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 = 0.02, 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} \begin {gather*} -\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} \end {gather*}
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*}
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Mathematica [A] time = 0.02, size = 26, normalized size = 0.58 \begin {gather*} -\frac {5400 x^3+1080 x^2-846 x+311}{2430 (3 x+2)^6} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {(1-2 x)^2 (3+5 x)}{(2+3 x)^7} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 1.32, size = 49, normalized size = 1.09 \begin {gather*} -\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 {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.21, size = 24, normalized size = 0.53 \begin {gather*} -\frac {5400 \, x^{3} + 1080 \, x^{2} - 846 \, x + 311}{2430 \, {\left (3 \, x + 2\right )}^{6}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 38, normalized size = 0.84 \begin {gather*} \frac {49}{486 \left (3 x +2\right )^{6}}-\frac {91}{135 \left (3 x +2\right )^{5}}+\frac {4}{9 \left (3 x +2\right )^{4}}-\frac {20}{243 \left (3 x +2\right )^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.68, size = 49, normalized size = 1.09 \begin {gather*} -\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 {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 37, normalized size = 0.82 \begin {gather*} \frac {4}{9\,{\left (3\,x+2\right )}^4}-\frac {20}{243\,{\left (3\,x+2\right )}^3}-\frac {91}{135\,{\left (3\,x+2\right )}^5}+\frac {49}{486\,{\left (3\,x+2\right )}^6} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.16, size = 44, normalized size = 0.98 \begin {gather*} \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 {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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