Optimal. Leaf size=54 \[ \frac{4}{1331 (1-2 x)}-\frac{20}{1331 (5 x+3)}-\frac{5}{242 (5 x+3)^2}-\frac{60 \log (1-2 x)}{14641}+\frac{60 \log (5 x+3)}{14641} \]
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Rubi [A] time = 0.0208356, antiderivative size = 54, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067, Rules used = {44} \[ \frac{4}{1331 (1-2 x)}-\frac{20}{1331 (5 x+3)}-\frac{5}{242 (5 x+3)^2}-\frac{60 \log (1-2 x)}{14641}+\frac{60 \log (5 x+3)}{14641} \]
Antiderivative was successfully verified.
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Rule 44
Rubi steps
\begin{align*} \int \frac{1}{(1-2 x)^2 (3+5 x)^3} \, dx &=\int \left (\frac{8}{1331 (-1+2 x)^2}-\frac{120}{14641 (-1+2 x)}+\frac{25}{121 (3+5 x)^3}+\frac{100}{1331 (3+5 x)^2}+\frac{300}{14641 (3+5 x)}\right ) \, dx\\ &=\frac{4}{1331 (1-2 x)}-\frac{5}{242 (3+5 x)^2}-\frac{20}{1331 (3+5 x)}-\frac{60 \log (1-2 x)}{14641}+\frac{60 \log (3+5 x)}{14641}\\ \end{align*}
Mathematica [A] time = 0.0210305, size = 47, normalized size = 0.87 \[ \frac{-\frac{11 \left (600 x^2+390 x-103\right )}{(2 x-1) (5 x+3)^2}-120 \log (1-2 x)+120 \log (10 x+6)}{29282} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.008, size = 45, normalized size = 0.8 \begin{align*} -{\frac{4}{2662\,x-1331}}-{\frac{60\,\ln \left ( 2\,x-1 \right ) }{14641}}-{\frac{5}{242\, \left ( 3+5\,x \right ) ^{2}}}-{\frac{20}{3993+6655\,x}}+{\frac{60\,\ln \left ( 3+5\,x \right ) }{14641}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.05222, size = 62, normalized size = 1.15 \begin{align*} -\frac{600 \, x^{2} + 390 \, x - 103}{2662 \,{\left (50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right )}} + \frac{60}{14641} \, \log \left (5 \, x + 3\right ) - \frac{60}{14641} \, \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 = 1.17036, size = 219, normalized size = 4.06 \begin{align*} -\frac{6600 \, x^{2} - 120 \,{\left (50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right )} \log \left (5 \, x + 3\right ) + 120 \,{\left (50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right )} \log \left (2 \, x - 1\right ) + 4290 \, x - 1133}{29282 \,{\left (50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.148568, size = 44, normalized size = 0.81 \begin{align*} - \frac{600 x^{2} + 390 x - 103}{133100 x^{3} + 93170 x^{2} - 31944 x - 23958} - \frac{60 \log{\left (x - \frac{1}{2} \right )}}{14641} + \frac{60 \log{\left (x + \frac{3}{5} \right )}}{14641} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.46827, size = 69, normalized size = 1.28 \begin{align*} -\frac{4}{1331 \,{\left (2 \, x - 1\right )}} + \frac{50 \,{\left (\frac{66}{2 \, x - 1} + 25\right )}}{14641 \,{\left (\frac{11}{2 \, x - 1} + 5\right )}^{2}} + \frac{60}{14641} \, \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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