Integrand size = 197, antiderivative size = 30 \[ \int e^{-3+25 e^{5 x} x^2-100 e^{4 x} x^3+e^{3 x} \left (200 x^2+150 x^4\right )+e^{2 x} \left (-400 x^3-100 x^5\right )+e^x \left (400 x^2+200 x^4+25 x^6\right )} \left (e^{5 x} \left (50 x+125 x^2\right )+e^{4 x} \left (-300 x^2-400 x^3\right )+e^{3 x} \left (400 x+600 x^2+600 x^3+450 x^4\right )+e^{2 x} \left (-1200 x^2-800 x^3-500 x^4-200 x^5\right )+e^x \left (800 x+400 x^2+800 x^3+200 x^4+150 x^5+25 x^6\right )\right ) \, dx=e^{-3-x+x \left (1+25 e^x x \left (4+\left (-e^x+x\right )^2\right )^2\right )} \] Output:
exp(x*(5*(4+(x-exp(x))^2)*(20+5*(x-exp(x))^2)*exp(x)*x+1)-3-x)
Leaf count is larger than twice the leaf count of optimal. \(71\) vs. \(2(30)=60\).
Time = 0.10 (sec) , antiderivative size = 71, normalized size of antiderivative = 2.37 \[ \int e^{-3+25 e^{5 x} x^2-100 e^{4 x} x^3+e^{3 x} \left (200 x^2+150 x^4\right )+e^{2 x} \left (-400 x^3-100 x^5\right )+e^x \left (400 x^2+200 x^4+25 x^6\right )} \left (e^{5 x} \left (50 x+125 x^2\right )+e^{4 x} \left (-300 x^2-400 x^3\right )+e^{3 x} \left (400 x+600 x^2+600 x^3+450 x^4\right )+e^{2 x} \left (-1200 x^2-800 x^3-500 x^4-200 x^5\right )+e^x \left (800 x+400 x^2+800 x^3+200 x^4+150 x^5+25 x^6\right )\right ) \, dx=e^{-3+25 e^{5 x} x^2-100 e^{4 x} x^3-100 e^{2 x} x^3 \left (4+x^2\right )+25 e^x x^2 \left (4+x^2\right )^2+50 e^{3 x} x^2 \left (4+3 x^2\right )} \] Input:
Integrate[E^(-3 + 25*E^(5*x)*x^2 - 100*E^(4*x)*x^3 + E^(3*x)*(200*x^2 + 15 0*x^4) + E^(2*x)*(-400*x^3 - 100*x^5) + E^x*(400*x^2 + 200*x^4 + 25*x^6))* (E^(5*x)*(50*x + 125*x^2) + E^(4*x)*(-300*x^2 - 400*x^3) + E^(3*x)*(400*x + 600*x^2 + 600*x^3 + 450*x^4) + E^(2*x)*(-1200*x^2 - 800*x^3 - 500*x^4 - 200*x^5) + E^x*(800*x + 400*x^2 + 800*x^3 + 200*x^4 + 150*x^5 + 25*x^6)),x ]
Output:
E^(-3 + 25*E^(5*x)*x^2 - 100*E^(4*x)*x^3 - 100*E^(2*x)*x^3*(4 + x^2) + 25* E^x*x^2*(4 + x^2)^2 + 50*E^(3*x)*x^2*(4 + 3*x^2))
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.
| \(\displaystyle \int \left (e^{5 x} \left (125 x^2+50 x\right )+e^{4 x} \left (-400 x^3-300 x^2\right )+e^{3 x} \left (450 x^4+600 x^3+600 x^2+400 x\right )+e^{2 x} \left (-200 x^5-500 x^4-800 x^3-1200 x^2\right )+e^x \left (25 x^6+150 x^5+200 x^4+800 x^3+400 x^2+800 x\right )\right ) \exp \left (-100 e^{4 x} x^3+25 e^{5 x} x^2+e^{2 x} \left (-100 x^5-400 x^3\right )+e^{3 x} \left (150 x^4+200 x^2\right )+e^x \left (25 x^6+200 x^4+400 x^2\right )-3\right ) \, dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-100 (4 x+3) x^2 \exp \left (-100 e^{4 x} x^3+25 e^{5 x} x^2+e^{2 x} \left (-100 x^5-400 x^3\right )+e^{3 x} \left (150 x^4+200 x^2\right )+e^x \left (25 x^6+200 x^4+400 x^2\right )+4 x-3\right )-100 \left (2 x^3+5 x^2+8 x+12\right ) x^2 \exp \left (-100 e^{4 x} x^3+25 e^{5 x} x^2+e^{2 x} \left (-100 x^5-400 x^3\right )+e^{3 x} \left (150 x^4+200 x^2\right )+e^x \left (25 x^6+200 x^4+400 x^2\right )+2 x-3\right )+25 (5 x+2) x \exp \left (-100 e^{4 x} x^3+25 e^{5 x} x^2+e^{2 x} \left (-100 x^5-400 x^3\right )+e^{3 x} \left (150 x^4+200 x^2\right )+e^x \left (25 x^6+200 x^4+400 x^2\right )+5 x-3\right )+50 \left (9 x^3+12 x^2+12 x+8\right ) x \exp \left (-100 e^{4 x} x^3+25 e^{5 x} x^2+e^{2 x} \left (-100 x^5-400 x^3\right )+e^{3 x} \left (150 x^4+200 x^2\right )+e^x \left (25 x^6+200 x^4+400 x^2\right )+3 x-3\right )+25 \left (x^5+6 x^4+8 x^3+32 x^2+16 x+32\right ) x \exp \left (-100 e^{4 x} x^3+25 e^{5 x} x^2+e^{2 x} \left (-100 x^5-400 x^3\right )+e^{3 x} \left (150 x^4+200 x^2\right )+e^x \left (25 x^6+200 x^4+400 x^2\right )+x-3\right )\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int 25 x \left (x^5+6 x^4+8 x^3+32 x^2-4 e^x \left (2 x^3+5 x^2+8 x+12\right ) x+2 e^{2 x} \left (9 x^3+12 x^2+12 x+8\right )-4 e^{3 x} (4 x+3) x+16 x+e^{4 x} (5 x+2)+32\right ) \exp \left (-100 e^{4 x} x^3+25 e^{5 x} x^2+25 e^x \left (x^2+4\right )^2 x^2+50 e^{3 x} \left (3 x^2+4\right ) x^2-100 e^{2 x} \left (x^2+4\right ) x^3+x-3\right )dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle 25 \int \exp \left (-100 e^{4 x} x^3-100 e^{2 x} \left (x^2+4\right ) x^3+25 e^{5 x} x^2+25 e^x \left (x^2+4\right )^2 x^2+50 e^{3 x} \left (3 x^2+4\right ) x^2+x-3\right ) x \left (x^5+6 x^4+8 x^3+32 x^2-4 e^{3 x} (4 x+3) x-4 e^x \left (2 x^3+5 x^2+8 x+12\right ) x+16 x+e^{4 x} (5 x+2)+2 e^{2 x} \left (9 x^3+12 