Optimal. Leaf size=88 \[ -\frac {3 (47 x+37)}{5 (2 x+3)^3 \left (3 x^2+5 x+2\right )}-\frac {16522}{625 (2 x+3)}-\frac {2212}{125 (2 x+3)^2}-\frac {1258}{75 (2 x+3)^3}-13 \log (x+1)+\frac {65816 \log (2 x+3)}{3125}-\frac {25191 \log (3 x+2)}{3125} \]
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Rubi [A] time = 0.06, antiderivative size = 88, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, integrand size = 25, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.080, Rules used = {822, 800} \begin {gather*} -\frac {3 (47 x+37)}{5 (2 x+3)^3 \left (3 x^2+5 x+2\right )}-\frac {16522}{625 (2 x+3)}-\frac {2212}{125 (2 x+3)^2}-\frac {1258}{75 (2 x+3)^3}-13 \log (x+1)+\frac {65816 \log (2 x+3)}{3125}-\frac {25191 \log (3 x+2)}{3125} \end {gather*}
Antiderivative was successfully verified.
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Rule 800
Rule 822
Rubi steps
\begin {align*} \int \frac {5-x}{(3+2 x)^4 \left (2+5 x+3 x^2\right )^2} \, dx &=-\frac {3 (37+47 x)}{5 (3+2 x)^3 \left (2+5 x+3 x^2\right )}-\frac {1}{5} \int \frac {1063+1128 x}{(3+2 x)^4 \left (2+5 x+3 x^2\right )} \, dx\\ &=-\frac {3 (37+47 x)}{5 (3+2 x)^3 \left (2+5 x+3 x^2\right )}-\frac {1}{5} \int \left (\frac {65}{1+x}-\frac {2516}{5 (3+2 x)^4}-\frac {8848}{25 (3+2 x)^3}-\frac {33044}{125 (3+2 x)^2}-\frac {131632}{625 (3+2 x)}+\frac {75573}{625 (2+3 x)}\right ) \, dx\\ &=-\frac {1258}{75 (3+2 x)^3}-\frac {2212}{125 (3+2 x)^2}-\frac {16522}{625 (3+2 x)}-\frac {3 (37+47 x)}{5 (3+2 x)^3 \left (2+5 x+3 x^2\right )}-13 \log (1+x)+\frac {65816 \log (3+2 x)}{3125}-\frac {25191 \log (2+3 x)}{3125}\\ \end {align*}
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Mathematica [A] time = 0.04, size = 75, normalized size = 0.85 \begin {gather*} \frac {-\frac {45 (4209 x+2959)}{3 x^2+5 x+2}-\frac {121560}{2 x+3}-\frac {30450}{(2 x+3)^2}-\frac {6500}{(2 x+3)^3}-75573 \log (-6 x-4)-121875 \log (-2 (x+1))+197448 \log (2 x+3)}{9375} \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 )^2} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 0.39, size = 146, normalized size = 1.66 \begin {gather*} -\frac {2973960 \, x^{4} + 14873880 \, x^{3} + 27167700 \, x^{2} + 75573 \, {\left (24 \, x^{5} + 148 \, x^{4} + 358 \, x^{3} + 423 \, x^{2} + 243 \, x + 54\right )} \log \left (3 \, x + 2\right ) - 197448 \, {\left (24 \, x^{5} + 148 \, x^{4} + 358 \, x^{3} + 423 \, x^{2} + 243 \, x + 54\right )} \log \left (2 \, x + 3\right ) + 121875 \, {\left (24 \, x^{5} + 148 \, x^{4} + 358 \, x^{3} + 423 \, x^{2} + 243 \, x + 54\right )} \log \left (x + 1\right ) + 21302995 \, x + 5978965}{9375 \, {\left (24 \, x^{5} + 148 \, x^{4} + 358 \, x^{3} + 423 \, x^{2} + 243 \, x + 54\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.17, size = 67, normalized size = 0.76 \begin {gather*} -\frac {594792 \, x^{4} + 2974776 \, x^{3} + 5433540 \, x^{2} + 4260599 \, x + 1195793}{1875 \, {\left (3 \, x + 2\right )} {\left (2 \, x + 3\right )}^{3} {\left (x + 1\right )}} - \frac {25191}{3125} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) + \frac {65816}{3125} \, \log \left ({\left | 2 \, x + 3 \right |}\right ) - 13 \, \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 = 0.06, size = 67, normalized size = 0.76 \begin {gather*} -\frac {25191 \ln \left (3 x +2\right )}{3125}+\frac {65816 \ln \left (2 x +3\right )}{3125}-13 \ln \left (x +1\right )-\frac {1377}{625 \left (3 x +2\right )}-\frac {52}{75 \left (2 x +3\right )^{3}}-\frac {406}{125 \left (2 x +3\right )^{2}}-\frac {8104}{625 \left (2 x +3\right )}-\frac {6}{x +1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.51, size = 72, normalized size = 0.82 \begin {gather*} -\frac {594792 \, x^{4} + 2974776 \, x^{3} + 5433540 \, x^{2} + 4260599 \, x + 1195793}{1875 \, {\left (24 \, x^{5} + 148 \, x^{4} + 358 \, x^{3} + 423 \, x^{2} + 243 \, x + 54\right )}} - \frac {25191}{3125} \, \log \left (3 \, x + 2\right ) + \frac {65816}{3125} \, \log \left (2 \, x + 3\right ) - 13 \, \log \left (x + 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 2.37, size = 66, normalized size = 0.75 \begin {gather*} \frac {65816\,\ln \left (x+\frac {3}{2}\right )}{3125}-\frac {25191\,\ln \left (x+\frac {2}{3}\right )}{3125}-13\,\ln \left (x+1\right )-\frac {\frac {8261\,x^4}{625}+\frac {123949\,x^3}{1875}+\frac {90559\,x^2}{750}+\frac {4260599\,x}{45000}+\frac {1195793}{45000}}{x^5+\frac {37\,x^4}{6}+\frac {179\,x^3}{12}+\frac {141\,x^2}{8}+\frac {81\,x}{8}+\frac {9}{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.23, size = 71, normalized size = 0.81 \begin {gather*} - \frac {594792 x^{4} + 2974776 x^{3} + 5433540 x^{2} + 4260599 x + 1195793}{45000 x^{5} + 277500 x^{4} + 671250 x^{3} + 793125 x^{2} + 455625 x + 101250} - \frac {25191 \log {\left (x + \frac {2}{3} \right )}}{3125} - 13 \log {\left (x + 1 \right )} + \frac {65816 \log {\left (x + \frac {3}{2} \right )}}{3125} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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