Integrand size = 206, antiderivative size = 38 \[ \int \frac {20-12 e^{10-8 x}-40 x-8 x^2+24 x^3-12 x^4+e^{5-4 x} \left (-76-8 x+24 x^2\right )}{25-10 x+31 x^2-36 x^3+15 x^4-18 x^5+9 x^6+e^{10-8 x} \left (e^6-6 e^3 x+9 x^2\right )+e^6 \left (x^2-2 x^3+x^4\right )+e^3 \left (-10 x+12 x^2-8 x^3+12 x^4-6 x^5\right )+e^{5-4 x} \left (30 x-6 x^2+18 x^3-18 x^4+e^6 \left (2 x-2 x^2\right )+e^3 \left (-10+2 x-12 x^2+12 x^3\right )\right )} \, dx=\frac {4}{-e^3+3 x-\frac {5-x}{-e^{5-4 x}-x+x^2}} \] Output:
4/(3*x-(5-x)/(x^2-x-exp(-4*x+5))-exp(3))
Time = 10.09 (sec) , antiderivative size = 61, normalized size of antiderivative = 1.61 \[ \int \frac {20-12 e^{10-8 x}-40 x-8 x^2+24 x^3-12 x^4+e^{5-4 x} \left (-76-8 x+24 x^2\right )}{25-10 x+31 x^2-36 x^3+15 x^4-18 x^5+9 x^6+e^{10-8 x} \left (e^6-6 e^3 x+9 x^2\right )+e^6 \left (x^2-2 x^3+x^4\right )+e^3 \left (-10 x+12 x^2-8 x^3+12 x^4-6 x^5\right )+e^{5-4 x} \left (30 x-6 x^2+18 x^3-18 x^4+e^6 \left (2 x-2 x^2\right )+e^3 \left (-10+2 x-12 x^2+12 x^3\right )\right )} \, dx=-\frac {4 \left (e^5-e^{4 x} (-1+x) x\right )}{e^8-3 e^5 x-e^{3+4 x} (-1+x) x+e^{4 x} \left (-5+x-3 x^2+3 x^3\right )} \] Input:
Integrate[(20 - 12*E^(10 - 8*x) - 40*x - 8*x^2 + 24*x^3 - 12*x^4 + E^(5 - 4*x)*(-76 - 8*x + 24*x^2))/(25 - 10*x + 31*x^2 - 36*x^3 + 15*x^4 - 18*x^5 + 9*x^6 + E^(10 - 8*x)*(E^6 - 6*E^3*x + 9*x^2) + E^6*(x^2 - 2*x^3 + x^4) + E^3*(-10*x + 12*x^2 - 8*x^3 + 12*x^4 - 6*x^5) + E^(5 - 4*x)*(30*x - 6*x^2 + 18*x^3 - 18*x^4 + E^6*(2*x - 2*x^2) + E^3*(-10 + 2*x - 12*x^2 + 12*x^3) )),x]
Output:
(-4*(E^5 - E^(4*x)*(-1 + x)*x))/(E^8 - 3*E^5*x - E^(3 + 4*x)*(-1 + x)*x + E^(4*x)*(-5 + x - 3*x^2 + 3*x^3))
Below are the steps used by Rubi to obtain the solution. The rule number used for the transformation is given above next to the arrow. The rules definitions used are listed below.
| \(\displaystyle \int \frac {-12 x^4+24 x^3-8 x^2+e^{5-4 x} \left (24 x^2-8 x-76\right )-40 x-12 e^{10-8 x}+20}{9 x^6-18 x^5+15 x^4-36 x^3+31 x^2+e^{10-8 x} \left (9 x^2-6 e^3 x+e^6\right )+e^6 \left (x^4-2 x^3+x^2\right )+e^{5-4 x} \left (-18 x^4+18 x^3-6 x^2+e^6 \left (2 x-2 x^2\right )+e^3 \left (12 x^3-12 x^2+2 x-10\right )+30 x\right )+e^3 \left (-6 x^5+12 x^4-8 x^3+12 x^2-10 x\right )-10 x+25} \, dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {4 \left (-e^{4 x+5} \left (-6 x^2+2 x+19\right )-e^{8 x} \left (3 x^4-6 x^3+2 x^2+10 x-5\right )-3 e^{10}\right )}{\left (e^{4 x} \left (3 x^3-3 x^2+x-5\right )-e^{4 x+3} (x-1) x-3 e^5 x+e^8\right )^2}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle 4 \int -\frac {e^{4 x+5} \left (-6 x^2+2 x+19\right )-e^{8 x} \left (-3 x^4+6 x^3-2 x^2-10 x+5\right )+3 e^{10}}{\left (e^{4 x+3} (1-x) x-3 e^5 x-e^{4 x} \left (-3 x^3+3 x^2-x+5\right )+e^8\right )^2}dx\) |
| \(\Big \downarrow \) 25 |
| \(\displaystyle -4 \int \frac {e^{4 x+5} \left (-6 x^2+2 x+19\right )-e^{8 x} \left (-3 x^4+6 x^3-2 x^2-10 x+5\right )+3 e^{10}}{\left (e^{4 x+3} (1-x) x-3 e^5 x-e^{4 x} \left (-3 x^3+3 x^2-x+5\right )+e^8\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -4 \int \left (\frac {e^5 \left (-12 x^4+\left (57+4 e^3\right ) x^3+7 \left (5-3 e^3\right ) x^2-\left (21+e^3\right ) x-5 \left (19-2 e^3\right )\right )}{\left (-3 x^3+\left (3+e^3\right ) x^2-\left (1+e^3\right ) x+5\right )^2 \left (3 e^{4 x} x^3-3 e^{4 x} \left (1+\frac {e^3}{3}\right ) x^2+e^{4 x} \left (1+e^3\right ) x-3 e^5 x-5 e^{4 x}+e^8\right )}+\frac {3 x^4-6 x^3+2 x^2+10 x-5}{\left (-3 x^3+\left (3+e^3\right ) x^2-\left (1+e^3\right ) x+5\right )^2}+\frac {e^{10} (5-x) \left (36 x^4-6 \left (3+4 e^3\right ) x^3+\left (3+12 e^3+4 e^6\right ) x^2-2 \left (30-e^3+e^6\right ) x-e^6+19 