Optimal. Leaf size=59 \[ \frac{605}{3 x+2}+\frac{121}{2 (3 x+2)^2}+\frac{217}{27 (3 x+2)^3}+\frac{49}{36 (3 x+2)^4}-3025 \log (3 x+2)+3025 \log (5 x+3) \]
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Rubi [A] time = 0.0231862, 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} \[ \frac{605}{3 x+2}+\frac{121}{2 (3 x+2)^2}+\frac{217}{27 (3 x+2)^3}+\frac{49}{36 (3 x+2)^4}-3025 \log (3 x+2)+3025 \log (5 x+3) \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin{align*} \int \frac{(1-2 x)^2}{(2+3 x)^5 (3+5 x)} \, dx &=\int \left (-\frac{49}{3 (2+3 x)^5}-\frac{217}{3 (2+3 x)^4}-\frac{363}{(2+3 x)^3}-\frac{1815}{(2+3 x)^2}-\frac{9075}{2+3 x}+\frac{15125}{3+5 x}\right ) \, dx\\ &=\frac{49}{36 (2+3 x)^4}+\frac{217}{27 (2+3 x)^3}+\frac{121}{2 (2+3 x)^2}+\frac{605}{2+3 x}-3025 \log (2+3 x)+3025 \log (3+5 x)\\ \end{align*}
Mathematica [A] time = 0.0271361, size = 45, normalized size = 0.76 \[ \frac{1764180 x^3+3587166 x^2+2433252 x+550739}{108 (3 x+2)^4}-3025 \log (5 (3 x+2))+3025 \log (5 x+3) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.007, size = 54, normalized size = 0.9 \begin{align*}{\frac{49}{36\, \left ( 2+3\,x \right ) ^{4}}}+{\frac{217}{27\, \left ( 2+3\,x \right ) ^{3}}}+{\frac{121}{2\, \left ( 2+3\,x \right ) ^{2}}}+605\, \left ( 2+3\,x \right ) ^{-1}-3025\,\ln \left ( 2+3\,x \right ) +3025\,\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 = 1.03409, size = 76, normalized size = 1.29 \begin{align*} \frac{1764180 \, x^{3} + 3587166 \, x^{2} + 2433252 \, x + 550739}{108 \,{\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )}} + 3025 \, \log \left (5 \, x + 3\right ) - 3025 \, \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 = 1.446, size = 301, normalized size = 5.1 \begin{align*} \frac{1764180 \, x^{3} + 3587166 \, x^{2} + 326700 \,{\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )} \log \left (5 \, x + 3\right ) - 326700 \,{\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )} \log \left (3 \, x + 2\right ) + 2433252 \, x + 550739}{108 \,{\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 = 0.160762, size = 51, normalized size = 0.86 \begin{align*} \frac{1764180 x^{3} + 3587166 x^{2} + 2433252 x + 550739}{8748 x^{4} + 23328 x^{3} + 23328 x^{2} + 10368 x + 1728} + 3025 \log{\left (x + \frac{3}{5} \right )} - 3025 \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 = 2.03797, size = 70, normalized size = 1.19 \begin{align*} \frac{605}{3 \, x + 2} + \frac{121}{2 \,{\left (3 \, x + 2\right )}^{2}} + \frac{217}{27 \,{\left (3 \, x + 2\right )}^{3}} + \frac{49}{36 \,{\left (3 \, x + 2\right )}^{4}} + 3025 \, \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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