Optimal. Leaf size=48 \[ \frac {125 x^4}{9}-\frac {800 x^3}{81}-\frac {305 x^2}{54}+\frac {1271 x}{243}+\frac {49}{729 (3 x+2)}+\frac {763}{729} \log (3 x+2) \]
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Rubi [A] time = 0.02, antiderivative size = 48, 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} \[ \frac {125 x^4}{9}-\frac {800 x^3}{81}-\frac {305 x^2}{54}+\frac {1271 x}{243}+\frac {49}{729 (3 x+2)}+\frac {763}{729} \log (3 x+2) \]
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)^2} \, dx &=\int \left (\frac {1271}{243}-\frac {305 x}{27}-\frac {800 x^2}{27}+\frac {500 x^3}{9}-\frac {49}{243 (2+3 x)^2}+\frac {763}{243 (2+3 x)}\right ) \, dx\\ &=\frac {1271 x}{243}-\frac {305 x^2}{54}-\frac {800 x^3}{81}+\frac {125 x^4}{9}+\frac {49}{729 (2+3 x)}+\frac {763}{729} \log (2+3 x)\\ \end {align*}
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Mathematica [A] time = 0.04, size = 49, normalized size = 1.02 \[ \frac {182250 x^5-8100 x^4-160515 x^3+19224 x^2+50052 x+4578 (3 x+2) \log (30 x+20)+3158}{4374 (3 x+2)} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.55, size = 47, normalized size = 0.98 \[ \frac {60750 \, x^{5} - 2700 \, x^{4} - 53505 \, x^{3} + 6408 \, x^{2} + 1526 \, {\left (3 \, x + 2\right )} \log \left (3 \, x + 2\right ) + 15252 \, x + 98}{1458 \, {\left (3 \, x + 2\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.03, size = 66, normalized size = 1.38 \[ -\frac {1}{4374} \, {\left (3 \, x + 2\right )}^{4} {\left (\frac {7600}{3 \, x + 2} - \frac {24855}{{\left (3 \, x + 2\right )}^{2}} + \frac {24594}{{\left (3 \, x + 2\right )}^{3}} - 750\right )} + \frac {49}{729 \, {\left (3 \, x + 2\right )}} - \frac {763}{729} \, \log \left (\frac {{\left | 3 \, x + 2 \right |}}{3 \, {\left (3 \, x + 2\right )}^{2}}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 37, normalized size = 0.77 \[ \frac {125 x^{4}}{9}-\frac {800 x^{3}}{81}-\frac {305 x^{2}}{54}+\frac {1271 x}{243}+\frac {763 \ln \left (3 x +2\right )}{729}+\frac {49}{729 \left (3 x +2\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.58, size = 36, normalized size = 0.75 \[ \frac {125}{9} \, x^{4} - \frac {800}{81} \, x^{3} - \frac {305}{54} \, x^{2} + \frac {1271}{243} \, x + \frac {49}{729 \, {\left (3 \, x + 2\right )}} + \frac {763}{729} \, \log \left (3 \, x + 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 34, normalized size = 0.71 \[ \frac {1271\,x}{243}+\frac {763\,\ln \left (x+\frac {2}{3}\right )}{729}+\frac {49}{2187\,\left (x+\frac {2}{3}\right )}-\frac {305\,x^2}{54}-\frac {800\,x^3}{81}+\frac {125\,x^4}{9} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.12, size = 41, normalized size = 0.85 \[ \frac {125 x^{4}}{9} - \frac {800 x^{3}}{81} - \frac {305 x^{2}}{54} + \frac {1271 x}{243} + \frac {763 \log {\left (3 x + 2 \right )}}{729} + \frac {49}{2187 x + 1458} \]
Verification of antiderivative is not currently implemented for this CAS.
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