e^3+15\right )}{\left (-3 x^3+\left (3+e^3\right ) x^2-\left (1+e^3\right ) x+5\right )^2 \left (3 e^{4 x} x^3-3 e^{4 x} \left (1+\frac {e^3}{3}\right ) x^2+e^{4 x} \left (1+e^3\right ) x-3 e^5 x-5 e^{4 x}+e^8\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -4 \int \frac {e^{4 x+5} \left (-6 x^2+2 x+19\right )+e^{8 x} \left (3 x^4-6 x^3+2 x^2+10 x-5\right )+3 e^{10}}{\left (-e^{4 x+3} (x-1) x-3 e^5 x+e^{4 x} \left (3 x^3-3 x^2+x-5\right )+e^8\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -4 \int \left (\frac {e^5 \left (-12 x^4+\left (57+4 e^3\right ) x^3+7 \left (5-3 e^3\right ) x^2-\left (21+e^3\right ) x-5 \left (19-2 e^3\right )\right )}{\left (-3 x^3+\left (3+e^3\right ) x^2-\left (1+e^3\right ) x+5\right )^2 \left (3 e^{4 x} x^3-3 e^{4 x} \left (1+\frac {e^3}{3}\right ) x^2+e^{4 x} \left (1+e^3\right ) x-3 e^5 x-5 e^{4 x}+e^8\right )}+\frac {3 x^4-6 x^3+2 x^2+10 x-5}{\left (-3 x^3+\left (3+e^3\right ) x^2-\left (1+e^3\right ) x+5\right )^2}+\frac {e^{10} (5-x) \left (36 x^4-6 \left (3+4 e^3\right ) x^3+\left (3+12 e^3+4 e^6\right ) x^2-2 \left (30-e^3+e^6\right ) x-e^6+19 e^3+15\right )}{\left (-3 x^3+\left (3+e^3\right ) x^2-\left (1+e^3\right ) x+5\right )^2 \left (3 e^{4 x} x^3-3 e^{4 x} \left (1+\frac {e^3}{3}\right ) x^2+e^{4 x} \left (1+e^3\right ) x-3 e^5 x-5 e^{4 x}+e^8\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -4 \int \frac {e^{4 x+5} \left (-6 x^2+2 x+19\right )+e^{8 x} \left (3 x^4-6 x^3+2 x^2+10 x-5\right )+3 e^{10}}{\left (-e^{4 x+3} (x-1) x-3 e^5 x+e^{4 x} \left (3 x^3-3 x^2+x-5\right )+e^8\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -4 \int \left (\frac {e^5 \left (-12 x^4+\left (57+4 e^3\right ) x^3+7 \left (5-3 e^3\right ) x^2-\left (21+e^3\right ) x-5 \left (19-2 e^3\right )\right )}{\left (-3 x^3+\left (3+e^3\right ) x^2-\left (1+e^3\right ) x+5\right )^2 \left (3 e^{4 x} x^3-3 e^{4 x} \left (1+\frac {e^3}{3}\right ) x^2+e^{4 x} \left (1+e^3\right ) x-3 e^5 x-5 e^{4 x}+e^8\right )}+\frac {3 x^4-6 x^3+2 x^2+10 x-5}{\left (-3 x^3+\left (3+e^3\right ) x^2-\left (1+e^3\right ) x+5\right )^2}+\frac {e^{10} (5-x) \left (36 x^4-6 \left (3+4 e^3\right ) x^3+\left (3+12 e^3+4 e^6\right ) x^2-2 \left (30-e^3+e^6\right ) x-e^6+19 e^3+15\right )}{\left (-3 x^3+\left (3+e^3\right ) x^2-\left (1+e^3\right ) x+5\right )^2 \left (3 e^{4 x} x^3-3 e^{4 x} \left (1+\frac {e^3}{3}\right ) x^2+e^{4 x} \left (1+e^3\right ) x-3 e^5 x-5 e^{4 x}+e^8\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -4 \int \frac {e^{4 x+5} \left (-6 x^2+2 x+19\right )+e^{8 x} \left (3 x^4-6 x^3+2 x^2+10 x-5\right )+3 e^{10}}{\left (-e^{4 x+3} (x-1) x-3 e^5 x+e^{4 x} \left (3 x^3-3 x^2+x-5\right )+e^8\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -4 \int \left (\frac {e^5 \left (-12 x^4+\left (57+4 e^3\right ) x^3+7 \left (5-3 e^3\right ) x^2-\left (21+e^3\right ) x-5 \left (19-2 e^3\right )\right )}{\left (-3 x^3+\left (3+e^3\right ) x^2-\left (1+e^3\right ) x+5\right )^2 \left (3 e^{4 x} x^3-3 e^{4 x} \left (1+\frac {e^3}{3}\right ) x^2+e^{4 x} \left (1+e^3\right ) x-3 e^5 x-5 e^{4 x}+e^8\right )}+\frac {3 x^4-6 x^3+2 x^2+10 x-5}{\left (-3 x^3+\left (3+e^3\right ) x^2-\left (1+e^3\right ) x+5\right )^2}+\frac {e^{10} (5-x) \left (36 x^4-6 \left (3+4 e^3\right ) x^3+\left (3+12 e^3+4 e^6\right ) x^2-2 \left (30-e^3+e^6\right ) x-e^6+19 e^3+15\right )}{\left (-3 x^3+\left (3+e^3\right ) x^2-\left (1+e^3\right ) x+5\right )^2 \left (3 e^{4 x} x^3-3 e^{4 x} \left (1+\frac {e^3}{3}\right ) x^2+e^{4 x} \left (1+e^3\right ) x-3 e^5 x-5 e^{4 x}+e^8\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -4 \int \frac {e^{4 x+5} \left (-6 x^2+2 x+19\right )+e^{8 