Optimal. Leaf size=73 \[ -\frac{10125 x^6}{16}-\frac{80595 x^5}{16}-\frac{629505 x^4}{32}-\frac{1661133 x^3}{32}-\frac{28504029 x^2}{256}-\frac{64029233 x}{256}-\frac{39220335}{256 (1-2 x)}+\frac{22370117}{1024 (1-2 x)^2}-\frac{60160485}{256} \log (1-2 x) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0382232, antiderivative size = 73, normalized size of antiderivative = 1., 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} \[ -\frac{10125 x^6}{16}-\frac{80595 x^5}{16}-\frac{629505 x^4}{32}-\frac{1661133 x^3}{32}-\frac{28504029 x^2}{256}-\frac{64029233 x}{256}-\frac{39220335}{256 (1-2 x)}+\frac{22370117}{1024 (1-2 x)^2}-\frac{60160485}{256} \log (1-2 x) \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 88
Rubi steps
\begin{align*} \int \frac{(2+3 x)^5 (3+5 x)^3}{(1-2 x)^3} \, dx &=\int \left (-\frac{64029233}{256}-\frac{28504029 x}{128}-\frac{4983399 x^2}{32}-\frac{629505 x^3}{8}-\frac{402975 x^4}{16}-\frac{30375 x^5}{8}-\frac{22370117}{256 (-1+2 x)^3}-\frac{39220335}{128 (-1+2 x)^2}-\frac{60160485}{128 (-1+2 x)}\right ) \, dx\\ &=\frac{22370117}{1024 (1-2 x)^2}-\frac{39220335}{256 (1-2 x)}-\frac{64029233 x}{256}-\frac{28504029 x^2}{256}-\frac{1661133 x^3}{32}-\frac{629505 x^4}{32}-\frac{80595 x^5}{16}-\frac{10125 x^6}{16}-\frac{60160485}{256} \log (1-2 x)\\ \end{align*}
Mathematica [A] time = 0.0211286, size = 66, normalized size = 0.9 \[ -\frac{2592000 x^8+18040320 x^7+60592320 x^6+137206464 x^5+263583600 x^4+621559520 x^3-1569001020 x^2+600903660 x+240641940 (1-2 x)^2 \log (1-2 x)-30126129}{1024 (1-2 x)^2} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.006, size = 56, normalized size = 0.8 \begin{align*} -{\frac{10125\,{x}^{6}}{16}}-{\frac{80595\,{x}^{5}}{16}}-{\frac{629505\,{x}^{4}}{32}}-{\frac{1661133\,{x}^{3}}{32}}-{\frac{28504029\,{x}^{2}}{256}}-{\frac{64029233\,x}{256}}-{\frac{60160485\,\ln \left ( 2\,x-1 \right ) }{256}}+{\frac{22370117}{1024\, \left ( 2\,x-1 \right ) ^{2}}}+{\frac{39220335}{512\,x-256}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 1.81977, size = 76, normalized size = 1.04 \begin{align*} -\frac{10125}{16} \, x^{6} - \frac{80595}{16} \, x^{5} - \frac{629505}{32} \, x^{4} - \frac{1661133}{32} \, x^{3} - \frac{28504029}{256} \, x^{2} - \frac{64029233}{256} \, x + \frac{290521 \,{\left (1080 \, x - 463\right )}}{1024 \,{\left (4 \, x^{2} - 4 \, x + 1\right )}} - \frac{60160485}{256} \, \log \left (2 \, x - 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.46917, size = 274, normalized size = 3.75 \begin{align*} -\frac{2592000 \, x^{8} + 18040320 \, x^{7} + 60592320 \, x^{6} + 137206464 \, x^{5} + 263583600 \, x^{4} + 621559520 \, x^{3} - 910451612 \, x^{2} + 240641940 \,{\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (2 \, x - 1\right ) - 57645748 \, x + 134511223}{1024 \,{\left (4 \, x^{2} - 4 \, x + 1\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.135292, size = 63, normalized size = 0.86 \begin{align*} - \frac{10125 x^{6}}{16} - \frac{80595 x^{5}}{16} - \frac{629505 x^{4}}{32} - \frac{1661133 x^{3}}{32} - \frac{28504029 x^{2}}{256} - \frac{64029233 x}{256} + \frac{313762680 x - 134511223}{4096 x^{2} - 4096 x + 1024} - \frac{60160485 \log{\left (2 x - 1 \right )}}{256} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 2.23665, size = 70, normalized size = 0.96 \begin{align*} -\frac{10125}{16} \, x^{6} - \frac{80595}{16} \, x^{5} - \frac{629505}{32} \, x^{4} - \frac{1661133}{32} \, x^{3} - \frac{28504029}{256} \, x^{2} - \frac{64029233}{256} \, x + \frac{290521 \,{\left (1080 \, x - 463\right )}}{1024 \,{\left (2 \, x - 1\right )}^{2}} - \frac{60160485}{256} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]