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 = 0.03, 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} \[ \frac {3800}{729 (3 x+2)}-\frac {8285}{1458 (3 x+2)^2}+\frac {4099}{2187 (3 x+2)^3}-\frac {763}{2916 (3 x+2)^4}+\frac {49}{3645 (3 x+2)^5}+\frac {500}{729} \log (3 x+2) \]
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*}
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Mathematica [A] time = 0.04, size = 46, normalized size = 0.70 \[ \frac {18468000 x^4+42537150 x^3+36564120 x^2+13889625 x+30000 (3 x+2)^5 \log (30 x+20)+1965218}{43740 (3 x+2)^5} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.74, size = 82, normalized size = 1.24 \[ \frac {18468000 \, x^{4} + 42537150 \, x^{3} + 36564120 \, x^{2} + 30000 \, {\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )} \log \left (3 \, x + 2\right ) + 13889625 \, x + 1965218}{43740 \, {\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.79, size = 39, normalized size = 0.59 \[ \frac {18468000 \, x^{4} + 42537150 \, x^{3} + 36564120 \, x^{2} + 13889625 \, x + 1965218}{43740 \, {\left (3 \, x + 2\right )}^{5}} + \frac {500}{729} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) \]
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 \[ \frac {500 \ln \left (3 x +2\right )}{729}+\frac {49}{3645 \left (3 x +2\right )^{5}}-\frac {763}{2916 \left (3 x +2\right )^{4}}+\frac {4099}{2187 \left (3 x +2\right )^{3}}-\frac {8285}{1458 \left (3 x +2\right )^{2}}+\frac {3800}{729 \left (3 x +2\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.52, size = 58, normalized size = 0.88 \[ \frac {18468000 \, x^{4} + 42537150 \, x^{3} + 36564120 \, x^{2} + 13889625 \, x + 1965218}{43740 \, {\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )}} + \frac {500}{729} \, \log \left (3 \, x + 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.11, size = 53, normalized size = 0.80 \[ \frac {500\,\ln \left (x+\frac {2}{3}\right )}{729}+\frac {\frac {3800\,x^4}{2187}+\frac {1945\,x^3}{486}+\frac {203134\,x^2}{59049}+\frac {925975\,x}{708588}+\frac {982609}{5314410}}{x^5+\frac {10\,x^4}{3}+\frac {40\,x^3}{9}+\frac {80\,x^2}{27}+\frac {80\,x}{81}+\frac {32}{243}} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.17, size = 54, normalized size = 0.82 \[ \frac {18468000 x^{4} + 42537150 x^{3} + 36564120 x^{2} + 13889625 x + 1965218}{10628820 x^{5} + 35429400 x^{4} + 47239200 x^{3} + 31492800 x^{2} + 10497600 x + 1399680} + \frac {500 \log {\left (3 x + 2 \right )}}{729} \]
Verification of antiderivative is not currently implemented for this CAS.
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