Integrand size = 22, antiderivative size = 67 \[ \int \frac {(1-2 x)^2 (3+5 x)^3}{(2+3 x)^8} \, dx=\frac {7}{729 (2+3 x)^7}-\frac {763}{4374 (2+3 x)^6}+\frac {4099}{3645 (2+3 x)^5}-\frac {8285}{2916 (2+3 x)^4}+\frac {3800}{2187 (2+3 x)^3}-\frac {250}{729 (2+3 x)^2} \]
[Out]
Time = 0.02 (sec) , antiderivative size = 67, 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} \[ \int \frac {(1-2 x)^2 (3+5 x)^3}{(2+3 x)^8} \, dx=-\frac {250}{729 (3 x+2)^2}+\frac {3800}{2187 (3 x+2)^3}-\frac {8285}{2916 (3 x+2)^4}+\frac {4099}{3645 (3 x+2)^5}-\frac {763}{4374 (3 x+2)^6}+\frac {7}{729 (3 x+2)^7} \]
[In]
[Out]
Rule 90
Rubi steps \begin{align*} \text {integral}& = \int \left (-\frac {49}{243 (2+3 x)^8}+\frac {763}{243 (2+3 x)^7}-\frac {4099}{243 (2+3 x)^6}+\frac {8285}{243 (2+3 x)^5}-\frac {3800}{243 (2+3 x)^4}+\frac {500}{243 (2+3 x)^3}\right ) \, dx \\ & = \frac {7}{729 (2+3 x)^7}-\frac {763}{4374 (2+3 x)^6}+\frac {4099}{3645 (2+3 x)^5}-\frac {8285}{2916 (2+3 x)^4}+\frac {3800}{2187 (2+3 x)^3}-\frac {250}{729 (2+3 x)^2} \\ \end{align*}
Time = 0.02 (sec) , antiderivative size = 36, normalized size of antiderivative = 0.54 \[ \int \frac {(1-2 x)^2 (3+5 x)^3}{(2+3 x)^8} \, dx=-\frac {76288+210534 x+652158 x^2+3139425 x^3+5994000 x^4+3645000 x^5}{43740 (2+3 x)^7} \]
[In]
[Out]
Time = 2.29 (sec) , antiderivative size = 34, normalized size of antiderivative = 0.51
method | result | size |
norman | \(\frac {-\frac {250}{3} x^{5}-\frac {3700}{27} x^{4}-\frac {23255}{324} x^{3}-\frac {12077}{810} x^{2}-\frac {35089}{7290} x -\frac {19072}{10935}}{\left (2+3 x \right )^{7}}\) | \(34\) |
gosper | \(-\frac {3645000 x^{5}+5994000 x^{4}+3139425 x^{3}+652158 x^{2}+210534 x +76288}{43740 \left (2+3 x \right )^{7}}\) | \(35\) |
risch | \(\frac {-\frac {250}{3} x^{5}-\frac {3700}{27} x^{4}-\frac {23255}{324} x^{3}-\frac {12077}{810} x^{2}-\frac {35089}{7290} x -\frac {19072}{10935}}{\left (2+3 x \right )^{7}}\) | \(35\) |
parallelrisch | \(\frac {57216 x^{7}+267008 x^{6}+374016 x^{5}+330240 x^{4}+257760 x^{3}+129600 x^{2}+25920 x}{1920 \left (2+3 x \right )^{7}}\) | \(44\) |
default | \(\frac {7}{729 \left (2+3 x \right )^{7}}-\frac {763}{4374 \left (2+3 x \right )^{6}}+\frac {4099}{3645 \left (2+3 x \right )^{5}}-\frac {8285}{2916 \left (2+3 x \right )^{4}}+\frac {3800}{2187 \left (2+3 x \right )^{3}}-\frac {250}{729 \left (2+3 x \right )^{2}}\) | \(56\) |
