Optimal. Leaf size=43 \[ \frac {5}{121 (1-2 x)}+\frac {1}{22 (1-2 x)^2}-\frac {25 \log (1-2 x)}{1331}+\frac {25 \log (5 x+3)}{1331} \]
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Rubi [A] time = 0.02, antiderivative size = 43, 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} \[ \frac {5}{121 (1-2 x)}+\frac {1}{22 (1-2 x)^2}-\frac {25 \log (1-2 x)}{1331}+\frac {25 \log (5 x+3)}{1331} \]
Antiderivative was successfully verified.
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Rule 44
Rubi steps
\begin {align*} \int \frac {1}{(1-2 x)^3 (3+5 x)} \, dx &=\int \left (-\frac {2}{11 (-1+2 x)^3}+\frac {10}{121 (-1+2 x)^2}-\frac {50}{1331 (-1+2 x)}+\frac {125}{1331 (3+5 x)}\right ) \, dx\\ &=\frac {1}{22 (1-2 x)^2}+\frac {5}{121 (1-2 x)}-\frac {25 \log (1-2 x)}{1331}+\frac {25 \log (3+5 x)}{1331}\\ \end {align*}
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Mathematica [A] time = 0.02, size = 46, normalized size = 1.07 \[ \frac {-220 x-50 (1-2 x)^2 \log (1-2 x)+50 (1-2 x)^2 \log (10 x+6)+231}{2662 (1-2 x)^2} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.65, size = 55, normalized size = 1.28 \[ \frac {50 \, {\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (5 \, x + 3\right ) - 50 \, {\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (2 \, x - 1\right ) - 220 \, x + 231}{2662 \, {\left (4 \, x^{2} - 4 \, x + 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.27, size = 33, normalized size = 0.77 \[ -\frac {20 \, x - 21}{242 \, {\left (2 \, x - 1\right )}^{2}} + \frac {25}{1331} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) - \frac {25}{1331} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 36, normalized size = 0.84 \[ -\frac {25 \ln \left (2 x -1\right )}{1331}+\frac {25 \ln \left (5 x +3\right )}{1331}+\frac {1}{22 \left (2 x -1\right )^{2}}-\frac {5}{121 \left (2 x -1\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.52, size = 36, normalized size = 0.84 \[ -\frac {20 \, x - 21}{242 \, {\left (4 \, x^{2} - 4 \, x + 1\right )}} + \frac {25}{1331} \, \log \left (5 \, x + 3\right ) - \frac {25}{1331} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 26, normalized size = 0.60 \[ \frac {50\,\mathrm {atanh}\left (\frac {20\,x}{11}+\frac {1}{11}\right )}{1331}-\frac {\frac {5\,x}{242}-\frac {21}{968}}{x^2-x+\frac {1}{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.16, size = 34, normalized size = 0.79 \[ - \frac {20 x - 21}{968 x^{2} - 968 x + 242} - \frac {25 \log {\left (x - \frac {1}{2} \right )}}{1331} + \frac {25 \log {\left (x + \frac {3}{5} \right )}}{1331} \]
Verification of antiderivative is not currently implemented for this CAS.
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