Optimal. Leaf size=66 \[ \frac{3800}{729 (3 x+2)}-\frac{8285}{1458 (3 x+2)^2}+\frac{4099}{2187 (3 x+2)^3}-\frac{763}{2916 (3 x+2)^4}+\frac{49}{3645 (3 x+2)^5}+\frac{500}{729} \log (3 x+2) \]
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Rubi [A] time = 0.0265225, 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} \[ \frac{3800}{729 (3 x+2)}-\frac{8285}{1458 (3 x+2)^2}+\frac{4099}{2187 (3 x+2)^3}-\frac{763}{2916 (3 x+2)^4}+\frac{49}{3645 (3 x+2)^5}+\frac{500}{729} \log (3 x+2) \]
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)^6} \, dx &=\int \left (-\frac{49}{243 (2+3 x)^6}+\frac{763}{243 (2+3 x)^5}-\frac{4099}{243 (2+3 x)^4}+\frac{8285}{243 (2+3 x)^3}-\frac{3800}{243 (2+3 x)^2}+\frac{500}{243 (2+3 x)}\right ) \, dx\\ &=\frac{49}{3645 (2+3 x)^5}-\frac{763}{2916 (2+3 x)^4}+\frac{4099}{2187 (2+3 x)^3}-\frac{8285}{1458 (2+3 x)^2}+\frac{3800}{729 (2+3 x)}+\frac{500}{729} \log (2+3 x)\\ \end{align*}
Mathematica [A] time = 0.0322137, size = 46, normalized size = 0.7 \[ \frac{18468000 x^4+42537150 x^3+36564120 x^2+13889625 x+30000 (3 x+2)^5 \log (30 x+20)+1965218}{43740 (3 x+2)^5} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.007, size = 55, normalized size = 0.8 \begin{align*}{\frac{49}{3645\, \left ( 2+3\,x \right ) ^{5}}}-{\frac{763}{2916\, \left ( 2+3\,x \right ) ^{4}}}+{\frac{4099}{2187\, \left ( 2+3\,x \right ) ^{3}}}-{\frac{8285}{1458\, \left ( 2+3\,x \right ) ^{2}}}+{\frac{3800}{1458+2187\,x}}+{\frac{500\,\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 = 1.05932, size = 78, normalized size = 1.18 \begin{align*} \frac{18468000 \, x^{4} + 42537150 \, x^{3} + 36564120 \, x^{2} + 13889625 \, x + 1965218}{43740 \,{\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )}} + \frac{500}{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 = 1.42957, size = 278, normalized size = 4.21 \begin{align*} \frac{18468000 \, x^{4} + 42537150 \, x^{3} + 36564120 \, x^{2} + 30000 \,{\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )} \log \left (3 \, x + 2\right ) + 13889625 \, x + 1965218}{43740 \,{\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 = 0.155683, size = 54, normalized size = 0.82 \begin{align*} \frac{18468000 x^{4} + 42537150 x^{3} + 36564120 x^{2} + 13889625 x + 1965218}{10628820 x^{5} + 35429400 x^{4} + 47239200 x^{3} + 31492800 x^{2} + 10497600 x + 1399680} + \frac{500 \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 = 1.64957, size = 53, normalized size = 0.8 \begin{align*} \frac{18468000 \, x^{4} + 42537150 \, x^{3} + 36564120 \, x^{2} + 13889625 \, x + 1965218}{43740 \,{\left (3 \, x + 2\right )}^{5}} + \frac{500}{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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