Optimal. Leaf size=98 \[ \frac {1936}{823543 (1-2 x)}-\frac {1}{882 (2+3 x)^6}+\frac {22}{1715 (2+3 x)^5}-\frac {319}{9604 (2+3 x)^4}-\frac {1364}{50421 (2+3 x)^3}-\frac {2090}{117649 (2+3 x)^2}-\frac {11264}{823543 (2+3 x)}-\frac {4048 \log (1-2 x)}{823543}+\frac {4048 \log (2+3 x)}{823543} \]
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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 {1936}{823543 (1-2 x)}-\frac {11264}{823543 (3 x+2)}-\frac {2090}{117649 (3 x+2)^2}-\frac {1364}{50421 (3 x+2)^3}-\frac {319}{9604 (3 x+2)^4}+\frac {22}{1715 (3 x+2)^5}-\frac {1}{882 (3 x+2)^6}-\frac {4048 \log (1-2 x)}{823543}+\frac {4048 \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)^2 (2+3 x)^7} \, dx &=\int \left (\frac {3872}{823543 (-1+2 x)^2}-\frac {8096}{823543 (-1+2 x)}+\frac {1}{49 (2+3 x)^7}-\frac {66}{343 (2+3 x)^6}+\frac {957}{2401 (2+3 x)^5}+\frac {4092}{16807 (2+3 x)^4}+\frac {12540}{117649 (2+3 x)^3}+\frac {33792}{823543 (2+3 x)^2}+\frac {12144}{823543 (2+3 x)}\right ) \, dx\\ &=\frac {1936}{823543 (1-2 x)}-\frac {1}{882 (2+3 x)^6}+\frac {22}{1715 (2+3 x)^5}-\frac {319}{9604 (2+3 x)^4}-\frac {1364}{50421 (2+3 x)^3}-\frac {2090}{117649 (2+3 x)^2}-\frac {11264}{823543 (2+3 x)}-\frac {4048 \log (1-2 x)}{823543}+\frac {4048 \log (2+3 x)}{823543}\\ \end {align*}
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Mathematica [A]
time = 0.06, size = 69, normalized size = 0.70 \begin {gather*} \frac {4 \left (-\frac {7 \left (-18979078-60874336 x+48220029 x^2+459657990 x^3+795948120 x^4+604953360 x^5+177059520 x^6\right )}{16 (-1+2 x) (2+3 x)^6}-45540 \log (1-2 x)+45540 \log (4+6 x)\right )}{37059435} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.10, size = 81, normalized size = 0.83
method | result | size |
risch | \(\frac {-\frac {983664}{117649} x^{6}-\frac {3360852}{117649} x^{5}-\frac {4421934}{117649} x^{4}-\frac {5107311}{235298} x^{3}-\frac {5357781}{2352980} x^{2}+\frac {15218584}{5294205} x +\frac {9489539}{10588410}}{\left (-1+2 x \right ) \left (2+3 x \right )^{6}}-\frac {4048 \ln \left (-1+2 x \right )}{823543}+\frac {4048 \ln \left (2+3 x \right )}{823543}\) | \(64\) |
norman | \(\frac {-\frac {15428467}{941192} x^{2}+\frac {57778431}{3764768} x^{4}+\frac {1255786551}{18823840} x^{5}+\frac {4751023653}{75295360} x^{6}-\frac {799769}{235298} x +\frac {768652659}{37647680} x^{7}-\frac {5107311}{235298} x^{3}}{\left (-1+2 x \right ) \left (2+3 x \right )^{6}}-\frac {4048 \ln \left (-1+2 x \right )}{823543}+\frac {4048 \ln \left (2+3 x \right )}{823543}\) | \(67\) |
