Optimal. Leaf size=37 \[ -\frac{27 x}{50}-\frac{1}{1375 (5 x+3)}-\frac{343}{484} \log (1-2 x)+\frac{101 \log (5 x+3)}{15125} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0153583, antiderivative size = 37, 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} \[ -\frac{27 x}{50}-\frac{1}{1375 (5 x+3)}-\frac{343}{484} \log (1-2 x)+\frac{101 \log (5 x+3)}{15125} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 88
Rubi steps
\begin{align*} \int \frac{(2+3 x)^3}{(1-2 x) (3+5 x)^2} \, dx &=\int \left (-\frac{27}{50}-\frac{343}{242 (-1+2 x)}+\frac{1}{275 (3+5 x)^2}+\frac{101}{3025 (3+5 x)}\right ) \, dx\\ &=-\frac{27 x}{50}-\frac{1}{1375 (3+5 x)}-\frac{343}{484} \log (1-2 x)+\frac{101 \log (3+5 x)}{15125}\\ \end{align*}
Mathematica [A] time = 0.0210582, size = 37, normalized size = 1. \[ \frac{16335 (1-2 x)-\frac{44}{5 x+3}-42875 \log (1-2 x)+404 \log (10 x+6)}{60500} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.006, size = 30, normalized size = 0.8 \begin{align*} -{\frac{27\,x}{50}}-{\frac{343\,\ln \left ( 2\,x-1 \right ) }{484}}-{\frac{1}{4125+6875\,x}}+{\frac{101\,\ln \left ( 3+5\,x \right ) }{15125}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 2.45823, size = 39, normalized size = 1.05 \begin{align*} -\frac{27}{50} \, x - \frac{1}{1375 \,{\left (5 \, x + 3\right )}} + \frac{101}{15125} \, \log \left (5 \, x + 3\right ) - \frac{343}{484} \, \log \left (2 \, x - 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.56202, size = 146, normalized size = 3.95 \begin{align*} -\frac{163350 \, x^{2} - 404 \,{\left (5 \, x + 3\right )} \log \left (5 \, x + 3\right ) + 42875 \,{\left (5 \, x + 3\right )} \log \left (2 \, x - 1\right ) + 98010 \, x + 44}{60500 \,{\left (5 \, x + 3\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.139723, size = 31, normalized size = 0.84 \begin{align*} - \frac{27 x}{50} - \frac{343 \log{\left (x - \frac{1}{2} \right )}}{484} + \frac{101 \log{\left (x + \frac{3}{5} \right )}}{15125} - \frac{1}{6875 x + 4125} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.38479, size = 63, normalized size = 1.7 \begin{align*} -\frac{27}{50} \, x - \frac{1}{1375 \,{\left (5 \, x + 3\right )}} + \frac{351}{500} \, \log \left (\frac{{\left | 5 \, x + 3 \right |}}{5 \,{\left (5 \, x + 3\right )}^{2}}\right ) - \frac{343}{484} \, \log \left ({\left | -\frac{11}{5 \, x + 3} + 2 \right |}\right ) - \frac{81}{250} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]