Optimal. Leaf size=75 \[ \frac {128634}{3 x+2}+\frac {103455}{5 x+3}+\frac {7854}{(3 x+2)^2}-\frac {6655}{2 (5 x+3)^2}+\frac {539}{(3 x+2)^3}+\frac {343}{12 (3 x+2)^4}-953535 \log (3 x+2)+953535 \log (5 x+3) \]
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Rubi [A] time = 0.04, antiderivative size = 75, 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} \[ \frac {128634}{3 x+2}+\frac {103455}{5 x+3}+\frac {7854}{(3 x+2)^2}-\frac {6655}{2 (5 x+3)^2}+\frac {539}{(3 x+2)^3}+\frac {343}{12 (3 x+2)^4}-953535 \log (3 x+2)+953535 \log (5 x+3) \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin {align*} \int \frac {(1-2 x)^3}{(2+3 x)^5 (3+5 x)^3} \, dx &=\int \left (-\frac {343}{(2+3 x)^5}-\frac {4851}{(2+3 x)^4}-\frac {47124}{(2+3 x)^3}-\frac {385902}{(2+3 x)^2}-\frac {2860605}{2+3 x}+\frac {33275}{(3+5 x)^3}-\frac {517275}{(3+5 x)^2}+\frac {4767675}{3+5 x}\right ) \, dx\\ &=\frac {343}{12 (2+3 x)^4}+\frac {539}{(2+3 x)^3}+\frac {7854}{(2+3 x)^2}+\frac {128634}{2+3 x}-\frac {6655}{2 (3+5 x)^2}+\frac {103455}{3+5 x}-953535 \log (2+3 x)+953535 \log (3+5 x)\\ \end {align*}
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Mathematica [A] time = 0.05, size = 77, normalized size = 1.03 \[ \frac {128634}{3 x+2}+\frac {103455}{5 x+3}+\frac {7854}{(3 x+2)^2}-\frac {6655}{2 (5 x+3)^2}+\frac {539}{(3 x+2)^3}+\frac {343}{12 (3 x+2)^4}-953535 \log (5 (3 x+2))+953535 \log (5 x+3) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.59, size = 135, normalized size = 1.80 \[ \frac {1544726700 \, x^{5} + 4994616330 \, x^{4} + 6455813364 \, x^{3} + 4169655991 \, x^{2} + 11442420 \, {\left (2025 \, x^{6} + 7830 \, x^{5} + 12609 \, x^{4} + 10824 \, x^{3} + 5224 \, x^{2} + 1344 \, x + 144\right )} \log \left (5 \, x + 3\right ) - 11442420 \, {\left (2025 \, x^{6} + 7830 \, x^{5} + 12609 \, x^{4} + 10824 \, x^{3} + 5224 \, x^{2} + 1344 \, x + 144\right )} \log \left (3 \, x + 2\right ) + 1345680462 \, x + 173603415}{12 \, {\left (2025 \, x^{6} + 7830 \, x^{5} + 12609 \, x^{4} + 10824 \, x^{3} + 5224 \, x^{2} + 1344 \, x + 144\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.87, size = 76, normalized size = 1.01 \[ \frac {128634}{3 \, x + 2} - \frac {27225 \, {\left (\frac {136}{3 \, x + 2} - 625\right )}}{2 \, {\left (\frac {1}{3 \, x + 2} - 5\right )}^{2}} + \frac {7854}{{\left (3 \, x + 2\right )}^{2}} + \frac {539}{{\left (3 \, x + 2\right )}^{3}} + \frac {343}{12 \, {\left (3 \, x + 2\right )}^{4}} + 953535 \, \log \left ({\left | -\frac {1}{3 \, x + 2} + 5 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 72, normalized size = 0.96 \[ -953535 \ln \left (3 x +2\right )+953535 \ln \left (5 x +3\right )+\frac {343}{12 \left (3 x +2\right )^{4}}+\frac {539}{\left (3 x +2\right )^{3}}+\frac {7854}{\left (3 x +2\right )^{2}}+\frac {128634}{3 x +2}-\frac {6655}{2 \left (5 x +3\right )^{2}}+\frac {103455}{5 x +3} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.57, size = 76, normalized size = 1.01 \[ \frac {1544726700 \, x^{5} + 4994616330 \, x^{4} + 6455813364 \, x^{3} + 4169655991 \, x^{2} + 1345680462 \, x + 173603415}{12 \, {\left (2025 \, x^{6} + 7830 \, x^{5} + 12609 \, x^{4} + 10824 \, x^{3} + 5224 \, x^{2} + 1344 \, x + 144\right )}} + 953535 \, \log \left (5 \, x + 3\right ) - 953535 \, \log \left (3 \, x + 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.05, size = 65, normalized size = 0.87 \[ \frac {63569\,x^5+\frac {6166193\,x^4}{30}+\frac {179328149\,x^3}{675}+\frac {4169655991\,x^2}{24300}+\frac {224280077\,x}{4050}+\frac {11573561}{1620}}{x^6+\frac {58\,x^5}{15}+\frac {467\,x^4}{75}+\frac {3608\,x^3}{675}+\frac {5224\,x^2}{2025}+\frac {448\,x}{675}+\frac {16}{225}}-1907070\,\mathrm {atanh}\left (30\,x+19\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.22, size = 73, normalized size = 0.97 \[ - \frac {- 1544726700 x^{5} - 4994616330 x^{4} - 6455813364 x^{3} - 4169655991 x^{2} - 1345680462 x - 173603415}{24300 x^{6} + 93960 x^{5} + 151308 x^{4} + 129888 x^{3} + 62688 x^{2} + 16128 x + 1728} + 953535 \log {\left (x + \frac {3}{5} \right )} - 953535 \log {\left (x + \frac {2}{3} \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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