Optimal. Leaf size=52 \[ \frac {36 x^3}{125}-\frac {216 x^2}{625}-\frac {153 x}{3125}-\frac {209}{3125 (5 x+3)}-\frac {121}{31250 (5 x+3)^2}+\frac {23}{125} \log (5 x+3) \]
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Rubi [A] time = 0.02, antiderivative size = 52, 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} \[ \frac {36 x^3}{125}-\frac {216 x^2}{625}-\frac {153 x}{3125}-\frac {209}{3125 (5 x+3)}-\frac {121}{31250 (5 x+3)^2}+\frac {23}{125} \log (5 x+3) \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin {align*} \int \frac {(1-2 x)^2 (2+3 x)^3}{(3+5 x)^3} \, dx &=\int \left (-\frac {153}{3125}-\frac {432 x}{625}+\frac {108 x^2}{125}+\frac {121}{3125 (3+5 x)^3}+\frac {209}{625 (3+5 x)^2}+\frac {23}{25 (3+5 x)}\right ) \, dx\\ &=-\frac {153 x}{3125}-\frac {216 x^2}{625}+\frac {36 x^3}{125}-\frac {121}{31250 (3+5 x)^2}-\frac {209}{3125 (3+5 x)}+\frac {23}{125} \log (3+5 x)\\ \end {align*}
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Mathematica [A] time = 0.05, size = 48, normalized size = 0.92 \[ \frac {45000 x^5-56250 x^3-4050 x^2+24640 x+1150 (5 x+3)^2 \log (6 (5 x+3))+7567}{6250 (5 x+3)^2} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.56, size = 52, normalized size = 1.00 \[ \frac {225000 \, x^{5} - 281250 \, x^{3} - 143100 \, x^{2} + 5750 \, {\left (25 \, x^{2} + 30 \, x + 9\right )} \log \left (5 \, x + 3\right ) - 24220 \, x - 6391}{31250 \, {\left (25 \, x^{2} + 30 \, x + 9\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.93, size = 37, normalized size = 0.71 \[ \frac {36}{125} \, x^{3} - \frac {216}{625} \, x^{2} - \frac {153}{3125} \, x - \frac {11 \, {\left (950 \, x + 581\right )}}{31250 \, {\left (5 \, x + 3\right )}^{2}} + \frac {23}{125} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 41, normalized size = 0.79 \[ \frac {36 x^{3}}{125}-\frac {216 x^{2}}{625}-\frac {153 x}{3125}+\frac {23 \ln \left (5 x +3\right )}{125}-\frac {121}{31250 \left (5 x +3\right )^{2}}-\frac {209}{3125 \left (5 x +3\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.53, size = 41, normalized size = 0.79 \[ \frac {36}{125} \, x^{3} - \frac {216}{625} \, x^{2} - \frac {153}{3125} \, x - \frac {11 \, {\left (950 \, x + 581\right )}}{31250 \, {\left (25 \, x^{2} + 30 \, x + 9\right )}} + \frac {23}{125} \, \log \left (5 \, x + 3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 37, normalized size = 0.71 \[ \frac {23\,\ln \left (x+\frac {3}{5}\right )}{125}-\frac {153\,x}{3125}-\frac {\frac {209\,x}{15625}+\frac {6391}{781250}}{x^2+\frac {6\,x}{5}+\frac {9}{25}}-\frac {216\,x^2}{625}+\frac {36\,x^3}{125} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.13, size = 44, normalized size = 0.85 \[ \frac {36 x^{3}}{125} - \frac {216 x^{2}}{625} - \frac {153 x}{3125} + \frac {- 10450 x - 6391}{781250 x^{2} + 937500 x + 281250} + \frac {23 \log {\left (5 x + 3 \right )}}{125} \]
Verification of antiderivative is not currently implemented for this CAS.
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