Optimal. Leaf size=34 \[ \frac {10}{81 (3 x+2)^3}-\frac {37}{108 (3 x+2)^4}+\frac {7}{135 (3 x+2)^5} \]
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Rubi [A] time = 0.01, antiderivative size = 34, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 18, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.056, Rules used = {77} \[ \frac {10}{81 (3 x+2)^3}-\frac {37}{108 (3 x+2)^4}+\frac {7}{135 (3 x+2)^5} \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin {align*} \int \frac {(1-2 x) (3+5 x)}{(2+3 x)^6} \, dx &=\int \left (-\frac {7}{9 (2+3 x)^6}+\frac {37}{9 (2+3 x)^5}-\frac {10}{9 (2+3 x)^4}\right ) \, dx\\ &=\frac {7}{135 (2+3 x)^5}-\frac {37}{108 (2+3 x)^4}+\frac {10}{81 (2+3 x)^3}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 21, normalized size = 0.62 \[ \frac {1800 x^2+735 x-226}{1620 (3 x+2)^5} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.57, size = 39, normalized size = 1.15 \[ \frac {1800 \, x^{2} + 735 \, x - 226}{1620 \, {\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.14, size = 19, normalized size = 0.56 \[ \frac {1800 \, x^{2} + 735 \, x - 226}{1620 \, {\left (3 \, x + 2\right )}^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 29, normalized size = 0.85 \[ \frac {7}{135 \left (3 x +2\right )^{5}}-\frac {37}{108 \left (3 x +2\right )^{4}}+\frac {10}{81 \left (3 x +2\right )^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.49, size = 39, normalized size = 1.15 \[ \frac {1800 \, x^{2} + 735 \, x - 226}{1620 \, {\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.12, size = 28, normalized size = 0.82 \[ \frac {10}{81\,{\left (3\,x+2\right )}^3}-\frac {37}{108\,{\left (3\,x+2\right )}^4}+\frac {7}{135\,{\left (3\,x+2\right )}^5} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.14, size = 36, normalized size = 1.06 \[ - \frac {- 1800 x^{2} - 735 x + 226}{393660 x^{5} + 1312200 x^{4} + 1749600 x^{3} + 1166400 x^{2} + 388800 x + 51840} \]
Verification of antiderivative is not currently implemented for this CAS.
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