Optimal. Leaf size=81 \[ \frac {33275}{3 x+2}+\frac {6655}{2 (3 x+2)^2}+\frac {1331}{3 (3 x+2)^3}+\frac {7189}{108 (3 x+2)^4}+\frac {1421}{135 (3 x+2)^5}+\frac {343}{162 (3 x+2)^6}-166375 \log (3 x+2)+166375 \log (5 x+3) \]
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Rubi [A] time = 0.03, antiderivative size = 81, 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} \[ \frac {33275}{3 x+2}+\frac {6655}{2 (3 x+2)^2}+\frac {1331}{3 (3 x+2)^3}+\frac {7189}{108 (3 x+2)^4}+\frac {1421}{135 (3 x+2)^5}+\frac {343}{162 (3 x+2)^6}-166375 \log (3 x+2)+166375 \log (5 x+3) \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin {align*} \int \frac {(1-2 x)^3}{(2+3 x)^7 (3+5 x)} \, dx &=\int \left (-\frac {343}{9 (2+3 x)^7}-\frac {1421}{9 (2+3 x)^6}-\frac {7189}{9 (2+3 x)^5}-\frac {3993}{(2+3 x)^4}-\frac {19965}{(2+3 x)^3}-\frac {99825}{(2+3 x)^2}-\frac {499125}{2+3 x}+\frac {831875}{3+5 x}\right ) \, dx\\ &=\frac {343}{162 (2+3 x)^6}+\frac {1421}{135 (2+3 x)^5}+\frac {7189}{108 (2+3 x)^4}+\frac {1331}{3 (2+3 x)^3}+\frac {6655}{2 (2+3 x)^2}+\frac {33275}{2+3 x}-166375 \log (2+3 x)+166375 \log (3+5 x)\\ \end {align*}
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Mathematica [A] time = 0.10, size = 75, normalized size = 0.93 \[ \frac {53905500 (3 x+2)^5+5390550 (3 x+2)^4+718740 (3 x+2)^3+107835 (3 x+2)^2+17052 (3 x+2)+3430}{1620 (3 x+2)^6}-166375 \log (5 (3 x+2))+166375 \log (5 x+3) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.67, size = 135, normalized size = 1.67 \[ \frac {13099036500 \, x^{5} + 44100089550 \, x^{4} + 59401704780 \, x^{3} + 40016101275 \, x^{2} + 269527500 \, {\left (729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right )} \log \left (5 \, x + 3\right ) - 269527500 \, {\left (729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right )} \log \left (3 \, x + 2\right ) + 13482032616 \, x + 1817443594}{1620 \, {\left (729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.06, size = 53, normalized size = 0.65 \[ \frac {13099036500 \, x^{5} + 44100089550 \, x^{4} + 59401704780 \, x^{3} + 40016101275 \, x^{2} + 13482032616 \, x + 1817443594}{1620 \, {\left (3 \, x + 2\right )}^{6}} + 166375 \, \log \left ({\left | 5 \, x + 3 \right |}\right ) - 166375 \, \log \left ({\left | 3 \, x + 2 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 72, normalized size = 0.89 \[ -166375 \ln \left (3 x +2\right )+166375 \ln \left (5 x +3\right )+\frac {343}{162 \left (3 x +2\right )^{6}}+\frac {1421}{135 \left (3 x +2\right )^{5}}+\frac {7189}{108 \left (3 x +2\right )^{4}}+\frac {1331}{3 \left (3 x +2\right )^{3}}+\frac {6655}{2 \left (3 x +2\right )^{2}}+\frac {33275}{3 x +2} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.60, size = 76, normalized size = 0.94 \[ \frac {13099036500 \, x^{5} + 44100089550 \, x^{4} + 59401704780 \, x^{3} + 40016101275 \, x^{2} + 13482032616 \, x + 1817443594}{1620 \, {\left (729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right )}} + 166375 \, \log \left (5 \, x + 3\right ) - 166375 \, \log \left (3 \, x + 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.12, size = 65, normalized size = 0.80 \[ \frac {\frac {33275\,x^5}{3}+\frac {672155\,x^4}{18}+\frac {4074191\,x^3}{81}+\frac {296415565\,x^2}{8748}+\frac {374500906\,x}{32805}+\frac {908721797}{590490}}{x^6+4\,x^5+\frac {20\,x^4}{3}+\frac {160\,x^3}{27}+\frac {80\,x^2}{27}+\frac {64\,x}{81}+\frac {64}{729}}-332750\,\mathrm {atanh}\left (30\,x+19\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.21, size = 73, normalized size = 0.90 \[ - \frac {- 13099036500 x^{5} - 44100089550 x^{4} - 59401704780 x^{3} - 40016101275 x^{2} - 13482032616 x - 1817443594}{1180980 x^{6} + 4723920 x^{5} + 7873200 x^{4} + 6998400 x^{3} + 3499200 x^{2} + 933120 x + 103680} + 166375 \log {\left (x + \frac {3}{5} \right )} - 166375 \log {\left (x + \frac {2}{3} \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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