Optimal. Leaf size=48 \[ -\frac {18 x^4}{25}+\frac {164 x^3}{125}-\frac {427 x^2}{625}-\frac {1179 x}{3125}-\frac {1331}{15625 (5 x+3)}+\frac {1452 \log (5 x+3)}{3125} \]
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Rubi [A] time = 0.02, antiderivative size = 48, 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} \[ -\frac {18 x^4}{25}+\frac {164 x^3}{125}-\frac {427 x^2}{625}-\frac {1179 x}{3125}-\frac {1331}{15625 (5 x+3)}+\frac {1452 \log (5 x+3)}{3125} \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin {align*} \int \frac {(1-2 x)^3 (2+3 x)^2}{(3+5 x)^2} \, dx &=\int \left (-\frac {1179}{3125}-\frac {854 x}{625}+\frac {492 x^2}{125}-\frac {72 x^3}{25}+\frac {1331}{3125 (3+5 x)^2}+\frac {1452}{625 (3+5 x)}\right ) \, dx\\ &=-\frac {1179 x}{3125}-\frac {427 x^2}{625}+\frac {164 x^3}{125}-\frac {18 x^4}{25}-\frac {1331}{15625 (3+5 x)}+\frac {1452 \log (3+5 x)}{3125}\\ \end {align*}
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Mathematica [A] time = 0.04, size = 51, normalized size = 1.06 \[ \frac {-11250 x^5+13750 x^4+1625 x^3-12300 x^2+2655 x+1452 (5 x+3) \log (6 (5 x+3))+3449}{3125 (5 x+3)} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.51, size = 47, normalized size = 0.98 \[ -\frac {56250 \, x^{5} - 68750 \, x^{4} - 8125 \, x^{3} + 61500 \, x^{2} - 7260 \, {\left (5 \, x + 3\right )} \log \left (5 \, x + 3\right ) + 17685 \, x + 1331}{15625 \, {\left (5 \, x + 3\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.02, size = 66, normalized size = 1.38 \[ \frac {1}{15625} \, {\left (5 \, x + 3\right )}^{4} {\left (\frac {380}{5 \, x + 3} - \frac {2875}{{\left (5 \, x + 3\right )}^{2}} + \frac {7755}{{\left (5 \, x + 3\right )}^{3}} - 18\right )} - \frac {1331}{15625 \, {\left (5 \, x + 3\right )}} - \frac {1452}{3125} \, \log \left (\frac {{\left | 5 \, x + 3 \right |}}{5 \, {\left (5 \, x + 3\right )}^{2}}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 37, normalized size = 0.77 \[ -\frac {18 x^{4}}{25}+\frac {164 x^{3}}{125}-\frac {427 x^{2}}{625}-\frac {1179 x}{3125}+\frac {1452 \ln \left (5 x +3\right )}{3125}-\frac {1331}{15625 \left (5 x +3\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.54, size = 36, normalized size = 0.75 \[ -\frac {18}{25} \, x^{4} + \frac {164}{125} \, x^{3} - \frac {427}{625} \, x^{2} - \frac {1179}{3125} \, x - \frac {1331}{15625 \, {\left (5 \, x + 3\right )}} + \frac {1452}{3125} \, \log \left (5 \, x + 3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 34, normalized size = 0.71 \[ \frac {1452\,\ln \left (x+\frac {3}{5}\right )}{3125}-\frac {1179\,x}{3125}-\frac {1331}{78125\,\left (x+\frac {3}{5}\right )}-\frac {427\,x^2}{625}+\frac {164\,x^3}{125}-\frac {18\,x^4}{25} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.12, size = 41, normalized size = 0.85 \[ - \frac {18 x^{4}}{25} + \frac {164 x^{3}}{125} - \frac {427 x^{2}}{625} - \frac {1179 x}{3125} + \frac {1452 \log {\left (5 x + 3 \right )}}{3125} - \frac {1331}{78125 x + 46875} \]
Verification of antiderivative is not currently implemented for this CAS.
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