Optimal. Leaf size=58 \[ -\frac{6075 x^7}{14}-\frac{20385 x^6}{8}-\frac{275103 x^5}{40}-\frac{736623 x^4}{64}-\frac{444581 x^3}{32}-\frac{1797103 x^2}{128}-\frac{1996783 x}{128}-\frac{2033647}{256} \log (1-2 x) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0259308, antiderivative size = 58, 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} \[ -\frac{6075 x^7}{14}-\frac{20385 x^6}{8}-\frac{275103 x^5}{40}-\frac{736623 x^4}{64}-\frac{444581 x^3}{32}-\frac{1797103 x^2}{128}-\frac{1996783 x}{128}-\frac{2033647}{256} \log (1-2 x) \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 88
Rubi steps
\begin{align*} \int \frac{(2+3 x)^5 (3+5 x)^2}{1-2 x} \, dx &=\int \left (-\frac{1996783}{128}-\frac{1797103 x}{64}-\frac{1333743 x^2}{32}-\frac{736623 x^3}{16}-\frac{275103 x^4}{8}-\frac{61155 x^5}{4}-\frac{6075 x^6}{2}-\frac{2033647}{128 (-1+2 x)}\right ) \, dx\\ &=-\frac{1996783 x}{128}-\frac{1797103 x^2}{128}-\frac{444581 x^3}{32}-\frac{736623 x^4}{64}-\frac{275103 x^5}{40}-\frac{20385 x^6}{8}-\frac{6075 x^7}{14}-\frac{2033647}{256} \log (1-2 x)\\ \end{align*}
Mathematica [A] time = 0.0125792, size = 47, normalized size = 0.81 \[ \frac{-15552000 x^7-91324800 x^6-246492288 x^5-412508880 x^4-497930720 x^3-503188840 x^2-559099240 x-284710580 \log (1-2 x)+502621309}{35840} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.003, size = 43, normalized size = 0.7 \begin{align*} -{\frac{6075\,{x}^{7}}{14}}-{\frac{20385\,{x}^{6}}{8}}-{\frac{275103\,{x}^{5}}{40}}-{\frac{736623\,{x}^{4}}{64}}-{\frac{444581\,{x}^{3}}{32}}-{\frac{1797103\,{x}^{2}}{128}}-{\frac{1996783\,x}{128}}-{\frac{2033647\,\ln \left ( 2\,x-1 \right ) }{256}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 1.07293, size = 57, normalized size = 0.98 \begin{align*} -\frac{6075}{14} \, x^{7} - \frac{20385}{8} \, x^{6} - \frac{275103}{40} \, x^{5} - \frac{736623}{64} \, x^{4} - \frac{444581}{32} \, x^{3} - \frac{1797103}{128} \, x^{2} - \frac{1996783}{128} \, x - \frac{2033647}{256} \, \log \left (2 \, x - 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.48291, size = 185, normalized size = 3.19 \begin{align*} -\frac{6075}{14} \, x^{7} - \frac{20385}{8} \, x^{6} - \frac{275103}{40} \, x^{5} - \frac{736623}{64} \, x^{4} - \frac{444581}{32} \, x^{3} - \frac{1797103}{128} \, x^{2} - \frac{1996783}{128} \, x - \frac{2033647}{256} \, \log \left (2 \, x - 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.101942, size = 56, normalized size = 0.97 \begin{align*} - \frac{6075 x^{7}}{14} - \frac{20385 x^{6}}{8} - \frac{275103 x^{5}}{40} - \frac{736623 x^{4}}{64} - \frac{444581 x^{3}}{32} - \frac{1797103 x^{2}}{128} - \frac{1996783 x}{128} - \frac{2033647 \log{\left (2 x - 1 \right )}}{256} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.18637, size = 58, normalized size = 1. \begin{align*} -\frac{6075}{14} \, x^{7} - \frac{20385}{8} \, x^{6} - \frac{275103}{40} \, x^{5} - \frac{736623}{64} \, x^{4} - \frac{444581}{32} \, x^{3} - \frac{1797103}{128} \, x^{2} - \frac{1996783}{128} \, x - \frac{2033647}{256} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]