Optimal. Leaf size=64 \[ \frac{8}{3773 (1-2 x)}+\frac{351}{343 (3 x+2)}+\frac{9}{98 (3 x+2)^2}-\frac{1072 \log (1-2 x)}{290521}-\frac{12393 \log (3 x+2)}{2401}+\frac{625}{121} \log (5 x+3) \]
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Rubi [A] time = 0.0323773, antiderivative size = 64, 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} \[ \frac{8}{3773 (1-2 x)}+\frac{351}{343 (3 x+2)}+\frac{9}{98 (3 x+2)^2}-\frac{1072 \log (1-2 x)}{290521}-\frac{12393 \log (3 x+2)}{2401}+\frac{625}{121} \log (5 x+3) \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin{align*} \int \frac{1}{(1-2 x)^2 (2+3 x)^3 (3+5 x)} \, dx &=\int \left (\frac{16}{3773 (-1+2 x)^2}-\frac{2144}{290521 (-1+2 x)}-\frac{27}{49 (2+3 x)^3}-\frac{1053}{343 (2+3 x)^2}-\frac{37179}{2401 (2+3 x)}+\frac{3125}{121 (3+5 x)}\right ) \, dx\\ &=\frac{8}{3773 (1-2 x)}+\frac{9}{98 (2+3 x)^2}+\frac{351}{343 (2+3 x)}-\frac{1072 \log (1-2 x)}{290521}-\frac{12393 \log (2+3 x)}{2401}+\frac{625}{121} \log (3+5 x)\\ \end{align*}
Mathematica [A] time = 0.0447408, size = 61, normalized size = 0.95 \[ \frac{-2144 \log (5-10 x)-2999106 \log (5 (3 x+2))+7 \left (\frac{176}{1-2 x}+\frac{84942}{3 x+2}+\frac{7623}{(3 x+2)^2}+428750 \log (5 x+3)\right )}{581042} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.01, size = 53, normalized size = 0.8 \begin{align*} -{\frac{8}{7546\,x-3773}}-{\frac{1072\,\ln \left ( 2\,x-1 \right ) }{290521}}+{\frac{9}{98\, \left ( 2+3\,x \right ) ^{2}}}+{\frac{351}{686+1029\,x}}-{\frac{12393\,\ln \left ( 2+3\,x \right ) }{2401}}+{\frac{625\,\ln \left ( 3+5\,x \right ) }{121}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.04119, size = 73, normalized size = 1.14 \begin{align*} \frac{46188 \, x^{2} + 8916 \, x - 16201}{7546 \,{\left (18 \, x^{3} + 15 \, x^{2} - 4 \, x - 4\right )}} + \frac{625}{121} \, \log \left (5 \, x + 3\right ) - \frac{12393}{2401} \, \log \left (3 \, x + 2\right ) - \frac{1072}{290521} \, \log \left (2 \, x - 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.19493, size = 301, normalized size = 4.7 \begin{align*} \frac{3556476 \, x^{2} + 3001250 \,{\left (18 \, x^{3} + 15 \, x^{2} - 4 \, x - 4\right )} \log \left (5 \, x + 3\right ) - 2999106 \,{\left (18 \, x^{3} + 15 \, x^{2} - 4 \, x - 4\right )} \log \left (3 \, x + 2\right ) - 2144 \,{\left (18 \, x^{3} + 15 \, x^{2} - 4 \, x - 4\right )} \log \left (2 \, x - 1\right ) + 686532 \, x - 1247477}{581042 \,{\left (18 \, x^{3} + 15 \, x^{2} - 4 \, x - 4\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.195513, size = 54, normalized size = 0.84 \begin{align*} \frac{46188 x^{2} + 8916 x - 16201}{135828 x^{3} + 113190 x^{2} - 30184 x - 30184} - \frac{1072 \log{\left (x - \frac{1}{2} \right )}}{290521} + \frac{625 \log{\left (x + \frac{3}{5} \right )}}{121} - \frac{12393 \log{\left (x + \frac{2}{3} \right )}}{2401} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.46821, size = 89, normalized size = 1.39 \begin{align*} -\frac{8}{3773 \,{\left (2 \, x - 1\right )}} - \frac{54 \,{\left (\frac{287}{2 \, x - 1} + 120\right )}}{2401 \,{\left (\frac{7}{2 \, x - 1} + 3\right )}^{2}} - \frac{12393}{2401} \, \log \left ({\left | -\frac{7}{2 \, x - 1} - 3 \right |}\right ) + \frac{625}{121} \, \log \left ({\left | -\frac{11}{2 \, x - 1} - 5 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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