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 = 0.02, antiderivative size = 54, normalized size of antiderivative = 1.00, 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*}
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Mathematica [A] time = 0.03, 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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fricas [A] time = 0.83, size = 75, normalized size = 1.39 \[ -\frac {6600 \, x^{2} - 120 \, {\left (50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right )} \log \left (5 \, x + 3\right ) + 120 \, {\left (50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right )} \log \left (2 \, x - 1\right ) + 4290 \, x - 1133}{29282 \, {\left (50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.18, size = 51, normalized size = 0.94 \[ -\frac {4}{1331 \, {\left (2 \, x - 1\right )}} + \frac {50 \, {\left (\frac {66}{2 \, x - 1} + 25\right )}}{14641 \, {\left (\frac {11}{2 \, x - 1} + 5\right )}^{2}} + \frac {60}{14641} \, \log \left ({\left | -\frac {11}{2 \, x - 1} - 5 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 45, normalized size = 0.83 \[ -\frac {60 \ln \left (2 x -1\right )}{14641}+\frac {60 \ln \left (5 x +3\right )}{14641}-\frac {5}{242 \left (5 x +3\right )^{2}}-\frac {20}{1331 \left (5 x +3\right )}-\frac {4}{1331 \left (2 x -1\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.62, size = 46, normalized size = 0.85 \[ -\frac {600 \, x^{2} + 390 \, x - 103}{2662 \, {\left (50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right )}} + \frac {60}{14641} \, \log \left (5 \, x + 3\right ) - \frac {60}{14641} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.06, size = 37, normalized size = 0.69 \[ \frac {120\,\mathrm {atanh}\left (\frac {20\,x}{11}+\frac {1}{11}\right )}{14641}+\frac {\frac {6\,x^2}{1331}+\frac {39\,x}{13310}-\frac {103}{133100}}{-x^3-\frac {7\,x^2}{10}+\frac {6\,x}{25}+\frac {9}{50}} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.17, size = 44, normalized size = 0.81 \[ \frac {- 600 x^{2} - 390 x + 103}{133100 x^{3} + 93170 x^{2} - 31944 x - 23958} - \frac {60 \log {\left (x - \frac {1}{2} \right )}}{14641} + \frac {60 \log {\left (x + \frac {3}{5} \right )}}{14641} \]
Verification of antiderivative is not currently implemented for this CAS.
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