Integrand size = 73, antiderivative size = 33 \[ \int \frac {e^{\frac {1}{9} \left (9-9 x+6 x^2-x^3-3750 x^4+1250 x^5-390625 x^7\right )} \left (-9-9 x+12 x^2-3 x^3-15000 x^4+6250 x^5-2734375 x^7\right )}{9 x^2} \, dx=\frac {e^{\frac {x-\frac {1}{9} x^2 \left (3-x \left (1-625 x^2\right )\right )^2}{x}}}{x} \]
[Out]
Leaf count is larger than twice the leaf count of optimal. \(96\) vs. \(2(33)=66\).
Time = 0.20 (sec) , antiderivative size = 96, normalized size of antiderivative = 2.91, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.027, Rules used = {12, 2326} \[ \int \frac {e^{\frac {1}{9} \left (9-9 x+6 x^2-x^3-3750 x^4+1250 x^5-390625 x^7\right )} \left (-9-9 x+12 x^2-3 x^3-15000 x^4+6250 x^5-2734375 x^7\right )}{9 x^2} \, dx=\frac {\left (2734375 x^7-6250 x^5+15000 x^4+3 x^3-12 x^2+9 x\right ) \exp \left (\frac {1}{9} \left (-390625 x^7+1250 x^5-3750 x^4-x^3+6 x^2-9 x+9\right )\right )}{x^2 \left (2734375 x^6-6250 x^4+15000 x^3+3 x^2-12 x+9\right )} \]
[In]
[Out]
Rule 12
Rule 2326
Rubi steps \begin{align*} \text {integral}& = \frac {1}{9} \int \frac {\exp \left (\frac {1}{9} \left (9-9 x+6 x^2-x^3-3750 x^4+1250 x^5-390625 x^7\right )\right ) \left (-9-9 x+12 x^2-3 x^3-15000 x^4+6250 x^5-2734375 x^7\right )}{x^2} \, dx \\ & = \frac {\exp \left (\frac {1}{9} \left (9-9 x+6 x^2-x^3-3750 x^4+1250 x^5-390625 x^7\right )\right ) \left (9 x-12 x^2+3 x^3+15000 x^4-6250 x^5+2734375 x^7\right )}{x^2 \left (9-12 x+3 x^2+15000 x^3-6250 x^4+2734375 x^6\right )} \\ \end{align*}
Time = 7.42 (sec) , antiderivative size = 40, normalized size of antiderivative = 1.21 \[ \int \frac {e^{\frac {1}{9} \left (9-9 x+6 x^2-x^3-3750 x^4+1250 x^5-390625 x^7\right )} \left (-9-9 x+12 x^2-3 x^3-15000 x^4+6250 x^5-2734375 x^7\right )}{9 x^2} \, dx=\frac {e^{\frac {1}{9} \left (9-9 x+6 x^2-x^3-3750 x^4+1250 x^5-390625 x^7\right )}}{x} \]
[In]
[Out]
Time = 0.15 (sec) , antiderivative size = 36, normalized size of antiderivative = 1.09
method | result | size |
gosper | \(\frac {{\mathrm e}^{-\frac {390625}{9} x^{7}+\frac {1250}{9} x^{5}-\frac {1250}{3} x^{4}-\frac {1}{9} x^{3}+\frac {2}{3} x^{2}-x +1}}{x}\) | \(36\) |
norman | \(\frac {{\mathrm e}^{-\frac {390625}{9} x^{7}+\frac {1250}{9} x^{5}-\frac {1250}{3} x^{4}-\frac {1}{9} x^{3}+\frac {2}{3} x^{2}-x +1}}{x}\) | \(36\) |
parallelrisch | \(\frac {{\mathrm e}^{-\frac {390625}{9} x^{7}+\frac {1250}{9} x^{5}-\frac {1250}{3} x^{4}-\frac {1}{9} x^{3}+\frac {2}{3} x^{2}-x +1}}{x}\) | \(36\) |
