Optimal. Leaf size=44 \[ \frac{100 x^5}{3}+\frac{50 x^4}{9}-\frac{2515 x^3}{81}-\frac{559 x^2}{162}+\frac{3305 x}{243}-\frac{49}{729} \log (3 x+2) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0187745, antiderivative size = 44, 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} \[ \frac{100 x^5}{3}+\frac{50 x^4}{9}-\frac{2515 x^3}{81}-\frac{559 x^2}{162}+\frac{3305 x}{243}-\frac{49}{729} \log (3 x+2) \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 88
Rubi steps
\begin{align*} \int \frac{(1-2 x)^2 (3+5 x)^3}{2+3 x} \, dx &=\int \left (\frac{3305}{243}-\frac{559 x}{81}-\frac{2515 x^2}{27}+\frac{200 x^3}{9}+\frac{500 x^4}{3}-\frac{49}{243 (2+3 x)}\right ) \, dx\\ &=\frac{3305 x}{243}-\frac{559 x^2}{162}-\frac{2515 x^3}{81}+\frac{50 x^4}{9}+\frac{100 x^5}{3}-\frac{49}{729} \log (2+3 x)\\ \end{align*}
Mathematica [A] time = 0.0102974, size = 37, normalized size = 0.84 \[ \frac{145800 x^5+24300 x^4-135810 x^3-15093 x^2+59490 x-294 \log (3 x+2)+20528}{4374} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.003, size = 33, normalized size = 0.8 \begin{align*}{\frac{3305\,x}{243}}-{\frac{559\,{x}^{2}}{162}}-{\frac{2515\,{x}^{3}}{81}}+{\frac{50\,{x}^{4}}{9}}+{\frac{100\,{x}^{5}}{3}}-{\frac{49\,\ln \left ( 2+3\,x \right ) }{729}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 1.03323, size = 43, normalized size = 0.98 \begin{align*} \frac{100}{3} \, x^{5} + \frac{50}{9} \, x^{4} - \frac{2515}{81} \, x^{3} - \frac{559}{162} \, x^{2} + \frac{3305}{243} \, x - \frac{49}{729} \, \log \left (3 \, x + 2\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.4836, size = 115, normalized size = 2.61 \begin{align*} \frac{100}{3} \, x^{5} + \frac{50}{9} \, x^{4} - \frac{2515}{81} \, x^{3} - \frac{559}{162} \, x^{2} + \frac{3305}{243} \, x - \frac{49}{729} \, \log \left (3 \, x + 2\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.087683, size = 41, normalized size = 0.93 \begin{align*} \frac{100 x^{5}}{3} + \frac{50 x^{4}}{9} - \frac{2515 x^{3}}{81} - \frac{559 x^{2}}{162} + \frac{3305 x}{243} - \frac{49 \log{\left (3 x + 2 \right )}}{729} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.65348, size = 45, normalized size = 1.02 \begin{align*} \frac{100}{3} \, x^{5} + \frac{50}{9} \, x^{4} - \frac{2515}{81} \, x^{3} - \frac{559}{162} \, x^{2} + \frac{3305}{243} \, x - \frac{49}{729} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]