Optimal. Leaf size=59 \[ \frac{1331}{3 x+2}+\frac{7189}{54 (3 x+2)^2}+\frac{1421}{81 (3 x+2)^3}+\frac{343}{108 (3 x+2)^4}-6655 \log (3 x+2)+6655 \log (5 x+3) \]
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Rubi [A] time = 0.0251028, antiderivative size = 59, 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} \[ \frac{1331}{3 x+2}+\frac{7189}{54 (3 x+2)^2}+\frac{1421}{81 (3 x+2)^3}+\frac{343}{108 (3 x+2)^4}-6655 \log (3 x+2)+6655 \log (5 x+3) \]
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)} \, dx &=\int \left (-\frac{343}{9 (2+3 x)^5}-\frac{1421}{9 (2+3 x)^4}-\frac{7189}{9 (2+3 x)^3}-\frac{3993}{(2+3 x)^2}-\frac{19965}{2+3 x}+\frac{33275}{3+5 x}\right ) \, dx\\ &=\frac{343}{108 (2+3 x)^4}+\frac{1421}{81 (2+3 x)^3}+\frac{7189}{54 (2+3 x)^2}+\frac{1331}{2+3 x}-6655 \log (2+3 x)+6655 \log (3+5 x)\\ \end{align*}
Mathematica [A] time = 0.0274584, size = 45, normalized size = 0.76 \[ \frac{11643588 x^3+23675382 x^2+16059444 x+3634885}{324 (3 x+2)^4}-6655 \log (5 (3 x+2))+6655 \log (5 x+3) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.006, size = 54, normalized size = 0.9 \begin{align*}{\frac{343}{108\, \left ( 2+3\,x \right ) ^{4}}}+{\frac{1421}{81\, \left ( 2+3\,x \right ) ^{3}}}+{\frac{7189}{54\, \left ( 2+3\,x \right ) ^{2}}}+1331\, \left ( 2+3\,x \right ) ^{-1}-6655\,\ln \left ( 2+3\,x \right ) +6655\,\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 = 1.00991, size = 76, normalized size = 1.29 \begin{align*} \frac{11643588 \, x^{3} + 23675382 \, x^{2} + 16059444 \, x + 3634885}{324 \,{\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )}} + 6655 \, \log \left (5 \, x + 3\right ) - 6655 \, \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 = 1.22758, size = 309, normalized size = 5.24 \begin{align*} \frac{11643588 \, x^{3} + 23675382 \, x^{2} + 2156220 \,{\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )} \log \left (5 \, x + 3\right ) - 2156220 \,{\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )} \log \left (3 \, x + 2\right ) + 16059444 \, x + 3634885}{324 \,{\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.165948, size = 51, normalized size = 0.86 \begin{align*} \frac{11643588 x^{3} + 23675382 x^{2} + 16059444 x + 3634885}{26244 x^{4} + 69984 x^{3} + 69984 x^{2} + 31104 x + 5184} + 6655 \log{\left (x + \frac{3}{5} \right )} - 6655 \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 = 3.21244, size = 70, normalized size = 1.19 \begin{align*} \frac{1331}{3 \, x + 2} + \frac{7189}{54 \,{\left (3 \, x + 2\right )}^{2}} + \frac{1421}{81 \,{\left (3 \, x + 2\right )}^{3}} + \frac{343}{108 \,{\left (3 \, x + 2\right )}^{4}} + 6655 \, \log \left ({\left | -\frac{1}{3 \, x + 2} + 5 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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