Optimal. Leaf size=50 \[ -\frac{3136}{9 (3 x+2)}-\frac{1331}{5 (5 x+3)}-\frac{343}{18 (3 x+2)^2}+2541 \log (3 x+2)-2541 \log (5 x+3) \]
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Rubi [A] time = 0.0258822, 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} \[ -\frac{3136}{9 (3 x+2)}-\frac{1331}{5 (5 x+3)}-\frac{343}{18 (3 x+2)^2}+2541 \log (3 x+2)-2541 \log (5 x+3) \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin{align*} \int \frac{(1-2 x)^3}{(2+3 x)^3 (3+5 x)^2} \, dx &=\int \left (\frac{343}{3 (2+3 x)^3}+\frac{3136}{3 (2+3 x)^2}+\frac{7623}{2+3 x}+\frac{1331}{(3+5 x)^2}-\frac{12705}{3+5 x}\right ) \, dx\\ &=-\frac{343}{18 (2+3 x)^2}-\frac{3136}{9 (2+3 x)}-\frac{1331}{5 (3+5 x)}+2541 \log (2+3 x)-2541 \log (3+5 x)\\ \end{align*}
Mathematica [A] time = 0.0331741, size = 47, normalized size = 0.94 \[ -\frac{686022 x^2+891911 x+289137}{90 (3 x+2)^2 (5 x+3)}+2541 \log (5 (3 x+2))-2541 \log (5 x+3) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.009, size = 45, normalized size = 0.9 \begin{align*} -{\frac{343}{18\, \left ( 2+3\,x \right ) ^{2}}}-{\frac{3136}{18+27\,x}}-{\frac{1331}{15+25\,x}}+2541\,\ln \left ( 2+3\,x \right ) -2541\,\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 = 1.02915, size = 62, normalized size = 1.24 \begin{align*} -\frac{686022 \, x^{2} + 891911 \, x + 289137}{90 \,{\left (45 \, x^{3} + 87 \, x^{2} + 56 \, x + 12\right )}} - 2541 \, \log \left (5 \, x + 3\right ) + 2541 \, \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 = 1.20537, size = 235, normalized size = 4.7 \begin{align*} -\frac{686022 \, x^{2} + 228690 \,{\left (45 \, x^{3} + 87 \, x^{2} + 56 \, x + 12\right )} \log \left (5 \, x + 3\right ) - 228690 \,{\left (45 \, x^{3} + 87 \, x^{2} + 56 \, x + 12\right )} \log \left (3 \, x + 2\right ) + 891911 \, x + 289137}{90 \,{\left (45 \, x^{3} + 87 \, x^{2} + 56 \, x + 12\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.156002, size = 41, normalized size = 0.82 \begin{align*} - \frac{686022 x^{2} + 891911 x + 289137}{4050 x^{3} + 7830 x^{2} + 5040 x + 1080} - 2541 \log{\left (x + \frac{3}{5} \right )} + 2541 \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 = 2.9028, size = 66, normalized size = 1.32 \begin{align*} -\frac{1331}{5 \,{\left (5 \, x + 3\right )}} + \frac{245 \,{\left (\frac{66}{5 \, x + 3} + 163\right )}}{2 \,{\left (\frac{1}{5 \, x + 3} + 3\right )}^{2}} + 2541 \, \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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