x} \left (3 x^4-6 x^3+2 x^2+10 x-5\right )+3 e^{10}}{\left (-e^{4 x+3} (x-1) x-3 e^5 x+e^{4 x} \left (3 x^3-3 x^2+x-5\right )+e^8\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -4 \int \left (\frac {e^5 \left (-12 x^4+\left (57+4 e^3\right ) x^3+7 \left (5-3 e^3\right ) x^2-\left (21+e^3\right ) x-5 \left (19-2 e^3\right )\right )}{\left (-3 x^3+\left (3+e^3\right ) x^2-\left (1+e^3\right ) x+5\right )^2 \left (3 e^{4 x} x^3-3 e^{4 x} \left (1+\frac {e^3}{3}\right ) x^2+e^{4 x} \left (1+e^3\right ) x-3 e^5 x-5 e^{4 x}+e^8\right )}+\frac {3 x^4-6 x^3+2 x^2+10 x-5}{\left (-3 x^3+\left (3+e^3\right ) x^2-\left (1+e^3\right ) x+5\right )^2}+\frac {e^{10} (5-x) \left (36 x^4-6 \left (3+4 e^3\right ) x^3+\left (3+12 e^3+4 e^6\right ) x^2-2 \left (30-e^3+e^6\right ) x-e^6+19 e^3+15\right )}{\left (-3 x^3+\left (3+e^3\right ) x^2-\left (1+e^3\right ) x+5\right )^2 \left (3 e^{4 x} x^3-3 e^{4 x} \left (1+\frac {e^3}{3}\right ) x^2+e^{4 x} \left (1+e^3\right ) x-3 e^5 x-5 e^{4 x}+e^8\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -4 \int \frac {e^{4 x+5} \left (-6 x^2+2 x+19\right )+e^{8 x} \left (3 x^4-6 x^3+2 x^2+10 x-5\right )+3 e^{10}}{\left (-e^{4 x+3} (x-1) x-3 e^5 x+e^{4 x} \left (3 x^3-3 x^2+x-5\right )+e^8\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -4 \int \left (\frac {e^5 \left (-12 x^4+\left (57+4 e^3\right ) x^3+7 \left (5-3 e^3\right ) x^2-\left (21+e^3\right ) x-5 \left (19-2 e^3\right )\right )}{\left (-3 x^3+\left (3+e^3\right ) x^2-\left (1+e^3\right ) x+5\right )^2 \left (3 e^{4 x} x^3-3 e^{4 x} \left (1+\frac {e^3}{3}\right ) x^2+e^{4 x} \left (1+e^3\right ) x-3 e^5 x-5 e^{4 x}+e^8\right )}+\frac {3 x^4-6 x^3+2 x^2+10 x-5}{\left (-3 x^3+\left (3+e^3\right ) x^2-\left (1+e^3\right ) x+5\right )^2}+\frac {e^{10} (5-x) \left (36 x^4-6 \left (3+4 e^3\right ) x^3+\left (3+12 e^3+4 e^6\right ) x^2-2 \left (30-e^3+e^6\right ) x-e^6+19 e^3+15\right )}{\left (-3 x^3+\left (3+e^3\right ) x^2-\left (1+e^3\right ) x+5\right )^2 \left (3 e^{4 x} x^3-3 e^{4 x} \left (1+\frac {e^3}{3}\right ) x^2+e^{4 x} \left (1+e^3\right ) x-3 e^5 x-5 e^{4 x}+e^8\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -4 \int \frac {e^{4 x+5} \left (-6 x^2+2 x+19\right )+e^{8 x} \left (3 x^4-6 x^3+2 x^2+10 x-5\right )+3 e^{10}}{\left (-e^{4 x+3} (x-1) x-3 e^5 x+e^{4 x} \left (3 x^3-3 x^2+x-5\right )+e^8\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -4 \int \left (\frac {e^5 \left (-12 x^4+\left (57+4 e^3\right ) x^3+7 \left (5-3 e^3\right ) x^2-\left (21+e^3\right ) x-5 \left (19-2 e^3\right )\right )}{\left (-3 x^3+\left (3+e^3\right ) x^2-\left (1+e^3\right ) x+5\right )^2 \left (3 e^{4 x} x^3-3 e^{4 x} \left (1+\frac {e^3}{3}\right ) x^2+e^{4 x} \left (1+e^3\right ) x-3 e^5 x-5 e^{4 x}+e^8\right )}+\frac {3 x^4-6 x^3+2 x^2+10 x-5}{\left (-3 x^3+\left (3+e^3\right ) x^2-\left (1+e^3\right ) x+5\right )^2}+\frac {e^{10} (5-x) \left (36 x^4-6 \left (3+4 e^3\right ) x^3+\left (3+12 e^3+4 e^6\right ) x^2-2 \left (30-e^3+e^6\right ) x-e^6+19 e^3+15\right )}{\left (-3 x^3+\left (3+e^3\right ) x^2-\left (1+e^3\right ) x+5\right )^2 \left (3 e^{4 x} x^3-3 e^{4 x} \left (1+\frac {e^3}{3}\right ) x^2+e^{4 x} \left (1+e^3\right ) x-3 e^5 x-5 e^{4 x}+e^8\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -4 \int \frac {e^{4 x+5} \left (-6 x^2+2 x+19\right )+e^{8 x} \left (3 x^4-6 x^3+2 x^2+10 x-5\right )+3 e^{10}}{\left (-e^{4 x+3} (x-1) x-3 e^5 x+e^{4 x} \left (3 x^3-3 x^2+x-5\right )+e^8\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -4 \int \left (\frac {e^5 \left (-12 x^4+\left (57+4 e^3\right ) x^3+7 \left (5-3 e^3\right ) x^2-\left (21+e^3\right ) x-5 \left (19-2 e^3\right )\right )}{\left (-3 x^3+\left (3+e^3\right ) x^2-\left (1+e^3\right ) x+5\right )^2 \left (3 e^{4 x} x^3-3 e^{4 x} \left (1+\frac {e^3}{3}\right ) x^2+e^{4 x} \left (1+e^3\right ) x-3 e^5 x-5 e^{4 x}+e^8\right )}+\frac {3 x^4-6 x^3+2 x^2+10 x-5}{\left (-3 x^3+\left (3+e^3\right ) x^2-\left (1+e^3\right ) x+5\right )^2}+\frac {e^{10} (5-x) \left (36 x^4-6 \left (3+4 e^3\right ) x^3+\left (3+12 e^3+4 e^6\right ) x^2-2 \left (30-e^3+e^6\right ) x-e^6+19 e^3+15\right )}{\left (-3 x^3+\left (3+e^3\right ) x^2-\left (1+e^3\right ) x+5\right )^2 \left (3 e^{4 x} x^3-3 e^{4 x} \left (1+\frac {e^3}{3}\right ) x^2+e^{4 x} \left (1+e^3\right ) x-3 e^5 x-5 e^{4 x}+e^8\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -4 \int \frac {e^{4 x+5} \left (-6 x^2+2 x+19\right )+e^{8 x} \left (3 x^4-6 x^3+2 x^2+10 x-5\right )+3 e^{10}}{\left (-e^{4 x+3} (x-1) x-3 e^5 x+e^{4 x} \left (3 x^3-3 x^2+x-5\right )+e^8\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -4 \int \left (\frac {e^5 \left (-12 x^4+\left (57+4 e^3\right ) x^3+7 \left (5-3 e^3\right ) x^2-\left (21+e^3\right ) x-5 \left (19-2 e^3\right )\right )}{\left (-3 x^3+\left (3+e^3\right ) x^2-\left (1+e^3\right ) x+5\right )^2 \left (3 e^{4 x} x^3-3 e^{4 x} \left (1+\frac {e^3}{3}\right ) x^2+e^{4 x} \left (1+e^3\right ) x-3 e^5 x-5 e^{4 x}+e^8\right )}+\frac {3 x^4-6 x^3+2 x^2+10 x-5}{\left (-3 x^3+\left (3+e^3\right ) x^2-\left (1+e^3\right ) x+5\right )^2}+\frac {e^{10} (5-x) \left (36 x^4-6 \left (3+4 e^3\right ) x^3+\left (3+12 e^3+4 e^6\right ) x^2-2 \left (30-e^3+e^6\right ) x-e^6+19 e^3+15\right )}{\left (-3 x^3+\left (3+e^3\right ) x^2-\left (1+e^3\right ) x+5\right )^2 \left (3 e^{4 x} x^3-3 e^{4 x} \left (1+\frac {e^3}{3}\right ) x^2+e^{4 x} \left (1+e^3\right ) x-3 e^5 x-5 e^{4 x}+e^8\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -4 \int \frac {e^{4 x+5} \left (-6 x^2+2 x+19\right )+e^{8 x} \left (3 x^4-6 x^3+2 x^2+10 x-5\right )+3 e^{10}}{\left (-e^{4 x+3} (x-1) x-3 e^5 x+e^{4 x} \left (3 x^3-3 x^2+x-5\right )+e^8\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -4 \int \left (\frac {e^5 \left (-12 x^4+\left (57+4 e^3\right ) x^3+7 \left (5-3 e^3\right ) x^2-\left (21+e^3\right ) x-5 \left (19-2 e^3\right )\right )}{\left (-3 x^3+\left (3+e^3\right ) x^2-\left (1+e^3\right ) x+5\right )^2 \left (3 e^{4 x} x^3-3 e^{4 x} \left (1+\frac {e^3}{3}\right ) x^2+e^{4 x} \left (1+e^3\right ) x-3 e^5 x-5 e^{4 x}+e^8\right )}+\frac {3 x^4-6 x^3+2 x^2+10 x-5}{\left (-3 x^3+\left (3+e^3\right ) x^2-\left (1+e^3\right ) x+5\right )^2}+\frac {e^{10} (5-x) \left (36 x^4-6 \left (3+4 e^3\right ) x^3+\left (3+12 e^3+4 e^6\right ) x^2-2 \left (30-e^3+e^6\right ) x-e^6+19 e^3+15\right )}{\left (-3 x^3+\left (3+e^3\right ) x^2-\left (1+e^3\right ) x+5\right )^2 \left (3 e^{4 x} x^3-3 e^{4 x} \left (1+\frac {e^3}{3}\right ) x^2+e^{4 x} \left (1+e^3\right ) x-3 e^5 x-5 e^{4 x}+e^8\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -4 \int \frac {e^{4 x+5} \left (-6 x^2+2 x+19\right )+e^{8 x} \left (3 x^4-6 x^3+2 x^2+10 x-5\right )+3 e^{10}}{\left (-e^{4 x+3} (x-1) x-3 e^5 x+e^{4 x} \left (3 x^3-3 x^2+x-5\right )+e^8\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -4 \int \left (\frac {e^5 \left (-12 x^4+\left (57+4 e^3\right ) x^3+7 \left (5-3 e^3\right ) x^2-\left (21+e^3\right ) x-5 \left (19-2 e^3\right )\right )}{\left (-3 x^3+\left (3+e^3\right ) x^2-\left (1+e^3\right ) x+5\right )^2 \left (3 e^{4 x} x^3-3 e^{4 x} \left (1+\frac {e^3}{3}\right ) x^2+e^{4 x} \left (1+e^3\right ) x-3 e^5 x-5 e^{4 x}+e^8\right )}+\frac {3 x^4-6 x^3+2 x^2+10 x-5}{\left (-3 x^3+\left (3+e^3\right ) x^2-\left (1+e^3\right ) x+5\right )^2}+\frac {e^{10} (5-x) \left (36 x^4-6 \left (3+4 e^3\right ) x^3+\left (3+12 e^3+4 e^6\right ) x^2-2 \left (30-e^3+e^6\right ) x-e^6+19 e^3+15\right )}{\left (-3 x^3+\left (3+e^3\right ) x^2-\left (1+e^3\right ) x+5\right )^2 \left (3 e^{4 x} x^3-3 e^{4 x} \left (1+\frac {e^3}{3}\right ) x^2+e^{4 x} \left (1+e^3\right ) x-3 e^5 x-5 e^{4 x}+e^8\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -4 \int \frac {e^{4 x+5} \left (-6 x^2+2 x+19\right )+e^{8 x} \left (3 x^4-6 x^3+2 x^2+10 x-5\right )+3 e^{10}}{\left (-e^{4 x+3} (x-1) x-3 e^5 x+e^{4 x} \left (3 x^3-3 x^2+x-5\right )+e^8\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -4 \int \left (\frac {e^5 \left (-12 x^4+\left (57+4 e^3\right ) x^3+7 \left (5-3 e^3\right ) x^2-\left (21+e^3\right ) x-5 \left (19-2 e^3\right )\right )}{\left (-3 x^3+\left (3+e^3\right ) x^2-\left (1+e^3\right ) x+5\right )^2 \left (3 e^{4 x} x^3-3 e^{4 x} \left (1+\frac {e^3}{3}\right ) x^2+e^{4 x} \left (1+e^3\right ) x-3 e^5 x-5 e^{4 x}+e^8\right )}+\frac {3 x^4-6 x^3+2 x^2+10 x-5}{\left (-3 x^3+\left (3+e^3\right ) x^2-\left (1+e^3\right ) x+5\right )^2}+\frac {e^{10} (5-x) \left (36 x^4-6 \left (3+4 e^3\right ) x^3+\left (3+12 e^3+4 e^6\right ) x^2-2 \left (30-e^3+e^6\right ) x-e^6+19 e^3+15\right )}{\left (-3 x^3+\left (3+e^3\right ) x^2-\left (1+e^3\right ) x+5\right )^2 \left (3 e^{4 x} x^3-3 e^{4 x} \left (1+\frac {e^3}{3}\right ) x^2+e^{4 x} \left (1+e^3\right ) x-3 e^5 x-5 e^{4 x}+e^8\right )^2}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle -4 \left (\frac {x^2}{-3 x^3+\left (3+e^3\right ) x^2-\left (1+e^3\right ) x+5}-\frac {x}{-3 x^3+\left (3+e^3\right ) x^2-\left (1+e^3\right ) x+5}+5 e^{10} \left (42+e^3-e^6\right ) \int \frac {1}{\left (-3 x^3+\left (3+e^3\right ) x^2-\left (1+e^3\right ) x+5\right )^2 \left (3 e^{4 x} x^3-3 e^{4 x} \left (1+\frac {e^3}{3}\right ) x^2+e^{4 x} \left (1+e^3\right ) x-3 e^5 x-5 e^{4 x}+e^8\right )^2}dx-e^{10} \left (72-2 e^3-9 e^6\right ) \int \frac {x}{\left (-3 x^3+\left (3+e^3\right ) x^2-\left (1+e^3\right ) x+5\right )^2 \left (3 e^{4 x} x^3-3 e^{4 x} \left (1+\frac {e^3}{3}\right ) x^2+e^{4 x} \left (1+e^3\right ) x-3 e^5 x-5 e^{4 x}+e^8\right )^2}dx+3 e^{10} \left (14-9 e^3\right ) \int \frac {x^2}{\left (-3 x^3+\left (3+e^3\right ) x^2-\left (1+e^3\right ) x+5\right )^2 \left (3 e^{4 x} x^3-3 e^{4 x} \left (1+\frac {e^3}{3}\right ) x^2+e^{4 x} \left (1+e^3\right ) x-3 e^5 x-5 e^{4 x}+e^8\right )^2}dx-9 e^{10} \left (3-2 e^3\right ) \int \frac {1}{\left (-3 x^3+\left (3+e^3\right ) x^2-\left (1+e^3\right ) x+5\right ) \left (3 e^{4 x} x^3-3 e^{4 x} \left (1+\frac {e^3}{3}\right ) x^2+e^{4 x} \left (1+e^3\right ) x-3 e^5 x-5 e^{4 x}+e^8\right )^2}dx-2 e^{10} \left (27+2 e^3\right ) \int \frac {x}{\left (-3 x^3+\left (3+e^3\right ) x^2-\left (1+e^3\right ) x+5\right ) \left (3 e^{4 x} x^3-3 e^{4 x} \left (1+\frac {e^3}{3}\right ) x^2+e^{4 x} \left (1+e^3\right ) x-3 e^5 x-5 e^{4 x}+e^8\right )^2}dx+12 e^{10} \int \frac {x^2}{\left (-3 x^3+\left (3+e^3\right ) x^2-\left (1+e^3\right ) x+5\right ) \left (3 e^{4 x} x^3-3 e^{4 x} \left (1+\frac {e^3}{3}\right ) x^2+e^{4 x} \left (1+e^3\right ) x-3 e^5 x-5 e^{4 x}+e^8\right )^2}dx-10 e^5 \left (2-e^3\right ) \int \frac {1}{\left (-3 x^3+\left (3+e^3\right ) x^2-\left (1+e^3\right ) x+5\right )^2 \left (3 e^{4 x} x^3-3 e^{4 x} \left (1+\frac {e^3}{3}\right ) x^2+e^{4 x} \left (1+e^3\right ) x-3 e^5 x-5 e^{4 x}+e^8\right )}dx-8 e^5 \left (7+2 e^3\right ) \int \frac {x}{\left (-3 x^3+\left (3+e^3\right ) x^2-\left (1+e^3\right ) x+5\right )^2 \left (3 e^{4 x} x^3-3 e^{4 x} \left (1+\frac {e^3}{3}\right ) x^2+e^{4 x} \left (1+e^3\right ) x-3 e^5 x-5 