Optimal. Leaf size=45 \[ \frac {25}{81 (3 x+2)^2}-\frac {65}{81 (3 x+2)^3}+\frac {2}{9 (3 x+2)^4}-\frac {7}{405 (3 x+2)^5} \]
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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} \[ \frac {25}{81 (3 x+2)^2}-\frac {65}{81 (3 x+2)^3}+\frac {2}{9 (3 x+2)^4}-\frac {7}{405 (3 x+2)^5} \]
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)^6} \, dx &=\int \left (\frac {7}{27 (2+3 x)^6}-\frac {8}{3 (2+3 x)^5}+\frac {65}{9 (2+3 x)^4}-\frac {50}{27 (2+3 x)^3}\right ) \, dx\\ &=-\frac {7}{405 (2+3 x)^5}+\frac {2}{9 (2+3 x)^4}-\frac {65}{81 (2+3 x)^3}+\frac {25}{81 (2+3 x)^2}\\ \end {align*}
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Mathematica [A] time = 0.02, size = 26, normalized size = 0.58 \[ \frac {3375 x^3+3825 x^2+870 x-127}{405 (3 x+2)^5} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.74, size = 44, normalized size = 0.98 \[ \frac {3375 \, x^{3} + 3825 \, x^{2} + 870 \, x - 127}{405 \, {\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.22, size = 24, normalized size = 0.53 \[ \frac {3375 \, x^{3} + 3825 \, x^{2} + 870 \, x - 127}{405 \, {\left (3 \, x + 2\right )}^{5}} \]
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 \[ -\frac {7}{405 \left (3 x +2\right )^{5}}+\frac {2}{9 \left (3 x +2\right )^{4}}-\frac {65}{81 \left (3 x +2\right )^{3}}+\frac {25}{81 \left (3 x +2\right )^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.49, size = 44, normalized size = 0.98 \[ \frac {3375 \, x^{3} + 3825 \, x^{2} + 870 \, x - 127}{405 \, {\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.10, size = 37, normalized size = 0.82 \[ \frac {25}{81\,{\left (3\,x+2\right )}^2}-\frac {65}{81\,{\left (3\,x+2\right )}^3}+\frac {2}{9\,{\left (3\,x+2\right )}^4}-\frac {7}{405\,{\left (3\,x+2\right )}^5} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.15, size = 41, normalized size = 0.91 \[ - \frac {- 3375 x^{3} - 3825 x^{2} - 870 x + 127}{98415 x^{5} + 328050 x^{4} + 437400 x^{3} + 291600 x^{2} + 97200 x + 12960} \]
Verification of antiderivative is not currently implemented for this CAS.
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