Optimal. Leaf size=52 \[ \frac {500 x^3}{81}-\frac {100 x^2}{9}+\frac {895 x}{81}-\frac {763}{729 (3 x+2)}+\frac {49}{1458 (3 x+2)^2}-\frac {4099}{729} \log (3 x+2) \]
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Rubi [A] time = 0.02, antiderivative size = 52, 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} \[ \frac {500 x^3}{81}-\frac {100 x^2}{9}+\frac {895 x}{81}-\frac {763}{729 (3 x+2)}+\frac {49}{1458 (3 x+2)^2}-\frac {4099}{729} \log (3 x+2) \]
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)^3} \, dx &=\int \left (\frac {895}{81}-\frac {200 x}{9}+\frac {500 x^2}{27}-\frac {49}{243 (2+3 x)^3}+\frac {763}{243 (2+3 x)^2}-\frac {4099}{243 (2+3 x)}\right ) \, dx\\ &=\frac {895 x}{81}-\frac {100 x^2}{9}+\frac {500 x^3}{81}+\frac {49}{1458 (2+3 x)^2}-\frac {763}{729 (2+3 x)}-\frac {4099}{729} \log (2+3 x)\\ \end {align*}
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Mathematica [A] time = 0.03, size = 51, normalized size = 0.98 \[ \frac {243000 x^5-113400 x^4-40230 x^3+941940 x^2+921426 x-24594 (3 x+2)^2 \log (30 x+20)+238271}{4374 (3 x+2)^2} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.71, size = 57, normalized size = 1.10 \[ \frac {81000 \, x^{5} - 37800 \, x^{4} - 13410 \, x^{3} + 128520 \, x^{2} - 8198 \, {\left (9 \, x^{2} + 12 \, x + 4\right )} \log \left (3 \, x + 2\right ) + 59862 \, x - 3003}{1458 \, {\left (9 \, x^{2} + 12 \, x + 4\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.88, size = 37, normalized size = 0.71 \[ \frac {500}{81} \, x^{3} - \frac {100}{9} \, x^{2} + \frac {895}{81} \, x - \frac {7 \, {\left (218 \, x + 143\right )}}{486 \, {\left (3 \, x + 2\right )}^{2}} - \frac {4099}{729} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 41, normalized size = 0.79 \[ \frac {500 x^{3}}{81}-\frac {100 x^{2}}{9}+\frac {895 x}{81}-\frac {4099 \ln \left (3 x +2\right )}{729}+\frac {49}{1458 \left (3 x +2\right )^{2}}-\frac {763}{729 \left (3 x +2\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.50, size = 41, normalized size = 0.79 \[ \frac {500}{81} \, x^{3} - \frac {100}{9} \, x^{2} + \frac {895}{81} \, x - \frac {7 \, {\left (218 \, x + 143\right )}}{486 \, {\left (9 \, x^{2} + 12 \, x + 4\right )}} - \frac {4099}{729} \, \log \left (3 \, x + 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 37, normalized size = 0.71 \[ \frac {895\,x}{81}-\frac {4099\,\ln \left (x+\frac {2}{3}\right )}{729}-\frac {\frac {763\,x}{2187}+\frac {1001}{4374}}{x^2+\frac {4\,x}{3}+\frac {4}{9}}-\frac {100\,x^2}{9}+\frac {500\,x^3}{81} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.13, size = 44, normalized size = 0.85 \[ \frac {500 x^{3}}{81} - \frac {100 x^{2}}{9} + \frac {895 x}{81} + \frac {- 1526 x - 1001}{4374 x^{2} + 5832 x + 1944} - \frac {4099 \log {\left (3 x + 2 \right )}}{729} \]
Verification of antiderivative is not currently implemented for this CAS.
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