x^2+12 x+8\right )+32\right )dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 25 \int \left (-4 \exp \left (-100 e^{4 x} x^3-100 e^{2 x} \left (x^2+4\right ) x^3+25 e^{5 x} x^2+25 e^x \left (x^2+4\right )^2 x^2+50 e^{3 x} \left (3 x^2+4\right ) x^2+4 x-3\right ) (4 x+3) x^2-4 \exp \left (-100 e^{4 x} x^3-100 e^{2 x} \left (x^2+4\right ) x^3+25 e^{5 x} x^2+25 e^x \left (x^2+4\right )^2 x^2+50 e^{3 x} \left (3 x^2+4\right ) x^2+2 x-3\right ) (x+2) \left (2 x^2+x+6\right ) x^2+\exp \left (-100 e^{4 x} x^3-100 e^{2 x} \left (x^2+4\right ) x^3+25 e^{5 x} x^2+25 e^x \left (x^2+4\right )^2 x^2+50 e^{3 x} \left (3 x^2+4\right ) x^2+5 x-3\right ) (5 x+2) x+2 \exp \left (-100 e^{4 x} x^3-100 e^{2 x} \left (x^2+4\right ) x^3+25 e^{5 x} x^2+25 e^x \left (x^2+4\right )^2 x^2+50 e^{3 x} \left (3 x^2+4\right ) x^2+3 x-3\right ) \left (9 x^3+12 x^2+12 x+8\right ) x+\exp \left (-100 e^{4 x} x^3-100 e^{2 x} \left (x^2+4\right ) x^3+25 e^{5 x} x^2+25 e^x \left (x^2+4\right )^2 x^2+50 e^{3 x} \left (3 x^2+4\right ) x^2+x-3\right ) \left (x^5+6 x^4+8 x^3+32 x^2+16 x+32\right ) x\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 25 \int \exp \left (-100 e^{4 x} x^3-100 e^{2 x} \left (x^2+4\right ) x^3+25 e^{5 x} x^2+25 e^x \left (x^2+4\right )^2 x^2+50 e^{3 x} \left (3 x^2+4\right ) x^2+x-3\right ) x \left (x^5+6 x^4+8 x^3+32 x^2-4 e^{3 x} (4 x+3) x-4 e^x (x+2) \left (2 x^2+x+6\right ) x+16 x+e^{4 x} (5 x+2)+2 e^{2 x} \left (9 x^3+12 x^2+12 x+8\right )+32\right )dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 25 \int \left (-4 \exp \left (-100 e^{4 x} x^3-100 e^{2 x} \left (x^2+4\right ) x^3+25 e^{5 x} x^2+25 e^x \left (x^2+4\right )^2 x^2+50 e^{3 x} \left (3 x^2+4\right ) x^2+4 x-3\right ) (4 x+3) x^2-4 \exp \left (-100 e^{4 x} x^3-100 e^{2 x} \left (x^2+4\right ) x^3+25 e^{5 x} x^2+25 e^x \left (x^2+4\right )^2 x^2+50 e^{3 x} \left (3 x^2+4\right ) x^2+2 x-3\right ) (x+2) \left (2 x^2+x+6\right ) x^2+\exp \left (-100 e^{4 x} x^3-100 e^{2 x} \left (x^2+4\right ) x^3+25 e^{5 x} x^2+25 e^x \left (x^2+4\right )^2 x^2+50 e^{3 x} \left (3 x^2+4\right ) x^2+5 x-3\right ) (5 x+2) x+2 \exp \left (-100 e^{4 x} x^3-100 e^{2 x} \left (x^2+4\right ) x^3+25 e^{5 x} x^2+25 e^x \left (x^2+4\right )^2 x^2+50 e^{3 x} \left (3 x^2+4\right ) x^2+3 x-3\right ) \left (9 x^3+12 x^2+12 x+8\right ) x+\exp \left (-100 e^{4 x} x^3-100 e^{2 x} \left (x^2+4\right ) x^3+25 e^{5 x} x^2+25 e^x \left (x^2+4\right )^2 x^2+50 e^{3 x} \left (3 x^2+4\right ) x^2+x-3\right ) \left (x^5+6 x^4+8 x^3+32 x^2+16 x+32\right ) x\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 25 \int \exp \left (-100 e^{4 x} x^3-100 e^{2 x} \left (x^2+4\right ) x^3+25 e^{5 x} x^2+25 e^x \left (x^2+4\right )^2 x^2+50 e^{3 x} \left (3 x^2+4\right ) x^2+x-3\right ) x \left (x^5+6 x^4+8 x^3+32 x^2-4 e^{3 x} (4 x+3) x-4 e^x (x+2) \left (2 x^2+x+6\right ) x+16 x+e^{4 x} (5 x+2)+2 e^{2 x} \left (9 x^3+12 x^2+12 x+8\right )+32\right )dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 25 \int \left (-4 \exp \left (-100 e^{4 x} x^3-100 e^{2 x} \left (x^2+4\right ) x^3+25 e^{5 x} x^2+25 e^x \left (x^2+4\right )^2 x^2+50 e^{3 x} \left (3 x^2+4\right ) x^2+4 x-3\right ) (4 x+3) x^2-4 \exp \left (-100 e^{4 x} x^3-100 e^{2 x} \left (x^2+4\right ) x^3+25 e^{5 x} x^2+25 e^x \left (x^2+4\right )^2 x^2+50 e^{3 x} \left (3 x^2+4\right ) x^2+2 x-3\right ) (x+2) \left (2 x^2+x+6\right ) x^2+\exp \left (-100 e^{4 x} x^3-100 e^{2 x} \left (x^2+4\right ) x^3+25 e^{5 x} x^2+25 e^x \left (x^2+4\right )^2 x^2+50 e^{3 x} \left (3 x^2+4\right ) x^2+5 x-3\right ) (5 x+2) x+2 \exp \left (-100 e^{4 x} x^3-100 e^{2 x} \left (x^2+4\right ) x^3+25 e^{5 x} x^2+25 e^x \left (x^2+4\right )^2 x^2+50 e^{3 x} \left (3 x^2+4\right ) x^2+3 x-3\right ) \left (9 x^3+12 x^2+12 x+8\right ) x+\exp \left (-100 e^{4 x} x^3-100 e^{2 x} \left (x^2+4\right ) x^3+25 e^{5 x} x^2+25 e^x \left (x^2+4\right )^2 x^2+50 e^{3 x} \left (3 x^2+4\right ) x^2+x-3\right ) \left (x^5+6 x^4+8 x^3+32 x^2+16 x+32\right ) x\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 25 \int \exp \left (-100 e^{4 x} x^3-100 e^{2 x} \left (x^2+4\right ) x^3+25 e^{5 x} x^2+25 e^x \left (x^2+4\right )^2 x^2+50 e^{3 x} \left (3 x^2+4\right ) x^2+x-3\right ) x \left (x^5+6 x^4+8 x^3+32 x^2-4 e^{3 x} (4 x+3) x-4 e^x (x+2) \left (2 x^2+x+6\right ) x+16 x+e^{4 x} (5 x+2)+2 