Optimal. Leaf size=86 \[ \frac {9}{7 (2+3 x)^3}+\frac {2889}{98 (2+3 x)^2}+\frac {204228}{343 (2+3 x)}-\frac {625}{22 (3+5 x)^2}+\frac {81250}{121 (3+5 x)}-\frac {64 \log (1-2 x)}{3195731}-\frac {11984706 \log (2+3 x)}{2401}+\frac {6643750 \log (3+5 x)}{1331} \]
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Rubi [A]
time = 0.03, antiderivative size = 86, 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 {204228}{343 (3 x+2)}+\frac {81250}{121 (5 x+3)}+\frac {2889}{98 (3 x+2)^2}-\frac {625}{22 (5 x+3)^2}+\frac {9}{7 (3 x+2)^3}-\frac {64 \log (1-2 x)}{3195731}-\frac {11984706 \log (3 x+2)}{2401}+\frac {6643750 \log (5 x+3)}{1331} \end {gather*}
Antiderivative was successfully verified.
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Rule 90
Rubi steps
\begin {align*} \int \frac {1}{(1-2 x) (2+3 x)^4 (3+5 x)^3} \, dx &=\int \left (-\frac {128}{3195731 (-1+2 x)}-\frac {81}{7 (2+3 x)^4}-\frac {8667}{49 (2+3 x)^3}-\frac {612684}{343 (2+3 x)^2}-\frac {35954118}{2401 (2+3 x)}+\frac {3125}{11 (3+5 x)^3}-\frac {406250}{121 (3+5 x)^2}+\frac {33218750}{1331 (3+5 x)}\right ) \, dx\\ &=\frac {9}{7 (2+3 x)^3}+\frac {2889}{98 (2+3 x)^2}+\frac {204228}{343 (2+3 x)}-\frac {625}{22 (3+5 x)^2}+\frac {81250}{121 (3+5 x)}-\frac {64 \log (1-2 x)}{3195731}-\frac {11984706 \log (2+3 x)}{2401}+\frac {6643750 \log (3+5 x)}{1331}\\ \end {align*}
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Mathematica [A]
time = 0.03, size = 84, normalized size = 0.98 \begin {gather*} \frac {9}{7 (2+3 x)^3}+\frac {2889}{98 (2+3 x)^2}+\frac {204228}{343 (2+3 x)}-\frac {625}{22 (3+5 x)^2}+\frac {81250}{363+605 x}-\frac {64 \log (1-2 x)}{3195731}-\frac {11984706 \log (4+6 x)}{2401}+\frac {6643750 \log (6+10 x)}{1331} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.09, size = 71, normalized size = 0.83
method | result | size |
risch | \(\frac {\frac {9322388550}{41503} x^{4}+\frac {23927463585}{41503} x^{3}+\frac {23009035068}{41503} x^{2}+\frac {19648830809}{83006} x +\frac {1571537764}{41503}}{\left (2+3 x \right )^{3} \left (3+5 x \right )^{2}}-\frac {64 \ln \left (-1+2 x \right )}{3195731}-\frac {11984706 \ln \left (2+3 x \right )}{2401}+\frac {6643750 \ln \left (3+5 x \right )}{1331}\) | \(62\) |
norman | \(\frac {-\frac {37823744370}{41503} x^{4}-\frac {14915782481}{249018} x -\frac {29466333075}{83006} x^{5}-\frac {72760596217}{83006} x^{3}-\frac {139835645791}{373527} x^{2}}{\left (2+3 x \right )^{3} \left (3+5 x \right )^{2}}-\frac {64 \ln \left (-1+2 x \right )}{3195731}-\frac {11984706 \ln \left (2+3 x \right )}{2401}+\frac {6643750 \ln \left (3+5 x \right )}{1331}\) | \(65\) |
default | \(-\frac {64 \ln \left (-1+2 x \right )}{3195731}+\frac {9}{7 \left (2+3 x \right )^{3}}+\frac {2889}{98 \left (2+3 x \right )^{2}}+\frac {204228}{343 \left (2+3 x \right )}-\frac {11984706 \ln \left (2+3 x \right )}{2401}-\frac {625}{22 \left (3+5 x \right )^{2}}+\frac {81250}{121 \left (3+5 x \right )}+\frac {6643750 \ln \left (3+5 x \right )}{1331}\) | \(71\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.32, size = 74, normalized size = 0.86 \begin {gather*} \frac {18644777100 \, x^{4} + 47854927170 \, x^{3} + 46018070136 \, x^{2} + 19648830809 \, x + 3143075528}{83006 \, {\left (675 \, x^{5} + 2160 \, x^{4} + 2763 \, x^{3} + 1766 \, x^{2} + 564 \, x + 72\right )}} + \frac {6643750}{1331} \, \log \left (5 \, x + 3\right ) - \frac {11984706}{2401} \, \log \left (3 \, x + 2\right ) - \frac {64}{3195731} \, \log \left (2 \, x - 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 148 vs.
