Optimal. Leaf size=109 \[ \frac {21296}{5764801 (1-2 x)}+\frac {1}{3087 (2+3 x)^7}-\frac {101}{18522 (2+3 x)^6}+\frac {363}{12005 (2+3 x)^5}-\frac {3267}{67228 (2+3 x)^4}-\frac {4840}{117649 (2+3 x)^3}-\frac {22506}{823543 (2+3 x)^2}-\frac {17424}{823543 (2+3 x)}-\frac {307824 \log (1-2 x)}{40353607}+\frac {307824 \log (2+3 x)}{40353607} \]
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Rubi [A]
time = 0.04, antiderivative size = 109, 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 {21296}{5764801 (1-2 x)}-\frac {17424}{823543 (3 x+2)}-\frac {22506}{823543 (3 x+2)^2}-\frac {4840}{117649 (3 x+2)^3}-\frac {3267}{67228 (3 x+2)^4}+\frac {363}{12005 (3 x+2)^5}-\frac {101}{18522 (3 x+2)^6}+\frac {1}{3087 (3 x+2)^7}-\frac {307824 \log (1-2 x)}{40353607}+\frac {307824 \log (3 x+2)}{40353607} \end {gather*}
Antiderivative was successfully verified.
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Rule 90
Rubi steps
\begin {align*} \int \frac {(3+5 x)^3}{(1-2 x)^2 (2+3 x)^8} \, dx &=\int \left (\frac {42592}{5764801 (-1+2 x)^2}-\frac {615648}{40353607 (-1+2 x)}-\frac {1}{147 (2+3 x)^8}+\frac {101}{1029 (2+3 x)^7}-\frac {1089}{2401 (2+3 x)^6}+\frac {9801}{16807 (2+3 x)^5}+\frac {43560}{117649 (2+3 x)^4}+\frac {135036}{823543 (2+3 x)^3}+\frac {52272}{823543 (2+3 x)^2}+\frac {923472}{40353607 (2+3 x)}\right ) \, dx\\ &=\frac {21296}{5764801 (1-2 x)}+\frac {1}{3087 (2+3 x)^7}-\frac {101}{18522 (2+3 x)^6}+\frac {363}{12005 (2+3 x)^5}-\frac {3267}{67228 (2+3 x)^4}-\frac {4840}{117649 (2+3 x)^3}-\frac {22506}{823543 (2+3 x)^2}-\frac {17424}{823543 (2+3 x)}-\frac {307824 \log (1-2 x)}{40353607}+\frac {307824 \log (2+3 x)}{40353607}\\ \end {align*}
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Mathematica [A]
time = 0.07, size = 74, normalized size = 0.68 \begin {gather*} \frac {4 \left (-\frac {7 \left (-8381276704-39853850134 x-18916696050 x^2+242725322763 x^3+677745912690 x^4+820756518120 x^5+494810149680 x^6+121177995840 x^7\right )}{16 (-1+2 x) (2+3 x)^7}-10389060 \log (1-2 x)+10389060 \log (4+6 x)\right )}{5447736945} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.09, size = 90, normalized size = 0.83
method | result | size |
risch | \(\frac {-\frac {224403696}{5764801} x^{7}-\frac {18700308}{117649} x^{6}-\frac {217131354}{823543} x^{5}-\frac {358595721}{1647086} x^{4}-\frac {1284260967}{16470860} x^{3}+\frac {90079505}{14823774} x^{2}+\frac {2846703581}{222356610} x +\frac {2095319176}{778248135}}{\left (-1+2 x \right ) \left (2+3 x \right )^{7}}-\frac {307824 \ln \left (-1+2 x \right )}{40353607}+\frac {307824 \ln \left (2+3 x \right )}{40353607}\) | \(69\) |
norman | \(\frac {-\frac {466384111}{3294172} x^{3}-\frac {106397787}{1647086} x^{2}-\frac {48340412}{823543} x^{4}+\frac {648327591}{1882384} x^{7}+\frac {4300564521}{16470860} x^{5}+\frac {15979020417}{32941720} x^{6}+\frac {21215106657}{230592040} x^{8}-\frac {116248155}{11529602} x}{\left (-1+2 x \right ) \left (2+3 x \right )^{7}}-\frac {307824 \ln \left (-1+2 x \right )}{40353607}+\frac {307824 \ln \left (2+3 x \right )}{40353607}\) | \(72\) |
