Optimal. Leaf size=66 \[ -\frac {2180}{729 (3 x+2)}+\frac {4099}{729 (3 x+2)^2}-\frac {11599}{2187 (3 x+2)^3}+\frac {931}{729 (3 x+2)^4}-\frac {343}{3645 (3 x+2)^5}-\frac {200}{729} \log (3 x+2) \]
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Rubi [A] time = 0.03, antiderivative size = 66, 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} \[ -\frac {2180}{729 (3 x+2)}+\frac {4099}{729 (3 x+2)^2}-\frac {11599}{2187 (3 x+2)^3}+\frac {931}{729 (3 x+2)^4}-\frac {343}{3645 (3 x+2)^5}-\frac {200}{729} \log (3 x+2) \]
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)^6} \, dx &=\int \left (\frac {343}{243 (2+3 x)^6}-\frac {3724}{243 (2+3 x)^5}+\frac {11599}{243 (2+3 x)^4}-\frac {8198}{243 (2+3 x)^3}+\frac {2180}{243 (2+3 x)^2}-\frac {200}{243 (2+3 x)}\right ) \, dx\\ &=-\frac {343}{3645 (2+3 x)^5}+\frac {931}{729 (2+3 x)^4}-\frac {11599}{2187 (2+3 x)^3}+\frac {4099}{729 (2+3 x)^2}-\frac {2180}{729 (2+3 x)}-\frac {200}{729} \log (2+3 x)\\ \end {align*}
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Mathematica [A] time = 0.05, size = 46, normalized size = 0.70 \[ -\frac {2648700 x^4+5403105 x^3+4264965 x^2+1579785 x+3000 (3 x+2)^5 \log (30 x+20)+236399}{10935 (3 x+2)^5} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.66, size = 82, normalized size = 1.24 \[ -\frac {2648700 \, x^{4} + 5403105 \, x^{3} + 4264965 \, x^{2} + 3000 \, {\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )} \log \left (3 \, x + 2\right ) + 1579785 \, x + 236399}{10935 \, {\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.80, size = 39, normalized size = 0.59 \[ -\frac {2648700 \, x^{4} + 5403105 \, x^{3} + 4264965 \, x^{2} + 1579785 \, x + 236399}{10935 \, {\left (3 \, x + 2\right )}^{5}} - \frac {200}{729} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 55, normalized size = 0.83 \[ -\frac {200 \ln \left (3 x +2\right )}{729}-\frac {343}{3645 \left (3 x +2\right )^{5}}+\frac {931}{729 \left (3 x +2\right )^{4}}-\frac {11599}{2187 \left (3 x +2\right )^{3}}+\frac {4099}{729 \left (3 x +2\right )^{2}}-\frac {2180}{729 \left (3 x +2\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.54, size = 58, normalized size = 0.88 \[ -\frac {2648700 \, x^{4} + 5403105 \, x^{3} + 4264965 \, x^{2} + 1579785 \, x + 236399}{10935 \, {\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )}} - \frac {200}{729} \, \log \left (3 \, x + 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 54, normalized size = 0.82 \[ -\frac {200\,\ln \left (x+\frac {2}{3}\right )}{729}-\frac {\frac {2180\,x^4}{2187}+\frac {4447\,x^3}{2187}+\frac {94777\,x^2}{59049}+\frac {105319\,x}{177147}+\frac {236399}{2657205}}{x^5+\frac {10\,x^4}{3}+\frac {40\,x^3}{9}+\frac {80\,x^2}{27}+\frac {80\,x}{81}+\frac {32}{243}} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.17, size = 56, normalized size = 0.85 \[ - \frac {2648700 x^{4} + 5403105 x^{3} + 4264965 x^{2} + 1579785 x + 236399}{2657205 x^{5} + 8857350 x^{4} + 11809800 x^{3} + 7873200 x^{2} + 2624400 x + 349920} - \frac {200 \log {\left (3 x + 2 \right )}}{729} \]
Verification of antiderivative is not currently implemented for this CAS.
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