Optimal. Leaf size=60 \[ -\frac {200 x}{243}+\frac {8198}{729 (3 x+2)}-\frac {11599}{1458 (3 x+2)^2}+\frac {3724}{2187 (3 x+2)^3}-\frac {343}{2916 (3 x+2)^4}+\frac {2180}{729} \log (3 x+2) \]
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Rubi [A] time = 0.03, antiderivative size = 60, 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} \[ -\frac {200 x}{243}+\frac {8198}{729 (3 x+2)}-\frac {11599}{1458 (3 x+2)^2}+\frac {3724}{2187 (3 x+2)^3}-\frac {343}{2916 (3 x+2)^4}+\frac {2180}{729} \log (3 x+2) \]
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)^5} \, dx &=\int \left (-\frac {200}{243}+\frac {343}{243 (2+3 x)^5}-\frac {3724}{243 (2+3 x)^4}+\frac {11599}{243 (2+3 x)^3}-\frac {8198}{243 (2+3 x)^2}+\frac {2180}{243 (2+3 x)}\right ) \, dx\\ &=-\frac {200 x}{243}-\frac {343}{2916 (2+3 x)^4}+\frac {3724}{2187 (2+3 x)^3}-\frac {11599}{1458 (2+3 x)^2}+\frac {8198}{729 (2+3 x)}+\frac {2180}{729} \log (2+3 x)\\ \end {align*}
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Mathematica [A] time = 0.04, size = 51, normalized size = 0.85 \[ \frac {-583200 x^5-1944000 x^4+64152 x^3+2957958 x^2+2175096 x+26160 (3 x+2)^4 \log (30 x+20)+460595}{8748 (3 x+2)^4} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.59, size = 77, normalized size = 1.28 \[ -\frac {583200 \, x^{5} + 1555200 \, x^{4} - 1100952 \, x^{3} - 3994758 \, x^{2} - 26160 \, {\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )} \log \left (3 \, x + 2\right ) - 2635896 \, x - 537395}{8748 \, {\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.15, size = 59, normalized size = 0.98 \[ -\frac {200}{243} \, x + \frac {8198}{729 \, {\left (3 \, x + 2\right )}} - \frac {11599}{1458 \, {\left (3 \, x + 2\right )}^{2}} + \frac {3724}{2187 \, {\left (3 \, x + 2\right )}^{3}} - \frac {343}{2916 \, {\left (3 \, x + 2\right )}^{4}} - \frac {2180}{729} \, \log \left (\frac {{\left | 3 \, x + 2 \right |}}{3 \, {\left (3 \, x + 2\right )}^{2}}\right ) - \frac {400}{729} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 49, normalized size = 0.82 \[ -\frac {200 x}{243}+\frac {2180 \ln \left (3 x +2\right )}{729}-\frac {343}{2916 \left (3 x +2\right )^{4}}+\frac {3724}{2187 \left (3 x +2\right )^{3}}-\frac {11599}{1458 \left (3 x +2\right )^{2}}+\frac {8198}{729 \left (3 x +2\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.58, size = 51, normalized size = 0.85 \[ -\frac {200}{243} \, x + \frac {2656152 \, x^{3} + 4685958 \, x^{2} + 2751096 \, x + 537395}{8748 \, {\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )}} + \frac {2180}{729} \, \log \left (3 \, x + 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.11, size = 46, normalized size = 0.77 \[ \frac {2180\,\ln \left (x+\frac {2}{3}\right )}{729}-\frac {200\,x}{243}+\frac {\frac {8198\,x^3}{2187}+\frac {86777\,x^2}{13122}+\frac {229258\,x}{59049}+\frac {537395}{708588}}{x^4+\frac {8\,x^3}{3}+\frac {8\,x^2}{3}+\frac {32\,x}{27}+\frac {16}{81}} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.16, size = 51, normalized size = 0.85 \[ - \frac {200 x}{243} - \frac {- 2656152 x^{3} - 4685958 x^{2} - 2751096 x - 537395}{708588 x^{4} + 1889568 x^{3} + 1889568 x^{2} + 839808 x + 139968} + \frac {2180 \log {\left (3 x + 2 \right )}}{729} \]
Verification of antiderivative is not currently implemented for this CAS.
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