Integrand size = 71, antiderivative size = 35 \[ \int \frac {-12800+1920 x-12800 e^{e^{x^2}+x^2} x}{625+6400 e^{2 e^{x^2}}+8000 x+25000 x^2-3840 x^3+144 x^4+e^{e^{x^2}} \left (4000+25600 x-1920 x^2\right )} \, dx=\frac {4}{\frac {5}{4}+x+4 \left (e^{e^{x^2}}+x-\frac {3}{4} \left (-x+\frac {x^2}{5}\right )\right )} \]
[Out]
Time = 0.16 (sec) , antiderivative size = 23, normalized size of antiderivative = 0.66, number of steps used = 3, number of rules used = 3, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.042, Rules used = {6820, 12, 6818} \[ \int \frac {-12800+1920 x-12800 e^{e^{x^2}+x^2} x}{625+6400 e^{2 e^{x^2}}+8000 x+25000 x^2-3840 x^3+144 x^4+e^{e^{x^2}} \left (4000+25600 x-1920 x^2\right )} \, dx=\frac {80}{-12 x^2+80 e^{e^{x^2}}+160 x+25} \]
[In]
[Out]
Rule 12
Rule 6818
Rule 6820
Rubi steps \begin{align*} \text {integral}& = \int \frac {640 \left (-20-\left (-3+20 e^{e^{x^2}+x^2}\right ) x\right )}{\left (25+80 e^{e^{x^2}}+160 x-12 x^2\right )^2} \, dx \\ & = 640 \int \frac {-20-\left (-3+20 e^{e^{x^2}+x^2}\right ) x}{\left (25+80 e^{e^{x^2}}+160 x-12 x^2\right )^2} \, dx \\ & = \frac {80}{25+80 e^{e^{x^2}}+160 x-12 x^2} \\ \end{align*}
Time = 0.06 (sec) , antiderivative size = 23, normalized size of antiderivative = 0.66 \[ \int \frac {-12800+1920 x-12800 e^{e^{x^2}+x^2} x}{625+6400 e^{2 e^{x^2}}+8000 x+25000 x^2-3840 x^3+144 x^4+e^{e^{x^2}} \left (4000+25600 x-1920 x^2\right )} \, dx=\frac {80}{25+80 e^{e^{x^2}}+160 x-12 x^2} \]
[In]
[Out]
Time = 0.21 (sec) , antiderivative size = 22, normalized size of antiderivative = 0.63
method | result | size |
norman | \(-\frac {80}{12 x^{2}-160 x -80 \,{\mathrm e}^{{\mathrm e}^{x^{2}}}-25}\) | \(22\) |
risch | \(-\frac {80}{12 x^{2}-160 x -80 \,{\mathrm e}^{{\mathrm e}^{x^{2}}}-25}\) | \(22\) |
parallelrisch | \(-\frac {80}{12 x^{2}-160 x -80 \,{\mathrm e}^{{\mathrm e}^{x^{2}}}-25}\) | \(22\) |
[In]
[Out]
none
Time = 0.24 (sec) , antiderivative size = 35, normalized size of antiderivative = 1.00 \[ \int \frac {-12800+1920 x-12800 e^{e^{x^2}+x^2} x}{625+6400 e^{2 e^{x^2}}+8000 x+25000 x^2-3840 x^3+144 x^4+e^{e^{x^2}} \left (4000+25600 x-1920 x^2\right )} \, dx=-\frac {80 \, e^{\left (x^{2}\right )}}{{\left (12 \, x^{2} - 160 \, x - 25\right )} e^{\left (x^{2}\right )} - 80 \, e^{\left (x^{2} + e^{\left (x^{2}\right )}\right )}} \]
[In]
[Out]
Time = 0.09 (sec) , antiderivative size = 20, normalized size of antiderivative = 0.57 \[ \int \frac {-12800+1920 x-12800 e^{e^{x^2}+x^2} x}{625+6400 e^{2 e^{x^2}}+8000 x+25000 x^2-3840 x^3+144 x^4+e^{e^{x^2}} \left (4000+25600 x-1920 x^2\right )} \, dx=\frac {1}{- \frac {3 x^{2}}{20} + 2 x + e^{e^{x^{2}}} + \frac {5}{16}} \]
[In]
[Out]
none
Time = 0.23 (sec) , antiderivative size = 21, normalized size of antiderivative = 0.60 \[ \int \frac {-12800+1920 x-12800 e^{e^{x^2}+x^2} x}{625+6400 e^{2 e^{x^2}}+8000 x+25000 x^2-3840 x^3+144 x^4+e^{e^{x^2}} \left (4000+25600 x-1920 x^2\right )} \, dx=-\frac {80}{12 \, x^{2} - 160 \, x - 80 \, e^{\left (e^{\left (x^{2}\right )}\right )} - 25} \]
[In]
[Out]
none
Time = 0.33 (sec) , antiderivative size = 21, normalized size of antiderivative = 0.60 \[ \int \frac {-12800+1920 x-12800 e^{e^{x^2}+x^2} x}{625+6400 e^{2 e^{x^2}}+8000 x+25000 x^2-3840 x^3+144 x^4+e^{e^{x^2}} \left (4000+25600 x-1920 x^2\right )} \, dx=-\frac {80}{12 \, x^{2} - 160 \, x - 80 \, e^{\left (e^{\left (x^{2}\right )}\right )} - 25} \]
[In]
[Out]
Time = 13.48 (sec) , antiderivative size = 21, normalized size of antiderivative = 0.60 \[ \int \frac {-12800+1920 x-12800 e^{e^{x^2}+x^2} x}{625+6400 e^{2 e^{x^2}}+8000 x+25000 x^2-3840 x^3+144 x^4+e^{e^{x^2}} \left (4000+25600 x-1920 x^2\right )} \, dx=\frac {80}{160\,x+80\,{\mathrm {e}}^{{\mathrm {e}}^{x^2}}-12\,x^2+25} \]
[In]
[Out]