e^{2 x} \left (9 x^3+12 x^2+12 x+8\right )+32\right )dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 25 \int \left (-4 \exp \left (-100 e^{4 x} x^3-100 e^{2 x} \left (x^2+4\right ) x^3+25 e^{5 x} x^2+25 e^x \left (x^2+4\right )^2 x^2+50 e^{3 x} \left (3 x^2+4\right ) x^2+4 x-3\right ) (4 x+3) x^2-4 \exp \left (-100 e^{4 x} x^3-100 e^{2 x} \left (x^2+4\right ) x^3+25 e^{5 x} x^2+25 e^x \left (x^2+4\right )^2 x^2+50 e^{3 x} \left (3 x^2+4\right ) x^2+2 x-3\right ) (x+2) \left (2 x^2+x+6\right ) x^2+\exp \left (-100 e^{4 x} x^3-100 e^{2 x} \left (x^2+4\right ) x^3+25 e^{5 x} x^2+25 e^x \left (x^2+4\right )^2 x^2+50 e^{3 x} \left (3 x^2+4\right ) x^2+5 x-3\right ) (5 x+2) x+2 \exp \left (-100 e^{4 x} x^3-100 e^{2 x} \left (x^2+4\right ) x^3+25 e^{5 x} x^2+25 e^x \left (x^2+4\right )^2 x^2+50 e^{3 x} \left (3 x^2+4\right ) x^2+3 x-3\right ) \left (9 x^3+12 x^2+12 x+8\right ) x+\exp \left (-100 e^{4 x} x^3-100 e^{2 x} \left (x^2+4\right ) x^3+25 e^{5 x} x^2+25 e^x \left (x^2+4\right )^2 x^2+50 e^{3 x} \left (3 x^2+4\right ) x^2+x-3\right ) \left (x^5+6 x^4+8 x^3+32 x^2+16 x+32\right ) x\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 25 \int \exp \left (-100 e^{4 x} x^3-100 e^{2 x} \left (x^2+4\right ) x^3+25 e^{5 x} x^2+25 e^x \left (x^2+4\right )^2 x^2+50 e^{3 x} \left (3 x^2+4\right ) x^2+x-3\right ) x \left (x^5+6 x^4+8 x^3+32 x^2-4 e^{3 x} (4 x+3) x-4 e^x (x+2) \left (2 x^2+x+6\right ) x+16 x+e^{4 x} (5 x+2)+2 e^{2 x} \left (9 x^3+12 x^2+12 x+8\right )+32\right )dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 25 \int \left (-4 \exp \left (-100 e^{4 x} x^3-100 e^{2 x} \left (x^2+4\right ) x^3+25 e^{5 x} x^2+25 e^x \left (x^2+4\right )^2 x^2+50 e^{3 x} \left (3 x^2+4\right ) x^2+4 x-3\right ) (4 x+3) x^2-4 \exp \left (-100 e^{4 x} x^3-100 e^{2 x} \left (x^2+4\right ) x^3+25 e^{5 x} x^2+25 e^x \left (x^2+4\right )^2 x^2+50 e^{3 x} \left (3 x^2+4\right ) x^2+2 x-3\right ) (x+2) \left (2 x^2+x+6\right ) x^2+\exp \left (-100 e^{4 x} x^3-100 e^{2 x} \left (x^2+4\right ) x^3+25 e^{5 x} x^2+25 e^x \left (x^2+4\right )^2 x^2+50 e^{3 x} \left (3 x^2+4\right ) x^2+5 x-3\right ) (5 x+2) x+2 \exp \left (-100 e^{4 x} x^3-100 e^{2 x} \left (x^2+4\right ) x^3+25 e^{5 x} x^2+25 e^x \left (x^2+4\right )^2 x^2+50 e^{3 x} \left (3 x^2+4\right ) x^2+3 x-3\right ) \left (9 x^3+12 x^2+12 x+8\right ) x+\exp \left (-100 e^{4 x} x^3-100 e^{2 x} \left (x^2+4\right ) x^3+25 e^{5 x} x^2+25 e^x \left (x^2+4\right )^2 x^2+50 e^{3 x} \left (3 x^2+4\right ) x^2+x-3\right ) \left (x^5+6 x^4+8 x^3+32 x^2+16 x+32\right ) x\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 25 \int \exp \left (-100 e^{4 x} x^3-100 e^{2 x} \left (x^2+4\right ) x^3+25 e^{5 x} x^2+25 e^x \left (x^2+4\right )^2 x^2+50 e^{3 x} \left (3 x^2+4\right ) x^2+x-3\right ) x \left (x^5+6 x^4+8 x^3+32 x^2-4 e^{3 x} (4 x+3) x-4 e^x (x+2) \left (2 x^2+x+6\right ) x+16 x+e^{4 x} (5 x+2)+2 e^{2 x} \left (9 x^3+12 x^2+12 x+8\right )+32\right )dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 25 \int \left (-4 \exp \left (-100 e^{4 x} x^3-100 e^{2 x} \left (x^2+4\right ) x^3+25 e^{5 x} x^2+25 e^x \left (x^2+4\right )^2 x^2+50 e^{3 x} \left (3 x^2+4\right ) x^2+4 x-3\right ) (4 x+3) x^2-4 \exp \left (-100 e^{4 x} x^3-100 e^{2 x} \left (x^2+4\right ) x^3+25 e^{5 x} x^2+25 e^x \left (x^2+4\right )^2 x^2+50 e^{3 x} \left (3 x^2+4\right ) x^2+2 x-3\right ) (x+2) \left (2 x^2+x+6\right ) x^2+\exp \left (-100 e^{4 x} x^3-100 e^{2 x} \left (x^2+4\right ) x^3+25 e^{5 x} x^2+25 e^x \left (x^2+4\right )^2 x^2+50 e^{3 x} \left (3 x^2+4\right ) x^2+5 x-3\right ) (5 x+2) x+2 \exp \left (-100 e^{4 x} x^3-100 e^{2 x} \left (x^2+4\right ) x^3+25 e^{5 x} x^2+25 e^x \left (x^2+4\right )^2 x^2+50 e^{3 x} \left (3 x^2+4\right ) x^2+3 x-3\right ) \left (9 x^3+12 x^2+12 x+8\right ) x+\exp \left (-100 e^{4 x} x^3-100 e^{2 x} \left (x^2+4\right ) x^3+25 e^{5 x} x^2+25 e^x \left (x^2+4\right )^2 x^2+50 e^{3 x} \left (3 x^2+4\right ) x^2+x-3\right ) \left (x^5+6 x^4+8 x^3+32 x^2+16 x+32\right ) x\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 25 \int \exp \left (-100 e^{4 x} x^3-100 e^{2 x} \left (x^2+4\right ) x^3+25 e^{5 x} x^2+25 e^x \left (x^2+4\right )^2 x^2+50 e^{3 x} \left (3 x^2+4\right ) x^2+x-3\right ) x \left (x^5+6 x^4+8 x^3+32 x^2-4 e^{3 x} (4 x+3) x-4 e^x (x+2) \left (2 x^2+x+6\right ) x+16 x+e^{4 x} (5 x+2)+2 e^{2 x} \left (9 x^3+12 x^2+12 x+8\right )+32\right )dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 25 \int \left (-4 \exp \left (-100 e^{4 x} x^3-100 e^{2 x} \left (x^2+4\right ) x^3+25 e^{5 x} x^2+25 e^x \left (x^2+4\right )^2 x^2+50 e^{3 x} \left (3 x^2+4\right ) x^2+4 x-3\right ) (4 x+3) x^2-4 \exp \left (-100 e^{4 x} x^3-100 e^{2 x} \left (x^2+4\right ) x^3+25 e^{5 x} x^2+25 e^x \left (x^2+4\right )^2 x^2+50 e^{3 x} \left (3 x^2+4\right ) x^2+2 x-3\right ) (x+2) \left (2 x^2+x+6\right ) x^2+\exp \left (-100 e^{4 x} x^3-100 e^{2 x} \left (x^2+4\right ) x^3+25 e^{5 x} x^2+25 e^x \left (x^2+4\right )^2 x^2+50 e^{3 x} \left (3 x^2+4\right ) x^2+5 x-3\right ) (5 x+2) x+2 \exp \left (-100 e^{4 x} x^3-100 e^{2 x} \left (x^2+4\right ) x^3+25 e^{5 x} x^2+25 e^x \left (x^2+4\right )^2 x^2+50 e^{3 x} \left (3 x^2+4\right ) x^2+3 x-3\right ) \left (9 x^3+12 x^2+12 x+8\right ) x+\exp \left (-100 e^{4 x} x^3-100 e^{2 x} \left (x^2+4\right ) x^3+25 e^{5 x} x^2+25 e^x \left (x^2+4\right )^2 x^2+50 e^{3 x} \left (3 x^2+4\right ) x^2+x-3\right ) \left (x^5+6 x^4+8 x^3+32 x^2+16 x+32\right ) x\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 25 \int \exp \left (-100 e^{4 x} x^3-100 e^{2 x} \left (x^2+4\right ) x^3+25 e^{5 x} x^2+25 e^x \left (x^2+4\right )^2 x^2+50 e^{3 x} \left (3 x^2+4\right ) x^2+x-3\right ) x \left (x^5+6 x^4+8 x^3+32 x^2-4 e^{3 x} (4 x+3) x-4 e^x (x+2) \left (2 x^2+x+6\right ) x+16 x+e^{4 x} (5 x+2)+2 e^{2 x} \left (9 x^3+12 x^2+12 x+8\right )+32\right )dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 25 \int \left (-4 \exp \left (-100 e^{4 x} x^3-100 e^{2 x} \left (x^2+4\right ) x^3+25 e^{5 x} x^2+25 e^x \left (x^2+4\right )^2 x^2+50 e^{3 x} \left (3 x^2+4\right ) x^2+4 x-3\right ) (4 x+3) x^2-4 \exp \left (-100 e^{4 x} x^3-100 e^{2 x} \left (x^2+4\right ) x^3+25 e^{5 x} x^2+25 e^x \left (x^2+4\right )^2 x^2+50 e^{3 x} \left (3 x^2+4\right ) x^2+2 x-3\right ) (x+2) \left (2 x^2+x+6\right ) x^2+\exp \left (-100 e^{4 x} x^3-100 e^{2 x} \left (x^2+4\right ) x^3+25 e^{5 x} x^2+25 e^x \left (x^2+4\right )^2 x^2+50 e^{3 x} \left (3 x^2+4\right ) x^2+5 x-3\right ) (5 x+2) x+2 \exp \left (-100 e^{4 x} x^3-100 e^{2 x} \left (x^2+4\right ) x^3+25 e^{5 x} x^2+25 e^x \left (x^2+4\right )^2 x^2+50 e^{3 x} \left (3 x^2+4\right ) x^2+3 x-3\right ) \left (9 x^3+12 x^2+12 x+8\right ) x+\exp \left (-100 e^{4 x} x^3-100 e^{2 x} \left (x^2+4\right ) x^3+25 e^{5 x} x^2+25 e^x \left (x^2+4\right )^2 x^2+50 e^{3 x} \left (3 x^2+4\right ) x^2+x-3\right ) \left (x^5+6 x^4+8 x^3+32 x^2+16 x+32\right ) x\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 25 \int \exp \left (-100 e^{4 x} x^3-100 e^{2 x} \left (x^2+4\right ) x^3+25 e^{5 x} x^2+25 e^x \left (x^2+4\right )^2 x^2+50 e^{3 x} \left (3 x^2+4\right ) x^2+x-3\right ) x \left (x^5+6 x^4+8 x^3+32 x^2-4 e^{3 x} (4 x+3) x-4 e^x (x+2) \left (2 x^2+x+6\right ) x+16 x+e^{4 x} (5 x+2)+2 e^{2 x} \left (9 x^3+12 x^2+12 x+8\right )+32\right )dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 25 \int \left (-4 \exp \left (-100 e^{4 x} x^3-100 e^{2 x} \left (x^2+4\right ) x^3+25 e^{5 x} x^2+25 e^x \left (x^2+4\right )^2 x^2+50 e^{3 x} \left (3 x^2+4\right ) x^2+4 x-3\right ) (4 x+3) x^2-4 \exp \left (-100 e^{4 x} x^3-100 e^{2 x} \left (x^2+4\right ) x^3+25 e^{5 x} x^2+25 e^x \left (x^2+4\right )^2 x^2+50 e^{3 x} \left (3 x^2+4\right ) x^2+2 x-3\right ) (x+2) \left (2 x^2+x+6\right ) x^2+\exp \left (-100 e^{4 x} x^3-100 e^{2 x} \left (x^2+4\right ) x^3+25 e^{5 x} x^2+25 e^x \left (x^2+4\right )^2 x^2+50 e^{3 x} \left (3 x^2+4\right ) x^2+5 x-3\right ) (5 x+2) x+2 \exp \left (-100 e^{4 x} x^3-100 e^{2 x} \left (x^2+4\right ) x^3+25 e^{5 x} x^2+25 e^x \left (x^2+4\right )^2 x^2+50 e^{3 x} \left (3 x^2+4\right ) x^2+3 x-3\right ) \left (9 x^3+12 x^2+12 x+8\right ) x+\exp \left (-100 e^{4 x} x^3-100 e^{2 x} \left (x^2+4\right ) x^3+25 e^{5 x} x^2+25 e^x \left (x^2+4\right )^2 x^2+50 e^{3 x} \left (3 x^2+4\right ) x^2+x-3\right ) \left (x^5+6 x^4+8 x^3+32 x^2+16 x+32\right ) x\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 25 \int \exp \left (-100 e^{4 x} x^3-100 e^{2 x} \left (x^2+4\right ) x^3+25 e^{5 x} x^2+25 e^x \left (x^2+4\right )^2 x^2+50 e^{3 x} \left (3 x^2+4\right ) x^2+x-3\right ) x \left (x^5+6 x^4+8 x^3+32 x^2-4 e^{3 x} (4 x+3) x-4 e^x (x+2) \left (2 x^2+x+6\right ) x+16 x+e^{4 x} (5 x+2)+2 e^{2 x} \left (9 x^3+12 x^2+12 x+8\right )+32\right )dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 25 \int \left (-4 \exp \left (-100 e^{4 x} x^3-100 e^{2 x} \left (x^2+4\right ) x^3+25 e^{5 x} x^2+25 e^x \left (x^2+4\right )^2 x^2+50 e^{3 x} \left (3 x^2+4\right ) x^2+4 x-3\right ) (4 x+3) x^2-4 \exp \left (-100 e^{4 x} x^3-100 e^{2 x} \left (x^2+4\right ) x^3+25 e^{5 x} x^2+25 e^x \left (x^2+4\right )^2 x^2+50 e^{3 x} \left (3 x^2+4\right ) x^2+2 x-3\right ) (x+2) \left (2 x^2+x+6\right ) x^2+\exp \left (-100 e^{4 x} x^3-100 e^{2 x} \left (x^2+4\right ) x^3+25 e^{5 x} x^2+25 e^x \left (x^2+4\right )^2 x^2+50 e^{3 x} \left (3 x^2+4\right ) x^2+5 x-3\right ) (5 x+2) x+2 \exp \left (-100 e^{4 x} x^3-100 e^{2 x} \left (x^2+4\right ) x^3+25 e^{5 x} x^2+25 e^x \left (x^2+4\right )^2 x^2+50 e^{3 x} \left (3 x^2+4\right ) x^2+3 x-3\right ) \left (9 x^3+12 x^2+12 x+8\right ) x+\exp \left (-100 e^{4 x} x^3-100 e^{2 x} \left (x^2+4\right ) x^3+25 e^{5 x} x^2+25 e^x \left (x^2+4\right )^2 x^2+50 e^{3 x} \left (3 x^2+4\right ) x^2+x-3\right ) \left (x^5+6 x^4+8 x^3+32 x^2+16 x+32\right ) x\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 25 \int \exp \left (-100 e^{4 x} x^3-100 e^{2 x} \left (x^2+4\right ) x^3+25 e^{5 x} x^2+25 e^x \left (x^2+4\right )^2 x^2+50 e^{3 x} \left (3 x^2+4\right ) x^2+x-3\right ) x \left (x^5+6 x^4+8 x^3+32 x^2-4 e^{3 x} (4 x+3) x-4 e^x (x+2) \left (2 x^2+x+6\right ) x+16 x+e^{4 x} (5 x+2)+2 e^{2 x} \left (9 x^3+12 x^2+12 x+8\right )+32\right )dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 25 \int \left (-4 \exp \left (-100 e^{4 x} x^3-100 e^{2 x} \left (x^2+4\right ) x^3+25 e^{5 x} x^2+25 e^x \left (x^2+4\right )^2 x^2+50 e^{3 x} \left (3 x^2+4\right ) x^2+4 x-3\right ) (4 x+3) x^2-4 \exp \left (-100 e^{4 x} x^3-100 e^{2 x} \left (x^2+4\right ) x^3+25 e^{5 x} x^2+25 e^x \left (x^2+4\right )^2 x^2+50 e^{3 x} \left (3 x^2+4\right ) x^2+2 x-3\right ) (x+2) \left (2 x^2+x+6\right ) x^2+\exp \left (-100 e^{4 x} x^3-100 e^{2 x} \left (x^2+4\right ) x^3+25 e^{5 x} x^2+25 e^x \left (x^2+4\right )^2 x^2+50 e^{3 x} \left (3 x^2+4\right ) x^2+5 x-3\right ) (5 x+2) x+2 \exp \left (-100 e^{4 x} x^3-100 e^{2 x} \left (x^2+4\right ) x^3+25 e^{5 x} x^2+25 e^x \left (x^2+4\right )^2 x^2+50 e^{3 x} \left (3 x^2+4\right ) x^2+3 x-3\right ) \left (9 x^3+12 x^2+12 x+8\right ) x+\exp \left (-100 e^{4 x} x^3-100 e^{2 x} \left (x^2+4\right ) x^3+25 e^{5 x} x^2+25 e^x \left (x^2+4\right )^2 x^2+50 e^{3 x} \left (3 x^2+4\right ) x^2+x-3\right ) \left (x^5+6 x^4+8 x^3+32 x^2+16 x+32\right ) x\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 25 \int \exp \left (-100 e^{4 x} x^3-100 e^{2 x} \left (x^2+4\right ) x^3+25 e^{5 x} x^2+25 e^x \left (x^2+4\right )^2 x^2+50 e^{3 x} \left (3 x^2+4\right ) x^2+x-3\right ) x \left (x^5+6 x^4+8 x^3+32 x^2-4 e^{3 x} (4 x+3) x-4 e^x (x+2) \left (2 x^2+x+6\right ) x+16 x+e^{4 x} (5 x+2)+2 e^{2 x} \left (9 x^3+12 x^2+12 x+8\right )+32\right )dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 25 \int \left (-4 \exp \left (-100 e^{4 x} x^3-100 e^{2 x} \left (x^2+4\right ) x^3+25 e^{5 x} x^2+25 e^x \left (x^2+4\right )^2 x^2+50 e^{3 x} \left (3 x^2+4\right ) x^2+4 x-3\right ) (4 x+3) x^2-4 \exp \left (-100 e^{4 x} x^3-100 e^{2 x} \left (x^2+4\right ) x^3+25 e^{5 x} x^2+25 e^x \left (x^2+4\right )^2 x^2+50 e^{3 x} \left (3 x^2+4\right ) x^2+2 x-3\right ) (x+2) \left (2 x^2+x+6\right ) x^2+\exp \left (-100 e^{4 x} x^3-100 e^{2 x} \left (x^2+4\right ) x^3+25 e^{5 x} x^2+25 e^x \left (x^2+4\right )^2 x^2+50 e^{3 x} \left (3 x^2+4\right ) x^2+5 x-3\right ) (5 x+2) x+2 \exp \left (-100 e^{4 x} x^3-100 e^{2 x} \left (x^2+4\right ) x^3+25 e^{5 x} x^2+25 e^x \left (x^2+4\right )^2 x^2+50 e^{3 x} \left (3 x^2+4\right ) x^2+3 x-3\right ) \left (9 x^3+12 x^2+12 x+8\right ) x+\exp \left (-100 e^{4 x} x^3-100 e^{2 x} \left (x^2+4\right ) x^3+25 e^{5 x} x^2+25 e^x \left (x^2+4\right )^2 x^2+50 e^{3 x} \left (3 x^2+4\right ) x^2+x-3\right ) \left (x^5+6 x^4+8 x^3+32 x^2+16 x+32\right ) x\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 25 \int \exp \left (-100 e^{4 x} x^3-100 e^{2 x} \left (x^2+4\right ) x^3+25 e^{5 x} x^2+25 e^x \left (x^2+4\right )^2 x^2+50 e^{3 x} \left (3 x^2+4\right ) x^2+x-3\right ) x \left (x^5+6 x^4+8 x^3+32 x^2-4 