default | \(-\frac {1936}{823543 \left (-1+2 x \right )}-\frac {4048 \ln \left (-1+2 x \right )}{823543}-\frac {1}{882 \left (2+3 x \right )^{6}}+\frac {22}{1715 \left (2+3 x \right )^{5}}-\frac {319}{9604 \left (2+3 x \right )^{4}}-\frac {1364}{50421 \left (2+3 x \right )^{3}}-\frac {2090}{117649 \left (2+3 x \right )^{2}}-\frac {11264}{823543 \left (2+3 x \right )}+\frac {4048 \ln \left (2+3 x \right )}{823543}\) | \(81\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.32, size = 81, normalized size = 0.83 \begin {gather*} -\frac {177059520 \, x^{6} + 604953360 \, x^{5} + 795948120 \, x^{4} + 459657990 \, x^{3} + 48220029 \, x^{2} - 60874336 \, x - 18979078}{21176820 \, {\left (1458 \, x^{7} + 5103 \, x^{6} + 6804 \, x^{5} + 3780 \, x^{4} - 1008 \, x^{2} - 448 \, x - 64\right )}} + \frac {4048}{823543} \, \log \left (3 \, x + 2\right ) - \frac {4048}{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 = 0.48, size = 140, normalized size = 1.43 \begin {gather*} -\frac {1239416640 \, x^{6} + 4234673520 \, x^{5} + 5571636840 \, x^{4} + 3217605930 \, x^{3} + 337540203 \, x^{2} - 728640 \, {\left (1458 \, x^{7} + 5103 \, x^{6} + 6804 \, x^{5} + 3780 \, x^{4} - 1008 \, x^{2} - 448 \, x - 64\right )} \log \left (3 \, x + 2\right ) + 728640 \, {\left (1458 \, x^{7} + 5103 \, x^{6} + 6804 \, x^{5} + 3780 \, x^{4} - 1008 \, x^{2} - 448 \, x - 64\right )} \log \left (2 \, x - 1\right ) - 426120352 \, x - 132853546}{148237740 \, {\left (1458 \, x^{7} + 5103 \, x^{6} + 6804 \, x^{5} + 3780 \, x^{4} - 1008 \, x^{2} - 448 \, x - 64\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.10, size = 80, normalized size = 0.82 \begin {gather*} \frac {- 177059520 x^{6} - 604953360 x^{5} - 795948120 x^{4} - 459657990 x^{3} - 48220029 x^{2} + 60874336 x + 18979078}{30875803560 x^{7} + 108065312460 x^{6} + 144087083280 x^{5} + 80048379600 x^{4} - 21346234560 x^{2} - 9487215360 x - 1355316480} - \frac {4048 \log {\left (x - \frac {1}{2} \right )}}{823543} + \frac {4048 \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 = 1.17, size = 87, normalized size = 0.89 \begin {gather*} -\frac {1936}{823543 \, {\left (2 \, x - 1\right )}} + \frac {4 \, {\left (\frac {407084454}{2 \, x - 1} + \frac {2053765665}{{\left (2 \, x - 1\right )}^{2}} + \frac {5220014100}{{\left (2 \, x - 1\right )}^{3}} + \frac {6680782500}{{\left (2 \, x - 1\right )}^{4}} + \frac {3440056760}{{\left (2 \, x - 1\right )}^{5}} + 32498901\right )}}{28824005 \, {\left (\frac {7}{2 \, x - 1} + 3\right )}^{6}} + \frac {4048}{823543} \, \log \left ({\left | -\frac {7}{2 \, x - 1} - 3 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.09, size = 71, normalized size = 0.72 \begin {gather*} \frac {8096\,\mathrm {atanh}\left (\frac {12\,x}{7}+\frac {1}{7}\right )}{823543}-\frac {\frac {2024\,x^6}{352947}+\frac {20746\,x^5}{1058841}+\frac {245663\,x^4}{9529569}+\frac {567479\,x^3}{38118276}+\frac {595309\,x^2}{381182760}-\frac {7609292\,x}{3859475445}-\frac {9489539}{15437901780}}{x^7+\frac {7\,x^6}{2}+\frac {14\,x^5}{3}+\frac {70\,x^4}{27}-\frac {56\,x^2}{81}-\frac {224\,x}{729}-\frac {32}{729}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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