Optimal. Leaf size=75 \[ \frac {16}{26411 (1-2 x)}+\frac {3}{49 (2+3 x)^3}+\frac {351}{686 (2+3 x)^2}+\frac {12393}{2401 (2+3 x)}-\frac {2672 \log (1-2 x)}{2033647}-\frac {434043 \log (2+3 x)}{16807}+\frac {3125}{121} \log (3+5 x) \]
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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 = {90}
\begin {gather*} \frac {16}{26411 (1-2 x)}+\frac {12393}{2401 (3 x+2)}+\frac {351}{686 (3 x+2)^2}+\frac {3}{49 (3 x+2)^3}-\frac {2672 \log (1-2 x)}{2033647}-\frac {434043 \log (3 x+2)}{16807}+\frac {3125}{121} \log (5 x+3) \end {gather*}
Antiderivative was successfully verified.
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Rule 90
Rubi steps
\begin {align*} \int \frac {1}{(1-2 x)^2 (2+3 x)^4 (3+5 x)} \, dx &=\int \left (\frac {32}{26411 (-1+2 x)^2}-\frac {5344}{2033647 (-1+2 x)}-\frac {27}{49 (2+3 x)^4}-\frac {1053}{343 (2+3 x)^3}-\frac {37179}{2401 (2+3 x)^2}-\frac {1302129}{16807 (2+3 x)}+\frac {15625}{121 (3+5 x)}\right ) \, dx\\ &=\frac {16}{26411 (1-2 x)}+\frac {3}{49 (2+3 x)^3}+\frac {351}{686 (2+3 x)^2}+\frac {12393}{2401 (2+3 x)}-\frac {2672 \log (1-2 x)}{2033647}-\frac {434043 \log (2+3 x)}{16807}+\frac {3125}{121} \log (3+5 x)\\ \end {align*}
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Mathematica [A]
time = 0.05, size = 70, normalized size = 0.93 \begin {gather*} \frac {77 \left (\frac {32}{1-2 x}+\frac {3234}{(2+3 x)^3}+\frac {27027}{(2+3 x)^2}+\frac {272646}{2+3 x}\right )-5344 \log (5-10 x)-105038406 \log (5 (2+3 x))+105043750 \log (3+5 x)}{4067294} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.09, size = 62, normalized size = 0.83
method | result | size |
risch | \(\frac {\frac {2453382}{26411} x^{3}+\frac {2125062}{26411} x^{2}-\frac {1058241}{52822} x -\frac {574064}{26411}}{\left (-1+2 x \right ) \left (2+3 x \right )^{3}}-\frac {2672 \ln \left (-1+2 x \right )}{2033647}-\frac {434043 \ln \left (2+3 x \right )}{16807}+\frac {3125 \ln \left (3+5 x \right )}{121}\) | \(57\) |
norman | \(\frac {-\frac {3359016}{26411} x^{3}-\frac {3874932}{26411} x^{4}+\frac {833418}{26411} x^{2}+\frac {1812079}{52822} x}{\left (-1+2 x \right ) \left (2+3 x \right )^{3}}-\frac {2672 \ln \left (-1+2 x \right )}{2033647}-\frac {434043 \ln \left (2+3 x \right )}{16807}+\frac {3125 \ln \left (3+5 x \right )}{121}\) | \(60\) |
default | \(-\frac {16}{26411 \left (-1+2 x \right )}-\frac {2672 \ln \left (-1+2 x \right )}{2033647}+\frac {3}{49 \left (2+3 x \right )^{3}}+\frac {351}{686 \left (2+3 x \right )^{2}}+\frac {12393}{2401 \left (2+3 x \right )}-\frac {434043 \ln \left (2+3 x \right )}{16807}+\frac {3125 \ln \left (3+5 x \right )}{121}\) | \(62\) |
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 {4906764 \, x^{3} + 4250124 \, x^{2} - 1058241 \, x - 1148128}{52822 \, {\left (54 \, x^{4} + 81 \, x^{3} + 18 \, x^{2} - 20 \, x - 8\right )}} + \frac {3125}{121} \, \log \left (5 \, x + 3\right ) - \frac {434043}{16807} \, \log \left (3 \, x + 2\right ) - \frac {2672}{2033647} \, \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 = 0.42, size = 123, normalized size = 1.64 \begin {gather*} \frac {377820828 \, x^{3} + 327259548 \, x^{2} + 105043750 \, {\left (54 \, x^{4} + 81 \, x^{3} + 18 \, x^{2} - 20 \, x - 8\right )} \log \left (5 \, x + 3\right ) - 105038406 \, {\left (54 \, x^{4} + 81 \, x^{3} + 18 \, x^{2} - 20 \, x - 8\right )} \log \left (3 \, x + 2\right ) - 5344 \, {\left (54 \, x^{4} + 81 \, x^{3} + 18 \, x^{2} - 20 \, x - 8\right )} \log \left (2 \, x - 1\right ) - 81484557 \, x - 88405856}{4067294 \, {\left (54 \, x^{4} + 81 \, x^{3} + 18 \, x^{2} - 20 \, x - 8\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.12, size = 65, normalized size = 0.87 \begin {gather*} \frac {4906764 x^{3} + 4250124 x^{2} - 1058241 x - 1148128}{2852388 x^{4} + 4278582 x^{3} + 950796 x^{2} - 1056440 x - 422576} - \frac {2672 \log {\left (x - \frac {1}{2} \right )}}{2033647} + \frac {3125 \log {\left (x + \frac {3}{5} \right )}}{121} - \frac {434043 \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 = 0.55, size = 75, normalized size = 1.00 \begin {gather*} -\frac {16}{26411 \, {\left (2 \, x - 1\right )}} - \frac {54 \, {\left (\frac {60375}{2 \, x - 1} + \frac {71491}{{\left (2 \, x - 1\right )}^{2}} + 12756\right )}}{16807 \, {\left (\frac {7}{2 \, x - 1} + 3\right )}^{3}} - \frac {434043}{16807} \, \log \left ({\left | -\frac {7}{2 \, x - 1} - 3 \right |}\right ) + \frac {3125}{121} \, \log \left ({\left | -\frac {11}{2 \, x - 1} - 5 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.04, size = 56, normalized size = 0.75 \begin {gather*} \frac {3125\,\ln \left (x+\frac {3}{5}\right )}{121}-\frac {434043\,\ln \left (x+\frac {2}{3}\right )}{16807}-\frac {2672\,\ln \left (x-\frac {1}{2}\right )}{2033647}-\frac {-\frac {45433\,x^3}{26411}-\frac {39353\,x^2}{26411}+\frac {352747\,x}{950796}+\frac {287032}{713097}}{x^4+\frac {3\,x^3}{2}+\frac {x^2}{3}-\frac {10\,x}{27}-\frac {4}{27}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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