Optimal. Leaf size=98 \[ \frac {484}{117649 (1-2 x)^2}+\frac {11264}{823543 (1-2 x)}-\frac {1}{1715 (2+3 x)^5}+\frac {16}{2401 (2+3 x)^4}-\frac {829}{50421 (2+3 x)^3}-\frac {2875}{117649 (2+3 x)^2}-\frac {24040}{823543 (2+3 x)}-\frac {11696 \log (1-2 x)}{823543}+\frac {11696 \log (2+3 x)}{823543} \]
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Rubi [A]
time = 0.03, antiderivative size = 98, 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 {11264}{823543 (1-2 x)}-\frac {24040}{823543 (3 x+2)}+\frac {484}{117649 (1-2 x)^2}-\frac {2875}{117649 (3 x+2)^2}-\frac {829}{50421 (3 x+2)^3}+\frac {16}{2401 (3 x+2)^4}-\frac {1}{1715 (3 x+2)^5}-\frac {11696 \log (1-2 x)}{823543}+\frac {11696 \log (3 x+2)}{823543} \end {gather*}
Antiderivative was successfully verified.
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Rule 90
Rubi steps
\begin {align*} \int \frac {(3+5 x)^2}{(1-2 x)^3 (2+3 x)^6} \, dx &=\int \left (-\frac {1936}{117649 (-1+2 x)^3}+\frac {22528}{823543 (-1+2 x)^2}-\frac {23392}{823543 (-1+2 x)}+\frac {3}{343 (2+3 x)^6}-\frac {192}{2401 (2+3 x)^5}+\frac {2487}{16807 (2+3 x)^4}+\frac {17250}{117649 (2+3 x)^3}+\frac {72120}{823543 (2+3 x)^2}+\frac {35088}{823543 (2+3 x)}\right ) \, dx\\ &=\frac {484}{117649 (1-2 x)^2}+\frac {11264}{823543 (1-2 x)}-\frac {1}{1715 (2+3 x)^5}+\frac {16}{2401 (2+3 x)^4}-\frac {829}{50421 (2+3 x)^3}-\frac {2875}{117649 (2+3 x)^2}-\frac {24040}{823543 (2+3 x)}-\frac {11696 \log (1-2 x)}{823543}+\frac {11696 \log (2+3 x)}{823543}\\ \end {align*}
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Mathematica [A]
time = 0.07, size = 69, normalized size = 0.70 \begin {gather*} \frac {4 \left (-\frac {7 \left (258089-4230956 x-19495039 x^2-14484765 x^3+36579240 x^4+63947880 x^5+28421280 x^6\right )}{4 (1-2 x)^2 (2+3 x)^5}-43860 \log (1-2 x)+43860 \log (4+6 x)\right )}{12353145} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.09, size = 81, normalized size = 0.83
method | result | size |
risch | \(\frac {-\frac {1894752}{117649} x^{6}-\frac {4263192}{117649} x^{5}-\frac {2438616}{117649} x^{4}+\frac {965651}{117649} x^{3}+\frac {19495039}{1764735} x^{2}+\frac {4230956}{1764735} x -\frac {258089}{1764735}}{\left (-1+2 x \right )^{2} \left (2+3 x \right )^{5}}-\frac {11696 \ln \left (-1+2 x \right )}{823543}+\frac {11696 \ln \left (2+3 x \right )}{823543}\) | \(64\) |
norman | \(\frac {-\frac {568293471}{18823840} x^{5}-\frac {44437725}{1882384} x^{4}-\frac {27011259}{4705960} x^{6}+\frac {2055981}{470596} x^{3}+\frac {2478897}{235298} x^{2}+\frac {20905209}{4705960} x^{7}+\frac {684569}{235298} x}{\left (-1+2 x \right )^{2} \left (2+3 x \right )^{5}}-\frac {11696 \ln \left (-1+2 x \right )}{823543}+\frac {11696 \ln \left (2+3 x \right )}{823543}\) | \(67\) |
