Optimal. Leaf size=69 \[ -\frac {3 (47 x+37)}{10 \left (3 x^2+5 x+2\right )^2}+\frac {11442 x+9587}{50 \left (3 x^2+5 x+2\right )}-233 \log (x+1)+\frac {208}{125} \log (2 x+3)+\frac {28917}{125} \log (3 x+2) \]
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Rubi [A] time = 0.05, antiderivative size = 69, normalized size of antiderivative = 1.00, number of steps used = 4, number of rules used = 2, integrand size = 25, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.080, Rules used = {822, 800} \[ -\frac {3 (47 x+37)}{10 \left (3 x^2+5 x+2\right )^2}+\frac {11442 x+9587}{50 \left (3 x^2+5 x+2\right )}-233 \log (x+1)+\frac {208}{125} \log (2 x+3)+\frac {28917}{125} \log (3 x+2) \]
Antiderivative was successfully verified.
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Rule 800
Rule 822
Rubi steps
\begin {align*} \int \frac {5-x}{(3+2 x) \left (2+5 x+3 x^2\right )^3} \, dx &=-\frac {3 (37+47 x)}{10 \left (2+5 x+3 x^2\right )^2}-\frac {1}{10} \int \frac {1217+846 x}{(3+2 x) \left (2+5 x+3 x^2\right )^2} \, dx\\ &=-\frac {3 (37+47 x)}{10 \left (2+5 x+3 x^2\right )^2}+\frac {9587+11442 x}{50 \left (2+5 x+3 x^2\right )}+\frac {1}{50} \int \frac {34534+22884 x}{(3+2 x) \left (2+5 x+3 x^2\right )} \, dx\\ &=-\frac {3 (37+47 x)}{10 \left (2+5 x+3 x^2\right )^2}+\frac {9587+11442 x}{50 \left (2+5 x+3 x^2\right )}+\frac {1}{50} \int \left (-\frac {11650}{1+x}+\frac {832}{5 (3+2 x)}+\frac {173502}{5 (2+3 x)}\right ) \, dx\\ &=-\frac {3 (37+47 x)}{10 \left (2+5 x+3 x^2\right )^2}+\frac {9587+11442 x}{50 \left (2+5 x+3 x^2\right )}-233 \log (1+x)+\frac {208}{125} \log (3+2 x)+\frac {28917}{125} \log (2+3 x)\\ \end {align*}
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Mathematica [A] time = 0.05, size = 68, normalized size = 0.99 \[ \frac {1}{125} \left (-\frac {75 (47 x+37)}{2 \left (3 x^2+5 x+2\right )^2}+\frac {57210 x+47935}{6 x^2+10 x+4}+28917 \log (-6 x-4)-29125 \log (-2 (x+1))+208 \log (2 x+3)\right ) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.71, size = 121, normalized size = 1.75 \[ \frac {171630 \, x^{3} + 429855 \, x^{2} + 57834 \, {\left (9 \, x^{4} + 30 \, x^{3} + 37 \, x^{2} + 20 \, x + 4\right )} \log \left (3 \, x + 2\right ) + 416 \, {\left (9 \, x^{4} + 30 \, x^{3} + 37 \, x^{2} + 20 \, x + 4\right )} \log \left (2 \, x + 3\right ) - 58250 \, {\left (9 \, x^{4} + 30 \, x^{3} + 37 \, x^{2} + 20 \, x + 4\right )} \log \left (x + 1\right ) + 350570 \, x + 93095}{250 \, {\left (9 \, x^{4} + 30 \, x^{3} + 37 \, x^{2} + 20 \, x + 4\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 55, normalized size = 0.80 \[ \frac {34326 \, x^{3} + 85971 \, x^{2} + 70114 \, x + 18619}{50 \, {\left (3 \, x + 2\right )}^{2} {\left (x + 1\right )}^{2}} + \frac {28917}{125} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) + \frac {208}{125} \, \log \left ({\left | 2 \, x + 3 \right |}\right ) - 233 \, \log \left ({\left | x + 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.05, size = 56, normalized size = 0.81 \[ \frac {28917 \ln \left (3 x +2\right )}{125}+\frac {208 \ln \left (2 x +3\right )}{125}-233 \ln \left (x +1\right )-\frac {153}{10 \left (3 x +2\right )^{2}}+\frac {2646}{25 \left (3 x +2\right )}+\frac {3}{\left (x +1\right )^{2}}+\frac {41}{x +1} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.59, size = 62, normalized size = 0.90 \[ \frac {34326 \, x^{3} + 85971 \, x^{2} + 70114 \, x + 18619}{50 \, {\left (9 \, x^{4} + 30 \, x^{3} + 37 \, x^{2} + 20 \, x + 4\right )}} + \frac {28917}{125} \, \log \left (3 \, x + 2\right ) + \frac {208}{125} \, \log \left (2 \, x + 3\right ) - 233 \, \log \left (x + 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 2.32, size = 55, normalized size = 0.80 \[ \frac {28917\,\ln \left (x+\frac {2}{3}\right )}{125}-233\,\ln \left (x+1\right )+\frac {208\,\ln \left (x+\frac {3}{2}\right )}{125}+\frac {\frac {1907\,x^3}{25}+\frac {28657\,x^2}{150}+\frac {35057\,x}{225}+\frac {18619}{450}}{x^4+\frac {10\,x^3}{3}+\frac {37\,x^2}{9}+\frac {20\,x}{9}+\frac {4}{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.21, size = 63, normalized size = 0.91 \[ - \frac {- 34326 x^{3} - 85971 x^{2} - 70114 x - 18619}{450 x^{4} + 1500 x^{3} + 1850 x^{2} + 1000 x + 200} + \frac {28917 \log {\left (x + \frac {2}{3} \right )}}{125} - 233 \log {\left (x + 1 \right )} + \frac {208 \log {\left (x + \frac {3}{2} \right )}}{125} \]
Verification of antiderivative is not currently implemented for this CAS.
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