Optimal. Leaf size=56 \[ \frac {40}{729 (3 x+2)^3}-\frac {107}{243 (3 x+2)^4}+\frac {518}{405 (3 x+2)^5}-\frac {2009}{1458 (3 x+2)^6}+\frac {49}{243 (3 x+2)^7} \]
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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 = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {77} \begin {gather*} \frac {40}{729 (3 x+2)^3}-\frac {107}{243 (3 x+2)^4}+\frac {518}{405 (3 x+2)^5}-\frac {2009}{1458 (3 x+2)^6}+\frac {49}{243 (3 x+2)^7} \end {gather*}
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin {align*} \int \frac {(1-2 x)^3 (3+5 x)}{(2+3 x)^8} \, dx &=\int \left (-\frac {343}{81 (2+3 x)^8}+\frac {2009}{81 (2+3 x)^7}-\frac {518}{27 (2+3 x)^6}+\frac {428}{81 (2+3 x)^5}-\frac {40}{81 (2+3 x)^4}\right ) \, dx\\ &=\frac {49}{243 (2+3 x)^7}-\frac {2009}{1458 (2+3 x)^6}+\frac {518}{405 (2+3 x)^5}-\frac {107}{243 (2+3 x)^4}+\frac {40}{729 (2+3 x)^3}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 31, normalized size = 0.55 \begin {gather*} \frac {32400 x^4-270 x^3-3024 x^2+4593 x-604}{7290 (3 x+2)^7} \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)^3 (3+5 x)}{(2+3 x)^8} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 1.10, size = 59, normalized size = 1.05 \begin {gather*} \frac {32400 \, x^{4} - 270 \, x^{3} - 3024 \, x^{2} + 4593 \, x - 604}{7290 \, {\left (2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.03, size = 29, normalized size = 0.52 \begin {gather*} \frac {32400 \, x^{4} - 270 \, x^{3} - 3024 \, x^{2} + 4593 \, x - 604}{7290 \, {\left (3 \, x + 2\right )}^{7}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 47, normalized size = 0.84 \begin {gather*} \frac {49}{243 \left (3 x +2\right )^{7}}-\frac {2009}{1458 \left (3 x +2\right )^{6}}+\frac {518}{405 \left (3 x +2\right )^{5}}-\frac {107}{243 \left (3 x +2\right )^{4}}+\frac {40}{729 \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 = 0.62, size = 59, normalized size = 1.05 \begin {gather*} \frac {32400 \, x^{4} - 270 \, x^{3} - 3024 \, x^{2} + 4593 \, x - 604}{7290 \, {\left (2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right )}} \end {gather*}
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 \begin {gather*} \frac {40}{729\,{\left (3\,x+2\right )}^3}-\frac {107}{243\,{\left (3\,x+2\right )}^4}+\frac {518}{405\,{\left (3\,x+2\right )}^5}-\frac {2009}{1458\,{\left (3\,x+2\right )}^6}+\frac {49}{243\,{\left (3\,x+2\right )}^7} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.18, size = 56, normalized size = 1.00 \begin {gather*} - \frac {- 32400 x^{4} + 270 x^{3} + 3024 x^{2} - 4593 x + 604}{15943230 x^{7} + 74401740 x^{6} + 148803480 x^{5} + 165337200 x^{4} + 110224800 x^{3} + 44089920 x^{2} + 9797760 x + 933120} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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