Optimal. Leaf size=53 \[ \frac{136}{5929 (1-2 x)}+\frac{1}{77 (1-2 x)^2}-\frac{6938 \log (1-2 x)}{456533}-\frac{27}{343} \log (3 x+2)+\frac{125 \log (5 x+3)}{1331} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0237475, 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 = {72} \[ \frac{136}{5929 (1-2 x)}+\frac{1}{77 (1-2 x)^2}-\frac{6938 \log (1-2 x)}{456533}-\frac{27}{343} \log (3 x+2)+\frac{125 \log (5 x+3)}{1331} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 72
Rubi steps
\begin{align*} \int \frac{1}{(1-2 x)^3 (2+3 x) (3+5 x)} \, dx &=\int \left (-\frac{4}{77 (-1+2 x)^3}+\frac{272}{5929 (-1+2 x)^2}-\frac{13876}{456533 (-1+2 x)}-\frac{81}{343 (2+3 x)}+\frac{625}{1331 (3+5 x)}\right ) \, dx\\ &=\frac{1}{77 (1-2 x)^2}+\frac{136}{5929 (1-2 x)}-\frac{6938 \log (1-2 x)}{456533}-\frac{27}{343} \log (2+3 x)+\frac{125 \log (3+5 x)}{1331}\\ \end{align*}
Mathematica [A] time = 0.0250934, size = 52, normalized size = 0.98 \[ \frac{-6938 \log (3-6 x)-35937 \log (3 x+2)+\frac{7 \left (-2992 x+6125 (1-2 x)^2 \log (-3 (5 x+3))+2343\right )}{(1-2 x)^2}}{456533} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.007, size = 44, normalized size = 0.8 \begin{align*}{\frac{1}{77\, \left ( 2\,x-1 \right ) ^{2}}}-{\frac{136}{11858\,x-5929}}-{\frac{6938\,\ln \left ( 2\,x-1 \right ) }{456533}}-{\frac{27\,\ln \left ( 2+3\,x \right ) }{343}}+{\frac{125\,\ln \left ( 3+5\,x \right ) }{1331}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 1.38795, size = 59, normalized size = 1.11 \begin{align*} -\frac{272 \, x - 213}{5929 \,{\left (4 \, x^{2} - 4 \, x + 1\right )}} + \frac{125}{1331} \, \log \left (5 \, x + 3\right ) - \frac{27}{343} \, \log \left (3 \, x + 2\right ) - \frac{6938}{456533} \, \log \left (2 \, x - 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.53099, size = 219, normalized size = 4.13 \begin{align*} \frac{42875 \,{\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (5 \, x + 3\right ) - 35937 \,{\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (3 \, x + 2\right ) - 6938 \,{\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (2 \, x - 1\right ) - 20944 \, x + 16401}{456533 \,{\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 = 0.177326, size = 44, normalized size = 0.83 \begin{align*} - \frac{272 x - 213}{23716 x^{2} - 23716 x + 5929} - \frac{6938 \log{\left (x - \frac{1}{2} \right )}}{456533} + \frac{125 \log{\left (x + \frac{3}{5} \right )}}{1331} - \frac{27 \log{\left (x + \frac{2}{3} \right )}}{343} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 3.00802, size = 57, normalized size = 1.08 \begin{align*} -\frac{272 \, x - 213}{5929 \,{\left (2 \, x - 1\right )}^{2}} + \frac{125}{1331} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) - \frac{27}{343} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) - \frac{6938}{456533} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]