Integrand size = 226, antiderivative size = 28 \[ \int \frac {-e^{3 x}+3375 x^6-10125 x^7+10125 x^8-3375 x^9+e^{\frac {16-2 e^{2 x}-450 x^4+900 x^5-450 x^6+e^x \left (60 x^2-60 x^3\right )}{e^{2 x}+225 x^4-450 x^5+225 x^6+e^x \left (-30 x^2+30 x^3\right )}} \left (32 e^x-960 x+1440 x^2\right )+e^{2 x} \left (45 x^2-45 x^3\right )+e^x \left (-675 x^4+1350 x^5-675 x^6\right )}{e^{3 x}-3375 x^6+10125 x^7-10125 x^8+3375 x^9+e^{2 x} \left (-45 x^2+45 x^3\right )+e^x \left (675 x^4-1350 x^5+675 x^6\right )} \, dx=-e^{-2+\frac {16}{\left (e^x+5 x^2 (-3+3 x)\right )^2}}-x \] Output:
-x-exp(16/(5*x^2*(-3+3*x)+exp(x))^2-2)
Time = 0.43 (sec) , antiderivative size = 28, normalized size of antiderivative = 1.00 \[ \int \frac {-e^{3 x}+3375 x^6-10125 x^7+10125 x^8-3375 x^9+e^{\frac {16-2 e^{2 x}-450 x^4+900 x^5-450 x^6+e^x \left (60 x^2-60 x^3\right )}{e^{2 x}+225 x^4-450 x^5+225 x^6+e^x \left (-30 x^2+30 x^3\right )}} \left (32 e^x-960 x+1440 x^2\right )+e^{2 x} \left (45 x^2-45 x^3\right )+e^x \left (-675 x^4+1350 x^5-675 x^6\right )}{e^{3 x}-3375 x^6+10125 x^7-10125 x^8+3375 x^9+e^{2 x} \left (-45 x^2+45 x^3\right )+e^x \left (675 x^4-1350 x^5+675 x^6\right )} \, dx=-e^{-2+\frac {16}{\left (e^x-15 x^2+15 x^3\right )^2}}-x \] Input:
Integrate[(-E^(3*x) + 3375*x^6 - 10125*x^7 + 10125*x^8 - 3375*x^9 + E^((16 - 2*E^(2*x) - 450*x^4 + 900*x^5 - 450*x^6 + E^x*(60*x^2 - 60*x^3))/(E^(2* x) + 225*x^4 - 450*x^5 + 225*x^6 + E^x*(-30*x^2 + 30*x^3)))*(32*E^x - 960* x + 1440*x^2) + E^(2*x)*(45*x^2 - 45*x^3) + E^x*(-675*x^4 + 1350*x^5 - 675 *x^6))/(E^(3*x) - 3375*x^6 + 10125*x^7 - 10125*x^8 + 3375*x^9 + E^(2*x)*(- 45*x^2 + 45*x^3) + E^x*(675*x^4 - 1350*x^5 + 675*x^6)),x]
Output:
-E^(-2 + 16/(E^x - 15*x^2 + 15*x^3)^2) - x
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.
| \(\displaystyle \int \frac {\left (1440 x^2-960 x+32 e^x\right ) \exp \left (\frac {-450 x^6+900 x^5-450 x^4+e^x \left (60 x^2-60 x^3\right )-2 e^{2 x}+16}{225 x^6-450 x^5+225 x^4+e^x \left (30 x^3-30 x^2\right )+e^{2 x}}\right )-3375 x^9+10125 x^8-10125 x^7+3375 x^6+e^{2 x} \left (45 x^2-45 x^3\right )+e^x \left (-675 x^6+1350 x^5-675 x^4\right )-e^{3 x}}{3375 x^9-10125 x^8+10125 x^7-3375 x^6+e^{2 x} \left (45 x^3-45 x^2\right )+e^x \left (675 x^6-1350 x^5+675 x^4\right )+e^{3 x}} \, dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {32 \left (15 x (3 x-2)+e^x\right ) \exp \left (-\frac {2 \left (225 x^6-450 x^5+225 x^4+30 e^x (x-1) x^2+e^{2 x}-8\right )}{\left (15 (x-1) x^2+e^x\right )^2}\right )-3375 x^9+10125 x^8-10125 x^7+3375 x^6-675 e^x (x-1)^2 x^4-45 e^{2 x} (x-1) x^2-e^{3 x}}{\left (15 (x-1) x^2+e^x\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {32 \left (45 x^2-30 x+e^x\right ) \exp \left (-\frac {2 \left (225 x^6-450 x^5+225 x^4+30 e^x x^3-30 e^x x^2+e^{2 x}-8\right )}{\left (15 x^3-15 x^2+e^x\right )^2}\right )}{\left (15 x^3-15 x^2+e^x\right )^3}-\frac {45 e^{2 x} (x-1) x^2}{\left (15 x^3-15 x^2+e^x\right )^3}-\frac {e^{3 x}}{\left (15 x^3-15 