\(2 (70) = 140\).
time = 1.33, size = 148, normalized size = 1.72 \begin {gather*} \frac {1435647836700 \, x^{4} + 3684829392090 \, x^{3} + 3543391400472 \, x^{2} + 31903287500 \, {\left (675 \, x^{5} + 2160 \, x^{4} + 2763 \, x^{3} + 1766 \, x^{2} + 564 \, x + 72\right )} \log \left (5 \, x + 3\right ) - 31903287372 \, {\left (675 \, x^{5} + 2160 \, x^{4} + 2763 \, x^{3} + 1766 \, x^{2} + 564 \, x + 72\right )} \log \left (3 \, x + 2\right ) - 128 \, {\left (675 \, x^{5} + 2160 \, x^{4} + 2763 \, x^{3} + 1766 \, x^{2} + 564 \, x + 72\right )} \log \left (2 \, x - 1\right ) + 1512959972293 \, x + 242016815656}{6391462 \, {\left (675 \, x^{5} + 2160 \, x^{4} + 2763 \, x^{3} + 1766 \, x^{2} + 564 \, x + 72\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.11, size = 76, normalized size = 0.88 \begin {gather*} - \frac {- 18644777100 x^{4} - 47854927170 x^{3} - 46018070136 x^{2} - 19648830809 x - 3143075528}{56029050 x^{5} + 179292960 x^{4} + 229345578 x^{3} + 146588596 x^{2} + 46815384 x + 5976432} - \frac {64 \log {\left (x - \frac {1}{2} \right )}}{3195731} + \frac {6643750 \log {\left (x + \frac {3}{5} \right )}}{1331} - \frac {11984706 \log {\left (x + \frac {2}{3} \right )}}{2401} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 2.08, size = 64, normalized size = 0.74 \begin {gather*} \frac {18644777100 \, x^{4} + 47854927170 \, x^{3} + 46018070136 \, x^{2} + 19648830809 \, x + 3143075528}{83006 \, {\left (5 \, x + 3\right )}^{2} {\left (3 \, x + 2\right )}^{3}} + \frac {6643750}{1331} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) - \frac {11984706}{2401} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) - \frac {64}{3195731} \, \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 = 1.12, size = 65, normalized size = 0.76 \begin {gather*} \frac {6643750\,\ln \left (x+\frac {3}{5}\right )}{1331}-\frac {11984706\,\ln \left (x+\frac {2}{3}\right )}{2401}-\frac {64\,\ln \left (x-\frac {1}{2}\right )}{3195731}+\frac {\frac {13810946\,x^4}{41503}+\frac {177240471\,x^3}{207515}+\frac {852186484\,x^2}{1037575}+\frac {19648830809\,x}{56029050}+\frac {1571537764}{28014525}}{x^5+\frac {16\,x^4}{5}+\frac {307\,x^3}{75}+\frac {1766\,x^2}{675}+\frac {188\,x}{225}+\frac {8}{75}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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