Optimal. Leaf size=50 \[ \frac{7189}{27 (3 x+2)}+\frac{1421}{54 (3 x+2)^2}+\frac{343}{81 (3 x+2)^3}-1331 \log (3 x+2)+1331 \log (5 x+3) \]
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Rubi [A] time = 0.0217267, antiderivative size = 50, 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} \[ \frac{7189}{27 (3 x+2)}+\frac{1421}{54 (3 x+2)^2}+\frac{343}{81 (3 x+2)^3}-1331 \log (3 x+2)+1331 \log (5 x+3) \]
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)} \, dx &=\int \left (-\frac{343}{9 (2+3 x)^4}-\frac{1421}{9 (2+3 x)^3}-\frac{7189}{9 (2+3 x)^2}-\frac{3993}{2+3 x}+\frac{6655}{3+5 x}\right ) \, dx\\ &=\frac{343}{81 (2+3 x)^3}+\frac{1421}{54 (2+3 x)^2}+\frac{7189}{27 (2+3 x)}-1331 \log (2+3 x)+1331 \log (3+5 x)\\ \end{align*}
Mathematica [A] time = 0.0251482, size = 40, normalized size = 0.8 \[ \frac{7 \left (55458 x^2+75771 x+25964\right )}{162 (3 x+2)^3}-1331 \log (5 (3 x+2))+1331 \log (5 x+3) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.007, size = 45, normalized size = 0.9 \begin{align*}{\frac{343}{81\, \left ( 2+3\,x \right ) ^{3}}}+{\frac{1421}{54\, \left ( 2+3\,x \right ) ^{2}}}+{\frac{7189}{54+81\,x}}-1331\,\ln \left ( 2+3\,x \right ) +1331\,\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 = 2.38946, size = 62, normalized size = 1.24 \begin{align*} \frac{7 \,{\left (55458 \, x^{2} + 75771 \, x + 25964\right )}}{162 \,{\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )}} + 1331 \, \log \left (5 \, x + 3\right ) - 1331 \, \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 = 1.29852, size = 231, normalized size = 4.62 \begin{align*} \frac{388206 \, x^{2} + 215622 \,{\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )} \log \left (5 \, x + 3\right ) - 215622 \,{\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )} \log \left (3 \, x + 2\right ) + 530397 \, x + 181748}{162 \,{\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.150603, size = 41, normalized size = 0.82 \begin{align*} \frac{388206 x^{2} + 530397 x + 181748}{4374 x^{3} + 8748 x^{2} + 5832 x + 1296} + 1331 \log{\left (x + \frac{3}{5} \right )} - 1331 \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 = 2.37139, size = 51, normalized size = 1.02 \begin{align*} \frac{7 \,{\left (55458 \, x^{2} + 75771 \, x + 25964\right )}}{162 \,{\left (3 \, x + 2\right )}^{3}} + 1331 \, \log \left ({\left | 5 \, x + 3 \right |}\right ) - 1331 \, \log \left ({\left | 3 \, x + 2 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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