Optimal. Leaf size=98 \[ \frac {2608}{823543 (1-2 x)}-\frac {7680}{823543 (3 x+2)}+\frac {88}{117649 (1-2 x)^2}-\frac {1140}{117649 (3 x+2)^2}-\frac {186}{16807 (3 x+2)^3}-\frac {87}{9604 (3 x+2)^4}+\frac {3}{1715 (3 x+2)^5}-\frac {3312 \log (1-2 x)}{823543}+\frac {3312 \log (3 x+2)}{823543} \]
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Rubi [A] time = 0.05, antiderivative size = 98, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {77} \[ \frac {2608}{823543 (1-2 x)}-\frac {7680}{823543 (3 x+2)}+\frac {88}{117649 (1-2 x)^2}-\frac {1140}{117649 (3 x+2)^2}-\frac {186}{16807 (3 x+2)^3}-\frac {87}{9604 (3 x+2)^4}+\frac {3}{1715 (3 x+2)^5}-\frac {3312 \log (1-2 x)}{823543}+\frac {3312 \log (3 x+2)}{823543} \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin {align*} \int \frac {3+5 x}{(1-2 x)^3 (2+3 x)^6} \, dx &=\int \left (-\frac {352}{117649 (-1+2 x)^3}+\frac {5216}{823543 (-1+2 x)^2}-\frac {6624}{823543 (-1+2 x)}-\frac {9}{343 (2+3 x)^6}+\frac {261}{2401 (2+3 x)^5}+\frac {1674}{16807 (2+3 x)^4}+\frac {6840}{117649 (2+3 x)^3}+\frac {23040}{823543 (2+3 x)^2}+\frac {9936}{823543 (2+3 x)}\right ) \, dx\\ &=\frac {88}{117649 (1-2 x)^2}+\frac {2608}{823543 (1-2 x)}+\frac {3}{1715 (2+3 x)^5}-\frac {87}{9604 (2+3 x)^4}-\frac {186}{16807 (2+3 x)^3}-\frac {1140}{117649 (2+3 x)^2}-\frac {7680}{823543 (2+3 x)}-\frac {3312 \log (1-2 x)}{823543}+\frac {3312 \log (2+3 x)}{823543}\\ \end {align*}
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Mathematica [A] time = 0.08, size = 69, normalized size = 0.70 \[ \frac {3 \left (-\frac {7 \left (10730880 x^6+24144480 x^5+13811040 x^4-5468940 x^3-7360644 x^2-1134751 x+381394\right )}{3 (1-2 x)^2 (3 x+2)^5}-22080 \log (3-6 x)+22080 \log (3 x+2)\right )}{16470860} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.69, size = 155, normalized size = 1.58 \[ -\frac {75116160 \, x^{6} + 169011360 \, x^{5} + 96677280 \, x^{4} - 38282580 \, x^{3} - 51524508 \, x^{2} - 66240 \, {\left (972 \, x^{7} + 2268 \, x^{6} + 1323 \, x^{5} - 630 \, x^{4} - 840 \, x^{3} - 112 \, x^{2} + 112 \, x + 32\right )} \log \left (3 \, x + 2\right ) + 66240 \, {\left (972 \, x^{7} + 2268 \, x^{6} + 1323 \, x^{5} - 630 \, x^{4} - 840 \, x^{3} - 112 \, x^{2} + 112 \, x + 32\right )} \log \left (2 \, x - 1\right ) - 7943257 \, x + 2669758}{16470860 \, {\left (972 \, x^{7} + 2268 \, x^{6} + 1323 \, x^{5} - 630 \, x^{4} - 840 \, x^{3} - 112 \, x^{2} + 112 \, x + 32\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.20, size = 65, normalized size = 0.66 \[ -\frac {10730880 \, x^{6} + 24144480 \, x^{5} + 13811040 \, x^{4} - 5468940 \, x^{3} - 7360644 \, x^{2} - 1134751 \, x + 381394}{2352980 \, {\left (3 \, x + 2\right )}^{5} {\left (2 \, x - 1\right )}^{2}} + \frac {3312}{823543} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) - \frac {3312}{823543} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 81, normalized size = 0.83 \[ -\frac {3312 \ln \left (2 x -1\right )}{823543}+\frac {3312 \ln \left (3 x +2\right )}{823543}+\frac {3}{1715 \left (3 x +2\right )^{5}}-\frac {87}{9604 \left (3 x +2\right )^{4}}-\frac {186}{16807 \left (3 x +2\right )^{3}}-\frac {1140}{117649 \left (3 x +2\right )^{2}}-\frac {7680}{823543 \left (3 x +2\right )}+\frac {88}{117649 \left (2 x -1\right )^{2}}-\frac {2608}{823543 \left (2 x -1\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.55, size = 86, normalized size = 0.88 \[ -\frac {10730880 \, x^{6} + 24144480 \, x^{5} + 13811040 \, x^{4} - 5468940 \, x^{3} - 7360644 \, x^{2} - 1134751 \, x + 381394}{2352980 \, {\left (972 \, x^{7} + 2268 \, x^{6} + 1323 \, x^{5} - 630 \, x^{4} - 840 \, x^{3} - 112 \, x^{2} + 112 \, x + 32\right )}} + \frac {3312}{823543} \, \log \left (3 \, x + 2\right ) - \frac {3312}{823543} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.07, size = 76, normalized size = 0.78 \[ \frac {6624\,\mathrm {atanh}\left (\frac {12\,x}{7}+\frac {1}{7}\right )}{823543}-\frac {\frac {552\,x^6}{117649}+\frac {1242\,x^5}{117649}+\frac {6394\,x^4}{1058841}-\frac {30383\,x^3}{12706092}-\frac {613387\,x^2}{190591380}-\frac {1134751\,x}{2287096560}+\frac {190697}{1143548280}}{x^7+\frac {7\,x^6}{3}+\frac {49\,x^5}{36}-\frac {35\,x^4}{54}-\frac {70\,x^3}{81}-\frac {28\,x^2}{243}+\frac {28\,x}{243}+\frac {8}{243}} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.22, size = 85, normalized size = 0.87 \[ - \frac {10730880 x^{6} + 24144480 x^{5} + 13811040 x^{4} - 5468940 x^{3} - 7360644 x^{2} - 1134751 x + 381394}{2287096560 x^{7} + 5336558640 x^{6} + 3112992540 x^{5} - 1482377400 x^{4} - 1976503200 x^{3} - 263533760 x^{2} + 263533760 x + 75295360} - \frac {3312 \log {\left (x - \frac {1}{2} \right )}}{823543} + \frac {3312 \log {\left (x + \frac {2}{3} \right )}}{823543} \]
Verification of antiderivative is not currently implemented for this CAS.
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