Optimal. Leaf size=45 \[ -\frac{20}{243 (3 x+2)^3}+\frac{4}{9 (3 x+2)^4}-\frac{91}{135 (3 x+2)^5}+\frac{49}{486 (3 x+2)^6} \]
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Rubi [A] time = 0.0166633, antiderivative size = 45, 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} \[ -\frac{20}{243 (3 x+2)^3}+\frac{4}{9 (3 x+2)^4}-\frac{91}{135 (3 x+2)^5}+\frac{49}{486 (3 x+2)^6} \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin{align*} \int \frac{(1-2 x)^2 (3+5 x)}{(2+3 x)^7} \, dx &=\int \left (-\frac{49}{27 (2+3 x)^7}+\frac{91}{9 (2+3 x)^6}-\frac{16}{3 (2+3 x)^5}+\frac{20}{27 (2+3 x)^4}\right ) \, dx\\ &=\frac{49}{486 (2+3 x)^6}-\frac{91}{135 (2+3 x)^5}+\frac{4}{9 (2+3 x)^4}-\frac{20}{243 (2+3 x)^3}\\ \end{align*}
Mathematica [A] time = 0.0123661, size = 26, normalized size = 0.58 \[ -\frac{5400 x^3+1080 x^2-846 x+311}{2430 (3 x+2)^6} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.005, size = 38, normalized size = 0.8 \begin{align*}{\frac{49}{486\, \left ( 2+3\,x \right ) ^{6}}}-{\frac{91}{135\, \left ( 2+3\,x \right ) ^{5}}}+{\frac{4}{9\, \left ( 2+3\,x \right ) ^{4}}}-{\frac{20}{243\, \left ( 2+3\,x \right ) ^{3}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.03467, size = 66, normalized size = 1.47 \begin{align*} -\frac{5400 \, x^{3} + 1080 \, x^{2} - 846 \, x + 311}{2430 \,{\left (729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.54151, size = 151, normalized size = 3.36 \begin{align*} -\frac{5400 \, x^{3} + 1080 \, x^{2} - 846 \, x + 311}{2430 \,{\left (729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.153905, size = 46, normalized size = 1.02 \begin{align*} - \frac{5400 x^{3} + 1080 x^{2} - 846 x + 311}{1771470 x^{6} + 7085880 x^{5} + 11809800 x^{4} + 10497600 x^{3} + 5248800 x^{2} + 1399680 x + 155520} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.28257, size = 32, normalized size = 0.71 \begin{align*} -\frac{5400 \, x^{3} + 1080 \, x^{2} - 846 \, x + 311}{2430 \,{\left (3 \, x + 2\right )}^{6}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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