Optimal. Leaf size=32 \[ \frac{45 x^2}{8}+33 x+\frac{539}{16 (1-2 x)}+\frac{707}{16} \log (1-2 x) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0163089, antiderivative size = 32, 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} \[ \frac{45 x^2}{8}+33 x+\frac{539}{16 (1-2 x)}+\frac{707}{16} \log (1-2 x) \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 77
Rubi steps
\begin{align*} \int \frac{(2+3 x)^2 (3+5 x)}{(1-2 x)^2} \, dx &=\int \left (33+\frac{45 x}{4}+\frac{539}{8 (-1+2 x)^2}+\frac{707}{8 (-1+2 x)}\right ) \, dx\\ &=\frac{539}{16 (1-2 x)}+33 x+\frac{45 x^2}{8}+\frac{707}{16} \log (1-2 x)\\ \end{align*}
Mathematica [A] time = 0.0096743, size = 36, normalized size = 1.12 \[ \frac{360 x^3+1932 x^2-2202 x+1414 (2 x-1) \log (1-2 x)-505}{64 x-32} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.007, size = 27, normalized size = 0.8 \begin{align*}{\frac{45\,{x}^{2}}{8}}+33\,x+{\frac{707\,\ln \left ( 2\,x-1 \right ) }{16}}-{\frac{539}{32\,x-16}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 1.05584, size = 35, normalized size = 1.09 \begin{align*} \frac{45}{8} \, x^{2} + 33 \, x - \frac{539}{16 \,{\left (2 \, x - 1\right )}} + \frac{707}{16} \, \log \left (2 \, x - 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.22375, size = 107, normalized size = 3.34 \begin{align*} \frac{180 \, x^{3} + 966 \, x^{2} + 707 \,{\left (2 \, x - 1\right )} \log \left (2 \, x - 1\right ) - 528 \, x - 539}{16 \,{\left (2 \, x - 1\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.098408, size = 26, normalized size = 0.81 \begin{align*} \frac{45 x^{2}}{8} + 33 x + \frac{707 \log{\left (2 x - 1 \right )}}{16} - \frac{539}{32 x - 16} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 2.95683, size = 65, normalized size = 2.03 \begin{align*} \frac{3}{32} \,{\left (2 \, x - 1\right )}^{2}{\left (\frac{206}{2 \, x - 1} + 15\right )} - \frac{539}{16 \,{\left (2 \, x - 1\right )}} - \frac{707}{16} \, \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]