Optimal. Leaf size=38 \[ -\frac{50 x}{27}+\frac{8}{9 (3 x+2)}-\frac{7}{162 (3 x+2)^2}+\frac{65}{27} \log (3 x+2) \]
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Rubi [A] time = 0.0162983, antiderivative size = 38, 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} \[ -\frac{50 x}{27}+\frac{8}{9 (3 x+2)}-\frac{7}{162 (3 x+2)^2}+\frac{65}{27} \log (3 x+2) \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin{align*} \int \frac{(1-2 x) (3+5 x)^2}{(2+3 x)^3} \, dx &=\int \left (-\frac{50}{27}+\frac{7}{27 (2+3 x)^3}-\frac{8}{3 (2+3 x)^2}+\frac{65}{9 (2+3 x)}\right ) \, dx\\ &=-\frac{50 x}{27}-\frac{7}{162 (2+3 x)^2}+\frac{8}{9 (2+3 x)}+\frac{65}{27} \log (2+3 x)\\ \end{align*}
Mathematica [A] time = 0.022794, size = 35, normalized size = 0.92 \[ \frac{1}{162} \left (-\frac{3 \left (600 x^2+656 x+173\right )}{(3 x+2)^2}-300 x+390 \log (3 x+2)\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.004, size = 31, normalized size = 0.8 \begin{align*} -{\frac{50\,x}{27}}-{\frac{7}{162\, \left ( 2+3\,x \right ) ^{2}}}+{\frac{8}{18+27\,x}}+{\frac{65\,\ln \left ( 2+3\,x \right ) }{27}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.17056, size = 42, normalized size = 1.11 \begin{align*} -\frac{50}{27} \, x + \frac{432 \, x + 281}{162 \,{\left (9 \, x^{2} + 12 \, x + 4\right )}} + \frac{65}{27} \, \log \left (3 \, x + 2\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.92503, size = 136, normalized size = 3.58 \begin{align*} -\frac{2700 \, x^{3} + 3600 \, x^{2} - 390 \,{\left (9 \, x^{2} + 12 \, x + 4\right )} \log \left (3 \, x + 2\right ) + 768 \, x - 281}{162 \,{\left (9 \, x^{2} + 12 \, x + 4\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.114663, size = 29, normalized size = 0.76 \begin{align*} - \frac{50 x}{27} + \frac{432 x + 281}{1458 x^{2} + 1944 x + 648} + \frac{65 \log{\left (3 x + 2 \right )}}{27} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.83135, size = 36, normalized size = 0.95 \begin{align*} -\frac{50}{27} \, x + \frac{432 \, x + 281}{162 \,{\left (3 \, x + 2\right )}^{2}} + \frac{65}{27} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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