Optimal. Leaf size=81 \[ \frac{15125}{3 x+2}+\frac{3025}{2 (3 x+2)^2}+\frac{605}{3 (3 x+2)^3}+\frac{121}{4 (3 x+2)^4}+\frac{217}{45 (3 x+2)^5}+\frac{49}{54 (3 x+2)^6}-75625 \log (3 x+2)+75625 \log (5 x+3) \]
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Rubi [A] time = 0.032481, 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} \[ \frac{15125}{3 x+2}+\frac{3025}{2 (3 x+2)^2}+\frac{605}{3 (3 x+2)^3}+\frac{121}{4 (3 x+2)^4}+\frac{217}{45 (3 x+2)^5}+\frac{49}{54 (3 x+2)^6}-75625 \log (3 x+2)+75625 \log (5 x+3) \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin{align*} \int \frac{(1-2 x)^2}{(2+3 x)^7 (3+5 x)} \, dx &=\int \left (-\frac{49}{3 (2+3 x)^7}-\frac{217}{3 (2+3 x)^6}-\frac{363}{(2+3 x)^5}-\frac{1815}{(2+3 x)^4}-\frac{9075}{(2+3 x)^3}-\frac{45375}{(2+3 x)^2}-\frac{226875}{2+3 x}+\frac{378125}{3+5 x}\right ) \, dx\\ &=\frac{49}{54 (2+3 x)^6}+\frac{217}{45 (2+3 x)^5}+\frac{121}{4 (2+3 x)^4}+\frac{605}{3 (2+3 x)^3}+\frac{3025}{2 (2+3 x)^2}+\frac{15125}{2+3 x}-75625 \log (2+3 x)+75625 \log (3+5 x)\\ \end{align*}
Mathematica [A] time = 0.0472763, size = 55, normalized size = 0.68 \[ \frac{1984702500 x^5+6681831750 x^4+9000258300 x^3+6063045615 x^2+2042732232 x+275370238}{540 (3 x+2)^6}-75625 \log (5 (3 x+2))+75625 \log (5 x+3) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.007, size = 72, normalized size = 0.9 \begin{align*}{\frac{49}{54\, \left ( 2+3\,x \right ) ^{6}}}+{\frac{217}{45\, \left ( 2+3\,x \right ) ^{5}}}+{\frac{121}{4\, \left ( 2+3\,x \right ) ^{4}}}+{\frac{605}{3\, \left ( 2+3\,x \right ) ^{3}}}+{\frac{3025}{2\, \left ( 2+3\,x \right ) ^{2}}}+15125\, \left ( 2+3\,x \right ) ^{-1}-75625\,\ln \left ( 2+3\,x \right ) +75625\,\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 = 1.21342, size = 103, normalized size = 1.27 \begin{align*} \frac{1984702500 \, x^{5} + 6681831750 \, x^{4} + 9000258300 \, x^{3} + 6063045615 \, x^{2} + 2042732232 \, x + 275370238}{540 \,{\left (729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right )}} + 75625 \, \log \left (5 \, x + 3\right ) - 75625 \, \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 = 1.52053, size = 474, normalized size = 5.85 \begin{align*} \frac{1984702500 \, x^{5} + 6681831750 \, x^{4} + 9000258300 \, x^{3} + 6063045615 \, x^{2} + 40837500 \,{\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 ) - 40837500 \,{\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 ) + 2042732232 \, x + 275370238}{540 \,{\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 = 0.187476, size = 71, normalized size = 0.88 \begin{align*} \frac{1984702500 x^{5} + 6681831750 x^{4} + 9000258300 x^{3} + 6063045615 x^{2} + 2042732232 x + 275370238}{393660 x^{6} + 1574640 x^{5} + 2624400 x^{4} + 2332800 x^{3} + 1166400 x^{2} + 311040 x + 34560} + 75625 \log{\left (x + \frac{3}{5} \right )} - 75625 \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 = 1.71114, size = 72, normalized size = 0.89 \begin{align*} \frac{1984702500 \, x^{5} + 6681831750 \, x^{4} + 9000258300 \, x^{3} + 6063045615 \, x^{2} + 2042732232 \, x + 275370238}{540 \,{\left (3 \, x + 2\right )}^{6}} + 75625 \, \log \left ({\left | 5 \, x + 3 \right |}\right ) - 75625 \, \log \left ({\left | 3 \, x + 2 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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