Optimal. Leaf size=70 \[ \frac {6655}{3 x+2}+\frac {1331}{2 (3 x+2)^2}+\frac {7189}{81 (3 x+2)^3}+\frac {1421}{108 (3 x+2)^4}+\frac {343}{135 (3 x+2)^5}-33275 \log (3 x+2)+33275 \log (5 x+3) \]
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Rubi [A] time = 0.03, antiderivative size = 70, 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} \[ \frac {6655}{3 x+2}+\frac {1331}{2 (3 x+2)^2}+\frac {7189}{81 (3 x+2)^3}+\frac {1421}{108 (3 x+2)^4}+\frac {343}{135 (3 x+2)^5}-33275 \log (3 x+2)+33275 \log (5 x+3) \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin {align*} \int \frac {(1-2 x)^3}{(2+3 x)^6 (3+5 x)} \, dx &=\int \left (-\frac {343}{9 (2+3 x)^6}-\frac {1421}{9 (2+3 x)^5}-\frac {7189}{9 (2+3 x)^4}-\frac {3993}{(2+3 x)^3}-\frac {19965}{(2+3 x)^2}-\frac {99825}{2+3 x}+\frac {166375}{3+5 x}\right ) \, dx\\ &=\frac {343}{135 (2+3 x)^5}+\frac {1421}{108 (2+3 x)^4}+\frac {7189}{81 (2+3 x)^3}+\frac {1331}{2 (2+3 x)^2}+\frac {6655}{2+3 x}-33275 \log (2+3 x)+33275 \log (3+5 x)\\ \end {align*}
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Mathematica [A] time = 0.08, size = 50, normalized size = 0.71 \[ \frac {873269100 x^4+2357826570 x^3+2388229560 x^2+1075586865 x+181744346}{1620 (3 x+2)^5}-33275 \log (5 (3 x+2))+33275 \log (5 x+3) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.54, size = 115, normalized size = 1.64 \[ \frac {873269100 \, x^{4} + 2357826570 \, x^{3} + 2388229560 \, x^{2} + 53905500 \, {\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )} \log \left (5 \, x + 3\right ) - 53905500 \, {\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )} \log \left (3 \, x + 2\right ) + 1075586865 \, x + 181744346}{1620 \, {\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.96, size = 48, normalized size = 0.69 \[ \frac {873269100 \, x^{4} + 2357826570 \, x^{3} + 2388229560 \, x^{2} + 1075586865 \, x + 181744346}{1620 \, {\left (3 \, x + 2\right )}^{5}} + 33275 \, \log \left ({\left | 5 \, x + 3 \right |}\right ) - 33275 \, \log \left ({\left | 3 \, x + 2 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 63, normalized size = 0.90 \[ -33275 \ln \left (3 x +2\right )+33275 \ln \left (5 x +3\right )+\frac {343}{135 \left (3 x +2\right )^{5}}+\frac {1421}{108 \left (3 x +2\right )^{4}}+\frac {7189}{81 \left (3 x +2\right )^{3}}+\frac {1331}{2 \left (3 x +2\right )^{2}}+\frac {6655}{3 x +2} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.50, size = 66, normalized size = 0.94 \[ \frac {873269100 \, x^{4} + 2357826570 \, x^{3} + 2388229560 \, x^{2} + 1075586865 \, x + 181744346}{1620 \, {\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )}} + 33275 \, \log \left (5 \, x + 3\right ) - 33275 \, \log \left (3 \, x + 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.05, size = 55, normalized size = 0.79 \[ \frac {\frac {6655\,x^4}{3}+\frac {11979\,x^3}{2}+\frac {13267942\,x^2}{2187}+\frac {71705791\,x}{26244}+\frac {90872173}{196830}}{x^5+\frac {10\,x^4}{3}+\frac {40\,x^3}{9}+\frac {80\,x^2}{27}+\frac {80\,x}{81}+\frac {32}{243}}-66550\,\mathrm {atanh}\left (30\,x+19\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.19, size = 63, normalized size = 0.90 \[ - \frac {- 873269100 x^{4} - 2357826570 x^{3} - 2388229560 x^{2} - 1075586865 x - 181744346}{393660 x^{5} + 1312200 x^{4} + 1749600 x^{3} + 1166400 x^{2} + 388800 x + 51840} + 33275 \log {\left (x + \frac {3}{5} \right )} - 33275 \log {\left (x + \frac {2}{3} \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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