default | \(-\frac {21296}{5764801 \left (-1+2 x \right )}-\frac {307824 \ln \left (-1+2 x \right )}{40353607}+\frac {1}{3087 \left (2+3 x \right )^{7}}-\frac {101}{18522 \left (2+3 x \right )^{6}}+\frac {363}{12005 \left (2+3 x \right )^{5}}-\frac {3267}{67228 \left (2+3 x \right )^{4}}-\frac {4840}{117649 \left (2+3 x \right )^{3}}-\frac {22506}{823543 \left (2+3 x \right )^{2}}-\frac {17424}{823543 \left (2+3 x \right )}+\frac {307824 \ln \left (2+3 x \right )}{40353607}\) | \(90\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.33, size = 96, normalized size = 0.88 \begin {gather*} -\frac {121177995840 \, x^{7} + 494810149680 \, x^{6} + 820756518120 \, x^{5} + 677745912690 \, x^{4} + 242725322763 \, x^{3} - 18916696050 \, x^{2} - 39853850134 \, x - 8381276704}{3112992540 \, {\left (4374 \, x^{8} + 18225 \, x^{7} + 30618 \, x^{6} + 24948 \, x^{5} + 7560 \, x^{4} - 3024 \, x^{3} - 3360 \, x^{2} - 1088 \, x - 128\right )}} + \frac {307824}{40353607} \, \log \left (3 \, x + 2\right ) - \frac {307824}{40353607} \, \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 = 0.38, size = 175, normalized size = 1.61 \begin {gather*} -\frac {848245970880 \, x^{7} + 3463671047760 \, x^{6} + 5745295626840 \, x^{5} + 4744221388830 \, x^{4} + 1699077259341 \, x^{3} - 132416872350 \, x^{2} - 166224960 \, {\left (4374 \, x^{8} + 18225 \, x^{7} + 30618 \, x^{6} + 24948 \, x^{5} + 7560 \, x^{4} - 3024 \, x^{3} - 3360 \, x^{2} - 1088 \, x - 128\right )} \log \left (3 \, x + 2\right ) + 166224960 \, {\left (4374 \, x^{8} + 18225 \, x^{7} + 30618 \, x^{6} + 24948 \, x^{5} + 7560 \, x^{4} - 3024 \, x^{3} - 3360 \, x^{2} - 1088 \, x - 128\right )} \log \left (2 \, x - 1\right ) - 278976950938 \, x - 58668936928}{21790947780 \, {\left (4374 \, x^{8} + 18225 \, x^{7} + 30618 \, x^{6} + 24948 \, x^{5} + 7560 \, x^{4} - 3024 \, x^{3} - 3360 \, x^{2} - 1088 \, x - 128\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.10, size = 95, normalized size = 0.87 \begin {gather*} \frac {- 121177995840 x^{7} - 494810149680 x^{6} - 820756518120 x^{5} - 677745912690 x^{4} - 242725322763 x^{3} + 18916696050 x^{2} + 39853850134 x + 8381276704}{13616229369960 x^{8} + 56734289041500 x^{7} + 95313605589720 x^{6} + 77662937887920 x^{5} + 23534223602400 x^{4} - 9413689440960 x^{3} - 10459654934400 x^{2} - 3386935883520 x - 398463045120} - \frac {307824 \log {\left (x - \frac {1}{2} \right )}}{40353607} + \frac {307824 \log {\left (x + \frac {2}{3} \right )}}{40353607} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.76, size = 96, normalized size = 0.88 \begin {gather*} -\frac {21296}{5764801 \, {\left (2 \, x - 1\right )}} + \frac {4 \, {\left (\frac {108987508287}{2 \, x - 1} + \frac {677288963799}{{\left (2 \, x - 1\right )}^{2}} + \frac {2255033089785}{{\left (2 \, x - 1\right )}^{3}} + \frac {4241269979800}{{\left (2 \, x - 1\right )}^{4}} + \frac {4269658683500}{{\left (2 \, x - 1\right )}^{5}} + \frac {1795850807520}{{\left (2 \, x - 1\right )}^{6}} + 7339564629\right )}}{1412376245 \, {\left (\frac {7}{2 \, x - 1} + 3\right )}^{7}} + \frac {307824}{40353607} \, \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 = 0.05, size = 86, normalized size = 0.79 \begin {gather*} \frac {615648\,\mathrm {atanh}\left (\frac {12\,x}{7}+\frac {1}{7}\right )}{40353607}-\frac {\frac {51304\,x^7}{5764801}+\frac {12826\,x^6}{352947}+\frac {1340317\,x^5}{22235661}+\frac {13281323\,x^4}{266827932}+\frac {47565221\,x^3}{2668279320}-\frac {90079505\,x^2}{64839187476}-\frac {2846703581\,x}{972587812140}-\frac {1047659588}{1702028671245}}{x^8+\frac {25\,x^7}{6}+7\,x^6+\frac {154\,x^5}{27}+\frac {140\,x^4}{81}-\frac {56\,x^3}{81}-\frac {560\,x^2}{729}-\frac {544\,x}{2187}-\frac {64}{2187}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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