e^{4 x}+e^8\right )}dx+2 e^5 \left (42-e^3\right ) \int \frac {x^2}{\left (-3 x^3+\left (3+e^3\right ) x^2-\left (1+e^3\right ) x+5\right )^2 \left (3 e^{4 x} x^3-3 e^{4 x} \left (1+\frac {e^3}{3}\right ) x^2+e^{4 x} \left (1+e^3\right ) x-3 e^5 x-5 e^{4 x}+e^8\right )}dx+4 e^5 \int \frac {x}{\left (-3 x^3+\left (3+e^3\right ) x^2-\left (1+e^3\right ) x+5\right ) \left (3 e^{4 x} x^3-3 e^{4 x} \left (1+\frac {e^3}{3}\right ) x^2+e^{4 x} \left (1+e^3\right ) x-3 e^5 x-5 e^{4 x}+e^8\right )}dx+15 e^5 \int \frac {1}{\left (3 x^3-\left (3+e^3\right ) x^2+\left (1+e^3\right ) x-5\right ) \left (3 e^{4 x} x^3-3 e^{4 x} \left (1+\frac {e^3}{3}\right ) x^2+e^{4 x} \left (1+e^3\right ) x-3 e^5 x-5 e^{4 x}+e^8\right )}dx\right )\) |
Input:
Int[(20 - 12*E^(10 - 8*x) - 40*x - 8*x^2 + 24*x^3 - 12*x^4 + E^(5 - 4*x)*( -76 - 8*x + 24*x^2))/(25 - 10*x + 31*x^2 - 36*x^3 + 15*x^4 - 18*x^5 + 9*x^ 6 + E^(10 - 8*x)*(E^6 - 6*E^3*x + 9*x^2) + E^6*(x^2 - 2*x^3 + x^4) + E^3*( -10*x + 12*x^2 - 8*x^3 + 12*x^4 - 6*x^5) + E^(5 - 4*x)*(30*x - 6*x^2 + 18* x^3 - 18*x^4 + E^6*(2*x - 2*x^2) + E^3*(-10 + 2*x - 12*x^2 + 12*x^3))),x]
Output:
$Aborted
Time = 0.84 (sec) , antiderivative size = 66, normalized size of antiderivative = 1.74
| method | result | size |
| norman | \(\frac {-4 x^{2}+4 x +4 \,{\mathrm e}^{-4 x +5}}{x^{2} {\mathrm e}^{3}-3 x^{3}-x \,{\mathrm e}^{3}-{\mathrm e}^{3} {\mathrm e}^{-4 x +5}+3 x^{2}+3 \,{\mathrm e}^{-4 x +5} x -x +5}\) | \(66\) |
| parallelrisch | \(\frac {-12 x^{2}+12 x +12 \,{\mathrm e}^{-4 x +5}}{3 x^{2} {\mathrm e}^{3}-9 x^{3}-3 x \,{\mathrm e}^{3}-3 \,{\mathrm e}^{3} {\mathrm e}^{-4 x +5}+9 x^{2}+9 \,{\mathrm e}^{-4 x +5} x -3 x +15}\) | \(67\) |
| risch | \(-\frac {4}{{\mathrm e}^{3}-3 x}-\frac {4 \left (-5+x \right )}{\left ({\mathrm e}^{3}-3 x \right ) \left (x^{2} {\mathrm e}^{3}-3 x^{3}-x \,{\mathrm e}^{3}-{\mathrm e}^{-4 x +8}+3 x^{2}+3 \,{\mathrm e}^{-4 x +5} x -x +5\right )}\) | \(70\) |
Input:
int((-12*exp(-4*x+5)^2+(24*x^2-8*x-76)*exp(-4*x+5)-12*x^4+24*x^3-8*x^2-40* x+20)/((exp(3)^2-6*x*exp(3)+9*x^2)*exp(-4*x+5)^2+((-2*x^2+2*x)*exp(3)^2+(1 2*x^3-12*x^2+2*x-10)*exp(3)-18*x^4+18*x^3-6*x^2+30*x)*exp(-4*x+5)+(x^4-2*x ^3+x^2)*exp(3)^2+(-6*x^5+12*x^4-8*x^3+12*x^2-10*x)*exp(3)+9*x^6-18*x^5+15* x^4-36*x^3+31*x^2-10*x+25),x,method=_RETURNVERBOSE)
Output:
(-4*x^2+4*x+4*exp(-4*x+5))/(x^2*exp(3)-3*x^3-x*exp(3)-exp(3)*exp(-4*x+5)+3 *x^2+3*exp(-4*x+5)*x-x+5)
Time = 0.09 (sec) , antiderivative size = 59, normalized size of antiderivative = 1.55 \[ \int \frac {20-12 e^{10-8 x}-40 x-8 x^2+24 x^3-12 x^4+e^{5-4 x} \left (-76-8 x+24 x^2\right )}{25-10 x+31 x^2-36 x^3+15 x^4-18 x^5+9 x^6+e^{10-8 x} \left (e^6-6 e^3 x+9 x^2\right )+e^6 \left (x^2-2 x^3+x^4\right )+e^3 \left (-10 x+12 x^2-8 x^3+12 x^4-6 x^5\right )+e^{5-4 x} \left (30 x-6 x^2+18 x^3-18 x^4+e^6 \left (2 x-2 x^2\right )+e^3 \left (-10+2 x-12 x^2+12 x^3\right )\right )} \, dx=\frac {4 \, {\left (x^{2} - x - e^{\left (-4 \, x + 5\right )}\right )}}{3 \, x^{3} - 3 \, x^{2} - {\left (x^{2} - x\right )} e^{3} - {\left (3 \, x - e^{3}\right )} e^{\left (-4 \, x + 5\right )} + x - 5} \] Input:
integrate((-12*exp(-4*x+5)^2+(24*x^2-8*x-76)*exp(-4*x+5)-12*x^4+24*x^3-8*x ^2-40*x+20)/((exp(3)^2-6*x*exp(3)+9*x^2)*exp(-4*x+5)^2+((-2*x^2+2*x)*exp(3 )^2+(12*x^3-12*x^2+2*x-10)*exp(3)-18*x^4+18*x^3-6*x^2+30*x)*exp(-4*x+5)+(x ^4-2*x^3+x^2)*exp(3)^2+(-6*x^5+12*x^4-8*x^3+12*x^2-10*x)*exp(3)+9*x^6-18*x ^5+15*x^4-36*x^3+31*x^2-10*x+25),x, algorithm="fricas")
Output:
4*(x^2 - x - e^(-4*x + 5))/(3*x^3 - 3*x^2 - (x^2 - x)*e^3 - (3*x - e^3)*e^ (-4*x + 5) + x - 5)
Leaf count of result is larger than twice the leaf count of optimal. 94 vs. \(2 (22) = 44\).
