Optimal. Leaf size=53 \[ \frac{4}{847 (1-2 x)}-\frac{25}{121 (5 x+3)}-\frac{412 \log (1-2 x)}{65219}+\frac{27}{49} \log (3 x+2)-\frac{725 \log (5 x+3)}{1331} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0252081, antiderivative size = 53, 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} \[ \frac{4}{847 (1-2 x)}-\frac{25}{121 (5 x+3)}-\frac{412 \log (1-2 x)}{65219}+\frac{27}{49} \log (3 x+2)-\frac{725 \log (5 x+3)}{1331} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 88
Rubi steps
\begin{align*} \int \frac{1}{(1-2 x)^2 (2+3 x) (3+5 x)^2} \, dx &=\int \left (\frac{8}{847 (-1+2 x)^2}-\frac{824}{65219 (-1+2 x)}+\frac{81}{49 (2+3 x)}+\frac{125}{121 (3+5 x)^2}-\frac{3625}{1331 (3+5 x)}\right ) \, dx\\ &=\frac{4}{847 (1-2 x)}-\frac{25}{121 (3+5 x)}-\frac{412 \log (1-2 x)}{65219}+\frac{27}{49} \log (2+3 x)-\frac{725 \log (3+5 x)}{1331}\\ \end{align*}
Mathematica [A] time = 0.0318662, size = 48, normalized size = 0.91 \[ \frac{-\frac{77 (370 x-163)}{10 x^2+x-3}-412 \log (3-6 x)+35937 \log (3 x+2)-35525 \log (-3 (5 x+3))}{65219} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.01, size = 44, normalized size = 0.8 \begin{align*} -{\frac{4}{1694\,x-847}}-{\frac{412\,\ln \left ( 2\,x-1 \right ) }{65219}}+{\frac{27\,\ln \left ( 2+3\,x \right ) }{49}}-{\frac{25}{363+605\,x}}-{\frac{725\,\ln \left ( 3+5\,x \right ) }{1331}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 1.95621, size = 57, normalized size = 1.08 \begin{align*} -\frac{370 \, x - 163}{847 \,{\left (10 \, x^{2} + x - 3\right )}} - \frac{725}{1331} \, \log \left (5 \, x + 3\right ) + \frac{27}{49} \, \log \left (3 \, x + 2\right ) - \frac{412}{65219} \, \log \left (2 \, x - 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.47198, size = 212, normalized size = 4. \begin{align*} -\frac{35525 \,{\left (10 \, x^{2} + x - 3\right )} \log \left (5 \, x + 3\right ) - 35937 \,{\left (10 \, x^{2} + x - 3\right )} \log \left (3 \, x + 2\right ) + 412 \,{\left (10 \, x^{2} + x - 3\right )} \log \left (2 \, x - 1\right ) + 28490 \, x - 12551}{65219 \,{\left (10 \, x^{2} + x - 3\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.181762, size = 44, normalized size = 0.83 \begin{align*} - \frac{370 x - 163}{8470 x^{2} + 847 x - 2541} - \frac{412 \log{\left (x - \frac{1}{2} \right )}}{65219} - \frac{725 \log{\left (x + \frac{3}{5} \right )}}{1331} + \frac{27 \log{\left (x + \frac{2}{3} \right )}}{49} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 3.28268, size = 74, normalized size = 1.4 \begin{align*} -\frac{25}{121 \,{\left (5 \, x + 3\right )}} + \frac{40}{9317 \,{\left (\frac{11}{5 \, x + 3} - 2\right )}} + \frac{27}{49} \, \log \left ({\left | -\frac{1}{5 \, x + 3} - 3 \right |}\right ) - \frac{412}{65219} \, \log \left ({\left | -\frac{11}{5 \, x + 3} + 2 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]