Optimal. Leaf size=44 \[ -\frac{65}{27 (3 x+2)}+\frac{4}{9 (3 x+2)^2}-\frac{7}{243 (3 x+2)^3}-\frac{50}{81} \log (3 x+2) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0174397, antiderivative size = 44, 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} \[ -\frac{65}{27 (3 x+2)}+\frac{4}{9 (3 x+2)^2}-\frac{7}{243 (3 x+2)^3}-\frac{50}{81} \log (3 x+2) \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 77
Rubi steps
\begin{align*} \int \frac{(1-2 x) (3+5 x)^2}{(2+3 x)^4} \, dx &=\int \left (\frac{7}{27 (2+3 x)^4}-\frac{8}{3 (2+3 x)^3}+\frac{65}{9 (2+3 x)^2}-\frac{50}{27 (2+3 x)}\right ) \, dx\\ &=-\frac{7}{243 (2+3 x)^3}+\frac{4}{9 (2+3 x)^2}-\frac{65}{27 (2+3 x)}-\frac{50}{81} \log (2+3 x)\\ \end{align*}
Mathematica [A] time = 0.0129345, size = 36, normalized size = 0.82 \[ -\frac{5265 x^2+6696 x+150 (3 x+2)^3 \log (3 x+2)+2131}{243 (3 x+2)^3} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.006, size = 37, normalized size = 0.8 \begin{align*} -{\frac{7}{243\, \left ( 2+3\,x \right ) ^{3}}}+{\frac{4}{9\, \left ( 2+3\,x \right ) ^{2}}}-{\frac{65}{54+81\,x}}-{\frac{50\,\ln \left ( 2+3\,x \right ) }{81}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 1.14627, size = 51, normalized size = 1.16 \begin{align*} -\frac{5265 \, x^{2} + 6696 \, x + 2131}{243 \,{\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )}} - \frac{50}{81} \, \log \left (3 \, x + 2\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.69936, size = 151, normalized size = 3.43 \begin{align*} -\frac{5265 \, x^{2} + 150 \,{\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )} \log \left (3 \, x + 2\right ) + 6696 \, x + 2131}{243 \,{\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.127129, size = 36, normalized size = 0.82 \begin{align*} - \frac{5265 x^{2} + 6696 x + 2131}{6561 x^{3} + 13122 x^{2} + 8748 x + 1944} - \frac{50 \log{\left (3 x + 2 \right )}}{81} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.88928, size = 39, normalized size = 0.89 \begin{align*} -\frac{5265 \, x^{2} + 6696 \, x + 2131}{243 \,{\left (3 \, x + 2\right )}^{3}} - \frac{50}{81} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]