Optimal. Leaf size=55 \[ -\frac{428}{243 (3 x+2)}+\frac{259}{81 (3 x+2)^2}-\frac{2009}{729 (3 x+2)^3}+\frac{343}{972 (3 x+2)^4}-\frac{40}{243} \log (3 x+2) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0200654, antiderivative size = 55, 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} \[ -\frac{428}{243 (3 x+2)}+\frac{259}{81 (3 x+2)^2}-\frac{2009}{729 (3 x+2)^3}+\frac{343}{972 (3 x+2)^4}-\frac{40}{243} \log (3 x+2) \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 77
Rubi steps
\begin{align*} \int \frac{(1-2 x)^3 (3+5 x)}{(2+3 x)^5} \, dx &=\int \left (-\frac{343}{81 (2+3 x)^5}+\frac{2009}{81 (2+3 x)^4}-\frac{518}{27 (2+3 x)^3}+\frac{428}{81 (2+3 x)^2}-\frac{40}{81 (2+3 x)}\right ) \, dx\\ &=\frac{343}{972 (2+3 x)^4}-\frac{2009}{729 (2+3 x)^3}+\frac{259}{81 (2+3 x)^2}-\frac{428}{243 (2+3 x)}-\frac{40}{243} \log (2+3 x)\\ \end{align*}
Mathematica [A] time = 0.0165141, size = 41, normalized size = 0.75 \[ -\frac{138672 x^3+193428 x^2+97116 x+480 (3 x+2)^4 \log (6 x+4)+18835}{2916 (3 x+2)^4} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.006, size = 46, normalized size = 0.8 \begin{align*}{\frac{343}{972\, \left ( 2+3\,x \right ) ^{4}}}-{\frac{2009}{729\, \left ( 2+3\,x \right ) ^{3}}}+{\frac{259}{81\, \left ( 2+3\,x \right ) ^{2}}}-{\frac{428}{486+729\,x}}-{\frac{40\,\ln \left ( 2+3\,x \right ) }{243}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 1.01201, size = 65, normalized size = 1.18 \begin{align*} -\frac{138672 \, x^{3} + 193428 \, x^{2} + 97116 \, x + 18835}{2916 \,{\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )}} - \frac{40}{243} \, \log \left (3 \, x + 2\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.24307, size = 208, normalized size = 3.78 \begin{align*} -\frac{138672 \, x^{3} + 193428 \, x^{2} + 480 \,{\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )} \log \left (3 \, x + 2\right ) + 97116 \, x + 18835}{2916 \,{\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.140471, size = 46, normalized size = 0.84 \begin{align*} - \frac{138672 x^{3} + 193428 x^{2} + 97116 x + 18835}{236196 x^{4} + 629856 x^{3} + 629856 x^{2} + 279936 x + 46656} - \frac{40 \log{\left (3 x + 2 \right )}}{243} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 2.83235, size = 74, normalized size = 1.35 \begin{align*} -\frac{428}{243 \,{\left (3 \, x + 2\right )}} + \frac{259}{81 \,{\left (3 \, x + 2\right )}^{2}} - \frac{2009}{729 \,{\left (3 \, x + 2\right )}^{3}} + \frac{343}{972 \,{\left (3 \, x + 2\right )}^{4}} + \frac{40}{243} \, \log \left (\frac{{\left | 3 \, x + 2 \right |}}{3 \,{\left (3 \, x + 2\right )}^{2}}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]