Optimal. Leaf size=55 \[ -\frac{1133}{3 x+2}-\frac{605}{5 x+3}-\frac{77}{(3 x+2)^2}-\frac{49}{9 (3 x+2)^3}+7480 \log (3 x+2)-7480 \log (5 x+3) \]
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Rubi [A] time = 0.0257409, antiderivative size = 55, 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} \[ -\frac{1133}{3 x+2}-\frac{605}{5 x+3}-\frac{77}{(3 x+2)^2}-\frac{49}{9 (3 x+2)^3}+7480 \log (3 x+2)-7480 \log (5 x+3) \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin{align*} \int \frac{(1-2 x)^2}{(2+3 x)^4 (3+5 x)^2} \, dx &=\int \left (\frac{49}{(2+3 x)^4}+\frac{462}{(2+3 x)^3}+\frac{3399}{(2+3 x)^2}+\frac{22440}{2+3 x}+\frac{3025}{(3+5 x)^2}-\frac{37400}{3+5 x}\right ) \, dx\\ &=-\frac{49}{9 (2+3 x)^3}-\frac{77}{(2+3 x)^2}-\frac{1133}{2+3 x}-\frac{605}{3+5 x}+7480 \log (2+3 x)-7480 \log (3+5 x)\\ \end{align*}
Mathematica [A] time = 0.0299482, size = 57, normalized size = 1.04 \[ -\frac{1133}{3 x+2}-\frac{605}{5 x+3}-\frac{77}{(3 x+2)^2}-\frac{49}{9 (3 x+2)^3}+7480 \log (5 (3 x+2))-7480 \log (5 x+3) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.009, size = 54, normalized size = 1. \begin{align*} -{\frac{49}{9\, \left ( 2+3\,x \right ) ^{3}}}-77\, \left ( 2+3\,x \right ) ^{-2}-1133\, \left ( 2+3\,x \right ) ^{-1}-605\, \left ( 3+5\,x \right ) ^{-1}+7480\,\ln \left ( 2+3\,x \right ) -7480\,\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 = 1.16357, size = 76, normalized size = 1.38 \begin{align*} -\frac{605880 \, x^{3} + 1191564 \, x^{2} + 780464 \, x + 170229}{9 \,{\left (135 \, x^{4} + 351 \, x^{3} + 342 \, x^{2} + 148 \, x + 24\right )}} - 7480 \, \log \left (5 \, x + 3\right ) + 7480 \, \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 = 1.2027, size = 302, normalized size = 5.49 \begin{align*} -\frac{605880 \, x^{3} + 1191564 \, x^{2} + 67320 \,{\left (135 \, x^{4} + 351 \, x^{3} + 342 \, x^{2} + 148 \, x + 24\right )} \log \left (5 \, x + 3\right ) - 67320 \,{\left (135 \, x^{4} + 351 \, x^{3} + 342 \, x^{2} + 148 \, x + 24\right )} \log \left (3 \, x + 2\right ) + 780464 \, x + 170229}{9 \,{\left (135 \, x^{4} + 351 \, x^{3} + 342 \, x^{2} + 148 \, x + 24\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.166759, size = 51, normalized size = 0.93 \begin{align*} - \frac{605880 x^{3} + 1191564 x^{2} + 780464 x + 170229}{1215 x^{4} + 3159 x^{3} + 3078 x^{2} + 1332 x + 216} - 7480 \log{\left (x + \frac{3}{5} \right )} + 7480 \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 = 2.27131, size = 78, normalized size = 1.42 \begin{align*} -\frac{605}{5 \, x + 3} + \frac{5 \,{\left (\frac{34464}{5 \, x + 3} + \frac{6934}{{\left (5 \, x + 3\right )}^{2}} + 44661\right )}}{{\left (\frac{1}{5 \, x + 3} + 3\right )}^{3}} + 7480 \, \log \left ({\left | -\frac{1}{5 \, x + 3} - 3 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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