Optimal. Leaf size=36 \[ -\frac{8 x^3}{9}+\frac{26 x^2}{9}+\frac{922 x}{27}-6 \log (x+1)+\frac{2125}{81} \log (3 x+2) \]
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Rubi [A] time = 0.0239243, antiderivative size = 36, normalized size of antiderivative = 1., number of steps used = 5, number of rules used = 3, integrand size = 25, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.12, Rules used = {800, 632, 31} \[ -\frac{8 x^3}{9}+\frac{26 x^2}{9}+\frac{922 x}{27}-6 \log (x+1)+\frac{2125}{81} \log (3 x+2) \]
Antiderivative was successfully verified.
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Rule 800
Rule 632
Rule 31
Rubi steps
\begin{align*} \int \frac{(5-x) (3+2 x)^3}{2+5 x+3 x^2} \, dx &=\int \left (\frac{922}{27}+\frac{52 x}{9}-\frac{8 x^2}{3}+\frac{1801+1639 x}{27 \left (2+5 x+3 x^2\right )}\right ) \, dx\\ &=\frac{922 x}{27}+\frac{26 x^2}{9}-\frac{8 x^3}{9}+\frac{1}{27} \int \frac{1801+1639 x}{2+5 x+3 x^2} \, dx\\ &=\frac{922 x}{27}+\frac{26 x^2}{9}-\frac{8 x^3}{9}-18 \int \frac{1}{3+3 x} \, dx+\frac{2125}{27} \int \frac{1}{2+3 x} \, dx\\ &=\frac{922 x}{27}+\frac{26 x^2}{9}-\frac{8 x^3}{9}-6 \log (1+x)+\frac{2125}{81} \log (2+3 x)\\ \end{align*}
Mathematica [A] time = 0.0172052, size = 35, normalized size = 0.97 \[ \frac{1}{162} \left (-144 x^3+468 x^2+5532 x+4250 \log (-6 x-4)-972 \log (-2 (x+1))+6759\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.007, size = 29, normalized size = 0.8 \begin{align*}{\frac{922\,x}{27}}+{\frac{26\,{x}^{2}}{9}}-{\frac{8\,{x}^{3}}{9}}-6\,\ln \left ( 1+x \right ) +{\frac{2125\,\ln \left ( 2+3\,x \right ) }{81}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.40739, size = 38, normalized size = 1.06 \begin{align*} -\frac{8}{9} \, x^{3} + \frac{26}{9} \, x^{2} + \frac{922}{27} \, x + \frac{2125}{81} \, \log \left (3 \, x + 2\right ) - 6 \, \log \left (x + 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 2.14085, size = 95, normalized size = 2.64 \begin{align*} -\frac{8}{9} \, x^{3} + \frac{26}{9} \, x^{2} + \frac{922}{27} \, x + \frac{2125}{81} \, \log \left (3 \, x + 2\right ) - 6 \, \log \left (x + 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.127632, size = 34, normalized size = 0.94 \begin{align*} - \frac{8 x^{3}}{9} + \frac{26 x^{2}}{9} + \frac{922 x}{27} + \frac{2125 \log{\left (x + \frac{2}{3} \right )}}{81} - 6 \log{\left (x + 1 \right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.09886, size = 41, normalized size = 1.14 \begin{align*} -\frac{8}{9} \, x^{3} + \frac{26}{9} \, x^{2} + \frac{922}{27} \, x + \frac{2125}{81} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) - 6 \, \log \left ({\left | x + 1 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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