Time = 0.33 (sec) , antiderivative size = 94, normalized size of antiderivative = 2.47 \[ \int \frac {20-12 e^{10-8 x}-40 x-8 x^2+24 x^3-12 x^4+e^{5-4 x} \left (-76-8 x+24 x^2\right )}{25-10 x+31 x^2-36 x^3+15 x^4-18 x^5+9 x^6+e^{10-8 x} \left (e^6-6 e^3 x+9 x^2\right )+e^6 \left (x^2-2 x^3+x^4\right )+e^3 \left (-10 x+12 x^2-8 x^3+12 x^4-6 x^5\right )+e^{5-4 x} \left (30 x-6 x^2+18 x^3-18 x^4+e^6 \left (2 x-2 x^2\right )+e^3 \left (-10+2 x-12 x^2+12 x^3\right )\right )} \, dx=\frac {4 x - 20}{- 9 x^{4} + 9 x^{3} + 6 x^{3} e^{3} - x^{2} e^{6} - 6 x^{2} e^{3} - 3 x^{2} + 15 x + x e^{3} + x e^{6} + \left (9 x^{2} - 6 x e^{3} + e^{6}\right ) e^{5 - 4 x} - 5 e^{3}} + \frac {12}{9 x - 3 e^{3}} \] Input:
integrate((-12*exp(-4*x+5)**2+(24*x**2-8*x-76)*exp(-4*x+5)-12*x**4+24*x**3 -8*x**2-40*x+20)/((exp(3)**2-6*x*exp(3)+9*x**2)*exp(-4*x+5)**2+((-2*x**2+2 *x)*exp(3)**2+(12*x**3-12*x**2+2*x-10)*exp(3)-18*x**4+18*x**3-6*x**2+30*x) *exp(-4*x+5)+(x**4-2*x**3+x**2)*exp(3)**2+(-6*x**5+12*x**4-8*x**3+12*x**2- 10*x)*exp(3)+9*x**6-18*x**5+15*x**4-36*x**3+31*x**2-10*x+25),x)
Output:
(4*x - 20)/(-9*x**4 + 9*x**3 + 6*x**3*exp(3) - x**2*exp(6) - 6*x**2*exp(3) - 3*x**2 + 15*x + x*exp(3) + x*exp(6) + (9*x**2 - 6*x*exp(3) + exp(6))*ex p(5 - 4*x) - 5*exp(3)) + 12/(9*x - 3*exp(3))
Time = 0.30 (sec) , antiderivative size = 59, normalized size of antiderivative = 1.55 \[ \int \frac {20-12 e^{10-8 x}-40 x-8 x^2+24 x^3-12 x^4+e^{5-4 x} \left (-76-8 x+24 x^2\right )}{25-10 x+31 x^2-36 x^3+15 x^4-18 x^5+9 x^6+e^{10-8 x} \left (e^6-6 e^3 x+9 x^2\right )+e^6 \left (x^2-2 x^3+x^4\right )+e^3 \left (-10 x+12 x^2-8 x^3+12 x^4-6 x^5\right )+e^{5-4 x} \left (30 x-6 x^2+18 x^3-18 x^4+e^6 \left (2 x-2 x^2\right )+e^3 \left (-10+2 x-12 x^2+12 x^3\right )\right )} \, dx=-\frac {4 \, {\left ({\left (x^{2} - x\right )} e^{\left (4 \, x\right )} - e^{5}\right )}}{3 \, x e^{5} - {\left (3 \, x^{3} - x^{2} {\left (e^{3} + 3\right )} + x {\left (e^{3} + 1\right )} - 5\right )} e^{\left (4 \, x\right )} - e^{8}} \] Input:
integrate((-12*exp(-4*x+5)^2+(24*x^2-8*x-76)*exp(-4*x+5)-12*x^4+24*x^3-8*x ^2-40*x+20)/((exp(3)^2-6*x*exp(3)+9*x^2)*exp(-4*x+5)^2+((-2*x^2+2*x)*exp(3 )^2+(12*x^3-12*x^2+2*x-10)*exp(3)-18*x^4+18*x^3-6*x^2+30*x)*exp(-4*x+5)+(x ^4-2*x^3+x^2)*exp(3)^2+(-6*x^5+12*x^4-8*x^3+12*x^2-10*x)*exp(3)+9*x^6-18*x ^5+15*x^4-36*x^3+31*x^2-10*x+25),x, algorithm="maxima")
Output:
-4*((x^2 - x)*e^(4*x) - e^5)/(3*x*e^5 - (3*x^3 - x^2*(e^3 + 3) + x*(e^3 + 1) - 5)*e^(4*x) - e^8)
Leaf count of result is larger than twice the leaf count of optimal. 100 vs. \(2 (33) = 66\).
Time = 0.22 (sec) , antiderivative size = 100, normalized size of antiderivative = 2.63 \[ \int \frac {20-12 e^{10-8 x}-40 x-8 x^2+24 x^3-12 x^4+e^{5-4 x} \left (-76-8 x+24 x^2\right )}{25-10 x+31 x^2-36 x^3+15 x^4-18 x^5+9 x^6+e^{10-8 x} \left (e^6-6 e^3 x+9 x^2\right )+e^6 \left (x^2-2 x^3+x^4\right )+e^3 \left (-10 x+12 x^2-8 x^3+12 x^4-6 x^5\right )+e^{5-4 x} \left (30 x-6 x^2+18 x^3-18 x^4+e^6 \left (2 x-2 x^2\right )+e^3 \left (-10+2 x-12 x^2+12 x^3\right )\right )} \, dx=\frac {16 \, {\left ({\left (4 \, x - 5\right )}^{2} + 24 \, x - 16 \, e^{\left (-4 \, x + 5\right )} - 25\right )}}{3 \, {\left (4 \, x - 5\right )}^{3} - 4 \, {\left (4 \, x - 5\right )}^{2} e^{3} + 33 \, {\left (4 \, x - 5\right )}^{2} - 24 \, {\left (4 \, x - 5\right )} e^{3} - 48 \, {\left (4 \, x - 5\right )} e^{\left (-4 \, x + 5\right )} + 484 \, x - 20 \, e^{3} + 64 \, e^{\left (-4 \, x + 8\right )} - 240 \, e^{\left (-4 \, x + 5\right )} - 770} \] Input:
