Optimal. Leaf size=37 \[ \frac{9 x^4}{5}-\frac{16 x^3}{25}-\frac{431 x^2}{250}+\frac{793 x}{625}+\frac{121 \log (5 x+3)}{3125} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0168758, 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} \[ \frac{9 x^4}{5}-\frac{16 x^3}{25}-\frac{431 x^2}{250}+\frac{793 x}{625}+\frac{121 \log (5 x+3)}{3125} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 88
Rubi steps
\begin{align*} \int \frac{(1-2 x)^2 (2+3 x)^2}{3+5 x} \, dx &=\int \left (\frac{793}{625}-\frac{431 x}{125}-\frac{48 x^2}{25}+\frac{36 x^3}{5}+\frac{121}{625 (3+5 x)}\right ) \, dx\\ &=\frac{793 x}{625}-\frac{431 x^2}{250}-\frac{16 x^3}{25}+\frac{9 x^4}{5}+\frac{121 \log (3+5 x)}{3125}\\ \end{align*}
Mathematica [A] time = 0.0100934, size = 35, normalized size = 0.95 \[ \frac{5 \left (2250 x^4-800 x^3-2155 x^2+1586 x+1263\right )+242 \log (5 x+3)}{6250} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.002, size = 28, normalized size = 0.8 \begin{align*}{\frac{793\,x}{625}}-{\frac{431\,{x}^{2}}{250}}-{\frac{16\,{x}^{3}}{25}}+{\frac{9\,{x}^{4}}{5}}+{\frac{121\,\ln \left ( 3+5\,x \right ) }{3125}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 0.98556, size = 36, normalized size = 0.97 \begin{align*} \frac{9}{5} \, x^{4} - \frac{16}{25} \, x^{3} - \frac{431}{250} \, x^{2} + \frac{793}{625} \, x + \frac{121}{3125} \, \log \left (5 \, x + 3\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.48669, size = 96, normalized size = 2.59 \begin{align*} \frac{9}{5} \, x^{4} - \frac{16}{25} \, x^{3} - \frac{431}{250} \, x^{2} + \frac{793}{625} \, x + \frac{121}{3125} \, \log \left (5 \, x + 3\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.085488, size = 34, normalized size = 0.92 \begin{align*} \frac{9 x^{4}}{5} - \frac{16 x^{3}}{25} - \frac{431 x^{2}}{250} + \frac{793 x}{625} + \frac{121 \log{\left (5 x + 3 \right )}}{3125} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 2.6876, size = 38, normalized size = 1.03 \begin{align*} \frac{9}{5} \, x^{4} - \frac{16}{25} \, x^{3} - \frac{431}{250} \, x^{2} + \frac{793}{625} \, x + \frac{121}{3125} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]