Optimal. Leaf size=43 \[ \frac{1331}{196 (1-2 x)}+\frac{1}{441 (3 x+2)}+\frac{4719 \log (1-2 x)}{1372}+\frac{101 \log (3 x+2)}{3087} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0185813, antiderivative size = 43, 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} \[ \frac{1331}{196 (1-2 x)}+\frac{1}{441 (3 x+2)}+\frac{4719 \log (1-2 x)}{1372}+\frac{101 \log (3 x+2)}{3087} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 88
Rubi steps
\begin{align*} \int \frac{(3+5 x)^3}{(1-2 x)^2 (2+3 x)^2} \, dx &=\int \left (\frac{1331}{98 (-1+2 x)^2}+\frac{4719}{686 (-1+2 x)}-\frac{1}{147 (2+3 x)^2}+\frac{101}{1029 (2+3 x)}\right ) \, dx\\ &=\frac{1331}{196 (1-2 x)}+\frac{1}{441 (2+3 x)}+\frac{4719 \log (1-2 x)}{1372}+\frac{101 \log (2+3 x)}{3087}\\ \end{align*}
Mathematica [A] time = 0.0222907, size = 40, normalized size = 0.93 \[ \frac{-\frac{7 (35929 x+23962)}{6 x^2+x-2}+42471 \log (5-10 x)+404 \log (5 (3 x+2))}{12348} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.009, size = 36, normalized size = 0.8 \begin{align*} -{\frac{1331}{392\,x-196}}+{\frac{4719\,\ln \left ( 2\,x-1 \right ) }{1372}}+{\frac{1}{882+1323\,x}}+{\frac{101\,\ln \left ( 2+3\,x \right ) }{3087}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 2.04313, size = 46, normalized size = 1.07 \begin{align*} -\frac{35929 \, x + 23962}{1764 \,{\left (6 \, x^{2} + x - 2\right )}} + \frac{101}{3087} \, \log \left (3 \, x + 2\right ) + \frac{4719}{1372} \, \log \left (2 \, x - 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.25605, size = 158, normalized size = 3.67 \begin{align*} \frac{404 \,{\left (6 \, x^{2} + x - 2\right )} \log \left (3 \, x + 2\right ) + 42471 \,{\left (6 \, x^{2} + x - 2\right )} \log \left (2 \, x - 1\right ) - 251503 \, x - 167734}{12348 \,{\left (6 \, x^{2} + x - 2\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.151601, size = 34, normalized size = 0.79 \begin{align*} - \frac{35929 x + 23962}{10584 x^{2} + 1764 x - 3528} + \frac{4719 \log{\left (x - \frac{1}{2} \right )}}{1372} + \frac{101 \log{\left (x + \frac{2}{3} \right )}}{3087} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 2.30383, size = 78, normalized size = 1.81 \begin{align*} \frac{1}{441 \,{\left (3 \, x + 2\right )}} + \frac{3993}{686 \,{\left (\frac{7}{3 \, x + 2} - 2\right )}} - \frac{125}{36} \, \log \left (\frac{{\left | 3 \, x + 2 \right |}}{3 \,{\left (3 \, x + 2\right )}^{2}}\right ) + \frac{4719}{1372} \, \log \left ({\left | -\frac{7}{3 \, x + 2} + 2 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]