Optimal. Leaf size=52 \[ -\frac {200 x^3}{81}+\frac {230 x^2}{27}-\frac {1546 x}{81}+\frac {3724}{729 (3 x+2)}-\frac {343}{1458 (3 x+2)^2}+\frac {11599}{729} \log (3 x+2) \]
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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} \[ -\frac {200 x^3}{81}+\frac {230 x^2}{27}-\frac {1546 x}{81}+\frac {3724}{729 (3 x+2)}-\frac {343}{1458 (3 x+2)^2}+\frac {11599}{729} \log (3 x+2) \]
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)^3} \, dx &=\int \left (-\frac {1546}{81}+\frac {460 x}{27}-\frac {200 x^2}{27}+\frac {343}{243 (2+3 x)^3}-\frac {3724}{243 (2+3 x)^2}+\frac {11599}{243 (2+3 x)}\right ) \, dx\\ &=-\frac {1546 x}{81}+\frac {230 x^2}{27}-\frac {200 x^3}{81}-\frac {343}{1458 (2+3 x)^2}+\frac {3724}{729 (2+3 x)}+\frac {11599}{729} \log (2+3 x)\\ \end {align*}
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Mathematica [A] time = 0.05, size = 51, normalized size = 0.98 \[ -\frac {97200 x^5-205740 x^4+347436 x^3+1531512 x^2+1171896 x-69594 (3 x+2)^2 \log (30 x+20)+258005}{4374 (3 x+2)^2} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.55, size = 57, normalized size = 1.10 \[ -\frac {32400 \, x^{5} - 68580 \, x^{4} + 115812 \, x^{3} + 284256 \, x^{2} - 23198 \, {\left (9 \, x^{2} + 12 \, x + 4\right )} \log \left (3 \, x + 2\right ) + 88968 \, x - 14553}{1458 \, {\left (9 \, x^{2} + 12 \, x + 4\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.84, size = 37, normalized size = 0.71 \[ -\frac {200}{81} \, x^{3} + \frac {230}{27} \, x^{2} - \frac {1546}{81} \, x + \frac {49 \, {\left (152 \, x + 99\right )}}{486 \, {\left (3 \, x + 2\right )}^{2}} + \frac {11599}{729} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) \]
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 \[ -\frac {200 x^{3}}{81}+\frac {230 x^{2}}{27}-\frac {1546 x}{81}+\frac {11599 \ln \left (3 x +2\right )}{729}-\frac {343}{1458 \left (3 x +2\right )^{2}}+\frac {3724}{729 \left (3 x +2\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.46, size = 41, normalized size = 0.79 \[ -\frac {200}{81} \, x^{3} + \frac {230}{27} \, x^{2} - \frac {1546}{81} \, x + \frac {49 \, {\left (152 \, x + 99\right )}}{486 \, {\left (9 \, x^{2} + 12 \, x + 4\right )}} + \frac {11599}{729} \, \log \left (3 \, x + 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 36, normalized size = 0.69 \[ \frac {11599\,\ln \left (x+\frac {2}{3}\right )}{729}-\frac {1546\,x}{81}+\frac {\frac {3724\,x}{2187}+\frac {539}{486}}{x^2+\frac {4\,x}{3}+\frac {4}{9}}+\frac {230\,x^2}{27}-\frac {200\,x^3}{81} \]
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 \[ - \frac {200 x^{3}}{81} + \frac {230 x^{2}}{27} - \frac {1546 x}{81} - \frac {- 7448 x - 4851}{4374 x^{2} + 5832 x + 1944} + \frac {11599 \log {\left (3 x + 2 \right )}}{729} \]
Verification of antiderivative is not currently implemented for this CAS.
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