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 = 0.02, antiderivative size = 45, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, 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*}
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Mathematica [A] time = 0.02, 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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fricas [A] time = 0.74, size = 54, normalized size = 1.20 \[ -\frac {1350 \, x^{3} + 108 \, x^{2} - 291 \, x + 88}{810 \, {\left (2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.16, size = 24, normalized size = 0.53 \[ -\frac {1350 \, x^{3} + 108 \, x^{2} - 291 \, x + 88}{810 \, {\left (3 \, x + 2\right )}^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 38, normalized size = 0.84 \[ \frac {7}{81 \left (3 x +2\right )^{7}}-\frac {91}{162 \left (3 x +2\right )^{6}}+\frac {16}{45 \left (3 x +2\right )^{5}}-\frac {5}{81 \left (3 x +2\right )^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.47, size = 54, normalized size = 1.20 \[ -\frac {1350 \, x^{3} + 108 \, x^{2} - 291 \, x + 88}{810 \, {\left (2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.11, size = 37, normalized size = 0.82 \[ \frac {16}{45\,{\left (3\,x+2\right )}^5}-\frac {5}{81\,{\left (3\,x+2\right )}^4}-\frac {91}{162\,{\left (3\,x+2\right )}^6}+\frac {7}{81\,{\left (3\,x+2\right )}^7} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.17, size = 49, normalized size = 1.09 \[ \frac {- 1350 x^{3} - 108 x^{2} + 291 x - 88}{1771470 x^{7} + 8266860 x^{6} + 16533720 x^{5} + 18370800 x^{4} + 12247200 x^{3} + 4898880 x^{2} + 1088640 x + 103680} \]
Verification of antiderivative is not currently implemented for this CAS.
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