Optimal. Leaf size=67 \[ \frac {100}{729 (3 x+2)^2}-\frac {2180}{2187 (3 x+2)^3}+\frac {4099}{1458 (3 x+2)^4}-\frac {11599}{3645 (3 x+2)^5}+\frac {1862}{2187 (3 x+2)^6}-\frac {49}{729 (3 x+2)^7} \]
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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} \begin {gather*} \frac {100}{729 (3 x+2)^2}-\frac {2180}{2187 (3 x+2)^3}+\frac {4099}{1458 (3 x+2)^4}-\frac {11599}{3645 (3 x+2)^5}+\frac {1862}{2187 (3 x+2)^6}-\frac {49}{729 (3 x+2)^7} \end {gather*}
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)^8} \, dx &=\int \left (\frac {343}{243 (2+3 x)^8}-\frac {3724}{243 (2+3 x)^7}+\frac {11599}{243 (2+3 x)^6}-\frac {8198}{243 (2+3 x)^5}+\frac {2180}{243 (2+3 x)^4}-\frac {200}{243 (2+3 x)^3}\right ) \, dx\\ &=-\frac {49}{729 (2+3 x)^7}+\frac {1862}{2187 (2+3 x)^6}-\frac {11599}{3645 (2+3 x)^5}+\frac {4099}{1458 (2+3 x)^4}-\frac {2180}{2187 (2+3 x)^3}+\frac {100}{729 (2+3 x)^2}\\ \end {align*}
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Mathematica [A] time = 0.03, size = 36, normalized size = 0.54 \begin {gather*} \frac {729000 x^5+664200 x^4+191295 x^3+145044 x^2+61392 x-3526}{21870 (3 x+2)^7} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {(1-2 x)^3 (3+5 x)^2}{(2+3 x)^8} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 1.06, size = 64, normalized size = 0.96 \begin {gather*} \frac {729000 \, x^{5} + 664200 \, x^{4} + 191295 \, x^{3} + 145044 \, x^{2} + 61392 \, x - 3526}{21870 \, {\left (2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right )}} \end {gather*}
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 \begin {gather*} \frac {729000 \, x^{5} + 664200 \, x^{4} + 191295 \, x^{3} + 145044 \, x^{2} + 61392 \, x - 3526}{21870 \, {\left (3 \, x + 2\right )}^{7}} \end {gather*}
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 \begin {gather*} -\frac {49}{729 \left (3 x +2\right )^{7}}+\frac {1862}{2187 \left (3 x +2\right )^{6}}-\frac {11599}{3645 \left (3 x +2\right )^{5}}+\frac {4099}{1458 \left (3 x +2\right )^{4}}-\frac {2180}{2187 \left (3 x +2\right )^{3}}+\frac {100}{729 \left (3 x +2\right )^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.66, size = 64, normalized size = 0.96 \begin {gather*} \frac {729000 \, x^{5} + 664200 \, x^{4} + 191295 \, x^{3} + 145044 \, x^{2} + 61392 \, x - 3526}{21870 \, {\left (2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 55, normalized size = 0.82 \begin {gather*} \frac {100}{729\,{\left (3\,x+2\right )}^2}-\frac {2180}{2187\,{\left (3\,x+2\right )}^3}+\frac {4099}{1458\,{\left (3\,x+2\right )}^4}-\frac {11599}{3645\,{\left (3\,x+2\right )}^5}+\frac {1862}{2187\,{\left (3\,x+2\right )}^6}-\frac {49}{729\,{\left (3\,x+2\right )}^7} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.18, size = 61, normalized size = 0.91 \begin {gather*} - \frac {- 729000 x^{5} - 664200 x^{4} - 191295 x^{3} - 145044 x^{2} - 61392 x + 3526}{47829690 x^{7} + 223205220 x^{6} + 446410440 x^{5} + 496011600 x^{4} + 330674400 x^{3} + 132269760 x^{2} + 29393280 x + 2799360} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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