Optimal. Leaf size=48 \[ \frac{1125 x^4}{16}+\frac{775 x^3}{2}+\frac{35135 x^2}{32}+\frac{41537 x}{16}+\frac{65219}{64 (1-2 x)}+\frac{144837}{64} \log (1-2 x) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0230594, antiderivative size = 48, 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} \[ \frac{1125 x^4}{16}+\frac{775 x^3}{2}+\frac{35135 x^2}{32}+\frac{41537 x}{16}+\frac{65219}{64 (1-2 x)}+\frac{144837}{64} \log (1-2 x) \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 88
Rubi steps
\begin{align*} \int \frac{(2+3 x)^2 (3+5 x)^3}{(1-2 x)^2} \, dx &=\int \left (\frac{41537}{16}+\frac{35135 x}{16}+\frac{2325 x^2}{2}+\frac{1125 x^3}{4}+\frac{65219}{32 (-1+2 x)^2}+\frac{144837}{32 (-1+2 x)}\right ) \, dx\\ &=\frac{65219}{64 (1-2 x)}+\frac{41537 x}{16}+\frac{35135 x^2}{32}+\frac{775 x^3}{2}+\frac{1125 x^4}{16}+\frac{144837}{64} \log (1-2 x)\\ \end{align*}
Mathematica [A] time = 0.0135248, size = 49, normalized size = 1.02 \[ \frac{36000 x^5+180400 x^4+462960 x^3+1048104 x^2-1496774 x+579348 (2 x-1) \log (1-2 x)+155215}{256 (2 x-1)} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.007, size = 37, normalized size = 0.8 \begin{align*}{\frac{1125\,{x}^{4}}{16}}+{\frac{775\,{x}^{3}}{2}}+{\frac{35135\,{x}^{2}}{32}}+{\frac{41537\,x}{16}}+{\frac{144837\,\ln \left ( 2\,x-1 \right ) }{64}}-{\frac{65219}{128\,x-64}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 1.16312, size = 49, normalized size = 1.02 \begin{align*} \frac{1125}{16} \, x^{4} + \frac{775}{2} \, x^{3} + \frac{35135}{32} \, x^{2} + \frac{41537}{16} \, x - \frac{65219}{64 \,{\left (2 \, x - 1\right )}} + \frac{144837}{64} \, \log \left (2 \, x - 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.18316, size = 157, normalized size = 3.27 \begin{align*} \frac{9000 \, x^{5} + 45100 \, x^{4} + 115740 \, x^{3} + 262026 \, x^{2} + 144837 \,{\left (2 \, x - 1\right )} \log \left (2 \, x - 1\right ) - 166148 \, x - 65219}{64 \,{\left (2 \, x - 1\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.102453, size = 41, normalized size = 0.85 \begin{align*} \frac{1125 x^{4}}{16} + \frac{775 x^{3}}{2} + \frac{35135 x^{2}}{32} + \frac{41537 x}{16} + \frac{144837 \log{\left (2 x - 1 \right )}}{64} - \frac{65219}{128 x - 64} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 3.035, size = 89, normalized size = 1.85 \begin{align*} \frac{1}{256} \,{\left (2 \, x - 1\right )}^{4}{\left (\frac{16900}{2 \, x - 1} + \frac{114220}{{\left (2 \, x - 1\right )}^{2}} + \frac{514536}{{\left (2 \, x - 1\right )}^{3}} + 1125\right )} - \frac{65219}{64 \,{\left (2 \, x - 1\right )}} - \frac{144837}{64} \, \log \left (\frac{{\left | 2 \, x - 1 \right |}}{2 \,{\left (2 \, x - 1\right )}^{2}}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]