risch | \(\frac {{\mathrm e}^{-\frac {\left (25 x^{2}+x +1\right ) \left (15625 x^{5}-625 x^{4}-650 x^{3}+201 x^{2}+18 x -9\right )}{9}}}{x}\) | \(41\) |
[In]
[Out]
none
Time = 0.24 (sec) , antiderivative size = 35, normalized size of antiderivative = 1.06 \[ \int \frac {e^{\frac {1}{9} \left (9-9 x+6 x^2-x^3-3750 x^4+1250 x^5-390625 x^7\right )} \left (-9-9 x+12 x^2-3 x^3-15000 x^4+6250 x^5-2734375 x^7\right )}{9 x^2} \, dx=\frac {e^{\left (-\frac {390625}{9} \, x^{7} + \frac {1250}{9} \, x^{5} - \frac {1250}{3} \, x^{4} - \frac {1}{9} \, x^{3} + \frac {2}{3} \, x^{2} - x + 1\right )}}{x} \]
[In]
[Out]
Time = 0.07 (sec) , antiderivative size = 37, normalized size of antiderivative = 1.12 \[ \int \frac {e^{\frac {1}{9} \left (9-9 x+6 x^2-x^3-3750 x^4+1250 x^5-390625 x^7\right )} \left (-9-9 x+12 x^2-3 x^3-15000 x^4+6250 x^5-2734375 x^7\right )}{9 x^2} \, dx=\frac {e^{- \frac {390625 x^{7}}{9} + \frac {1250 x^{5}}{9} - \frac {1250 x^{4}}{3} - \frac {x^{3}}{9} + \frac {2 x^{2}}{3} - x + 1}}{x} \]
[In]
[Out]
none
Time = 0.36 (sec) , antiderivative size = 35, normalized size of antiderivative = 1.06 \[ \int \frac {e^{\frac {1}{9} \left (9-9 x+6 x^2-x^3-3750 x^4+1250 x^5-390625 x^7\right )} \left (-9-9 x+12 x^2-3 x^3-15000 x^4+6250 x^5-2734375 x^7\right )}{9 x^2} \, dx=\frac {e^{\left (-\frac {390625}{9} \, x^{7} + \frac {1250}{9} \, x^{5} - \frac {1250}{3} \, x^{4} - \frac {1}{9} \, x^{3} + \frac {2}{3} \, x^{2} - x + 1\right )}}{x} \]
[In]
[Out]
none
Time = 0.32 (sec) , antiderivative size = 35, normalized size of antiderivative = 1.06 \[ \int \frac {e^{\frac {1}{9} \left (9-9 x+6 x^2-x^3-3750 x^4+1250 x^5-390625 x^7\right )} \left (-9-9 x+12 x^2-3 x^3-15000 x^4+6250 x^5-2734375 x^7\right )}{9 x^2} \, dx=\frac {e^{\left (-\frac {390625}{9} \, x^{7} + \frac {1250}{9} \, x^{5} - \frac {1250}{3} \, x^{4} - \frac {1}{9} \, x^{3} + \frac {2}{3} \, x^{2} - x + 1\right )}}{x} \]
[In]
[Out]
Time = 14.19 (sec) , antiderivative size = 40, normalized size of antiderivative = 1.21 \[ \int \frac {e^{\frac {1}{9} \left (9-9 x+6 x^2-x^3-3750 x^4+1250 x^5-390625 x^7\right )} \left (-9-9 x+12 x^2-3 x^3-15000 x^4+6250 x^5-2734375 x^7\right )}{9 x^2} \, dx=\frac {{\mathrm {e}}^{-x}\,\mathrm {e}\,{\mathrm {e}}^{\frac {2\,x^2}{3}}\,{\mathrm {e}}^{-\frac {x^3}{9}}\,{\mathrm {e}}^{-\frac {1250\,x^4}{3}}\,{\mathrm {e}}^{\frac {1250\,x^5}{9}}\,{\mathrm {e}}^{-\frac {390625\,x^7}{9}}}{x} \]
[In]
[Out]