e^{3 x} (4 x+3) x-4 e^x (x+2) \left (2 x^2+x+6\right ) x+16 x+e^{4 x} (5 x+2)+2 e^{2 x} \left (9 x^3+12 x^2+12 x+8\right )+32\right )dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 25 \int \left (-4 \exp \left (-100 e^{4 x} x^3-100 e^{2 x} \left (x^2+4\right ) x^3+25 e^{5 x} x^2+25 e^x \left (x^2+4\right )^2 x^2+50 e^{3 x} \left (3 x^2+4\right ) x^2+4 x-3\right ) (4 x+3) x^2-4 \exp \left (-100 e^{4 x} x^3-100 e^{2 x} \left (x^2+4\right ) x^3+25 e^{5 x} x^2+25 e^x \left (x^2+4\right )^2 x^2+50 e^{3 x} \left (3 x^2+4\right ) x^2+2 x-3\right ) (x+2) \left (2 x^2+x+6\right ) x^2+\exp \left (-100 e^{4 x} x^3-100 e^{2 x} \left (x^2+4\right ) x^3+25 e^{5 x} x^2+25 e^x \left (x^2+4\right )^2 x^2+50 e^{3 x} \left (3 x^2+4\right ) x^2+5 x-3\right ) (5 x+2) x+2 \exp \left (-100 e^{4 x} x^3-100 e^{2 x} \left (x^2+4\right ) x^3+25 e^{5 x} x^2+25 e^x \left (x^2+4\right )^2 x^2+50 e^{3 x} \left (3 x^2+4\right ) x^2+3 x-3\right ) \left (9 x^3+12 x^2+12 x+8\right ) x+\exp \left (-100 e^{4 x} x^3-100 e^{2 x} \left (x^2+4\right ) x^3+25 e^{5 x} x^2+25 e^x \left (x^2+4\right )^2 x^2+50 e^{3 x} \left (3 x^2+4\right ) x^2+x-3\right ) \left (x^5+6 x^4+8 x^3+32 x^2+16 x+32\right ) x\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 25 \int \exp \left (-100 e^{4 x} x^3-100 e^{2 x} \left (x^2+4\right ) x^3+25 e^{5 x} x^2+25 e^x \left (x^2+4\right )^2 x^2+50 e^{3 x} \left (3 x^2+4\right ) x^2+x-3\right ) x \left (x^5+6 x^4+8 x^3+32 x^2-4 e^{3 x} (4 x+3) x-4 e^x (x+2) \left (2 x^2+x+6\right ) x+16 x+e^{4 x} (5 x+2)+2 e^{2 x} \left (9 x^3+12 x^2+12 x+8\right )+32\right )dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 25 \int \left (-4 \exp \left (-100 e^{4 x} x^3-100 e^{2 x} \left (x^2+4\right ) x^3+25 e^{5 x} x^2+25 e^x \left (x^2+4\right )^2 x^2+50 e^{3 x} \left (3 x^2+4\right ) x^2+4 x-3\right ) (4 x+3) x^2-4 \exp \left (-100 e^{4 x} x^3-100 e^{2 x} \left (x^2+4\right ) x^3+25 e^{5 x} x^2+25 e^x \left (x^2+4\right )^2 x^2+50 e^{3 x} \left (3 x^2+4\right ) x^2+2 x-3\right ) (x+2) \left (2 x^2+x+6\right ) x^2+\exp \left (-100 e^{4 x} x^3-100 e^{2 x} \left (x^2+4\right ) x^3+25 e^{5 x} x^2+25 e^x \left (x^2+4\right )^2 x^2+50 e^{3 x} \left (3 x^2+4\right ) x^2+5 x-3\right ) (5 x+2) x+2 \exp \left (-100 e^{4 x} x^3-100 e^{2 x} \left (x^2+4\right ) x^3+25 e^{5 x} x^2+25 e^x \left (x^2+4\right )^2 x^2+50 e^{3 x} \left (3 x^2+4\right ) x^2+3 x-3\right ) \left (9 x^3+12 x^2+12 x+8\right ) x+\exp \left (-100 e^{4 x} x^3-100 e^{2 x} \left (x^2+4\right ) x^3+25 e^{5 x} x^2+25 e^x \left (x^2+4\right )^2 x^2+50 e^{3 x} \left (3 x^2+4\right ) x^2+x-3\right ) \left (x^5+6 x^4+8 x^3+32 x^2+16 x+32\right ) x\right )dx\) |
Input:
Int[E^(-3 + 25*E^(5*x)*x^2 - 100*E^(4*x)*x^3 + E^(3*x)*(200*x^2 + 150*x^4) + E^(2*x)*(-400*x^3 - 100*x^5) + E^x*(400*x^2 + 200*x^4 + 25*x^6))*(E^(5* x)*(50*x + 125*x^2) + E^(4*x)*(-300*x^2 - 400*x^3) + E^(3*x)*(400*x + 600* x^2 + 600*x^3 + 450*x^4) + E^(2*x)*(-1200*x^2 - 800*x^3 - 500*x^4 - 200*x^ 5) + E^x*(800*x + 400*x^2 + 800*x^3 + 200*x^4 + 150*x^5 + 25*x^6)),x]
Output:
$Aborted
Time = 0.77 (sec) , antiderivative size = 73, normalized size of antiderivative = 2.43
| method | result | size |
| parallelrisch | \({\mathrm e}^{25 x^{2} {\mathrm e}^{5 x}-100 x^{3} {\mathrm e}^{4 x}+\left (150 x^{4}+200 x^{2}\right ) {\mathrm e}^{3 x}+\left (-100 x^{5}-400 x^{3}\right ) {\mathrm e}^{2 x}+\left (25 x^{6}+200 x^{4}+400 x^{2}\right ) {\mathrm e}^{x}-3}\) | \(73\) |
| risch | \({\mathrm e}^{25 \,{\mathrm e}^{x} x^{6}-100 \,{\mathrm e}^{2 x} x^{5}+200 \,{\mathrm e}^{x} x^{4}+150 \,{\mathrm e}^{3 x} x^{4}-100 x^{3} {\mathrm e}^{4 x}-400 \,{\mathrm e}^{2 x} x^{3}+400 \,{\mathrm e}^{x} x^{2}+25 x^{2} {\mathrm e}^{5 x}+200 x^{2} {\mathrm e}^{3 x}-3}\) | \(79\) |
Input:
int(((125*x^2+50*x)*exp(x)^5+(-400*x^3-300*x^2)*exp(x)^4+(450*x^4+600*x^3+ 600*x^2+400*x)*exp(x)^3+(-200*x^5-500*x^4-800*x^3-1200*x^2)*exp(x)^2+(25*x ^6+150*x^5+200*x^4+800*x^3+400*x^2+800*x)*exp(x))*exp(25*x^2*exp(x)^5-100* x^3*exp(x)^4+(150*x^4+200*x^2)*exp(x)^3+(-100*x^5-400*x^3)*exp(x)^2+(25*x^ 6+200*x^4+400*x^2)*exp(x)-3),x,method=_RETURNVERBOSE)
Output:
exp(25*x^2*exp(x)^5-100*x^3*exp(x)^4+(150*x^4+200*x^2)*exp(x)^3+(-100*x^5- 400*x^3)*exp(x)^2+(25*x^6+200*x^4+400*x^2)*exp(x)-3)
Leaf count of result is larger than twice the leaf count of optimal. 71 vs. \(2 (27) = 54\).
