Integrand size = 25, antiderivative size = 77 \[ \int \frac {5-x}{(3+2 x)^3 \left (2+5 x+3 x^2\right )^2} \, dx=-\frac {428}{25 (3+2 x)^2}-\frac {2618}{125 (3+2 x)}-\frac {3 (37+47 x)}{5 (3+2 x)^2 \left (2+5 x+3 x^2\right )}-\log (1+x)+\frac {8104}{625} \log (3+2 x)-\frac {7479}{625} \log (2+3 x) \]
[Out]
Time = 0.03 (sec) , antiderivative size = 77, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.080, Rules used = {836, 814} \[ \int \frac {5-x}{(3+2 x)^3 \left (2+5 x+3 x^2\right )^2} \, dx=-\frac {3 (47 x+37)}{5 (2 x+3)^2 \left (3 x^2+5 x+2\right )}-\frac {2618}{125 (2 x+3)}-\frac {428}{25 (2 x+3)^2}-\log (x+1)+\frac {8104}{625} \log (2 x+3)-\frac {7479}{625} \log (3 x+2) \]
[In]
[Out]
Rule 814
Rule 836
Rubi steps \begin{align*} \text {integral}& = -\frac {3 (37+47 x)}{5 (3+2 x)^2 \left (2+5 x+3 x^2\right )}-\frac {1}{5} \int \frac {841+846 x}{(3+2 x)^3 \left (2+5 x+3 x^2\right )} \, dx \\ & = -\frac {3 (37+47 x)}{5 (3+2 x)^2 \left (2+5 x+3 x^2\right )}-\frac {1}{5} \int \left (\frac {5}{1+x}-\frac {1712}{5 (3+2 x)^3}-\frac {5236}{25 (3+2 x)^2}-\frac {16208}{125 (3+2 x)}+\frac {22437}{125 (2+3 x)}\right ) \, dx \\ & = -\frac {428}{25 (3+2 x)^2}-\frac {2618}{125 (3+2 x)}-\frac {3 (37+47 x)}{5 (3+2 x)^2 \left (2+5 x+3 x^2\right )}-\log (1+x)+\frac {8104}{625} \log (3+2 x)-\frac {7479}{625} \log (2+3 x) \\ \end{align*}
Time = 0.02 (sec) , antiderivative size = 66, normalized size of antiderivative = 0.86 \[ \int \frac {5-x}{(3+2 x)^3 \left (2+5 x+3 x^2\right )^2} \, dx=\frac {1}{625} \left (-\frac {650}{(3+2 x)^2}-\frac {4060}{3+2 x}-\frac {15 (653+903 x)}{2+5 x+3 x^2}-7479 \log (-4-6 x)-625 \log (-2 (1+x))+8104 \log (3+2 x)\right ) \]
[In]
[Out]
Time = 0.32 (sec) , antiderivative size = 58, normalized size of antiderivative = 0.75
method | result | size |
default | \(-\frac {459}{125 \left (2+3 x \right )}-\frac {7479 \ln \left (2+3 x \right )}{625}-\frac {26}{25 \left (3+2 x \right )^{2}}-\frac {812}{125 \left (3+2 x \right )}+\frac {8104 \ln \left (3+2 x \right )}{625}-\frac {6}{1+x}-\ln \left (1+x \right )\) | \(58\) |
norman | \(\frac {-\frac {63967}{125} x -\frac {56162}{125} x^{2}-\frac {15708}{125} x^{3}-\frac {22763}{125}}{\left (3+2 x \right )^{2} \left (3 x^{2}+5 x +2\right )}+\frac {8104 \ln \left (3+2 x \right )}{625}-\ln \left (1+x \right )-\frac {7479 \ln \left (2+3 x \right )}{625}\) | \(59\) |
risch | \(\frac {-\frac {63967}{125} x -\frac {56162}{125} x^{2}-\frac {15708}{125} x^{3}-\frac {22763}{125}}{\left (3+2 x \right )^{2} \left (3 x^{2}+5 x +2\right )}+\frac {8104 \ln \left (3+2 x \right )}{625}-\ln \left (1+x \right )-\frac {7479 \ln \left (2+3 x \right )}{625}\) | \(60\) |
