Optimal. Leaf size=33 \[ -\frac{55}{4 (1-2 x)}+\frac{121}{16 (1-2 x)^2}-\frac{25}{8} \log (1-2 x) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.012367, antiderivative size = 33, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067, Rules used = {43} \[ -\frac{55}{4 (1-2 x)}+\frac{121}{16 (1-2 x)^2}-\frac{25}{8} \log (1-2 x) \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 43
Rubi steps
\begin{align*} \int \frac{(3+5 x)^2}{(1-2 x)^3} \, dx &=\int \left (-\frac{121}{4 (-1+2 x)^3}-\frac{55}{2 (-1+2 x)^2}-\frac{25}{4 (-1+2 x)}\right ) \, dx\\ &=\frac{121}{16 (1-2 x)^2}-\frac{55}{4 (1-2 x)}-\frac{25}{8} \log (1-2 x)\\ \end{align*}
Mathematica [A] time = 0.0074873, size = 33, normalized size = 1. \[ -\frac{55}{4 (1-2 x)}+\frac{121}{16 (1-2 x)^2}-\frac{25}{8} \log (1-2 x) \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.006, size = 28, normalized size = 0.9 \begin{align*} -{\frac{25\,\ln \left ( 2\,x-1 \right ) }{8}}+{\frac{121}{16\, \left ( 2\,x-1 \right ) ^{2}}}+{\frac{55}{8\,x-4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 1.05154, size = 38, normalized size = 1.15 \begin{align*} \frac{11 \,{\left (40 \, x - 9\right )}}{16 \,{\left (4 \, x^{2} - 4 \, x + 1\right )}} - \frac{25}{8} \, \log \left (2 \, x - 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.49271, size = 100, normalized size = 3.03 \begin{align*} -\frac{50 \,{\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (2 \, x - 1\right ) - 440 \, x + 99}{16 \,{\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 = 0.109294, size = 24, normalized size = 0.73 \begin{align*} \frac{440 x - 99}{64 x^{2} - 64 x + 16} - \frac{25 \log{\left (2 x - 1 \right )}}{8} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 2.6247, size = 32, normalized size = 0.97 \begin{align*} \frac{11 \,{\left (40 \, x - 9\right )}}{16 \,{\left (2 \, x - 1\right )}^{2}} - \frac{25}{8} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]