Optimal. Leaf size=45 \[ \frac {50}{243 (3 x+2)^3}-\frac {65}{108 (3 x+2)^4}+\frac {8}{45 (3 x+2)^5}-\frac {7}{486 (3 x+2)^6} \]
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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} \[ \frac {50}{243 (3 x+2)^3}-\frac {65}{108 (3 x+2)^4}+\frac {8}{45 (3 x+2)^5}-\frac {7}{486 (3 x+2)^6} \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin {align*} \int \frac {(1-2 x) (3+5 x)^2}{(2+3 x)^7} \, dx &=\int \left (\frac {7}{27 (2+3 x)^7}-\frac {8}{3 (2+3 x)^6}+\frac {65}{9 (2+3 x)^5}-\frac {50}{27 (2+3 x)^4}\right ) \, dx\\ &=-\frac {7}{486 (2+3 x)^6}+\frac {8}{45 (2+3 x)^5}-\frac {65}{108 (2+3 x)^4}+\frac {50}{243 (2+3 x)^3}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 26, normalized size = 0.58 \[ \frac {27000 x^3+27675 x^2+3492 x-2042}{4860 (3 x+2)^6} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.68, size = 49, normalized size = 1.09 \[ \frac {27000 \, x^{3} + 27675 \, x^{2} + 3492 \, x - 2042}{4860 \, {\left (729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.23, size = 24, normalized size = 0.53 \[ \frac {27000 \, x^{3} + 27675 \, x^{2} + 3492 \, x - 2042}{4860 \, {\left (3 \, x + 2\right )}^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 38, normalized size = 0.84 \[ -\frac {7}{486 \left (3 x +2\right )^{6}}+\frac {8}{45 \left (3 x +2\right )^{5}}-\frac {65}{108 \left (3 x +2\right )^{4}}+\frac {50}{243 \left (3 x +2\right )^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.53, size = 49, normalized size = 1.09 \[ \frac {27000 \, x^{3} + 27675 \, x^{2} + 3492 \, x - 2042}{4860 \, {\left (729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 37, normalized size = 0.82 \[ \frac {50}{243\,{\left (3\,x+2\right )}^3}-\frac {65}{108\,{\left (3\,x+2\right )}^4}+\frac {8}{45\,{\left (3\,x+2\right )}^5}-\frac {7}{486\,{\left (3\,x+2\right )}^6} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.16, size = 46, normalized size = 1.02 \[ - \frac {- 27000 x^{3} - 27675 x^{2} - 3492 x + 2042}{3542940 x^{6} + 14171760 x^{5} + 23619600 x^{4} + 20995200 x^{3} + 10497600 x^{2} + 2799360 x + 311040} \]
Verification of antiderivative is not currently implemented for this CAS.
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