Optimal. Leaf size=60 \[ -\frac {597}{125 (2 x+3)}-\frac {99}{50 (2 x+3)^2}-\frac {13}{15 (2 x+3)^3}-6 \log (x+1)+\frac {3291}{625} \log (2 x+3)+\frac {459}{625} \log (3 x+2) \]
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Rubi [A] time = 0.04, antiderivative size = 60, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 25, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.040, Rules used = {800} \begin {gather*} -\frac {597}{125 (2 x+3)}-\frac {99}{50 (2 x+3)^2}-\frac {13}{15 (2 x+3)^3}-6 \log (x+1)+\frac {3291}{625} \log (2 x+3)+\frac {459}{625} \log (3 x+2) \end {gather*}
Antiderivative was successfully verified.
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Rule 800
Rubi steps
\begin {align*} \int \frac {5-x}{(3+2 x)^4 \left (2+5 x+3 x^2\right )} \, dx &=\int \left (-\frac {6}{1+x}+\frac {26}{5 (3+2 x)^4}+\frac {198}{25 (3+2 x)^3}+\frac {1194}{125 (3+2 x)^2}+\frac {6582}{625 (3+2 x)}+\frac {1377}{625 (2+3 x)}\right ) \, dx\\ &=-\frac {13}{15 (3+2 x)^3}-\frac {99}{50 (3+2 x)^2}-\frac {597}{125 (3+2 x)}-6 \log (1+x)+\frac {3291}{625} \log (3+2 x)+\frac {459}{625} \log (2+3 x)\\ \end {align*}
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Mathematica [A] time = 0.03, size = 62, normalized size = 1.03 \begin {gather*} -\frac {597}{125 (2 x+3)}-\frac {99}{50 (2 x+3)^2}-\frac {13}{15 (2 x+3)^3}+\frac {459}{625} \log (-6 x-4)-6 \log (-2 (x+1))+\frac {3291}{625} \log (2 x+3) \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)^4 \left (2+5 x+3 x^2\right )} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 0.39, size = 96, normalized size = 1.60 \begin {gather*} -\frac {71640 \, x^{2} - 2754 \, {\left (8 \, x^{3} + 36 \, x^{2} + 54 \, x + 27\right )} \log \left (3 \, x + 2\right ) - 19746 \, {\left (8 \, x^{3} + 36 \, x^{2} + 54 \, x + 27\right )} \log \left (2 \, x + 3\right ) + 22500 \, {\left (8 \, x^{3} + 36 \, x^{2} + 54 \, x + 27\right )} \log \left (x + 1\right ) + 229770 \, x + 186715}{3750 \, {\left (8 \, x^{3} + 36 \, x^{2} + 54 \, x + 27\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.17, size = 45, normalized size = 0.75 \begin {gather*} -\frac {14328 \, x^{2} + 45954 \, x + 37343}{750 \, {\left (2 \, x + 3\right )}^{3}} + \frac {459}{625} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) + \frac {3291}{625} \, \log \left ({\left | 2 \, x + 3 \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 = 51, normalized size = 0.85 \begin {gather*} \frac {459 \ln \left (3 x +2\right )}{625}+\frac {3291 \ln \left (2 x +3\right )}{625}-6 \ln \left (x +1\right )-\frac {13}{15 \left (2 x +3\right )^{3}}-\frac {99}{50 \left (2 x +3\right )^{2}}-\frac {597}{125 \left (2 x +3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.55, size = 52, normalized size = 0.87 \begin {gather*} -\frac {14328 \, x^{2} + 45954 \, x + 37343}{750 \, {\left (8 \, x^{3} + 36 \, x^{2} + 54 \, x + 27\right )}} + \frac {459}{625} \, \log \left (3 \, x + 2\right ) + \frac {3291}{625} \, \log \left (2 \, x + 3\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 = 0.04, size = 46, normalized size = 0.77 \begin {gather*} \frac {459\,\ln \left (x+\frac {2}{3}\right )}{625}-6\,\ln \left (x+1\right )+\frac {3291\,\ln \left (x+\frac {3}{2}\right )}{625}-\frac {\frac {597\,x^2}{250}+\frac {7659\,x}{1000}+\frac {37343}{6000}}{x^3+\frac {9\,x^2}{2}+\frac {27\,x}{4}+\frac {27}{8}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.20, size = 51, normalized size = 0.85 \begin {gather*} - \frac {14328 x^{2} + 45954 x + 37343}{6000 x^{3} + 27000 x^{2} + 40500 x + 20250} + \frac {459 \log {\left (x + \frac {2}{3} \right )}}{625} - 6 \log {\left (x + 1 \right )} + \frac {3291 \log {\left (x + \frac {3}{2} \right )}}{625} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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