Optimal. Leaf size=54 \[ \frac {343}{968 (1-2 x)^2}-\frac {1421}{5324 (1-2 x)}-\frac {1}{6655 (3+5 x)}-\frac {21 \log (1-2 x)}{14641}+\frac {21 \log (3+5 x)}{14641} \]
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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 = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.045, Rules used = {90}
\begin {gather*} -\frac {1421}{5324 (1-2 x)}-\frac {1}{6655 (5 x+3)}+\frac {343}{968 (1-2 x)^2}-\frac {21 \log (1-2 x)}{14641}+\frac {21 \log (5 x+3)}{14641} \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)^2} \, dx &=\int \left (-\frac {343}{242 (-1+2 x)^3}-\frac {1421}{2662 (-1+2 x)^2}-\frac {42}{14641 (-1+2 x)}+\frac {1}{1331 (3+5 x)^2}+\frac {105}{14641 (3+5 x)}\right ) \, dx\\ &=\frac {343}{968 (1-2 x)^2}-\frac {1421}{5324 (1-2 x)}-\frac {1}{6655 (3+5 x)}-\frac {21 \log (1-2 x)}{14641}+\frac {21 \log (3+5 x)}{14641}\\ \end {align*}
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Mathematica [A]
time = 0.03, size = 47, normalized size = 0.87 \begin {gather*} \frac {\frac {11 \left (13957+108567 x+142068 x^2\right )}{(1-2 x)^2 (3+5 x)}-840 \log (1-2 x)+840 \log (6+10 x)}{585640} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.10, size = 45, normalized size = 0.83
method | result | size |
risch | \(\frac {\frac {35517}{13310} x^{2}+\frac {108567}{53240} x +\frac {13957}{53240}}{\left (-1+2 x \right )^{2} \left (3+5 x \right )}-\frac {21 \ln \left (-1+2 x \right )}{14641}+\frac {21 \ln \left (3+5 x \right )}{14641}\) | \(44\) |
default | \(\frac {343}{968 \left (-1+2 x \right )^{2}}+\frac {1421}{5324 \left (-1+2 x \right )}-\frac {21 \ln \left (-1+2 x \right )}{14641}-\frac {1}{6655 \left (3+5 x \right )}+\frac {21 \ln \left (3+5 x \right )}{14641}\) | \(45\) |
norman | \(\frac {-\frac {13957}{7986} x^{3}+\frac {26893}{7986} x^{2}+\frac {10585}{3993} x}{\left (-1+2 x \right )^{2} \left (3+5 x \right )}-\frac {21 \ln \left (-1+2 x \right )}{14641}+\frac {21 \ln \left (3+5 x \right )}{14641}\) | \(47\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.30, size = 46, normalized size = 0.85 \begin {gather*} \frac {142068 \, x^{2} + 108567 \, x + 13957}{53240 \, {\left (20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right )}} + \frac {21}{14641} \, \log \left (5 \, x + 3\right ) - \frac {21}{14641} \, \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 = 0.90, size = 75, normalized size = 1.39 \begin {gather*} \frac {1562748 \, x^{2} + 840 \, {\left (20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right )} \log \left (5 \, x + 3\right ) - 840 \, {\left (20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right )} \log \left (2 \, x - 1\right ) + 1194237 \, x + 153527}{585640 \, {\left (20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.08, size = 46, normalized size = 0.85 \begin {gather*} - \frac {- 142068 x^{2} - 108567 x - 13957}{1064800 x^{3} - 425920 x^{2} - 372680 x + 159720} - \frac {21 \log {\left (x - \frac {1}{2} \right )}}{14641} + \frac {21 \log {\left (x + \frac {3}{5} \right )}}{14641} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 2.37, size = 51, normalized size = 0.94 \begin {gather*} -\frac {1}{6655 \, {\left (5 \, x + 3\right )}} + \frac {245 \, {\left (\frac {66}{5 \, x + 3} + 23\right )}}{29282 \, {\left (\frac {11}{5 \, x + 3} - 2\right )}^{2}} - \frac {21}{14641} \, \log \left ({\left | -\frac {11}{5 \, x + 3} + 2 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.04, size = 38, normalized size = 0.70 \begin {gather*} \frac {42\,\mathrm {atanh}\left (\frac {20\,x}{11}+\frac {1}{11}\right )}{14641}-\frac {\frac {35517\,x^2}{266200}+\frac {108567\,x}{1064800}+\frac {13957}{1064800}}{-x^3+\frac {2\,x^2}{5}+\frac {7\,x}{20}-\frac {3}{20}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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