Optimal. Leaf size=44 \[ -\frac {72 x^5}{25}+\frac {69 x^4}{25}+\frac {622 x^3}{375}-\frac {3741 x^2}{1250}+\frac {3723 x}{3125}+\frac {1331 \log (5 x+3)}{15625} \]
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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 {72 x^5}{25}+\frac {69 x^4}{25}+\frac {622 x^3}{375}-\frac {3741 x^2}{1250}+\frac {3723 x}{3125}+\frac {1331 \log (5 x+3)}{15625} \end {gather*}
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} \, dx &=\int \left (\frac {3723}{3125}-\frac {3741 x}{625}+\frac {622 x^2}{125}+\frac {276 x^3}{25}-\frac {72 x^4}{5}+\frac {1331}{3125 (3+5 x)}\right ) \, dx\\ &=\frac {3723 x}{3125}-\frac {3741 x^2}{1250}+\frac {622 x^3}{375}+\frac {69 x^4}{25}-\frac {72 x^5}{25}+\frac {1331 \log (3+5 x)}{15625}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 37, normalized size = 0.84 \begin {gather*} \frac {-1350000 x^5+1293750 x^4+777500 x^3-1402875 x^2+558450 x+39930 \log (5 x+3)+735399}{468750} \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)^3 (2+3 x)^2}{3+5 x} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 1.35, size = 32, normalized size = 0.73 \begin {gather*} -\frac {72}{25} \, x^{5} + \frac {69}{25} \, x^{4} + \frac {622}{375} \, x^{3} - \frac {3741}{1250} \, x^{2} + \frac {3723}{3125} \, x + \frac {1331}{15625} \, \log \left (5 \, x + 3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.86, size = 33, normalized size = 0.75 \begin {gather*} -\frac {72}{25} \, x^{5} + \frac {69}{25} \, x^{4} + \frac {622}{375} \, x^{3} - \frac {3741}{1250} \, x^{2} + \frac {3723}{3125} \, x + \frac {1331}{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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maple [A] time = 0.00, size = 33, normalized size = 0.75 \begin {gather*} -\frac {72 x^{5}}{25}+\frac {69 x^{4}}{25}+\frac {622 x^{3}}{375}-\frac {3741 x^{2}}{1250}+\frac {3723 x}{3125}+\frac {1331 \ln \left (5 x +3\right )}{15625} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.52, size = 32, normalized size = 0.73 \begin {gather*} -\frac {72}{25} \, x^{5} + \frac {69}{25} \, x^{4} + \frac {622}{375} \, x^{3} - \frac {3741}{1250} \, x^{2} + \frac {3723}{3125} \, x + \frac {1331}{15625} \, \log \left (5 \, x + 3\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 {3723\,x}{3125}+\frac {1331\,\ln \left (x+\frac {3}{5}\right )}{15625}-\frac {3741\,x^2}{1250}+\frac {622\,x^3}{375}+\frac {69\,x^4}{25}-\frac {72\,x^5}{25} \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 {72 x^{5}}{25} + \frac {69 x^{4}}{25} + \frac {622 x^{3}}{375} - \frac {3741 x^{2}}{1250} + \frac {3723 x}{3125} + \frac {1331 \log {\left (5 x + 3 \right )}}{15625} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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