Optimal. Leaf size=43 \[ \frac{121}{98 (1-2 x)}-\frac{1}{147 (3 x+2)}+\frac{22}{343} \log (1-2 x)-\frac{22}{343} \log (3 x+2) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0178059, 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} \[ \frac{121}{98 (1-2 x)}-\frac{1}{147 (3 x+2)}+\frac{22}{343} \log (1-2 x)-\frac{22}{343} \log (3 x+2) \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 88
Rubi steps
\begin{align*} \int \frac{(3+5 x)^2}{(1-2 x)^2 (2+3 x)^2} \, dx &=\int \left (\frac{121}{49 (-1+2 x)^2}+\frac{44}{343 (-1+2 x)}+\frac{1}{49 (2+3 x)^2}-\frac{66}{343 (2+3 x)}\right ) \, dx\\ &=\frac{121}{98 (1-2 x)}-\frac{1}{147 (2+3 x)}+\frac{22}{343} \log (1-2 x)-\frac{22}{343} \log (2+3 x)\\ \end{align*}
Mathematica [A] time = 0.0264893, size = 38, normalized size = 0.88 \[ \frac{-\frac{7 (1093 x+724)}{6 x^2+x-2}+132 \log (1-2 x)-132 \log (3 x+2)}{2058} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.009, size = 36, normalized size = 0.8 \begin{align*} -{\frac{121}{196\,x-98}}+{\frac{22\,\ln \left ( 2\,x-1 \right ) }{343}}-{\frac{1}{294+441\,x}}-{\frac{22\,\ln \left ( 2+3\,x \right ) }{343}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 1.09904, size = 46, normalized size = 1.07 \begin{align*} -\frac{1093 \, x + 724}{294 \,{\left (6 \, x^{2} + x - 2\right )}} - \frac{22}{343} \, \log \left (3 \, x + 2\right ) + \frac{22}{343} \, \log \left (2 \, x - 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.25124, size = 150, normalized size = 3.49 \begin{align*} -\frac{132 \,{\left (6 \, x^{2} + x - 2\right )} \log \left (3 \, x + 2\right ) - 132 \,{\left (6 \, x^{2} + x - 2\right )} \log \left (2 \, x - 1\right ) + 7651 \, x + 5068}{2058 \,{\left (6 \, x^{2} + x - 2\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.133014, size = 34, normalized size = 0.79 \begin{align*} - \frac{1093 x + 724}{1764 x^{2} + 294 x - 588} + \frac{22 \log{\left (x - \frac{1}{2} \right )}}{343} - \frac{22 \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 = 2.00916, size = 54, normalized size = 1.26 \begin{align*} -\frac{1}{147 \,{\left (3 \, x + 2\right )}} + \frac{363}{343 \,{\left (\frac{7}{3 \, x + 2} - 2\right )}} + \frac{22}{343} \, \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]