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 = 0.0250362, antiderivative size = 66, normalized size of antiderivative = 1., 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*}
Mathematica [A] time = 0.0345439, size = 46, normalized size = 0.7 \[ -\frac{2648700 x^4+5403105 x^3+4264965 x^2+1579785 x+3000 (3 x+2)^5 \log (30 x+20)+236399}{10935 (3 x+2)^5} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.005, size = 55, normalized size = 0.8 \begin{align*} -{\frac{343}{3645\, \left ( 2+3\,x \right ) ^{5}}}+{\frac{931}{729\, \left ( 2+3\,x \right ) ^{4}}}-{\frac{11599}{2187\, \left ( 2+3\,x \right ) ^{3}}}+{\frac{4099}{729\, \left ( 2+3\,x \right ) ^{2}}}-{\frac{2180}{1458+2187\,x}}-{\frac{200\,\ln \left ( 2+3\,x \right ) }{729}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.00284, size = 78, normalized size = 1.18 \begin{align*} -\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 ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.34583, size = 271, normalized size = 4.11 \begin{align*} -\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 )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.160259, size = 56, normalized size = 0.85 \begin{align*} - \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} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.68774, size = 53, normalized size = 0.8 \begin{align*} -\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 ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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