Optimal. Leaf size=43 \[ \frac {343}{176 (1-2 x)^2}-\frac {392}{121 (1-2 x)}-\frac {7189 \log (1-2 x)}{10648}+\frac {\log (3+5 x)}{6655} \]
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Rubi [A]
time = 0.01, antiderivative size = 43, 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 = {90}
\begin {gather*} -\frac {392}{121 (1-2 x)}+\frac {343}{176 (1-2 x)^2}-\frac {7189 \log (1-2 x)}{10648}+\frac {\log (5 x+3)}{6655} \end {gather*}
Antiderivative was successfully verified.
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Rule 90
Rubi steps
\begin {align*} \int \frac {(2+3 x)^3}{(1-2 x)^3 (3+5 x)} \, dx &=\int \left (-\frac {343}{44 (-1+2 x)^3}-\frac {784}{121 (-1+2 x)^2}-\frac {7189}{5324 (-1+2 x)}+\frac {1}{1331 (3+5 x)}\right ) \, dx\\ &=\frac {343}{176 (1-2 x)^2}-\frac {392}{121 (1-2 x)}-\frac {7189 \log (1-2 x)}{10648}+\frac {\log (3+5 x)}{6655}\\ \end {align*}
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Mathematica [A]
time = 0.02, size = 35, normalized size = 0.81 \begin {gather*} \frac {\frac {2695 (-51+256 x)}{(1-2 x)^2}-71890 \log (5-10 x)+16 \log (3+5 x)}{106480} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.10, size = 36, normalized size = 0.84
method | result | size |
risch | \(\frac {\frac {784 x}{121}-\frac {2499}{1936}}{\left (-1+2 x \right )^{2}}-\frac {7189 \ln \left (-1+2 x \right )}{10648}+\frac {\ln \left (3+5 x \right )}{6655}\) | \(32\) |
norman | \(\frac {\frac {637}{484} x +\frac {2499}{484} x^{2}}{\left (-1+2 x \right )^{2}}-\frac {7189 \ln \left (-1+2 x \right )}{10648}+\frac {\ln \left (3+5 x \right )}{6655}\) | \(35\) |
default | \(\frac {343}{176 \left (-1+2 x \right )^{2}}+\frac {392}{121 \left (-1+2 x \right )}-\frac {7189 \ln \left (-1+2 x \right )}{10648}+\frac {\ln \left (3+5 x \right )}{6655}\) | \(36\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, size = 36, normalized size = 0.84 \begin {gather*} \frac {49 \, {\left (256 \, x - 51\right )}}{1936 \, {\left (4 \, x^{2} - 4 \, x + 1\right )}} + \frac {1}{6655} \, \log \left (5 \, x + 3\right ) - \frac {7189}{10648} \, \log \left (2 \, x - 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.44, size = 55, normalized size = 1.28 \begin {gather*} \frac {16 \, {\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (5 \, x + 3\right ) - 71890 \, {\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (2 \, x - 1\right ) + 689920 \, x - 137445}{106480 \, {\left (4 \, x^{2} - 4 \, x + 1\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.07, size = 32, normalized size = 0.74 \begin {gather*} - \frac {2499 - 12544 x}{7744 x^{2} - 7744 x + 1936} - \frac {7189 \log {\left (x - \frac {1}{2} \right )}}{10648} + \frac {\log {\left (x + \frac {3}{5} \right )}}{6655} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.23, size = 33, normalized size = 0.77 \begin {gather*} \frac {49 \, {\left (256 \, x - 51\right )}}{1936 \, {\left (2 \, x - 1\right )}^{2}} + \frac {1}{6655} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) - \frac {7189}{10648} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.08, size = 29, normalized size = 0.67 \begin {gather*} \frac {\ln \left (x+\frac {3}{5}\right )}{6655}-\frac {7189\,\ln \left (x-\frac {1}{2}\right )}{10648}+\frac {\frac {196\,x}{121}-\frac {2499}{7744}}{x^2-x+\frac {1}{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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