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 = 0.02, antiderivative size = 56, normalized size of antiderivative = 1.00, 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*}
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Mathematica [A] time = 0.01, 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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fricas [A] time = 0.70, size = 59, normalized size = 1.05 \[ -\frac {40500 \, x^{4} + 33075 \, x^{3} - 1107 \, x^{2} - 1461 \, x + 1423}{3645 \, {\left (2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.13, size = 29, normalized size = 0.52 \[ -\frac {40500 \, x^{4} + 33075 \, x^{3} - 1107 \, x^{2} - 1461 \, x + 1423}{3645 \, {\left (3 \, x + 2\right )}^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 47, normalized size = 0.84 \[ -\frac {7}{243 \left (3 x +2\right )^{7}}+\frac {259}{729 \left (3 x +2\right )^{6}}-\frac {503}{405 \left (3 x +2\right )^{5}}+\frac {185}{243 \left (3 x +2\right )^{4}}-\frac {100}{729 \left (3 x +2\right )^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.50, size = 59, normalized size = 1.05 \[ -\frac {40500 \, x^{4} + 33075 \, x^{3} - 1107 \, x^{2} - 1461 \, x + 1423}{3645 \, {\left (2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.09, size = 46, normalized size = 0.82 \[ \frac {185}{243\,{\left (3\,x+2\right )}^4}-\frac {100}{729\,{\left (3\,x+2\right )}^3}-\frac {503}{405\,{\left (3\,x+2\right )}^5}+\frac {259}{729\,{\left (3\,x+2\right )}^6}-\frac {7}{243\,{\left (3\,x+2\right )}^7} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.19, size = 54, normalized size = 0.96 \[ \frac {- 40500 x^{4} - 33075 x^{3} + 1107 x^{2} + 1461 x - 1423}{7971615 x^{7} + 37200870 x^{6} + 74401740 x^{5} + 82668600 x^{4} + 55112400 x^{3} + 22044960 x^{2} + 4898880 x + 466560} \]
Verification of antiderivative is not currently implemented for this CAS.
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