Optimal. Leaf size=67 \[ -\frac {250}{729 (3 x+2)^2}+\frac {3800}{2187 (3 x+2)^3}-\frac {8285}{2916 (3 x+2)^4}+\frac {4099}{3645 (3 x+2)^5}-\frac {763}{4374 (3 x+2)^6}+\frac {7}{729 (3 x+2)^7} \]
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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} \[ -\frac {250}{729 (3 x+2)^2}+\frac {3800}{2187 (3 x+2)^3}-\frac {8285}{2916 (3 x+2)^4}+\frac {4099}{3645 (3 x+2)^5}-\frac {763}{4374 (3 x+2)^6}+\frac {7}{729 (3 x+2)^7} \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin {align*} \int \frac {(1-2 x)^2 (3+5 x)^3}{(2+3 x)^8} \, dx &=\int \left (-\frac {49}{243 (2+3 x)^8}+\frac {763}{243 (2+3 x)^7}-\frac {4099}{243 (2+3 x)^6}+\frac {8285}{243 (2+3 x)^5}-\frac {3800}{243 (2+3 x)^4}+\frac {500}{243 (2+3 x)^3}\right ) \, dx\\ &=\frac {7}{729 (2+3 x)^7}-\frac {763}{4374 (2+3 x)^6}+\frac {4099}{3645 (2+3 x)^5}-\frac {8285}{2916 (2+3 x)^4}+\frac {3800}{2187 (2+3 x)^3}-\frac {250}{729 (2+3 x)^2}\\ \end {align*}
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Mathematica [A] time = 0.03, size = 36, normalized size = 0.54 \[ -\frac {3645000 x^5+5994000 x^4+3139425 x^3+652158 x^2+210534 x+76288}{43740 (3 x+2)^7} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.59, size = 64, normalized size = 0.96 \[ -\frac {3645000 \, x^{5} + 5994000 \, x^{4} + 3139425 \, x^{3} + 652158 \, x^{2} + 210534 \, x + 76288}{43740 \, {\left (2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.90, size = 34, normalized size = 0.51 \[ -\frac {3645000 \, x^{5} + 5994000 \, x^{4} + 3139425 \, x^{3} + 652158 \, x^{2} + 210534 \, x + 76288}{43740 \, {\left (3 \, x + 2\right )}^{7}} \]
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 \[ \frac {7}{729 \left (3 x +2\right )^{7}}-\frac {763}{4374 \left (3 x +2\right )^{6}}+\frac {4099}{3645 \left (3 x +2\right )^{5}}-\frac {8285}{2916 \left (3 x +2\right )^{4}}+\frac {3800}{2187 \left (3 x +2\right )^{3}}-\frac {250}{729 \left (3 x +2\right )^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.55, size = 64, normalized size = 0.96 \[ -\frac {3645000 \, x^{5} + 5994000 \, x^{4} + 3139425 \, x^{3} + 652158 \, x^{2} + 210534 \, x + 76288}{43740 \, {\left (2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.09, size = 55, normalized size = 0.82 \[ \frac {3800}{2187\,{\left (3\,x+2\right )}^3}-\frac {250}{729\,{\left (3\,x+2\right )}^2}-\frac {8285}{2916\,{\left (3\,x+2\right )}^4}+\frac {4099}{3645\,{\left (3\,x+2\right )}^5}-\frac {763}{4374\,{\left (3\,x+2\right )}^6}+\frac {7}{729\,{\left (3\,x+2\right )}^7} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.19, size = 61, normalized size = 0.91 \[ \frac {- 3645000 x^{5} - 5994000 x^{4} - 3139425 x^{3} - 652158 x^{2} - 210534 x - 76288}{95659380 x^{7} + 446410440 x^{6} + 892820880 x^{5} + 992023200 x^{4} + 661348800 x^{3} + 264539520 x^{2} + 58786560 x + 5598720} \]
Verification of antiderivative is not currently implemented for this CAS.
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