Optimal. Leaf size=36 \[ -\frac {8 x^3}{9}+\frac {26 x^2}{9}+\frac {922 x}{27}-6 \log (x+1)+\frac {2125}{81} \log (3 x+2) \]
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Rubi [A] time = 0.02, antiderivative size = 36, normalized size of antiderivative = 1.00, number of steps used = 5, number of rules used = 3, integrand size = 25, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.120, Rules used = {800, 632, 31} \begin {gather*} -\frac {8 x^3}{9}+\frac {26 x^2}{9}+\frac {922 x}{27}-6 \log (x+1)+\frac {2125}{81} \log (3 x+2) \end {gather*}
Antiderivative was successfully verified.
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Rule 31
Rule 632
Rule 800
Rubi steps
\begin {align*} \int \frac {(5-x) (3+2 x)^3}{2+5 x+3 x^2} \, dx &=\int \left (\frac {922}{27}+\frac {52 x}{9}-\frac {8 x^2}{3}+\frac {1801+1639 x}{27 \left (2+5 x+3 x^2\right )}\right ) \, dx\\ &=\frac {922 x}{27}+\frac {26 x^2}{9}-\frac {8 x^3}{9}+\frac {1}{27} \int \frac {1801+1639 x}{2+5 x+3 x^2} \, dx\\ &=\frac {922 x}{27}+\frac {26 x^2}{9}-\frac {8 x^3}{9}-18 \int \frac {1}{3+3 x} \, dx+\frac {2125}{27} \int \frac {1}{2+3 x} \, dx\\ &=\frac {922 x}{27}+\frac {26 x^2}{9}-\frac {8 x^3}{9}-6 \log (1+x)+\frac {2125}{81} \log (2+3 x)\\ \end {align*}
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Mathematica [A] time = 0.01, size = 35, normalized size = 0.97 \begin {gather*} \frac {1}{162} \left (-144 x^3+468 x^2+5532 x+4250 \log (-6 x-4)-972 \log (-2 (x+1))+6759\right ) \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 {(5-x) (3+2 x)^3}{2+5 x+3 x^2} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 0.50, size = 28, normalized size = 0.78 \begin {gather*} -\frac {8}{9} \, x^{3} + \frac {26}{9} \, x^{2} + \frac {922}{27} \, x + \frac {2125}{81} \, \log \left (3 \, x + 2\right ) - 6 \, \log \left (x + 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 30, normalized size = 0.83 \begin {gather*} -\frac {8}{9} \, x^{3} + \frac {26}{9} \, x^{2} + \frac {922}{27} \, x + \frac {2125}{81} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) - 6 \, \log \left ({\left | x + 1 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.05, size = 29, normalized size = 0.81 \begin {gather*} -\frac {8 x^{3}}{9}+\frac {26 x^{2}}{9}+\frac {922 x}{27}+\frac {2125 \ln \left (3 x +2\right )}{81}-6 \ln \left (x +1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.50, size = 28, normalized size = 0.78 \begin {gather*} -\frac {8}{9} \, x^{3} + \frac {26}{9} \, x^{2} + \frac {922}{27} \, x + \frac {2125}{81} \, \log \left (3 \, x + 2\right ) - 6 \, \log \left (x + 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 2.31, size = 26, normalized size = 0.72 \begin {gather*} \frac {922\,x}{27}-6\,\ln \left (x+1\right )+\frac {2125\,\ln \left (x+\frac {2}{3}\right )}{81}+\frac {26\,x^2}{9}-\frac {8\,x^3}{9} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.13, size = 34, normalized size = 0.94 \begin {gather*} - \frac {8 x^{3}}{9} + \frac {26 x^{2}}{9} + \frac {922 x}{27} + \frac {2125 \log {\left (x + \frac {2}{3} \right )}}{81} - 6 \log {\left (x + 1 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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