Time = 0.09 (sec) , antiderivative size = 71, normalized size of antiderivative = 2.37 \[ \int e^{-3+25 e^{5 x} x^2-100 e^{4 x} x^3+e^{3 x} \left (200 x^2+150 x^4\right )+e^{2 x} \left (-400 x^3-100 x^5\right )+e^x \left (400 x^2+200 x^4+25 x^6\right )} \left (e^{5 x} \left (50 x+125 x^2\right )+e^{4 x} \left (-300 x^2-400 x^3\right )+e^{3 x} \left (400 x+600 x^2+600 x^3+450 x^4\right )+e^{2 x} \left (-1200 x^2-800 x^3-500 x^4-200 x^5\right )+e^x \left (800 x+400 x^2+800 x^3+200 x^4+150 x^5+25 x^6\right )\right ) \, dx=e^{\left (-100 \, x^{3} e^{\left (4 \, x\right )} + 25 \, x^{2} e^{\left (5 \, x\right )} + 50 \, {\left (3 \, x^{4} + 4 \, x^{2}\right )} e^{\left (3 \, x\right )} - 100 \, {\left (x^{5} + 4 \, x^{3}\right )} e^{\left (2 \, x\right )} + 25 \, {\left (x^{6} + 8 \, x^{4} + 16 \, x^{2}\right )} e^{x} - 3\right )} \] Input:
integrate(((125*x^2+50*x)*exp(x)^5+(-400*x^3-300*x^2)*exp(x)^4+(450*x^4+60 0*x^3+600*x^2+400*x)*exp(x)^3+(-200*x^5-500*x^4-800*x^3-1200*x^2)*exp(x)^2 +(25*x^6+150*x^5+200*x^4+800*x^3+400*x^2+800*x)*exp(x))*exp(25*x^2*exp(x)^ 5-100*x^3*exp(x)^4+(150*x^4+200*x^2)*exp(x)^3+(-100*x^5-400*x^3)*exp(x)^2+ (25*x^6+200*x^4+400*x^2)*exp(x)-3),x, algorithm="fricas")
Output:
e^(-100*x^3*e^(4*x) + 25*x^2*e^(5*x) + 50*(3*x^4 + 4*x^2)*e^(3*x) - 100*(x ^5 + 4*x^3)*e^(2*x) + 25*(x^6 + 8*x^4 + 16*x^2)*e^x - 3)
Leaf count of result is larger than twice the leaf count of optimal. 73 vs. \(2 (24) = 48\).
Time = 0.32 (sec) , antiderivative size = 73, normalized size of antiderivative = 2.43 \[ \int e^{-3+25 e^{5 x} x^2-100 e^{4 x} x^3+e^{3 x} \left (200 x^2+150 x^4\right )+e^{2 x} \left (-400 x^3-100 x^5\right )+e^x \left (400 x^2+200 x^4+25 x^6\right )} \left (e^{5 x} \left (50 x+125 x^2\right )+e^{4 x} \left (-300 x^2-400 x^3\right )+e^{3 x} \left (400 x+600 x^2+600 x^3+450 x^4\right )+e^{2 x} \left (-1200 x^2-800 x^3-500 x^4-200 x^5\right )+e^x \left (800 x+400 x^2+800 x^3+200 x^4+150 x^5+25 x^6\right )\right ) \, dx=e^{- 100 x^{3} e^{4 x} + 25 x^{2} e^{5 x} + \left (150 x^{4} + 200 x^{2}\right ) e^{3 x} + \left (- 100 x^{5} - 400 x^{3}\right ) e^{2 x} + \left (25 x^{6} + 200 x^{4} + 400 x^{2}\right ) e^{x} - 3} \] Input:
integrate(((125*x**2+50*x)*exp(x)**5+(-400*x**3-300*x**2)*exp(x)**4+(450*x **4+600*x**3+600*x**2+400*x)*exp(x)**3+(-200*x**5-500*x**4-800*x**3-1200*x **2)*exp(x)**2+(25*x**6+150*x**5+200*x**4+800*x**3+400*x**2+800*x)*exp(x)) *exp(25*x**2*exp(x)**5-100*x**3*exp(x)**4+(150*x**4+200*x**2)*exp(x)**3+(- 100*x**5-400*x**3)*exp(x)**2+(25*x**6+200*x**4+400*x**2)*exp(x)-3),x)
Output:
exp(-100*x**3*exp(4*x) + 25*x**2*exp(5*x) + (150*x**4 + 200*x**2)*exp(3*x) + (-100*x**5 - 400*x**3)*exp(2*x) + (25*x**6 + 200*x**4 + 400*x**2)*exp(x ) - 3)
Leaf count of result is larger than twice the leaf count of optimal. 78 vs. \(2 (27) = 54\).
Time = 0.39 (sec) , antiderivative size = 78, normalized size of antiderivative = 2.60 \[ \int e^{-3+25 e^{5 x} x^2-100 e^{4 x} x^3+e^{3 x} \left (200 x^2+150 x^4\right )+e^{2 x} \left (-400 x^3-100 x^5\right )+e^x \left (400 x^2+200 x^4+25 x^6\right )} \left (e^{5 x} \left (50 x+125 x^2\right )+e^{4 x} \left (-300 x^2-400 x^3\right )+e^{3 x} \left (400 x+600 x^2+600 x^3+450 x^4\right )+e^{2 x} \left (-1200 x^2-800 x^3-500 x^4-200 x^5\right )+e^x \left (800 x+400 x^2+800 x^3+200 x^4+150 x^5+25 x^6\right )\right ) \, dx=e^{\left (25 \, x^{6} e^{x} - 100 \, x^{5} e^{\left (2 \, x\right )} + 150 \, x^{4} e^{\left (3 \, x\right )} + 200 \, x^{4} e^{x} - 100 \, x^{3} e^{\left (4 \, x\right )} - 400 \, x^{3} e^{\left (2 \, x\right )} + 25 \, x^{2} e^{\left (5 \, x\right )} + 200 \, x^{2} e^{\left (3 \, x\right )} + 400 \, x^{2} e^{x} - 3\right )} \] Input:
integrate(((125*x^2+50*x)*exp(x)^5+(-400*x^3-300*x^2)*exp(x)^4+(450*x^4+60 0*x^3+600*x^2+400*x)*exp(x)^3+(-200*x^5-500*x^4-800*x^3-1200*x^2)*exp(x)^2 +(25*x^6+150*x^5+200*x^4+800*x^3+400*x^2+800*x)*exp(x))*exp(25*x^2*exp(x)^ 5-100*x^3*exp(x)^4+(150*x^4+200*x^2)*exp(x)^3+(-100*x^5-400*x^3)*exp(x)^2+ (25*x^6+200*x^4+400*x^2)*exp(x)-3),x, algorithm="maxima")
Output:
e^(25*x^6*e^x - 100*x^5*e^(2*x) + 150*x^4*e^(3*x) + 200*x^4*e^x - 100*x^3* e^(4*x) - 400*x^3*e^(2*x) + 25*x^2*e^(5*x) + 200*x^2*e^(3*x) + 400*x^2*e^x - 3)