default | \(\frac {484}{117649 \left (-1+2 x \right )^{2}}-\frac {11264}{823543 \left (-1+2 x \right )}-\frac {11696 \ln \left (-1+2 x \right )}{823543}-\frac {1}{1715 \left (2+3 x \right )^{5}}+\frac {16}{2401 \left (2+3 x \right )^{4}}-\frac {829}{50421 \left (2+3 x \right )^{3}}-\frac {2875}{117649 \left (2+3 x \right )^{2}}-\frac {24040}{823543 \left (2+3 x \right )}+\frac {11696 \ln \left (2+3 x \right )}{823543}\) | \(81\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.44, size = 86, normalized size = 0.88 \begin {gather*} -\frac {28421280 \, x^{6} + 63947880 \, x^{5} + 36579240 \, x^{4} - 14484765 \, x^{3} - 19495039 \, x^{2} - 4230956 \, x + 258089}{1764735 \, {\left (972 \, x^{7} + 2268 \, x^{6} + 1323 \, x^{5} - 630 \, x^{4} - 840 \, x^{3} - 112 \, x^{2} + 112 \, x + 32\right )}} + \frac {11696}{823543} \, \log \left (3 \, x + 2\right ) - \frac {11696}{823543} \, \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 = 0.39, size = 155, normalized size = 1.58 \begin {gather*} -\frac {198948960 \, x^{6} + 447635160 \, x^{5} + 256054680 \, x^{4} - 101393355 \, x^{3} - 136465273 \, x^{2} - 175440 \, {\left (972 \, x^{7} + 2268 \, x^{6} + 1323 \, x^{5} - 630 \, x^{4} - 840 \, x^{3} - 112 \, x^{2} + 112 \, x + 32\right )} \log \left (3 \, x + 2\right ) + 175440 \, {\left (972 \, x^{7} + 2268 \, x^{6} + 1323 \, x^{5} - 630 \, x^{4} - 840 \, x^{3} - 112 \, x^{2} + 112 \, x + 32\right )} \log \left (2 \, x - 1\right ) - 29616692 \, x + 1806623}{12353145 \, {\left (972 \, x^{7} + 2268 \, x^{6} + 1323 \, x^{5} - 630 \, x^{4} - 840 \, x^{3} - 112 \, x^{2} + 112 \, x + 32\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.12, size = 85, normalized size = 0.87 \begin {gather*} - \frac {28421280 x^{6} + 63947880 x^{5} + 36579240 x^{4} - 14484765 x^{3} - 19495039 x^{2} - 4230956 x + 258089}{1715322420 x^{7} + 4002418980 x^{6} + 2334744405 x^{5} - 1111783050 x^{4} - 1482377400 x^{3} - 197650320 x^{2} + 197650320 x + 56471520} - \frac {11696 \log {\left (x - \frac {1}{2} \right )}}{823543} + \frac {11696 \log {\left (x + \frac {2}{3} \right )}}{823543} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.06, size = 65, normalized size = 0.66 \begin {gather*} -\frac {28421280 \, x^{6} + 63947880 \, x^{5} + 36579240 \, x^{4} - 14484765 \, x^{3} - 19495039 \, x^{2} - 4230956 \, x + 258089}{1764735 \, {\left (3 \, x + 2\right )}^{5} {\left (2 \, x - 1\right )}^{2}} + \frac {11696}{823543} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) - \frac {11696}{823543} \, \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 = 1.06, size = 76, normalized size = 0.78 \begin {gather*} \frac {23392\,\mathrm {atanh}\left (\frac {12\,x}{7}+\frac {1}{7}\right )}{823543}-\frac {\frac {5848\,x^6}{352947}+\frac {4386\,x^5}{117649}+\frac {203218\,x^4}{9529569}-\frac {965651\,x^3}{114354828}-\frac {19495039\,x^2}{1715322420}-\frac {1057739\,x}{428830605}+\frac {258089}{1715322420}}{x^7+\frac {7\,x^6}{3}+\frac {49\,x^5}{36}-\frac {35\,x^4}{54}-\frac {70\,x^3}{81}-\frac {28\,x^2}{243}+\frac {28\,x}{243}+\frac {8}{243}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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