Optimal. Leaf size=34 \[ -\frac {25 x^2}{9}+\frac {95 x}{27}-\frac {7}{81 (3 x+2)}-\frac {8}{9} \log (3 x+2) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.02, antiderivative size = 34, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {77} \[ -\frac {25 x^2}{9}+\frac {95 x}{27}-\frac {7}{81 (3 x+2)}-\frac {8}{9} \log (3 x+2) \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 77
Rubi steps
\begin {align*} \int \frac {(1-2 x) (3+5 x)^2}{(2+3 x)^2} \, dx &=\int \left (\frac {95}{27}-\frac {50 x}{9}+\frac {7}{27 (2+3 x)^2}-\frac {8}{3 (2+3 x)}\right ) \, dx\\ &=\frac {95 x}{27}-\frac {25 x^2}{9}-\frac {7}{81 (2+3 x)}-\frac {8}{9} \log (2+3 x)\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.02, size = 36, normalized size = 1.06 \[ \frac {-225 x^3+135 x^2+480 x-24 (3 x+2) \log (3 x+2)+191}{81 x+54} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.63, size = 37, normalized size = 1.09 \[ -\frac {675 \, x^{3} - 405 \, x^{2} + 72 \, {\left (3 \, x + 2\right )} \log \left (3 \, x + 2\right ) - 570 \, x + 7}{81 \, {\left (3 \, x + 2\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 1.20, size = 48, normalized size = 1.41 \[ \frac {5}{81} \, {\left (3 \, x + 2\right )}^{2} {\left (\frac {39}{3 \, x + 2} - 5\right )} - \frac {7}{81 \, {\left (3 \, x + 2\right )}} + \frac {8}{9} \, \log \left (\frac {{\left | 3 \, x + 2 \right |}}{3 \, {\left (3 \, x + 2\right )}^{2}}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.01, size = 27, normalized size = 0.79 \[ -\frac {25 x^{2}}{9}+\frac {95 x}{27}-\frac {8 \ln \left (3 x +2\right )}{9}-\frac {7}{81 \left (3 x +2\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.55, size = 26, normalized size = 0.76 \[ -\frac {25}{9} \, x^{2} + \frac {95}{27} \, x - \frac {7}{81 \, {\left (3 \, x + 2\right )}} - \frac {8}{9} \, \log \left (3 \, x + 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.03, size = 24, normalized size = 0.71 \[ \frac {95\,x}{27}-\frac {8\,\ln \left (x+\frac {2}{3}\right )}{9}-\frac {7}{243\,\left (x+\frac {2}{3}\right )}-\frac {25\,x^2}{9} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.10, size = 27, normalized size = 0.79 \[ - \frac {25 x^{2}}{9} + \frac {95 x}{27} - \frac {8 \log {\left (3 x + 2 \right )}}{9} - \frac {7}{243 x + 162} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________