Optimal. Leaf size=67 \[ \frac {200}{729 (3 x+2)}-\frac {1090}{729 (3 x+2)^2}+\frac {8198}{2187 (3 x+2)^3}-\frac {11599}{2916 (3 x+2)^4}+\frac {3724}{3645 (3 x+2)^5}-\frac {343}{4374 (3 x+2)^6} \]
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Rubi [A] time = 0.02, antiderivative size = 67, 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} \[ \frac {200}{729 (3 x+2)}-\frac {1090}{729 (3 x+2)^2}+\frac {8198}{2187 (3 x+2)^3}-\frac {11599}{2916 (3 x+2)^4}+\frac {3724}{3645 (3 x+2)^5}-\frac {343}{4374 (3 x+2)^6} \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin {align*} \int \frac {(1-2 x)^3 (3+5 x)^2}{(2+3 x)^7} \, dx &=\int \left (\frac {343}{243 (2+3 x)^7}-\frac {3724}{243 (2+3 x)^6}+\frac {11599}{243 (2+3 x)^5}-\frac {8198}{243 (2+3 x)^4}+\frac {2180}{243 (2+3 x)^3}-\frac {200}{243 (2+3 x)^2}\right ) \, dx\\ &=-\frac {343}{4374 (2+3 x)^6}+\frac {3724}{3645 (2+3 x)^5}-\frac {11599}{2916 (2+3 x)^4}+\frac {8198}{2187 (2+3 x)^3}-\frac {1090}{729 (2+3 x)^2}+\frac {200}{729 (2+3 x)}\\ \end {align*}
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Mathematica [A] time = 0.04, size = 36, normalized size = 0.54 \[ \frac {2916000 x^5+4422600 x^4+3260520 x^3+1801575 x^2+550404 x+39286}{43740 (3 x+2)^6} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.66, size = 59, normalized size = 0.88 \[ \frac {2916000 \, x^{5} + 4422600 \, x^{4} + 3260520 \, x^{3} + 1801575 \, x^{2} + 550404 \, x + 39286}{43740 \, {\left (729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.83, size = 34, normalized size = 0.51 \[ \frac {2916000 \, x^{5} + 4422600 \, x^{4} + 3260520 \, x^{3} + 1801575 \, x^{2} + 550404 \, x + 39286}{43740 \, {\left (3 \, x + 2\right )}^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 56, normalized size = 0.84 \[ -\frac {343}{4374 \left (3 x +2\right )^{6}}+\frac {3724}{3645 \left (3 x +2\right )^{5}}-\frac {11599}{2916 \left (3 x +2\right )^{4}}+\frac {8198}{2187 \left (3 x +2\right )^{3}}-\frac {1090}{729 \left (3 x +2\right )^{2}}+\frac {200}{729 \left (3 x +2\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.57, size = 59, normalized size = 0.88 \[ \frac {2916000 \, x^{5} + 4422600 \, x^{4} + 3260520 \, x^{3} + 1801575 \, x^{2} + 550404 \, x + 39286}{43740 \, {\left (729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.11, size = 55, normalized size = 0.82 \[ \frac {200}{729\,\left (3\,x+2\right )}-\frac {1090}{729\,{\left (3\,x+2\right )}^2}+\frac {8198}{2187\,{\left (3\,x+2\right )}^3}-\frac {11599}{2916\,{\left (3\,x+2\right )}^4}+\frac {3724}{3645\,{\left (3\,x+2\right )}^5}-\frac {343}{4374\,{\left (3\,x+2\right )}^6} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.18, size = 58, normalized size = 0.87 \[ - \frac {- 2916000 x^{5} - 4422600 x^{4} - 3260520 x^{3} - 1801575 x^{2} - 550404 x - 39286}{31886460 x^{6} + 127545840 x^{5} + 212576400 x^{4} + 188956800 x^{3} + 94478400 x^{2} + 25194240 x + 2799360} \]
Verification of antiderivative is not currently implemented for this CAS.
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