Optimal. Leaf size=37 \[ -\frac{125 x^4}{6}-\frac{475 x^3}{27}+\frac{545 x^2}{54}+\frac{1097 x}{81}-\frac{7}{243} \log (3 x+2) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0137501, antiderivative size = 37, 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} \[ -\frac{125 x^4}{6}-\frac{475 x^3}{27}+\frac{545 x^2}{54}+\frac{1097 x}{81}-\frac{7}{243} \log (3 x+2) \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 77
Rubi steps
\begin{align*} \int \frac{(1-2 x) (3+5 x)^3}{2+3 x} \, dx &=\int \left (\frac{1097}{81}+\frac{545 x}{27}-\frac{475 x^2}{9}-\frac{250 x^3}{3}-\frac{7}{81 (2+3 x)}\right ) \, dx\\ &=\frac{1097 x}{81}+\frac{545 x^2}{54}-\frac{475 x^3}{27}-\frac{125 x^4}{6}-\frac{7}{243} \log (2+3 x)\\ \end{align*}
Mathematica [A] time = 0.01178, size = 32, normalized size = 0.86 \[ \frac{-30375 x^4-25650 x^3+14715 x^2+19746 x-42 \log (3 x+2)+5024}{1458} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.001, size = 28, normalized size = 0.8 \begin{align*}{\frac{1097\,x}{81}}+{\frac{545\,{x}^{2}}{54}}-{\frac{475\,{x}^{3}}{27}}-{\frac{125\,{x}^{4}}{6}}-{\frac{7\,\ln \left ( 2+3\,x \right ) }{243}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 1.07793, size = 36, normalized size = 0.97 \begin{align*} -\frac{125}{6} \, x^{4} - \frac{475}{27} \, x^{3} + \frac{545}{54} \, x^{2} + \frac{1097}{81} \, x - \frac{7}{243} \, \log \left (3 \, x + 2\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.81489, size = 96, normalized size = 2.59 \begin{align*} -\frac{125}{6} \, x^{4} - \frac{475}{27} \, x^{3} + \frac{545}{54} \, x^{2} + \frac{1097}{81} \, x - \frac{7}{243} \, \log \left (3 \, x + 2\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.086983, size = 34, normalized size = 0.92 \begin{align*} - \frac{125 x^{4}}{6} - \frac{475 x^{3}}{27} + \frac{545 x^{2}}{54} + \frac{1097 x}{81} - \frac{7 \log{\left (3 x + 2 \right )}}{243} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 2.27813, size = 38, normalized size = 1.03 \begin{align*} -\frac{125}{6} \, x^{4} - \frac{475}{27} \, x^{3} + \frac{545}{54} \, x^{2} + \frac{1097}{81} \, x - \frac{7}{243} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]