Optimal. Leaf size=44 \[ \frac {100 x^5}{3}+\frac {50 x^4}{9}-\frac {2515 x^3}{81}-\frac {559 x^2}{162}+\frac {3305 x}{243}-\frac {49}{729} \log (3 x+2) \]
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Rubi [A] time = 0.02, antiderivative size = 44, 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} \begin {gather*} \frac {100 x^5}{3}+\frac {50 x^4}{9}-\frac {2515 x^3}{81}-\frac {559 x^2}{162}+\frac {3305 x}{243}-\frac {49}{729} \log (3 x+2) \end {gather*}
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin {align*} \int \frac {(1-2 x)^2 (3+5 x)^3}{2+3 x} \, dx &=\int \left (\frac {3305}{243}-\frac {559 x}{81}-\frac {2515 x^2}{27}+\frac {200 x^3}{9}+\frac {500 x^4}{3}-\frac {49}{243 (2+3 x)}\right ) \, dx\\ &=\frac {3305 x}{243}-\frac {559 x^2}{162}-\frac {2515 x^3}{81}+\frac {50 x^4}{9}+\frac {100 x^5}{3}-\frac {49}{729} \log (2+3 x)\\ \end {align*}
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Mathematica [A] time = 0.02, size = 37, normalized size = 0.84 \begin {gather*} \frac {145800 x^5+24300 x^4-135810 x^3-15093 x^2+59490 x-294 \log (3 x+2)+20528}{4374} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {(1-2 x)^2 (3+5 x)^3}{2+3 x} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 0.69, size = 32, normalized size = 0.73 \begin {gather*} \frac {100}{3} \, x^{5} + \frac {50}{9} \, x^{4} - \frac {2515}{81} \, x^{3} - \frac {559}{162} \, x^{2} + \frac {3305}{243} \, x - \frac {49}{729} \, \log \left (3 \, x + 2\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.99, size = 33, normalized size = 0.75 \begin {gather*} \frac {100}{3} \, x^{5} + \frac {50}{9} \, x^{4} - \frac {2515}{81} \, x^{3} - \frac {559}{162} \, x^{2} + \frac {3305}{243} \, x - \frac {49}{729} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 33, normalized size = 0.75 \begin {gather*} \frac {100 x^{5}}{3}+\frac {50 x^{4}}{9}-\frac {2515 x^{3}}{81}-\frac {559 x^{2}}{162}+\frac {3305 x}{243}-\frac {49 \ln \left (3 x +2\right )}{729} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.57, size = 32, normalized size = 0.73 \begin {gather*} \frac {100}{3} \, x^{5} + \frac {50}{9} \, x^{4} - \frac {2515}{81} \, x^{3} - \frac {559}{162} \, x^{2} + \frac {3305}{243} \, x - \frac {49}{729} \, \log \left (3 \, x + 2\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 30, normalized size = 0.68 \begin {gather*} \frac {3305\,x}{243}-\frac {49\,\ln \left (x+\frac {2}{3}\right )}{729}-\frac {559\,x^2}{162}-\frac {2515\,x^3}{81}+\frac {50\,x^4}{9}+\frac {100\,x^5}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.10, size = 41, normalized size = 0.93 \begin {gather*} \frac {100 x^{5}}{3} + \frac {50 x^{4}}{9} - \frac {2515 x^{3}}{81} - \frac {559 x^{2}}{162} + \frac {3305 x}{243} - \frac {49 \log {\left (3 x + 2 \right )}}{729} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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