integrate((-12*exp(-4*x+5)^2+(24*x^2-8*x-76)*exp(-4*x+5)-12*x^4+24*x^3-8*x ^2-40*x+20)/((exp(3)^2-6*x*exp(3)+9*x^2)*exp(-4*x+5)^2+((-2*x^2+2*x)*exp(3 )^2+(12*x^3-12*x^2+2*x-10)*exp(3)-18*x^4+18*x^3-6*x^2+30*x)*exp(-4*x+5)+(x ^4-2*x^3+x^2)*exp(3)^2+(-6*x^5+12*x^4-8*x^3+12*x^2-10*x)*exp(3)+9*x^6-18*x ^5+15*x^4-36*x^3+31*x^2-10*x+25),x, algorithm="giac")
Output:
16*((4*x - 5)^2 + 24*x - 16*e^(-4*x + 5) - 25)/(3*(4*x - 5)^3 - 4*(4*x - 5 )^2*e^3 + 33*(4*x - 5)^2 - 24*(4*x - 5)*e^3 - 48*(4*x - 5)*e^(-4*x + 5) + 484*x - 20*e^3 + 64*e^(-4*x + 8) - 240*e^(-4*x + 5) - 770)
Timed out. \[ \int \frac {20-12 e^{10-8 x}-40 x-8 x^2+24 x^3-12 x^4+e^{5-4 x} \left (-76-8 x+24 x^2\right )}{25-10 x+31 x^2-36 x^3+15 x^4-18 x^5+9 x^6+e^{10-8 x} \left (e^6-6 e^3 x+9 x^2\right )+e^6 \left (x^2-2 x^3+x^4\right )+e^3 \left (-10 x+12 x^2-8 x^3+12 x^4-6 x^5\right )+e^{5-4 x} \left (30 x-6 x^2+18 x^3-18 x^4+e^6 \left (2 x-2 x^2\right )+e^3 \left (-10+2 x-12 x^2+12 x^3\right )\right )} \, dx=\int -\frac {40\,x+12\,{\mathrm {e}}^{10-8\,x}+{\mathrm {e}}^{5-4\,x}\,\left (-24\,x^2+8\,x+76\right )+8\,x^2-24\,x^3+12\,x^4-20}{{\mathrm {e}}^6\,\left (x^4-2\,x^3+x^2\right )-10\,x+{\mathrm {e}}^{10-8\,x}\,\left (9\,x^2-6\,{\mathrm {e}}^3\,x+{\mathrm {e}}^6\right )+{\mathrm {e}}^{5-4\,x}\,\left (30\,x+{\mathrm {e}}^6\,\left (2\,x-2\,x^2\right )+{\mathrm {e}}^3\,\left (12\,x^3-12\,x^2+2\,x-10\right )-6\,x^2+18\,x^3-18\,x^4\right )-{\mathrm {e}}^3\,\left (6\,x^5-12\,x^4+8\,x^3-12\,x^2+10\,x\right )+31\,x^2-36\,x^3+15\,x^4-18\,x^5+9\,x^6+25} \,d x \] Input:
int(-(40*x + 12*exp(10 - 8*x) + exp(5 - 4*x)*(8*x - 24*x^2 + 76) + 8*x^2 - 24*x^3 + 12*x^4 - 20)/(exp(6)*(x^2 - 2*x^3 + x^4) - 10*x + exp(10 - 8*x)* (exp(6) - 6*x*exp(3) + 9*x^2) + exp(5 - 4*x)*(30*x + exp(6)*(2*x - 2*x^2) + exp(3)*(2*x - 12*x^2 + 12*x^3 - 10) - 6*x^2 + 18*x^3 - 18*x^4) - exp(3)* (10*x - 12*x^2 + 8*x^3 - 12*x^4 + 6*x^5) + 31*x^2 - 36*x^3 + 15*x^4 - 18*x ^5 + 9*x^6 + 25),x)
Output:
int(-(40*x + 12*exp(10 - 8*x) + exp(5 - 4*x)*(8*x - 24*x^2 + 76) + 8*x^2 - 24*x^3 + 12*x^4 - 20)/(exp(6)*(x^2 - 2*x^3 + x^4) - 10*x + exp(10 - 8*x)* (exp(6) - 6*x*exp(3) + 9*x^2) + exp(5 - 4*x)*(30*x + exp(6)*(2*x - 2*x^2) + exp(3)*(2*x - 12*x^2 + 12*x^3 - 10) - 6*x^2 + 18*x^3 - 18*x^4) - exp(3)* (10*x - 12*x^2 + 8*x^3 - 12*x^4 + 6*x^5) + 31*x^2 - 36*x^3 + 15*x^4 - 18*x ^5 + 9*x^6 + 25), x)
Time = 1.74 (sec) , antiderivative size = 95, normalized size of antiderivative = 2.50 \[ \int \frac {20-12 e^{10-8 x}-40 x-8 x^2+24 x^3-12 x^4+e^{5-4 x} \left (-76-8 x+24 x^2\right )}{25-10 x+31 x^2-36 x^3+15 x^4-18 x^5+9 x^6+e^{10-8 x} \left (e^6-6 e^3 x+9 x^2\right )+e^6 \left (x^2-2 x^3+x^4\right )+e^3 \left (-10 x+12 x^2-8 x^3+12 x^4-6 x^5\right )+e^{5-4 x} \left (30 x-6 x^2+18 x^3-18 x^4+e^6 \left (2 x-2 x^2\right )+e^3 \left (-10+2 x-12 x^2+12 x^3\right )\right )} \, dx=\frac {-4 e^{4 x} x^{2}+4 e^{4 x} x +4 e^{5}}{e^{4 x} e^{3} x^{2}-e^{4 x} e^{3} x -3 e^{4 x} x^{3}+3 e^{4 x} x^{2}-e^{4 x} x +5 e^{4 x}-e^{8}+3 e^{5} x} \] Input:
int((-12*exp(-4*x+5)^2+(24*x^2-8*x-76)*exp(-4*x+5)-12*x^4+24*x^3-8*x^2-40* x+20)/((exp(3)^2-6*x*exp(3)+9*x^2)*exp(-4*x+5)^2+((-2*x^2+2*x)*exp(3)^2+(1 2*x^3-12*x^2+2*x-10)*exp(3)-18*x^4+18*x^3-6*x^2+30*x)*exp(-4*x+5)+(x^4-2*x ^3+x^2)*exp(3)^2+(-6*x^5+12*x^4-8*x^3+12*x^2-10*x)*exp(3)+9*x^6-18*x^5+15* x^4-36*x^3+31*x^2-10*x+25),x)
Output:
(4*( - e**(4*x)*x**2 + e**(4*x)*x + e**5))/(e**(4*x)*e**3*x**2 - e**(4*x)* e**3*x - 3*e**(4*x)*x**3 + 3*e**(4*x)*x**2 - e**(4*x)*x + 5*e**(4*x) - e** 8 + 3*e**5*x)