parallelrisch | \(-\frac {90000 \ln \left (1+x \right ) x^{4}-1166976 \ln \left (x +\frac {3}{2}\right ) x^{4}+1076976 \ln \left (x +\frac {2}{3}\right ) x^{4}+1365780+420000 \ln \left (1+x \right ) x^{3}-5445888 \ln \left (x +\frac {3}{2}\right ) x^{3}+5025888 \ln \left (x +\frac {2}{3}\right ) x^{3}+712500 \ln \left (1+x \right ) x^{2}-9238560 \ln \left (x +\frac {3}{2}\right ) x^{2}+8526060 \ln \left (x +\frac {2}{3}\right ) x^{2}+942480 x^{3}+517500 \ln \left (1+x \right ) x -6710112 \ln \left (x +\frac {3}{2}\right ) x +6192612 \ln \left (x +\frac {2}{3}\right ) x +3369720 x^{2}+135000 \ln \left (1+x \right )-1750464 \ln \left (x +\frac {3}{2}\right )+1615464 \ln \left (x +\frac {2}{3}\right )+3838020 x}{7500 \left (3+2 x \right )^{2} \left (3 x^{2}+5 x +2\right )}\) | \(157\) |
[In]
[Out]
none
Time = 0.28 (sec) , antiderivative size = 121, normalized size of antiderivative = 1.57 \[ \int \frac {5-x}{(3+2 x)^3 \left (2+5 x+3 x^2\right )^2} \, dx=-\frac {78540 \, x^{3} + 280810 \, x^{2} + 7479 \, {\left (12 \, x^{4} + 56 \, x^{3} + 95 \, x^{2} + 69 \, x + 18\right )} \log \left (3 \, x + 2\right ) - 8104 \, {\left (12 \, x^{4} + 56 \, x^{3} + 95 \, x^{2} + 69 \, x + 18\right )} \log \left (2 \, x + 3\right ) + 625 \, {\left (12 \, x^{4} + 56 \, x^{3} + 95 \, x^{2} + 69 \, x + 18\right )} \log \left (x + 1\right ) + 319835 \, x + 113815}{625 \, {\left (12 \, x^{4} + 56 \, x^{3} + 95 \, x^{2} + 69 \, x + 18\right )}} \]
[In]
[Out]
Time = 0.10 (sec) , antiderivative size = 60, normalized size of antiderivative = 0.78 \[ \int \frac {5-x}{(3+2 x)^3 \left (2+5 x+3 x^2\right )^2} \, dx=- \frac {15708 x^{3} + 56162 x^{2} + 63967 x + 22763}{1500 x^{4} + 7000 x^{3} + 11875 x^{2} + 8625 x + 2250} - \frac {7479 \log {\left (x + \frac {2}{3} \right )}}{625} - \log {\left (x + 1 \right )} + \frac {8104 \log {\left (x + \frac {3}{2} \right )}}{625} \]
[In]
[Out]
none
Time = 0.18 (sec) , antiderivative size = 62, normalized size of antiderivative = 0.81 \[ \int \frac {5-x}{(3+2 x)^3 \left (2+5 x+3 x^2\right )^2} \, dx=-\frac {15708 \, x^{3} + 56162 \, x^{2} + 63967 \, x + 22763}{125 \, {\left (12 \, x^{4} + 56 \, x^{3} + 95 \, x^{2} + 69 \, x + 18\right )}} - \frac {7479}{625} \, \log \left (3 \, x + 2\right ) + \frac {8104}{625} \, \log \left (2 \, x + 3\right ) - \log \left (x + 1\right ) \]
[In]
[Out]
none
Time = 0.26 (sec) , antiderivative size = 62, normalized size of antiderivative = 0.81 \[ \int \frac {5-x}{(3+2 x)^3 \left (2+5 x+3 x^2\right )^2} \, dx=-\frac {15708 \, x^{3} + 56162 \, x^{2} + 63967 \, x + 22763}{125 \, {\left (3 \, x + 2\right )} {\left (2 \, x + 3\right )}^{2} {\left (x + 1\right )}} - \frac {7479}{625} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) + \frac {8104}{625} \, \log \left ({\left | 2 \, x + 3 \right |}\right ) - \log \left ({\left | x + 1 \right |}\right ) \]
[In]
[Out]
Time = 11.33 (sec) , antiderivative size = 56, normalized size of antiderivative = 0.73 \[ \int \frac {5-x}{(3+2 x)^3 \left (2+5 x+3 x^2\right )^2} \, dx=\frac {8104\,\ln \left (x+\frac {3}{2}\right )}{625}-\frac {7479\,\ln \left (x+\frac {2}{3}\right )}{625}-\ln \left (x+1\right )-\frac {\frac {1309\,x^3}{125}+\frac {28081\,x^2}{750}+\frac {63967\,x}{1500}+\frac {22763}{1500}}{x^4+\frac {14\,x^3}{3}+\frac {95\,x^2}{12}+\frac {23\,x}{4}+\frac {3}{2}} \]
[In]
[Out]