Optimal. Leaf size=59 \[ -\frac {54 x^4}{125}+\frac {468 x^3}{625}-\frac {927 x^2}{3125}-\frac {1303 x}{3125}-\frac {11253}{78125 (5 x+3)}-\frac {1331}{156250 (5 x+3)^2}+\frac {5907 \log (5 x+3)}{15625} \]
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Rubi [A] time = 0.03, 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 = {88} \[ -\frac {54 x^4}{125}+\frac {468 x^3}{625}-\frac {927 x^2}{3125}-\frac {1303 x}{3125}-\frac {11253}{78125 (5 x+3)}-\frac {1331}{156250 (5 x+3)^2}+\frac {5907 \log (5 x+3)}{15625} \]
Antiderivative was successfully verified.
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Rule 88
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 = 0.02, size = 56, normalized size = 0.95 \[ -\frac {337500 x^6-180000 x^5-348750 x^4+393250 x^3+416250 x^2+70080 x-11814 (5 x+3)^2 \log (5 x+3)-7139}{31250 (5 x+3)^2} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.62, size = 62, normalized size = 1.05 \[ -\frac {1687500 \, x^{6} - 900000 \, x^{5} - 1743750 \, x^{4} + 1966250 \, x^{3} + 2371650 \, x^{2} - 59070 \, {\left (25 \, x^{2} + 30 \, x + 9\right )} \log \left (5 \, x + 3\right ) + 698880 \, x + 68849}{156250 \, {\left (25 \, x^{2} + 30 \, x + 9\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.78, size = 42, normalized size = 0.71 \[ -\frac {54}{125} \, x^{4} + \frac {468}{625} \, x^{3} - \frac {927}{3125} \, x^{2} - \frac {1303}{3125} \, x - \frac {121 \, {\left (930 \, x + 569\right )}}{156250 \, {\left (5 \, x + 3\right )}^{2}} + \frac {5907}{15625} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 46, normalized size = 0.78 \[ -\frac {54 x^{4}}{125}+\frac {468 x^{3}}{625}-\frac {927 x^{2}}{3125}-\frac {1303 x}{3125}+\frac {5907 \ln \left (5 x +3\right )}{15625}-\frac {1331}{156250 \left (5 x +3\right )^{2}}-\frac {11253}{78125 \left (5 x +3\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.54, size = 46, normalized size = 0.78 \[ -\frac {54}{125} \, x^{4} + \frac {468}{625} \, x^{3} - \frac {927}{3125} \, x^{2} - \frac {1303}{3125} \, x - \frac {121 \, {\left (930 \, x + 569\right )}}{156250 \, {\left (25 \, x^{2} + 30 \, x + 9\right )}} + \frac {5907}{15625} \, \log \left (5 \, x + 3\right ) \]
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 \[ \frac {5907\,\ln \left (x+\frac {3}{5}\right )}{15625}-\frac {1303\,x}{3125}-\frac {\frac {11253\,x}{390625}+\frac {68849}{3906250}}{x^2+\frac {6\,x}{5}+\frac {9}{25}}-\frac {927\,x^2}{3125}+\frac {468\,x^3}{625}-\frac {54\,x^4}{125} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.14, size = 49, normalized size = 0.83 \[ - \frac {54 x^{4}}{125} + \frac {468 x^{3}}{625} - \frac {927 x^{2}}{3125} - \frac {1303 x}{3125} - \frac {112530 x + 68849}{3906250 x^{2} + 4687500 x + 1406250} + \frac {5907 \log {\left (5 x + 3 \right )}}{15625} \]
Verification of antiderivative is not currently implemented for this CAS.
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