meijerg | \(\frac {27 x \left (\frac {729}{64} x^{6}+\frac {1701}{32} x^{5}+\frac {1701}{16} x^{4}+\frac {945}{8} x^{3}+\frac {315}{4} x^{2}+\frac {63}{2} x +7\right )}{1792 \left (1+\frac {3 x}{2}\right )^{7}}+\frac {9 x^{2} \left (\frac {243}{32} x^{5}+\frac {567}{16} x^{4}+\frac {567}{8} x^{3}+\frac {315}{4} x^{2}+\frac {105}{2} x +21\right )}{3584 \left (1+\frac {3 x}{2}\right )^{7}}-\frac {69 x^{3} \left (\frac {81}{16} x^{4}+\frac {189}{8} x^{3}+\frac {189}{4} x^{2}+\frac {105}{2} x +35\right )}{8960 \left (1+\frac {3 x}{2}\right )^{7}}-\frac {47 x^{4} \left (\frac {27}{8} x^{3}+\frac {63}{4} x^{2}+\frac {63}{2} x +35\right )}{7168 \left (1+\frac {3 x}{2}\right )^{7}}+\frac {5 x^{5} \left (\frac {9}{4} x^{2}+\frac {21}{2} x +21\right )}{336 \left (1+\frac {3 x}{2}\right )^{7}}+\frac {125 x^{6} \left (\frac {3 x}{2}+7\right )}{2688 \left (1+\frac {3 x}{2}\right )^{7}}\) | \(177\) |
[In]
[Out]
none
Time = 0.22 (sec) , antiderivative size = 64, normalized size of antiderivative = 0.96 \[ \int \frac {(1-2 x)^2 (3+5 x)^3}{(2+3 x)^8} \, dx=-\frac {3645000 \, x^{5} + 5994000 \, x^{4} + 3139425 \, x^{3} + 652158 \, x^{2} + 210534 \, x + 76288}{43740 \, {\left (2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right )}} \]
[In]
[Out]
Time = 0.08 (sec) , antiderivative size = 61, normalized size of antiderivative = 0.91 \[ \int \frac {(1-2 x)^2 (3+5 x)^3}{(2+3 x)^8} \, dx=\frac {- 3645000 x^{5} - 5994000 x^{4} - 3139425 x^{3} - 652158 x^{2} - 210534 x - 76288}{95659380 x^{7} + 446410440 x^{6} + 892820880 x^{5} + 992023200 x^{4} + 661348800 x^{3} + 264539520 x^{2} + 58786560 x + 5598720} \]
[In]
[Out]
none
Time = 0.20 (sec) , antiderivative size = 64, normalized size of antiderivative = 0.96 \[ \int \frac {(1-2 x)^2 (3+5 x)^3}{(2+3 x)^8} \, dx=-\frac {3645000 \, x^{5} + 5994000 \, x^{4} + 3139425 \, x^{3} + 652158 \, x^{2} + 210534 \, x + 76288}{43740 \, {\left (2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right )}} \]
[In]
[Out]
none
Time = 0.27 (sec) , antiderivative size = 34, normalized size of antiderivative = 0.51 \[ \int \frac {(1-2 x)^2 (3+5 x)^3}{(2+3 x)^8} \, dx=-\frac {3645000 \, x^{5} + 5994000 \, x^{4} + 3139425 \, x^{3} + 652158 \, x^{2} + 210534 \, x + 76288}{43740 \, {\left (3 \, x + 2\right )}^{7}} \]
[In]
[Out]
Time = 1.16 (sec) , antiderivative size = 55, normalized size of antiderivative = 0.82 \[ \int \frac {(1-2 x)^2 (3+5 x)^3}{(2+3 x)^8} \, dx=\frac {3800}{2187\,{\left (3\,x+2\right )}^3}-\frac {250}{729\,{\left (3\,x+2\right )}^2}-\frac {8285}{2916\,{\left (3\,x+2\right )}^4}+\frac {4099}{3645\,{\left (3\,x+2\right )}^5}-\frac {763}{4374\,{\left (3\,x+2\right )}^6}+\frac {7}{729\,{\left (3\,x+2\right )}^7} \]
[In]
[Out]