Optimal. Leaf size=57 \[ -\frac{2541}{3 x+2}-\frac{1331}{5 x+3}-\frac{1568}{9 (3 x+2)^2}-\frac{343}{27 (3 x+2)^3}+16698 \log (3 x+2)-16698 \log (5 x+3) \]
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Rubi [A] time = 0.0289954, antiderivative size = 57, 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} \[ -\frac{2541}{3 x+2}-\frac{1331}{5 x+3}-\frac{1568}{9 (3 x+2)^2}-\frac{343}{27 (3 x+2)^3}+16698 \log (3 x+2)-16698 \log (5 x+3) \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin{align*} \int \frac{(1-2 x)^3}{(2+3 x)^4 (3+5 x)^2} \, dx &=\int \left (\frac{343}{3 (2+3 x)^4}+\frac{3136}{3 (2+3 x)^3}+\frac{7623}{(2+3 x)^2}+\frac{50094}{2+3 x}+\frac{6655}{(3+5 x)^2}-\frac{83490}{3+5 x}\right ) \, dx\\ &=-\frac{343}{27 (2+3 x)^3}-\frac{1568}{9 (2+3 x)^2}-\frac{2541}{2+3 x}-\frac{1331}{3+5 x}+16698 \log (2+3 x)-16698 \log (3+5 x)\\ \end{align*}
Mathematica [A] time = 0.0277352, size = 59, normalized size = 1.04 \[ -\frac{2541}{3 x+2}-\frac{1331}{5 x+3}-\frac{1568}{9 (3 x+2)^2}-\frac{343}{27 (3 x+2)^3}+16698 \log (5 (3 x+2))-16698 \log (5 x+3) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.01, size = 54, normalized size = 1. \begin{align*} -{\frac{343}{27\, \left ( 2+3\,x \right ) ^{3}}}-{\frac{1568}{9\, \left ( 2+3\,x \right ) ^{2}}}-2541\, \left ( 2+3\,x \right ) ^{-1}-1331\, \left ( 3+5\,x \right ) ^{-1}+16698\,\ln \left ( 2+3\,x \right ) -16698\,\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 = 1.39668, size = 76, normalized size = 1.33 \begin{align*} -\frac{4057614 \, x^{3} + 7979967 \, x^{2} + 5226815 \, x + 1140033}{27 \,{\left (135 \, x^{4} + 351 \, x^{3} + 342 \, x^{2} + 148 \, x + 24\right )}} - 16698 \, \log \left (5 \, x + 3\right ) + 16698 \, \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 = 1.26535, size = 311, normalized size = 5.46 \begin{align*} -\frac{4057614 \, x^{3} + 7979967 \, x^{2} + 450846 \,{\left (135 \, x^{4} + 351 \, x^{3} + 342 \, x^{2} + 148 \, x + 24\right )} \log \left (5 \, x + 3\right ) - 450846 \,{\left (135 \, x^{4} + 351 \, x^{3} + 342 \, x^{2} + 148 \, x + 24\right )} \log \left (3 \, x + 2\right ) + 5226815 \, x + 1140033}{27 \,{\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 = 0.169026, size = 51, normalized size = 0.89 \begin{align*} - \frac{4057614 x^{3} + 7979967 x^{2} + 5226815 x + 1140033}{3645 x^{4} + 9477 x^{3} + 9234 x^{2} + 3996 x + 648} - 16698 \log{\left (x + \frac{3}{5} \right )} + 16698 \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 = 1.74613, size = 78, normalized size = 1.37 \begin{align*} -\frac{1331}{5 \, x + 3} + \frac{35 \,{\left (\frac{11119}{5 \, x + 3} + \frac{2244}{{\left (5 \, x + 3\right )}^{2}} + 14386\right )}}{{\left (\frac{1}{5 \, x + 3} + 3\right )}^{3}} + 16698 \, \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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