Optimal. Leaf size=56 \[ -\frac{100}{729 (3 x+2)^3}+\frac{185}{243 (3 x+2)^4}-\frac{503}{405 (3 x+2)^5}+\frac{259}{729 (3 x+2)^6}-\frac{7}{243 (3 x+2)^7} \]
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Rubi [A] time = 0.0197464, antiderivative size = 56, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 22, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.045, Rules used = {88} \[ -\frac{100}{729 (3 x+2)^3}+\frac{185}{243 (3 x+2)^4}-\frac{503}{405 (3 x+2)^5}+\frac{259}{729 (3 x+2)^6}-\frac{7}{243 (3 x+2)^7} \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin{align*} \int \frac{(1-2 x)^2 (3+5 x)^2}{(2+3 x)^8} \, dx &=\int \left (\frac{49}{81 (2+3 x)^8}-\frac{518}{81 (2+3 x)^7}+\frac{503}{27 (2+3 x)^6}-\frac{740}{81 (2+3 x)^5}+\frac{100}{81 (2+3 x)^4}\right ) \, dx\\ &=-\frac{7}{243 (2+3 x)^7}+\frac{259}{729 (2+3 x)^6}-\frac{503}{405 (2+3 x)^5}+\frac{185}{243 (2+3 x)^4}-\frac{100}{729 (2+3 x)^3}\\ \end{align*}
Mathematica [A] time = 0.0113724, size = 31, normalized size = 0.55 \[ \frac{-40500 x^4-33075 x^3+1107 x^2+1461 x-1423}{3645 (3 x+2)^7} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.004, size = 47, normalized size = 0.8 \begin{align*} -{\frac{7}{243\, \left ( 2+3\,x \right ) ^{7}}}+{\frac{259}{729\, \left ( 2+3\,x \right ) ^{6}}}-{\frac{503}{405\, \left ( 2+3\,x \right ) ^{5}}}+{\frac{185}{243\, \left ( 2+3\,x \right ) ^{4}}}-{\frac{100}{729\, \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 = 1.07262, size = 80, normalized size = 1.43 \begin{align*} -\frac{40500 \, x^{4} + 33075 \, x^{3} - 1107 \, x^{2} - 1461 \, x + 1423}{3645 \,{\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 = 1.70604, size = 196, normalized size = 3.5 \begin{align*} -\frac{40500 \, x^{4} + 33075 \, x^{3} - 1107 \, x^{2} - 1461 \, x + 1423}{3645 \,{\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 = 0.169625, size = 56, normalized size = 1. \begin{align*} - \frac{40500 x^{4} + 33075 x^{3} - 1107 x^{2} - 1461 x + 1423}{7971615 x^{7} + 37200870 x^{6} + 74401740 x^{5} + 82668600 x^{4} + 55112400 x^{3} + 22044960 x^{2} + 4898880 x + 466560} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.29221, size = 39, normalized size = 0.7 \begin{align*} -\frac{40500 \, x^{4} + 33075 \, x^{3} - 1107 \, x^{2} - 1461 \, x + 1423}{3645 \,{\left (3 \, x + 2\right )}^{7}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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