\[ \int e^{-3+25 e^{5 x} x^2-100 e^{4 x} x^3+e^{3 x} \left (200 x^2+150 x^4\right )+e^{2 x} \left (-400 x^3-100 x^5\right )+e^x \left (400 x^2+200 x^4+25 x^6\right )} \left (e^{5 x} \left (50 x+125 x^2\right )+e^{4 x} \left (-300 x^2-400 x^3\right )+e^{3 x} \left (400 x+600 x^2+600 x^3+450 x^4\right )+e^{2 x} \left (-1200 x^2-800 x^3-500 x^4-200 x^5\right )+e^x \left (800 x+400 x^2+800 x^3+200 x^4+150 x^5+25 x^6\right )\right ) \, dx=\int { 25 \, {\left ({\left (5 \, x^{2} + 2 \, x\right )} e^{\left (5 \, x\right )} - 4 \, {\left (4 \, x^{3} + 3 \, x^{2}\right )} e^{\left (4 \, x\right )} + 2 \, {\left (9 \, x^{4} + 12 \, x^{3} + 12 \, x^{2} + 8 \, x\right )} e^{\left (3 \, x\right )} - 4 \, {\left (2 \, x^{5} + 5 \, x^{4} + 8 \, x^{3} + 12 \, x^{2}\right )} e^{\left (2 \, x\right )} + {\left (x^{6} + 6 \, x^{5} + 8 \, x^{4} + 32 \, x^{3} + 16 \, x^{2} + 32 \, x\right )} e^{x}\right )} e^{\left (-100 \, x^{3} e^{\left (4 \, x\right )} + 25 \, x^{2} e^{\left (5 \, x\right )} + 50 \, {\left (3 \, x^{4} + 4 \, x^{2}\right )} e^{\left (3 \, x\right )} - 100 \, {\left (x^{5} + 4 \, x^{3}\right )} e^{\left (2 \, x\right )} + 25 \, {\left (x^{6} + 8 \, x^{4} + 16 \, x^{2}\right )} e^{x} - 3\right )} \,d x } \] Input:
integrate(((125*x^2+50*x)*exp(x)^5+(-400*x^3-300*x^2)*exp(x)^4+(450*x^4+60 0*x^3+600*x^2+400*x)*exp(x)^3+(-200*x^5-500*x^4-800*x^3-1200*x^2)*exp(x)^2 +(25*x^6+150*x^5+200*x^4+800*x^3+400*x^2+800*x)*exp(x))*exp(25*x^2*exp(x)^ 5-100*x^3*exp(x)^4+(150*x^4+200*x^2)*exp(x)^3+(-100*x^5-400*x^3)*exp(x)^2+ (25*x^6+200*x^4+400*x^2)*exp(x)-3),x, algorithm="giac")
Output:
integrate(25*((5*x^2 + 2*x)*e^(5*x) - 4*(4*x^3 + 3*x^2)*e^(4*x) + 2*(9*x^4 + 12*x^3 + 12*x^2 + 8*x)*e^(3*x) - 4*(2*x^5 + 5*x^4 + 8*x^3 + 12*x^2)*e^( 2*x) + (x^6 + 6*x^5 + 8*x^4 + 32*x^3 + 16*x^2 + 32*x)*e^x)*e^(-100*x^3*e^( 4*x) + 25*x^2*e^(5*x) + 50*(3*x^4 + 4*x^2)*e^(3*x) - 100*(x^5 + 4*x^3)*e^( 2*x) + 25*(x^6 + 8*x^4 + 16*x^2)*e^x - 3), x)
Time = 4.15 (sec) , antiderivative size = 87, normalized size of antiderivative = 2.90 \[ \int e^{-3+25 e^{5 x} x^2-100 e^{4 x} x^3+e^{3 x} \left (200 x^2+150 x^4\right )+e^{2 x} \left (-400 x^3-100 x^5\right )+e^x \left (400 x^2+200 x^4+25 x^6\right )} \left (e^{5 x} \left (50 x+125 x^2\right )+e^{4 x} \left (-300 x^2-400 x^3\right )+e^{3 x} \left (400 x+600 x^2+600 x^3+450 x^4\right )+e^{2 x} \left (-1200 x^2-800 x^3-500 x^4-200 x^5\right )+e^x \left (800 x+400 x^2+800 x^3+200 x^4+150 x^5+25 x^6\right )\right ) \, dx={\mathrm {e}}^{-3}\,{\mathrm {e}}^{25\,x^6\,{\mathrm {e}}^x}\,{\mathrm {e}}^{200\,x^4\,{\mathrm {e}}^x}\,{\mathrm {e}}^{400\,x^2\,{\mathrm {e}}^x}\,{\mathrm {e}}^{25\,x^2\,{\mathrm {e}}^{5\,x}}\,{\mathrm {e}}^{-100\,x^3\,{\mathrm {e}}^{4\,x}}\,{\mathrm {e}}^{-100\,x^5\,{\mathrm {e}}^{2\,x}}\,{\mathrm {e}}^{150\,x^4\,{\mathrm {e}}^{3\,x}}\,{\mathrm {e}}^{200\,x^2\,{\mathrm {e}}^{3\,x}}\,{\mathrm {e}}^{-400\,x^3\,{\mathrm {e}}^{2\,x}} \] Input:
int(exp(exp(x)*(400*x^2 + 200*x^4 + 25*x^6) + exp(3*x)*(200*x^2 + 150*x^4) - exp(2*x)*(400*x^3 + 100*x^5) + 25*x^2*exp(5*x) - 100*x^3*exp(4*x) - 3)* (exp(5*x)*(50*x + 125*x^2) - exp(4*x)*(300*x^2 + 400*x^3) + exp(3*x)*(400* x + 600*x^2 + 600*x^3 + 450*x^4) + exp(x)*(800*x + 400*x^2 + 800*x^3 + 200 *x^4 + 150*x^5 + 25*x^6) - exp(2*x)*(1200*x^2 + 800*x^3 + 500*x^4 + 200*x^ 5)),x)
Output:
exp(-3)*exp(25*x^6*exp(x))*exp(200*x^4*exp(x))*exp(400*x^2*exp(x))*exp(25* x^2*exp(5*x))*exp(-100*x^3*exp(4*x))*exp(-100*x^5*exp(2*x))*exp(150*x^4*ex p(3*x))*exp(200*x^2*exp(3*x))*exp(-400*x^3*exp(2*x))
Time = 0.18 (sec) , antiderivative size = 96, normalized size of antiderivative = 3.20 \[ \int e^{-3+25 e^{5 x} x^2-100 e^{4 x} x^3+e^{3 x} \left (200 x^2+150 x^4\right )+e^{2 x} \left (-400 x^3-100 x^5\right )+e^x \left (400 x^2+200 x^4+25 x^6\right )} \left (e^{5 x} \left (50 x+125 x^2\right )+e^{4 x} \left (-300 x^2-400 x^3\right )+e^{3 x} \left (400 x+600 x^2+600 x^3+450 x^4\right )+e^{2 x} \left (-1200 x^2-800 x^3-500 x^4-200 x^5\right )+e^x \left (800 x+400 x^2+800 x^3+200 x^4+150 x^5+25 x^6\right )\right ) \, dx=\frac {e^{25 e^{5 x} x^{2}+150 e^{3 x} x^{4}+200 e^{3 x} x^{2}+25 e^{x} x^{6}+200 e^{x} x^{4}+400 e^{x} x^{2}}}{e^{100 e^{4 x} x^{3}+100 e^{2 x} x^{5}+400 e^{2 x} x^{3}} e^{3}} \] Input:
int(((125*x^2+50*x)*exp(x)^5+(-400*x^3-300*x^2)*exp(x)^4+(450*x^4+600*x^3+ 600*x^2+400*x)*exp(x)^3+(-200*x^5-500*x^4-800*x^3-1200*x^2)*exp(x)^2+(25*x ^6+150*x^5+200*x^4+800*x^3+400*x^2+800*x)*exp(x))*exp(25*x^2*exp(x)^5-100* x^3*exp(x)^4+(150*x^4+200*x^2)*exp(x)^3+(-100*x^5-400*x^3)*exp(x)^2+(25*x^ 6+200*x^4+400*x^2)*exp(x)-3),x)
Output:
e**(25*e**(5*x)*x**2 + 150*e**(3*x)*x**4 + 200*e**(3*x)*x**2 + 25*e**x*x** 6 + 200*e**x*x**4 + 400*e**x*x**2)/(e**(100*e**(4*x)*x**3 + 100*e**(2*x)*x **5 + 400*e**(2*x)*x**3)*e**3)