Integrand size = 22, antiderivative size = 54 \[ \int \frac {(3+5 x)^3}{(1-2 x) (2+3 x)^4} \, dx=\frac {1}{567 (2+3 x)^3}-\frac {103}{2646 (2+3 x)^2}+\frac {3469}{9261 (2+3 x)}-\frac {1331 \log (1-2 x)}{2401}+\frac {1331 \log (2+3 x)}{2401} \]
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Time = 0.02 (sec) , antiderivative size = 54, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.045, Rules used = {90} \[ \int \frac {(3+5 x)^3}{(1-2 x) (2+3 x)^4} \, dx=\frac {3469}{9261 (3 x+2)}-\frac {103}{2646 (3 x+2)^2}+\frac {1}{567 (3 x+2)^3}-\frac {1331 \log (1-2 x)}{2401}+\frac {1331 \log (3 x+2)}{2401} \]
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Rule 90
Rubi steps \begin{align*} \text {integral}& = \int \left (-\frac {2662}{2401 (-1+2 x)}-\frac {1}{63 (2+3 x)^4}+\frac {103}{441 (2+3 x)^3}-\frac {3469}{3087 (2+3 x)^2}+\frac {3993}{2401 (2+3 x)}\right ) \, dx \\ & = \frac {1}{567 (2+3 x)^3}-\frac {103}{2646 (2+3 x)^2}+\frac {3469}{9261 (2+3 x)}-\frac {1331 \log (1-2 x)}{2401}+\frac {1331 \log (2+3 x)}{2401} \\ \end{align*}
Time = 0.02 (sec) , antiderivative size = 40, normalized size of antiderivative = 0.74 \[ \int \frac {(3+5 x)^3}{(1-2 x) (2+3 x)^4} \, dx=\frac {\frac {7 \left (79028+243279 x+187326 x^2\right )}{(2+3 x)^3}-215622 \log (1-2 x)+215622 \log (4+6 x)}{388962} \]
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Time = 2.51 (sec) , antiderivative size = 36, normalized size of antiderivative = 0.67
method | result | size |
norman | \(\frac {\frac {3469}{1029} x^{2}+\frac {27031}{6174} x +\frac {39514}{27783}}{\left (2+3 x \right )^{3}}-\frac {1331 \ln \left (-1+2 x \right )}{2401}+\frac {1331 \ln \left (2+3 x \right )}{2401}\) | \(36\) |
risch | \(\frac {\frac {3469}{1029} x^{2}+\frac {27031}{6174} x +\frac {39514}{27783}}{\left (2+3 x \right )^{3}}-\frac {1331 \ln \left (-1+2 x \right )}{2401}+\frac {1331 \ln \left (2+3 x \right )}{2401}\) | \(37\) |
default | \(-\frac {1331 \ln \left (-1+2 x \right )}{2401}+\frac {1}{567 \left (2+3 x \right )^{3}}-\frac {103}{2646 \left (2+3 x \right )^{2}}+\frac {3469}{9261 \left (2+3 x \right )}+\frac {1331 \ln \left (2+3 x \right )}{2401}\) | \(45\) |
parallelrisch | \(\frac {862488 \ln \left (\frac {2}{3}+x \right ) x^{3}-862488 \ln \left (x -\frac {1}{2}\right ) x^{3}+1724976 \ln \left (\frac {2}{3}+x \right ) x^{2}-1724976 \ln \left (x -\frac {1}{2}\right ) x^{2}-276598 x^{3}+1149984 \ln \left (\frac {2}{3}+x \right ) x -1149984 \ln \left (x -\frac {1}{2}\right ) x -358932 x^{2}+255552 \ln \left (\frac {2}{3}+x \right )-255552 \ln \left (x -\frac {1}{2}\right )-116508 x}{57624 \left (2+3 x \right )^{3}}\) | \(86\) |
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Time = 0.22 (sec) , antiderivative size = 75, normalized size of antiderivative = 1.39 \[ \int \frac {(3+5 x)^3}{(1-2 x) (2+3 x)^4} \, dx=\frac {1311282 \, x^{2} + 215622 \, {\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )} \log \left (3 \, x + 2\right ) - 215622 \, {\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )} \log \left (2 \, x - 1\right ) + 1702953 \, x + 553196}{388962 \, {\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )}} \]
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Time = 0.08 (sec) , antiderivative size = 46, normalized size of antiderivative = 0.85 \[ \int \frac {(3+5 x)^3}{(1-2 x) (2+3 x)^4} \, dx=- \frac {- 187326 x^{2} - 243279 x - 79028}{1500282 x^{3} + 3000564 x^{2} + 2000376 x + 444528} - \frac {1331 \log {\left (x - \frac {1}{2} \right )}}{2401} + \frac {1331 \log {\left (x + \frac {2}{3} \right )}}{2401} \]
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Time = 0.21 (sec) , antiderivative size = 46, normalized size of antiderivative = 0.85 \[ \int \frac {(3+5 x)^3}{(1-2 x) (2+3 x)^4} \, dx=\frac {187326 \, x^{2} + 243279 \, x + 79028}{55566 \, {\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )}} + \frac {1331}{2401} \, \log \left (3 \, x + 2\right ) - \frac {1331}{2401} \, \log \left (2 \, x - 1\right ) \]
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Time = 0.28 (sec) , antiderivative size = 38, normalized size of antiderivative = 0.70 \[ \int \frac {(3+5 x)^3}{(1-2 x) (2+3 x)^4} \, dx=\frac {187326 \, x^{2} + 243279 \, x + 79028}{55566 \, {\left (3 \, x + 2\right )}^{3}} + \frac {1331}{2401} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) - \frac {1331}{2401} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \]
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Time = 1.36 (sec) , antiderivative size = 35, normalized size of antiderivative = 0.65 \[ \int \frac {(3+5 x)^3}{(1-2 x) (2+3 x)^4} \, dx=\frac {2662\,\mathrm {atanh}\left (\frac {12\,x}{7}+\frac {1}{7}\right )}{2401}+\frac {\frac {3469\,x^2}{27783}+\frac {27031\,x}{166698}+\frac {39514}{750141}}{x^3+2\,x^2+\frac {4\,x}{3}+\frac {8}{27}} \]
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