Optimal. Leaf size=45 \[ -\frac{5}{81 (3 x+2)^4}+\frac{16}{45 (3 x+2)^5}-\frac{91}{162 (3 x+2)^6}+\frac{7}{81 (3 x+2)^7} \]
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Rubi [A] time = 0.0170339, 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} \[ -\frac{5}{81 (3 x+2)^4}+\frac{16}{45 (3 x+2)^5}-\frac{91}{162 (3 x+2)^6}+\frac{7}{81 (3 x+2)^7} \]
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)^8} \, dx &=\int \left (-\frac{49}{27 (2+3 x)^8}+\frac{91}{9 (2+3 x)^7}-\frac{16}{3 (2+3 x)^6}+\frac{20}{27 (2+3 x)^5}\right ) \, dx\\ &=\frac{7}{81 (2+3 x)^7}-\frac{91}{162 (2+3 x)^6}+\frac{16}{45 (2+3 x)^5}-\frac{5}{81 (2+3 x)^4}\\ \end{align*}
Mathematica [A] time = 0.0106047, size = 26, normalized size = 0.58 \[ -\frac{1350 x^3+108 x^2-291 x+88}{810 (3 x+2)^7} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.005, size = 38, normalized size = 0.8 \begin{align*}{\frac{7}{81\, \left ( 2+3\,x \right ) ^{7}}}-{\frac{91}{162\, \left ( 2+3\,x \right ) ^{6}}}+{\frac{16}{45\, \left ( 2+3\,x \right ) ^{5}}}-{\frac{5}{81\, \left ( 2+3\,x \right ) ^{4}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 2.66469, size = 73, normalized size = 1.62 \begin{align*} -\frac{1350 \, x^{3} + 108 \, x^{2} - 291 \, x + 88}{810 \,{\left (2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.39078, size = 171, normalized size = 3.8 \begin{align*} -\frac{1350 \, x^{3} + 108 \, x^{2} - 291 \, x + 88}{810 \,{\left (2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.161907, size = 51, normalized size = 1.13 \begin{align*} - \frac{1350 x^{3} + 108 x^{2} - 291 x + 88}{1771470 x^{7} + 8266860 x^{6} + 16533720 x^{5} + 18370800 x^{4} + 12247200 x^{3} + 4898880 x^{2} + 1088640 x + 103680} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 4.14265, size = 32, normalized size = 0.71 \begin{align*} -\frac{1350 \, x^{3} + 108 \, x^{2} - 291 \, x + 88}{810 \,{\left (3 \, x + 2\right )}^{7}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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