Integrand size = 20, antiderivative size = 45 \[ \int \frac {(1-2 x) (3+5 x)^2}{(2+3 x)^7} \, dx=-\frac {7}{486 (2+3 x)^6}+\frac {8}{45 (2+3 x)^5}-\frac {65}{108 (2+3 x)^4}+\frac {50}{243 (2+3 x)^3} \]
[Out]
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} \[ \int \frac {(1-2 x) (3+5 x)^2}{(2+3 x)^7} \, dx=\frac {50}{243 (3 x+2)^3}-\frac {65}{108 (3 x+2)^4}+\frac {8}{45 (3 x+2)^5}-\frac {7}{486 (3 x+2)^6} \]
[In]
[Out]
Rule 78
Rubi steps \begin{align*} \text {integral}& = \int \left (\frac {7}{27 (2+3 x)^7}-\frac {8}{3 (2+3 x)^6}+\frac {65}{9 (2+3 x)^5}-\frac {50}{27 (2+3 x)^4}\right ) \, dx \\ & = -\frac {7}{486 (2+3 x)^6}+\frac {8}{45 (2+3 x)^5}-\frac {65}{108 (2+3 x)^4}+\frac {50}{243 (2+3 x)^3} \\ \end{align*}
Time = 0.01 (sec) , antiderivative size = 26, normalized size of antiderivative = 0.58 \[ \int \frac {(1-2 x) (3+5 x)^2}{(2+3 x)^7} \, dx=\frac {-2042+3492 x+27675 x^2+27000 x^3}{4860 (2+3 x)^6} \]
[In]
[Out]
Time = 2.19 (sec) , antiderivative size = 24, normalized size of antiderivative = 0.53
method | result | size |
norman | \(\frac {\frac {50}{9} x^{3}+\frac {97}{135} x +\frac {205}{36} x^{2}-\frac {1021}{2430}}{\left (2+3 x \right )^{6}}\) | \(24\) |
gosper | \(\frac {27000 x^{3}+27675 x^{2}+3492 x -2042}{4860 \left (2+3 x \right )^{6}}\) | \(25\) |
risch | \(\frac {\frac {50}{9} x^{3}+\frac {97}{135} x +\frac {205}{36} x^{2}-\frac {1021}{2430}}{\left (2+3 x \right )^{6}}\) | \(25\) |
default | \(-\frac {7}{486 \left (2+3 x \right )^{6}}+\frac {8}{45 \left (2+3 x \right )^{5}}-\frac {65}{108 \left (2+3 x \right )^{4}}+\frac {50}{243 \left (2+3 x \right )^{3}}\) | \(38\) |
parallelrisch | \(\frac {9189 x^{6}+36756 x^{5}+61260 x^{4}+65120 x^{3}+38160 x^{2}+8640 x}{1920 \left (2+3 x \right )^{6}}\) | \(39\) |
meijerg | \(\frac {3 x \left (\frac {243}{32} x^{5}+\frac {243}{8} x^{4}+\frac {405}{8} x^{3}+45 x^{2}+\frac {45}{2} x +6\right )}{256 \left (1+\frac {3 x}{2}\right )^{6}}+\frac {x^{2} \left (\frac {81}{16} x^{4}+\frac {81}{4} x^{3}+\frac {135}{4} x^{2}+30 x +15\right )}{320 \left (1+\frac {3 x}{2}\right )^{6}}-\frac {7 x^{3} \left (\frac {27}{8} x^{3}+\frac {27}{2} x^{2}+\frac {45}{2} x +20\right )}{1536 \left (1+\frac {3 x}{2}\right )^{6}}-\frac {5 x^{4} \left (\frac {9}{4} x^{2}+9 x +15\right )}{768 \left (1+\frac {3 x}{2}\right )^{6}}\) | \(118\) |
[In]
[Out]
none
Time = 0.22 (sec) , antiderivative size = 49, normalized size of antiderivative = 1.09 \[ \int \frac {(1-2 x) (3+5 x)^2}{(2+3 x)^7} \, dx=\frac {27000 \, x^{3} + 27675 \, x^{2} + 3492 \, x - 2042}{4860 \, {\left (729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right )}} \]
[In]
[Out]
Time = 0.07 (sec) , antiderivative size = 46, normalized size of antiderivative = 1.02 \[ \int \frac {(1-2 x) (3+5 x)^2}{(2+3 x)^7} \, dx=- \frac {- 27000 x^{3} - 27675 x^{2} - 3492 x + 2042}{3542940 x^{6} + 14171760 x^{5} + 23619600 x^{4} + 20995200 x^{3} + 10497600 x^{2} + 2799360 x + 311040} \]
[In]
[Out]
none
Time = 0.21 (sec) , antiderivative size = 49, normalized size of antiderivative = 1.09 \[ \int \frac {(1-2 x) (3+5 x)^2}{(2+3 x)^7} \, dx=\frac {27000 \, x^{3} + 27675 \, x^{2} + 3492 \, x - 2042}{4860 \, {\left (729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right )}} \]
[In]
[Out]
none
Time = 0.29 (sec) , antiderivative size = 24, normalized size of antiderivative = 0.53 \[ \int \frac {(1-2 x) (3+5 x)^2}{(2+3 x)^7} \, dx=\frac {27000 \, x^{3} + 27675 \, x^{2} + 3492 \, x - 2042}{4860 \, {\left (3 \, x + 2\right )}^{6}} \]
[In]
[Out]
Time = 0.05 (sec) , antiderivative size = 37, normalized size of antiderivative = 0.82 \[ \int \frac {(1-2 x) (3+5 x)^2}{(2+3 x)^7} \, dx=\frac {50}{243\,{\left (3\,x+2\right )}^3}-\frac {65}{108\,{\left (3\,x+2\right )}^4}+\frac {8}{45\,{\left (3\,x+2\right )}^5}-\frac {7}{486\,{\left (3\,x+2\right )}^6} \]
[In]
[Out]