Optimal. Leaf size=47 \[ -\frac{243 x^4}{40}-\frac{2619 x^3}{100}-\frac{107433 x^2}{2000}-\frac{848277 x}{10000}-\frac{16807}{352} \log (1-2 x)+\frac{\log (5 x+3)}{34375} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0200036, antiderivative size = 47, 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} \[ -\frac{243 x^4}{40}-\frac{2619 x^3}{100}-\frac{107433 x^2}{2000}-\frac{848277 x}{10000}-\frac{16807}{352} \log (1-2 x)+\frac{\log (5 x+3)}{34375} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 72
Rubi steps
\begin{align*} \int \frac{(2+3 x)^5}{(1-2 x) (3+5 x)} \, dx &=\int \left (-\frac{848277}{10000}-\frac{107433 x}{1000}-\frac{7857 x^2}{100}-\frac{243 x^3}{10}-\frac{16807}{176 (-1+2 x)}+\frac{1}{6875 (3+5 x)}\right ) \, dx\\ &=-\frac{848277 x}{10000}-\frac{107433 x^2}{2000}-\frac{2619 x^3}{100}-\frac{243 x^4}{40}-\frac{16807}{352} \log (1-2 x)+\frac{\log (3+5 x)}{34375}\\ \end{align*}
Mathematica [A] time = 0.0156134, size = 45, normalized size = 0.96 \[ \frac{-110 \left (60750 x^4+261900 x^3+537165 x^2+848277 x+392378\right )-52521875 \log (3-6 x)+32 \log (-3 (5 x+3))}{1100000} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.005, size = 36, normalized size = 0.8 \begin{align*} -{\frac{243\,{x}^{4}}{40}}-{\frac{2619\,{x}^{3}}{100}}-{\frac{107433\,{x}^{2}}{2000}}-{\frac{848277\,x}{10000}}-{\frac{16807\,\ln \left ( 2\,x-1 \right ) }{352}}+{\frac{\ln \left ( 3+5\,x \right ) }{34375}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 1.0413, size = 47, normalized size = 1. \begin{align*} -\frac{243}{40} \, x^{4} - \frac{2619}{100} \, x^{3} - \frac{107433}{2000} \, x^{2} - \frac{848277}{10000} \, x + \frac{1}{34375} \, \log \left (5 \, x + 3\right ) - \frac{16807}{352} \, \log \left (2 \, x - 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.27854, size = 150, normalized size = 3.19 \begin{align*} -\frac{243}{40} \, x^{4} - \frac{2619}{100} \, x^{3} - \frac{107433}{2000} \, x^{2} - \frac{848277}{10000} \, x + \frac{1}{34375} \, \log \left (5 \, x + 3\right ) - \frac{16807}{352} \, \log \left (2 \, x - 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.127128, size = 42, normalized size = 0.89 \begin{align*} - \frac{243 x^{4}}{40} - \frac{2619 x^{3}}{100} - \frac{107433 x^{2}}{2000} - \frac{848277 x}{10000} - \frac{16807 \log{\left (x - \frac{1}{2} \right )}}{352} + \frac{\log{\left (x + \frac{3}{5} \right )}}{34375} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.28696, size = 50, normalized size = 1.06 \begin{align*} -\frac{243}{40} \, x^{4} - \frac{2619}{100} \, x^{3} - \frac{107433}{2000} \, x^{2} - \frac{848277}{10000} \, x + \frac{1}{34375} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) - \frac{16807}{352} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]