Optimal. Leaf size=54 \[ -\frac {10633}{5324 (1-2 x)}-\frac {1}{33275 (5 x+3)}+\frac {2401}{1936 (1-2 x)^2}-\frac {47481 \log (1-2 x)}{117128}+\frac {138 \log (5 x+3)}{366025} \]
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Rubi [A] time = 0.03, antiderivative size = 54, normalized size of antiderivative = 1.00, 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} \[ -\frac {10633}{5324 (1-2 x)}-\frac {1}{33275 (5 x+3)}+\frac {2401}{1936 (1-2 x)^2}-\frac {47481 \log (1-2 x)}{117128}+\frac {138 \log (5 x+3)}{366025} \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin {align*} \int \frac {(2+3 x)^4}{(1-2 x)^3 (3+5 x)^2} \, dx &=\int \left (-\frac {2401}{484 (-1+2 x)^3}-\frac {10633}{2662 (-1+2 x)^2}-\frac {47481}{58564 (-1+2 x)}+\frac {1}{6655 (3+5 x)^2}+\frac {138}{73205 (3+5 x)}\right ) \, dx\\ &=\frac {2401}{1936 (1-2 x)^2}-\frac {10633}{5324 (1-2 x)}-\frac {1}{33275 (3+5 x)}-\frac {47481 \log (1-2 x)}{117128}+\frac {138 \log (3+5 x)}{366025}\\ \end {align*}
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Mathematica [A] time = 0.04, size = 48, normalized size = 0.89 \[ \frac {\frac {11696300}{2 x-1}-\frac {176}{5 x+3}+\frac {7263025}{(1-2 x)^2}-2374050 \log (1-2 x)+2208 \log (10 x+6)}{5856400} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.62, size = 75, normalized size = 1.39 \[ \frac {116962296 \, x^{2} + 2208 \, {\left (20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right )} \log \left (5 \, x + 3\right ) - 2374050 \, {\left (20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right )} \log \left (2 \, x - 1\right ) + 48012129 \, x - 13300001}{5856400 \, {\left (20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.17, size = 69, normalized size = 1.28 \[ -\frac {1}{33275 \, {\left (5 \, x + 3\right )}} - \frac {1715 \, {\left (\frac {297}{5 \, x + 3} - 89\right )}}{58564 \, {\left (\frac {11}{5 \, x + 3} - 2\right )}^{2}} + \frac {81}{200} \, \log \left (\frac {{\left | 5 \, x + 3 \right |}}{5 \, {\left (5 \, x + 3\right )}^{2}}\right ) - \frac {47481}{117128} \, \log \left ({\left | -\frac {11}{5 \, x + 3} + 2 \right |}\right ) \]
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 \[ -\frac {47481 \ln \left (2 x -1\right )}{117128}+\frac {138 \ln \left (5 x +3\right )}{366025}-\frac {1}{33275 \left (5 x +3\right )}+\frac {2401}{1936 \left (2 x -1\right )^{2}}+\frac {10633}{5324 \left (2 x -1\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.50, size = 46, normalized size = 0.85 \[ \frac {10632936 \, x^{2} + 4364739 \, x - 1209091}{532400 \, {\left (20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right )}} + \frac {138}{366025} \, \log \left (5 \, x + 3\right ) - \frac {47481}{117128} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.15, size = 42, normalized size = 0.78 \[ \frac {138\,\ln \left (x+\frac {3}{5}\right )}{366025}-\frac {47481\,\ln \left (x-\frac {1}{2}\right )}{117128}-\frac {\frac {1329117\,x^2}{1331000}+\frac {4364739\,x}{10648000}-\frac {1209091}{10648000}}{-x^3+\frac {2\,x^2}{5}+\frac {7\,x}{20}-\frac {3}{20}} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.20, size = 44, normalized size = 0.81 \[ - \frac {- 10632936 x^{2} - 4364739 x + 1209091}{10648000 x^{3} - 4259200 x^{2} - 3726800 x + 1597200} - \frac {47481 \log {\left (x - \frac {1}{2} \right )}}{117128} + \frac {138 \log {\left (x + \frac {3}{5} \right )}}{366025} \]
Verification of antiderivative is not currently implemented for this CAS.
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