Optimal. Leaf size=41 \[ -\frac{8 x^3}{25}+\frac{122 x^2}{125}-\frac{1098 x}{625}-\frac{1331}{3125 (5 x+3)}+\frac{3267 \log (5 x+3)}{3125} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0185232, antiderivative size = 41, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05, Rules used = {77} \[ -\frac{8 x^3}{25}+\frac{122 x^2}{125}-\frac{1098 x}{625}-\frac{1331}{3125 (5 x+3)}+\frac{3267 \log (5 x+3)}{3125} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 77
Rubi steps
\begin{align*} \int \frac{(1-2 x)^3 (2+3 x)}{(3+5 x)^2} \, dx &=\int \left (-\frac{1098}{625}+\frac{244 x}{125}-\frac{24 x^2}{25}+\frac{1331}{625 (3+5 x)^2}+\frac{3267}{625 (3+5 x)}\right ) \, dx\\ &=-\frac{1098 x}{625}+\frac{122 x^2}{125}-\frac{8 x^3}{25}-\frac{1331}{3125 (3+5 x)}+\frac{3267 \log (3+5 x)}{3125}\\ \end{align*}
Mathematica [A] time = 0.0149918, size = 44, normalized size = 1.07 \[ \frac{-10000 x^4+24500 x^3-36600 x^2-11865 x+6534 (5 x+3) \log (10 x+6)+9983}{6250 (5 x+3)} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.005, size = 32, normalized size = 0.8 \begin{align*} -{\frac{1098\,x}{625}}+{\frac{122\,{x}^{2}}{125}}-{\frac{8\,{x}^{3}}{25}}-{\frac{1331}{9375+15625\,x}}+{\frac{3267\,\ln \left ( 3+5\,x \right ) }{3125}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 1.00383, size = 42, normalized size = 1.02 \begin{align*} -\frac{8}{25} \, x^{3} + \frac{122}{125} \, x^{2} - \frac{1098}{625} \, x - \frac{1331}{3125 \,{\left (5 \, x + 3\right )}} + \frac{3267}{3125} \, \log \left (5 \, x + 3\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.44526, size = 136, normalized size = 3.32 \begin{align*} -\frac{5000 \, x^{4} - 12250 \, x^{3} + 18300 \, x^{2} - 3267 \,{\left (5 \, x + 3\right )} \log \left (5 \, x + 3\right ) + 16470 \, x + 1331}{3125 \,{\left (5 \, x + 3\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.100907, size = 34, normalized size = 0.83 \begin{align*} - \frac{8 x^{3}}{25} + \frac{122 x^{2}}{125} - \frac{1098 x}{625} + \frac{3267 \log{\left (5 x + 3 \right )}}{3125} - \frac{1331}{15625 x + 9375} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 3.11655, size = 77, normalized size = 1.88 \begin{align*} \frac{2}{3125} \,{\left (5 \, x + 3\right )}^{3}{\left (\frac{97}{5 \, x + 3} - \frac{1023}{{\left (5 \, x + 3\right )}^{2}} - 4\right )} - \frac{1331}{3125 \,{\left (5 \, x + 3\right )}} - \frac{3267}{3125} \, \log \left (\frac{{\left | 5 \, x + 3 \right |}}{5 \,{\left (5 \, x + 3\right )}^{2}}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]