Optimal. Leaf size=87 \[ -\frac {968}{117649 (3 x+2)}-\frac {242}{16807 (3 x+2)^2}-\frac {242}{7203 (3 x+2)^3}-\frac {121}{1372 (3 x+2)^4}+\frac {68}{2205 (3 x+2)^5}-\frac {1}{378 (3 x+2)^6}-\frac {1936 \log (1-2 x)}{823543}+\frac {1936 \log (3 x+2)}{823543} \]
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Rubi [A] time = 0.03, antiderivative size = 87, 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} \[ -\frac {968}{117649 (3 x+2)}-\frac {242}{16807 (3 x+2)^2}-\frac {242}{7203 (3 x+2)^3}-\frac {121}{1372 (3 x+2)^4}+\frac {68}{2205 (3 x+2)^5}-\frac {1}{378 (3 x+2)^6}-\frac {1936 \log (1-2 x)}{823543}+\frac {1936 \log (3 x+2)}{823543} \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin {align*} \int \frac {(3+5 x)^2}{(1-2 x) (2+3 x)^7} \, dx &=\int \left (-\frac {3872}{823543 (-1+2 x)}+\frac {1}{21 (2+3 x)^7}-\frac {68}{147 (2+3 x)^6}+\frac {363}{343 (2+3 x)^5}+\frac {726}{2401 (2+3 x)^4}+\frac {1452}{16807 (2+3 x)^3}+\frac {2904}{117649 (2+3 x)^2}+\frac {5808}{823543 (2+3 x)}\right ) \, dx\\ &=-\frac {1}{378 (2+3 x)^6}+\frac {68}{2205 (2+3 x)^5}-\frac {121}{1372 (2+3 x)^4}-\frac {242}{7203 (2+3 x)^3}-\frac {242}{16807 (2+3 x)^2}-\frac {968}{117649 (2+3 x)}-\frac {1936 \log (1-2 x)}{823543}+\frac {1936 \log (2+3 x)}{823543}\\ \end {align*}
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Mathematica [A] time = 0.10, size = 57, normalized size = 0.66 \[ \frac {4 \left (-\frac {7 \left (127020960 x^5+497498760 x^4+819755640 x^3+739632465 x^2+351466812 x+67099978\right )}{16 (3 x+2)^6}-65340 \log (1-2 x)+65340 \log (6 x+4)\right )}{111178305} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.82, size = 135, normalized size = 1.55 \[ -\frac {889146720 \, x^{5} + 3482491320 \, x^{4} + 5738289480 \, x^{3} + 5177427255 \, x^{2} - 1045440 \, {\left (729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right )} \log \left (3 \, x + 2\right ) + 1045440 \, {\left (729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right )} \log \left (2 \, x - 1\right ) + 2460267684 \, x + 469699846}{444713220 \, {\left (729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.07, size = 53, normalized size = 0.61 \[ -\frac {127020960 \, x^{5} + 497498760 \, x^{4} + 819755640 \, x^{3} + 739632465 \, x^{2} + 351466812 \, x + 67099978}{63530460 \, {\left (3 \, x + 2\right )}^{6}} + \frac {1936}{823543} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) - \frac {1936}{823543} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 72, normalized size = 0.83 \[ -\frac {1936 \ln \left (2 x -1\right )}{823543}+\frac {1936 \ln \left (3 x +2\right )}{823543}-\frac {1}{378 \left (3 x +2\right )^{6}}+\frac {68}{2205 \left (3 x +2\right )^{5}}-\frac {121}{1372 \left (3 x +2\right )^{4}}-\frac {242}{7203 \left (3 x +2\right )^{3}}-\frac {242}{16807 \left (3 x +2\right )^{2}}-\frac {968}{117649 \left (3 x +2\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.60, size = 76, normalized size = 0.87 \[ -\frac {127020960 \, x^{5} + 497498760 \, x^{4} + 819755640 \, x^{3} + 739632465 \, x^{2} + 351466812 \, x + 67099978}{63530460 \, {\left (729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right )}} + \frac {1936}{823543} \, \log \left (3 \, x + 2\right ) - \frac {1936}{823543} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.14, size = 66, normalized size = 0.76 \[ \frac {3872\,\mathrm {atanh}\left (\frac {12\,x}{7}+\frac {1}{7}\right )}{823543}-\frac {\frac {968\,x^5}{352947}+\frac {11374\,x^4}{1058841}+\frac {168674\,x^3}{9529569}+\frac {67639\,x^2}{4235364}+\frac {9762967\,x}{1286491815}+\frac {33549989}{23156852670}}{x^6+4\,x^5+\frac {20\,x^4}{3}+\frac {160\,x^3}{27}+\frac {80\,x^2}{27}+\frac {64\,x}{81}+\frac {64}{729}} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.21, size = 75, normalized size = 0.86 \[ - \frac {127020960 x^{5} + 497498760 x^{4} + 819755640 x^{3} + 739632465 x^{2} + 351466812 x + 67099978}{46313705340 x^{6} + 185254821360 x^{5} + 308758035600 x^{4} + 274451587200 x^{3} + 137225793600 x^{2} + 36593544960 x + 4065949440} - \frac {1936 \log {\left (x - \frac {1}{2} \right )}}{823543} + \frac {1936 \log {\left (x + \frac {2}{3} \right )}}{823543} \]
Verification of antiderivative is not currently implemented for this CAS.
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