Optimal. Leaf size=43 \[ -\frac{217}{484 (1-2 x)}+\frac{49}{88 (1-2 x)^2}-\frac{\log (1-2 x)}{1331}+\frac{\log (5 x+3)}{1331} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0178942, 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} \[ -\frac{217}{484 (1-2 x)}+\frac{49}{88 (1-2 x)^2}-\frac{\log (1-2 x)}{1331}+\frac{\log (5 x+3)}{1331} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 88
Rubi steps
\begin{align*} \int \frac{(2+3 x)^2}{(1-2 x)^3 (3+5 x)} \, dx &=\int \left (-\frac{49}{22 (-1+2 x)^3}-\frac{217}{242 (-1+2 x)^2}-\frac{2}{1331 (-1+2 x)}+\frac{5}{1331 (3+5 x)}\right ) \, dx\\ &=\frac{49}{88 (1-2 x)^2}-\frac{217}{484 (1-2 x)}-\frac{\log (1-2 x)}{1331}+\frac{\log (3+5 x)}{1331}\\ \end{align*}
Mathematica [A] time = 0.0206069, size = 35, normalized size = 0.81 \[ \frac{\frac{77 (124 x+15)}{(1-2 x)^2}-8 \log (5-10 x)+8 \log (5 x+3)}{10648} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.006, size = 36, normalized size = 0.8 \begin{align*}{\frac{49}{88\, \left ( 2\,x-1 \right ) ^{2}}}+{\frac{217}{968\,x-484}}-{\frac{\ln \left ( 2\,x-1 \right ) }{1331}}+{\frac{\ln \left ( 3+5\,x \right ) }{1331}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 1.01137, size = 49, normalized size = 1.14 \begin{align*} \frac{7 \,{\left (124 \, x + 15\right )}}{968 \,{\left (4 \, x^{2} - 4 \, x + 1\right )}} + \frac{1}{1331} \, \log \left (5 \, x + 3\right ) - \frac{1}{1331} \, \log \left (2 \, x - 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.57349, size = 153, normalized size = 3.56 \begin{align*} \frac{8 \,{\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (5 \, x + 3\right ) - 8 \,{\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (2 \, x - 1\right ) + 9548 \, x + 1155}{10648 \,{\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 = 0.137814, size = 31, normalized size = 0.72 \begin{align*} \frac{868 x + 105}{3872 x^{2} - 3872 x + 968} - \frac{\log{\left (x - \frac{1}{2} \right )}}{1331} + \frac{\log{\left (x + \frac{3}{5} \right )}}{1331} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.84607, size = 45, normalized size = 1.05 \begin{align*} \frac{7 \,{\left (124 \, x + 15\right )}}{968 \,{\left (2 \, x - 1\right )}^{2}} + \frac{1}{1331} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) - \frac{1}{1331} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]