Optimal. Leaf size=105 \[ -\frac {3 (47 x+37)}{10 (2 x+3)^2 \left (3 x^2+5 x+2\right )^2}+\frac {10254 x+8999}{50 (2 x+3)^2 \left (3 x^2+5 x+2\right )}+\frac {35886}{625 (2 x+3)}+\frac {11856}{125 (2 x+3)^2}-141 \log (x+1)+\frac {68592 \log (2 x+3)}{3125}+\frac {372033 \log (3 x+2)}{3125} \]
________________________________________________________________________________________
Rubi [A] time = 0.07, antiderivative size = 105, 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} \begin {gather*} -\frac {3 (47 x+37)}{10 (2 x+3)^2 \left (3 x^2+5 x+2\right )^2}+\frac {10254 x+8999}{50 (2 x+3)^2 \left (3 x^2+5 x+2\right )}+\frac {35886}{625 (2 x+3)}+\frac {11856}{125 (2 x+3)^2}-141 \log (x+1)+\frac {68592 \log (2 x+3)}{3125}+\frac {372033 \log (3 x+2)}{3125} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 800
Rule 822
Rubi steps
\begin {align*} \int \frac {5-x}{(3+2 x)^3 \left (2+5 x+3 x^2\right )^3} \, dx &=-\frac {3 (37+47 x)}{10 (3+2 x)^2 \left (2+5 x+3 x^2\right )^2}-\frac {1}{10} \int \frac {1661+1410 x}{(3+2 x)^3 \left (2+5 x+3 x^2\right )^2} \, dx\\ &=-\frac {3 (37+47 x)}{10 (3+2 x)^2 \left (2+5 x+3 x^2\right )^2}+\frac {8999+10254 x}{50 (3+2 x)^2 \left (2+5 x+3 x^2\right )}+\frac {1}{50} \int \frac {68574+61524 x}{(3+2 x)^3 \left (2+5 x+3 x^2\right )} \, dx\\ &=-\frac {3 (37+47 x)}{10 (3+2 x)^2 \left (2+5 x+3 x^2\right )^2}+\frac {8999+10254 x}{50 (3+2 x)^2 \left (2+5 x+3 x^2\right )}+\frac {1}{50} \int \left (-\frac {7050}{1+x}-\frac {94848}{5 (3+2 x)^3}-\frac {143544}{25 (3+2 x)^2}+\frac {274368}{125 (3+2 x)}+\frac {2232198}{125 (2+3 x)}\right ) \, dx\\ &=\frac {11856}{125 (3+2 x)^2}+\frac {35886}{625 (3+2 x)}-\frac {3 (37+47 x)}{10 (3+2 x)^2 \left (2+5 x+3 x^2\right )^2}+\frac {8999+10254 x}{50 (3+2 x)^2 \left (2+5 x+3 x^2\right )}-141 \log (1+x)+\frac {68592 \log (3+2 x)}{3125}+\frac {372033 \log (2+3 x)}{3125}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.05, size = 86, normalized size = 0.82 \begin {gather*} \frac {-\frac {75 (903 x+653)}{2 \left (3 x^2+5 x+2\right )^2}+\frac {611970 x+550495}{6 x^2+10 x+4}-\frac {24560}{2 x+3}-\frac {2600}{(2 x+3)^2}+372033 \log (-6 x-4)-440625 \log (-2 (x+1))+68592 \log (2 x+3)}{3125} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {5-x}{(3+2 x)^3 \left (2+5 x+3 x^2\right )^3} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.39, size = 171, normalized size = 1.63 \begin {gather*} \frac {6459480 \, x^{5} + 36556020 \, x^{4} + 80482290 \, x^{3} + 85904835 \, x^{2} + 744066 \, {\left (36 \, x^{6} + 228 \, x^{5} + 589 \, x^{4} + 794 \, x^{3} + 589 \, x^{2} + 228 \, x + 36\right )} \log \left (3 \, x + 2\right ) + 137184 \, {\left (36 \, x^{6} + 228 \, x^{5} + 589 \, x^{4} + 794 \, x^{3} + 589 \, x^{2} + 228 \, x + 36\right )} \log \left (2 \, x + 3\right ) - 881250 \, {\left (36 \, x^{6} + 228 \, x^{5} + 589 \, x^{4} + 794 \, x^{3} + 589 \, x^{2} + 228 \, x + 36\right )} \log \left (x + 1\right ) + 44358230 \, x + 8857895}{6250 \, {\left (36 \, x^{6} + 228 \, x^{5} + 589 \, x^{4} + 794 \, x^{3} + 589 \, x^{2} + 228 \, x + 36\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.16, size = 70, normalized size = 0.67 \begin {gather*} \frac {1291896 \, x^{5} + 7311204 \, x^{4} + 16096458 \, x^{3} + 17180967 \, x^{2} + 8871646 \, x + 1771579}{1250 \, {\left (6 \, x^{3} + 19 \, x^{2} + 19 \, x + 6\right )}^{2}} + \frac {372033}{3125} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) + \frac {68592}{3125} \, \log \left ({\left | 2 \, x + 3 \right |}\right ) - 141 \, \log \left ({\left | x + 1 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.06, size = 74, normalized size = 0.70 \begin {gather*} \frac {372033 \ln \left (3 x +2\right )}{3125}+\frac {68592 \ln \left (2 x +3\right )}{3125}-141 \ln \left (x +1\right )-\frac {1377}{250 \left (3 x +2\right )^{2}}+\frac {29322}{625 \left (3 x +2\right )}-\frac {104}{125 \left (2 x +3\right )^{2}}-\frac {4912}{625 \left (2 x +3\right )}+\frac {3}{\left (x +1\right )^{2}}+\frac {17}{x +1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.59, size = 82, normalized size = 0.78 \begin {gather*} \frac {1291896 \, x^{5} + 7311204 \, x^{4} + 16096458 \, x^{3} + 17180967 \, x^{2} + 8871646 \, x + 1771579}{1250 \, {\left (36 \, x^{6} + 228 \, x^{5} + 589 \, x^{4} + 794 \, x^{3} + 589 \, x^{2} + 228 \, x + 36\right )}} + \frac {372033}{3125} \, \log \left (3 \, x + 2\right ) + \frac {68592}{3125} \, \log \left (2 \, x + 3\right ) - 141 \, \log \left (x + 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 2.29, size = 75, normalized size = 0.71 \begin {gather*} \frac {372033\,\ln \left (x+\frac {2}{3}\right )}{3125}-141\,\ln \left (x+1\right )+\frac {68592\,\ln \left (x+\frac {3}{2}\right )}{3125}+\frac {\frac {17943\,x^5}{625}+\frac {203089\,x^4}{1250}+\frac {2682743\,x^3}{7500}+\frac {5726989\,x^2}{15000}+\frac {4435823\,x}{22500}+\frac {1771579}{45000}}{x^6+\frac {19\,x^5}{3}+\frac {589\,x^4}{36}+\frac {397\,x^3}{18}+\frac {589\,x^2}{36}+\frac {19\,x}{3}+1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.24, size = 83, normalized size = 0.79 \begin {gather*} - \frac {- 1291896 x^{5} - 7311204 x^{4} - 16096458 x^{3} - 17180967 x^{2} - 8871646 x - 1771579}{45000 x^{6} + 285000 x^{5} + 736250 x^{4} + 992500 x^{3} + 736250 x^{2} + 285000 x + 45000} + \frac {372033 \log {\left (x + \frac {2}{3} \right )}}{3125} - 141 \log {\left (x + 1 \right )} + \frac {68592 \log {\left (x + \frac {3}{2} \right )}}{3125} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________