{512} \, x - \frac{63412811}{1024} \, \log \left (2 \, x - 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.30488, size = 247, normalized size = 3.43 \begin{align*} -\frac{3645}{2} \, x^{9} - \frac{422091}{32} \, x^{8} - \frac{353565}{8} \, x^{7} - \frac{2929689}{32} \, x^{6} - \frac{21272139}{160} \, x^{5} - \frac{37722699}{256} \, x^{4} - \frac{17391129}{128} \, x^{3} - \frac{60332619}{512} \, x^{2} - \frac{63019595}{512} \, x - \frac{63412811}{1024} \, \log \left (2 \, x - 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.105237, size = 70, normalized size = 0.97 \begin{align*} - \frac{3645 x^{9}}{2} - \frac{422091 x^{8}}{32} - \frac{353565 x^{7}}{8} - \frac{2929689 x^{6}}{32} - \frac{21272139 x^{5}}{160} - \frac{37722699 x^{4}}{256} - \frac{17391129 x^{3}}{128} - \frac{60332619 x^{2}}{512} - \frac{63019595 x}{512} - \frac{63412811 \log{\left (2 x - 1 \right )}}{1024} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.94187, size = 72, normalized size = 1. \begin{align*} -\frac{3645}{2} \, x^{9} - \frac{422091}{32} \, x^{8} - \frac{353565}{8} \, x^{7} - \frac{2929689}{32} \, x^{6} - \frac{21272139}{160} \, x^{5} - \frac{37722699}{256} \, x^{4} - \frac{17391129}{128} \, x^{3} - \frac{60332619}{512} \, x^{2} - \frac{63019595}{512} \, x - \frac{63412811}{1024} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]