Integrand size = 20, antiderivative size = 45 \[ \int \frac {(1-2 x)^2 (3+5 x)}{(2+3 x)^6} \, dx=\frac {49}{405 (2+3 x)^5}-\frac {91}{108 (2+3 x)^4}+\frac {16}{27 (2+3 x)^3}-\frac {10}{81 (2+3 x)^2} \]
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Time = 0.01 (sec) , antiderivative size = 45, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {78} \[ \int \frac {(1-2 x)^2 (3+5 x)}{(2+3 x)^6} \, dx=-\frac {10}{81 (3 x+2)^2}+\frac {16}{27 (3 x+2)^3}-\frac {91}{108 (3 x+2)^4}+\frac {49}{405 (3 x+2)^5} \]
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Rule 78
Rubi steps \begin{align*} \text {integral}& = \int \left (-\frac {49}{27 (2+3 x)^6}+\frac {91}{9 (2+3 x)^5}-\frac {16}{3 (2+3 x)^4}+\frac {20}{27 (2+3 x)^3}\right ) \, dx \\ & = \frac {49}{405 (2+3 x)^5}-\frac {91}{108 (2+3 x)^4}+\frac {16}{27 (2+3 x)^3}-\frac {10}{81 (2+3 x)^2} \\ \end{align*}
Time = 0.01 (sec) , antiderivative size = 26, normalized size of antiderivative = 0.58 \[ \int \frac {(1-2 x)^2 (3+5 x)}{(2+3 x)^6} \, dx=-\frac {98-75 x+720 x^2+1800 x^3}{540 (2+3 x)^5} \]
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Time = 2.27 (sec) , antiderivative size = 24, normalized size of antiderivative = 0.53
method | result | size |
norman | \(\frac {-\frac {10}{3} x^{3}-\frac {4}{3} x^{2}+\frac {5}{36} x -\frac {49}{270}}{\left (2+3 x \right )^{5}}\) | \(24\) |
gosper | \(-\frac {1800 x^{3}+720 x^{2}-75 x +98}{540 \left (2+3 x \right )^{5}}\) | \(25\) |
risch | \(\frac {-\frac {10}{3} x^{3}-\frac {4}{3} x^{2}+\frac {5}{36} x -\frac {49}{270}}{\left (2+3 x \right )^{5}}\) | \(25\) |
parallelrisch | \(\frac {1323 x^{5}+4410 x^{4}+2680 x^{3}+2640 x^{2}+1440 x}{960 \left (2+3 x \right )^{5}}\) | \(34\) |
default | \(\frac {49}{405 \left (2+3 x \right )^{5}}-\frac {91}{108 \left (2+3 x \right )^{4}}+\frac {16}{27 \left (2+3 x \right )^{3}}-\frac {10}{81 \left (2+3 x \right )^{2}}\) | \(38\) |
meijerg | \(\frac {3 x \left (\frac {81}{16} x^{4}+\frac {135}{8} x^{3}+\frac {45}{2} x^{2}+15 x +5\right )}{320 \left (1+\frac {3 x}{2}\right )^{5}}-\frac {7 x^{2} \left (\frac {27}{8} x^{3}+\frac {45}{4} x^{2}+15 x +10\right )}{1280 \left (1+\frac {3 x}{2}\right )^{5}}-\frac {x^{3} \left (\frac {9}{4} x^{2}+\frac {15}{2} x +10\right )}{240 \left (1+\frac {3 x}{2}\right )^{5}}+\frac {x^{4} \left (\frac {3 x}{2}+5\right )}{64 \left (1+\frac {3 x}{2}\right )^{5}}\) | \(98\) |
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Time = 0.22 (sec) , antiderivative size = 44, normalized size of antiderivative = 0.98 \[ \int \frac {(1-2 x)^2 (3+5 x)}{(2+3 x)^6} \, dx=-\frac {1800 \, x^{3} + 720 \, x^{2} - 75 \, x + 98}{540 \, {\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )}} \]
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Time = 0.06 (sec) , antiderivative size = 39, normalized size of antiderivative = 0.87 \[ \int \frac {(1-2 x)^2 (3+5 x)}{(2+3 x)^6} \, dx=\frac {- 1800 x^{3} - 720 x^{2} + 75 x - 98}{131220 x^{5} + 437400 x^{4} + 583200 x^{3} + 388800 x^{2} + 129600 x + 17280} \]
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Time = 0.20 (sec) , antiderivative size = 44, normalized size of antiderivative = 0.98 \[ \int \frac {(1-2 x)^2 (3+5 x)}{(2+3 x)^6} \, dx=-\frac {1800 \, x^{3} + 720 \, x^{2} - 75 \, x + 98}{540 \, {\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )}} \]
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Time = 0.26 (sec) , antiderivative size = 24, normalized size of antiderivative = 0.53 \[ \int \frac {(1-2 x)^2 (3+5 x)}{(2+3 x)^6} \, dx=-\frac {1800 \, x^{3} + 720 \, x^{2} - 75 \, x + 98}{540 \, {\left (3 \, x + 2\right )}^{5}} \]
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Time = 1.31 (sec) , antiderivative size = 37, normalized size of antiderivative = 0.82 \[ \int \frac {(1-2 x)^2 (3+5 x)}{(2+3 x)^6} \, dx=\frac {16}{27\,{\left (3\,x+2\right )}^3}-\frac {10}{81\,{\left (3\,x+2\right )}^2}-\frac {91}{108\,{\left (3\,x+2\right )}^4}+\frac {49}{405\,{\left (3\,x+2\right )}^5} \]
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