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 = 0.0336496, antiderivative size = 81, 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} \[ \frac{33275}{3 x+2}+\frac{6655}{2 (3 x+2)^2}+\frac{1331}{3 (3 x+2)^3}+\frac{7189}{108 (3 x+2)^4}+\frac{1421}{135 (3 x+2)^5}+\frac{343}{162 (3 x+2)^6}-166375 \log (3 x+2)+166375 \log (5 x+3) \]
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*}
Mathematica [A] time = 0.055875, 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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Maple [A] time = 0.009, size = 72, normalized size = 0.9 \begin{align*}{\frac{343}{162\, \left ( 2+3\,x \right ) ^{6}}}+{\frac{1421}{135\, \left ( 2+3\,x \right ) ^{5}}}+{\frac{7189}{108\, \left ( 2+3\,x \right ) ^{4}}}+{\frac{1331}{3\, \left ( 2+3\,x \right ) ^{3}}}+{\frac{6655}{2\, \left ( 2+3\,x \right ) ^{2}}}+33275\, \left ( 2+3\,x \right ) ^{-1}-166375\,\ln \left ( 2+3\,x \right ) +166375\,\ln \left ( 3+5\,x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.03953, size = 103, normalized size = 1.27 \begin{align*} \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 ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.21099, size = 486, normalized size = 6. \begin{align*} \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 )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.194197, size = 71, normalized size = 0.88 \begin{align*} \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 )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.38606, size = 72, normalized size = 0.89 \begin{align*} \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 ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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