Optimal. Leaf size=59 \[ -\frac {1303 x}{3125}-\frac {927 x^2}{3125}+\frac {468 x^3}{625}-\frac {54 x^4}{125}-\frac {1331}{156250 (3+5 x)^2}-\frac {11253}{78125 (3+5 x)}+\frac {5907 \log (3+5 x)}{15625} \]
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Rubi [A]
time = 0.02, antiderivative size = 59, 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 {54 x^4}{125}+\frac {468 x^3}{625}-\frac {927 x^2}{3125}-\frac {1303 x}{3125}-\frac {11253}{78125 (5 x+3)}-\frac {1331}{156250 (5 x+3)^2}+\frac {5907 \log (5 x+3)}{15625} \end {gather*}
Antiderivative was successfully verified.
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Rule 90
Rubi steps
\begin {align*} \int \frac {(1-2 x)^3 (2+3 x)^3}{(3+5 x)^3} \, dx &=\int \left (-\frac {1303}{3125}-\frac {1854 x}{3125}+\frac {1404 x^2}{625}-\frac {216 x^3}{125}+\frac {1331}{15625 (3+5 x)^3}+\frac {11253}{15625 (3+5 x)^2}+\frac {5907}{3125 (3+5 x)}\right ) \, dx\\ &=-\frac {1303 x}{3125}-\frac {927 x^2}{3125}+\frac {468 x^3}{625}-\frac {54 x^4}{125}-\frac {1331}{156250 (3+5 x)^2}-\frac {11253}{78125 (3+5 x)}+\frac {5907 \log (3+5 x)}{15625}\\ \end {align*}
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Mathematica [A]
time = 0.01, size = 56, normalized size = 0.95 \begin {gather*} -\frac {-7139+70080 x+416250 x^2+393250 x^3-348750 x^4-180000 x^5+337500 x^6-11814 (3+5 x)^2 \log (3+5 x)}{31250 (3+5 x)^2} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.11, size = 46, normalized size = 0.78
method | result | size |
risch | \(-\frac {54 x^{4}}{125}+\frac {468 x^{3}}{625}-\frac {927 x^{2}}{3125}-\frac {1303 x}{3125}+\frac {-\frac {11253 x}{15625}-\frac {68849}{156250}}{\left (3+5 x \right )^{2}}+\frac {5907 \ln \left (3+5 x \right )}{15625}\) | \(42\) |
default | \(-\frac {1303 x}{3125}-\frac {927 x^{2}}{3125}+\frac {468 x^{3}}{625}-\frac {54 x^{4}}{125}-\frac {1331}{156250 \left (3+5 x \right )^{2}}-\frac {11253}{78125 \left (3+5 x \right )}+\frac {5907 \ln \left (3+5 x \right )}{15625}\) | \(46\) |
norman | \(\frac {-\frac {28163}{9375} x -\frac {156989}{11250} x^{2}-\frac {1573}{125} x^{3}+\frac {279}{25} x^{4}+\frac {144}{25} x^{5}-\frac {54}{5} x^{6}}{\left (3+5 x \right )^{2}}+\frac {5907 \ln \left (3+5 x \right )}{15625}\) | \(47\) |
meijerg | \(\frac {4 x \left (\frac {5 x}{3}+2\right )}{27 \left (1+\frac {5 x}{3}\right )^{2}}-\frac {2 x^{2}}{9 \left (1+\frac {5 x}{3}\right )^{2}}+\frac {11 x \left (15 x +6\right )}{75 \left (1+\frac {5 x}{3}\right )^{2}}+\frac {5907 \ln \left (1+\frac {5 x}{3}\right )}{15625}+\frac {71 x \left (\frac {100}{9} x^{2}+30 x +12\right )}{500 \left (1+\frac {5 x}{3}\right )^{2}}-\frac {297 x \left (-\frac {625}{27} x^{3}+\frac {500}{9} x^{2}+150 x +60\right )}{3125 \left (1+\frac {5 x}{3}\right )^{2}}-\frac {162 x \left (\frac {1250}{81} x^{4}-\frac {625}{27} x^{3}+\frac {500}{9} x^{2}+150 x +60\right )}{3125 \left (1+\frac {5 x}{3}\right )^{2}}+\frac {1458 x \left (-\frac {21875}{243} x^{5}+\frac {8750}{81} x^{4}-\frac {4375}{27} x^{3}+\frac {3500}{9} x^{2}+1050 x +420\right )}{109375 \left (1+\frac {5 x}{3}\right )^{2}}\) | \(162\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 46, normalized size = 0.78 \begin {gather*} -\frac {54}{125} \, x^{4} + \frac {468}{625} \, x^{3} - \frac {927}{3125} \, x^{2} - \frac {1303}{3125} \, x - \frac {121 \, {\left (930 \, x + 569\right )}}{156250 \, {\left (25 \, x^{2} + 30 \, x + 9\right )}} + \frac {5907}{15625} \, \log \left (5 \, x + 3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.41, size = 62, normalized size = 1.05 \begin {gather*} -\frac {1687500 \, x^{6} - 900000 \, x^{5} - 1743750 \, x^{4} + 1966250 \, x^{3} + 2371650 \, x^{2} - 59070 \, {\left (25 \, x^{2} + 30 \, x + 9\right )} \log \left (5 \, x + 3\right ) + 698880 \, x + 68849}{156250 \, {\left (25 \, x^{2} + 30 \, x + 9\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.05, size = 49, normalized size = 0.83 \begin {gather*} - \frac {54 x^{4}}{125} + \frac {468 x^{3}}{625} - \frac {927 x^{2}}{3125} - \frac {1303 x}{3125} - \frac {112530 x + 68849}{3906250 x^{2} + 4687500 x + 1406250} + \frac {5907 \log {\left (5 x + 3 \right )}}{15625} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.73, size = 42, normalized size = 0.71 \begin {gather*} -\frac {54}{125} \, x^{4} + \frac {468}{625} \, x^{3} - \frac {927}{3125} \, x^{2} - \frac {1303}{3125} \, x - \frac {121 \, {\left (930 \, x + 569\right )}}{156250 \, {\left (5 \, x + 3\right )}^{2}} + \frac {5907}{15625} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.03, size = 42, normalized size = 0.71 \begin {gather*} \frac {5907\,\ln \left (x+\frac {3}{5}\right )}{15625}-\frac {1303\,x}{3125}-\frac {\frac {11253\,x}{390625}+\frac {68849}{3906250}}{x^2+\frac {6\,x}{5}+\frac {9}{25}}-\frac {927\,x^2}{3125}+\frac {468\,x^3}{625}-\frac {54\,x^4}{125} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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