Optimal. Leaf size=75 \[ \frac {3}{28 (2+3 x)^4}+\frac {37}{49 (2+3 x)^3}+\frac {3897}{686 (2+3 x)^2}+\frac {136419}{2401 (2+3 x)}-\frac {32 \log (1-2 x)}{184877}-\frac {4774713 \log (2+3 x)}{16807}+\frac {3125}{11} \log (3+5 x) \]
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Rubi [A]
time = 0.02, antiderivative size = 75, 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 = {84}
\begin {gather*} \frac {136419}{2401 (3 x+2)}+\frac {3897}{686 (3 x+2)^2}+\frac {37}{49 (3 x+2)^3}+\frac {3}{28 (3 x+2)^4}-\frac {32 \log (1-2 x)}{184877}-\frac {4774713 \log (3 x+2)}{16807}+\frac {3125}{11} \log (5 x+3) \end {gather*}
Antiderivative was successfully verified.
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Rule 84
Rubi steps
\begin {align*} \int \frac {1}{(1-2 x) (2+3 x)^5 (3+5 x)} \, dx &=\int \left (-\frac {64}{184877 (-1+2 x)}-\frac {9}{7 (2+3 x)^5}-\frac {333}{49 (2+3 x)^4}-\frac {11691}{343 (2+3 x)^3}-\frac {409257}{2401 (2+3 x)^2}-\frac {14324139}{16807 (2+3 x)}+\frac {15625}{11 (3+5 x)}\right ) \, dx\\ &=\frac {3}{28 (2+3 x)^4}+\frac {37}{49 (2+3 x)^3}+\frac {3897}{686 (2+3 x)^2}+\frac {136419}{2401 (2+3 x)}-\frac {32 \log (1-2 x)}{184877}-\frac {4774713 \log (2+3 x)}{16807}+\frac {3125}{11} \log (3+5 x)\\ \end {align*}
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Mathematica [A]
time = 0.06, size = 55, normalized size = 0.73 \begin {gather*} \frac {\frac {77 \left (4599173+20320788 x+29957526 x^2+14733252 x^3\right )}{4 (2+3 x)^4}-32 \log (1-2 x)-52521843 \log (4+6 x)+52521875 \log (6+10 x)}{184877} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.11, size = 62, normalized size = 0.83
method | result | size |
risch | \(\frac {\frac {3683313}{2401} x^{3}+\frac {14978763}{4802} x^{2}+\frac {5080197}{2401} x +\frac {4599173}{9604}}{\left (2+3 x \right )^{4}}-\frac {32 \ln \left (-1+2 x \right )}{184877}-\frac {4774713 \ln \left (2+3 x \right )}{16807}+\frac {3125 \ln \left (3+5 x \right )}{11}\) | \(50\) |
norman | \(\frac {-\frac {3637125}{4802} x -\frac {94711167}{19208} x^{3}-\frac {64262619}{19208} x^{2}-\frac {372533013}{153664} x^{4}}{\left (2+3 x \right )^{4}}-\frac {32 \ln \left (-1+2 x \right )}{184877}-\frac {4774713 \ln \left (2+3 x \right )}{16807}+\frac {3125 \ln \left (3+5 x \right )}{11}\) | \(53\) |
default | \(-\frac {32 \ln \left (-1+2 x \right )}{184877}+\frac {3}{28 \left (2+3 x \right )^{4}}+\frac {37}{49 \left (2+3 x \right )^{3}}+\frac {3897}{686 \left (2+3 x \right )^{2}}+\frac {136419}{2401 \left (2+3 x \right )}-\frac {4774713 \ln \left (2+3 x \right )}{16807}+\frac {3125 \ln \left (3+5 x \right )}{11}\) | \(62\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.31, size = 64, normalized size = 0.85 \begin {gather*} \frac {14733252 \, x^{3} + 29957526 \, x^{2} + 20320788 \, x + 4599173}{9604 \, {\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )}} + \frac {3125}{11} \, \log \left (5 \, x + 3\right ) - \frac {4774713}{16807} \, \log \left (3 \, x + 2\right ) - \frac {32}{184877} \, \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. 123 vs.
\(2 (61) = 122\).
time = 0.58, size = 123, normalized size = 1.64 \begin {gather*} \frac {1134460404 \, x^{3} + 2306729502 \, x^{2} + 210087500 \, {\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )} \log \left (5 \, x + 3\right ) - 210087372 \, {\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )} \log \left (3 \, x + 2\right ) - 128 \, {\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )} \log \left (2 \, x - 1\right ) + 1564700676 \, x + 354136321}{739508 \, {\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.24, size = 66, normalized size = 0.88 \begin {gather*} - \frac {- 14733252 x^{3} - 29957526 x^{2} - 20320788 x - 4599173}{777924 x^{4} + 2074464 x^{3} + 2074464 x^{2} + 921984 x + 153664} - \frac {32 \log {\left (x - \frac {1}{2} \right )}}{184877} + \frac {3125 \log {\left (x + \frac {3}{5} \right )}}{11} - \frac {4774713 \log {\left (x + \frac {2}{3} \right )}}{16807} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.76, size = 67, normalized size = 0.89 \begin {gather*} \frac {136419}{2401 \, {\left (3 \, x + 2\right )}} + \frac {3897}{686 \, {\left (3 \, x + 2\right )}^{2}} + \frac {37}{49 \, {\left (3 \, x + 2\right )}^{3}} + \frac {3}{28 \, {\left (3 \, x + 2\right )}^{4}} + \frac {3125}{11} \, \log \left ({\left | -\frac {1}{3 \, x + 2} + 5 \right |}\right ) - \frac {32}{184877} \, \log \left ({\left | -\frac {7}{3 \, x + 2} + 2 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.12, size = 55, normalized size = 0.73 \begin {gather*} \frac {3125\,\ln \left (x+\frac {3}{5}\right )}{11}-\frac {4774713\,\ln \left (x+\frac {2}{3}\right )}{16807}-\frac {32\,\ln \left (x-\frac {1}{2}\right )}{184877}+\frac {\frac {45473\,x^3}{2401}+\frac {184923\,x^2}{4802}+\frac {1693399\,x}{64827}+\frac {4599173}{777924}}{x^4+\frac {8\,x^3}{3}+\frac {8\,x^2}{3}+\frac {32\,x}{27}+\frac {16}{81}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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