x^2+e^x\right )^3}-\frac {3375 x^9}{\left (15 x^3-15 x^2+e^x\right )^3}+\frac {10125 x^8}{\left (15 x^3-15 x^2+e^x\right )^3}-\frac {10125 x^7}{\left (15 x^3-15 x^2+e^x\right )^3}+\frac {3375 x^6}{\left (15 x^3-15 x^2+e^x\right )^3}-\frac {675 e^x (x-1)^2 x^4}{\left (15 x^3-15 x^2+e^x\right )^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {32 \left (15 x (3 x-2)+e^x\right ) \exp \left (-\frac {2 \left (225 x^6-450 x^5+225 x^4+30 e^x (x-1) x^2+e^{2 x}-8\right )}{\left (15 (x-1) x^2+e^x\right )^2}\right )-3375 x^9+10125 x^8-10125 x^7+3375 x^6-675 e^x (x-1)^2 x^4-45 e^{2 x} (x-1) x^2-e^{3 x}}{\left (15 (x-1) x^2+e^x\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {32 \left (45 x^2-30 x+e^x\right ) \exp \left (-\frac {2 \left (225 x^6-450 x^5+225 x^4+30 e^x x^3-30 e^x x^2+e^{2 x}-8\right )}{\left (15 x^3-15 x^2+e^x\right )^2}\right )}{\left (15 x^3-15 x^2+e^x\right )^3}-\frac {45 e^{2 x} (x-1) x^2}{\left (15 x^3-15 x^2+e^x\right )^3}-\frac {e^{3 x}}{\left (15 x^3-15 x^2+e^x\right )^3}-\frac {3375 x^9}{\left (15 x^3-15 x^2+e^x\right )^3}+\frac {10125 x^8}{\left (15 x^3-15 x^2+e^x\right )^3}-\frac {10125 x^7}{\left (15 x^3-15 x^2+e^x\right )^3}+\frac {3375 x^6}{\left (15 x^3-15 x^2+e^x\right )^3}-\frac {675 e^x (x-1)^2 x^4}{\left (15 x^3-15 x^2+e^x\right )^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {32 \left (15 x (3 x-2)+e^x\right ) \exp \left (-\frac {2 \left (225 x^6-450 x^5+225 x^4+30 e^x (x-1) x^2+e^{2 x}-8\right )}{\left (15 (x-1) x^2+e^x\right )^2}\right )-3375 x^9+10125 x^8-10125 x^7+3375 x^6-675 e^x (x-1)^2 x^4-45 e^{2 x} (x-1) x^2-e^{3 x}}{\left (15 (x-1) x^2+e^x\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {32 \left (45 x^2-30 x+e^x\right ) \exp \left (-\frac {2 \left (225 x^6-450 x^5+225 x^4+30 e^x x^3-30 e^x x^2+e^{2 x}-8\right )}{\left (15 x^3-15 x^2+e^x\right )^2}\right )}{\left (15 x^3-15 x^2+e^x\right )^3}-\frac {45 e^{2 x} (x-1) x^2}{\left (15 x^3-15 x^2+e^x\right )^3}-\frac {e^{3 x}}{\left (15 x^3-15 x^2+e^x\right )^3}-\frac {3375 x^9}{\left (15 x^3-15 x^2+e^x\right )^3}+\frac {10125 x^8}{\left (15 x^3-15 x^2+e^x\right )^3}-\frac {10125 x^7}{\left (15 x^3-15 x^2+e^x\right )^3}+\frac {3375 x^6}{\left (15 x^3-15 x^2+e^x\right )^3}-\frac {675 e^x (x-1)^2 x^4}{\left (15 x^3-15 x^2+e^x\right )^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {32 \left (15 x (3 x-2)+e^x\right ) \exp \left (-\frac {2 \left (225 x^6-450 x^5+225 x^4+30 e^x (x-1) x^2+e^{2 x}-8\right )}{\left (15 (x-1) x^2+e^x\right )^2}\right )-3375 x^9+10125 x^8-10125 x^7+3375 x^6-675 e^x (x-1)^2 x^4-45 e^{2 x} (x-1) x^2-e^{3 x}}{\left (15 (x-1) x^2+e^x\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {32 \left (45 x^2-30 x+e^x\right ) \exp \left (-\frac {2 \left (225 x^6-450 x^5+225 x^4+30 e^x x^3-30 e^x x^2+e^{2 x}-8\right )}{\left (15 x^3-15 x^2+e^x\right )^2}\right )}{\left (15 x^3-15 x^2+e^x\right )^3}-\frac {45 e^{2 x} (x-1) x^2}{\left (15 x^3-15 x^2+e^x\right )^3}-\frac {e^{3 x}}{\left (15 x^3-15 x^2+e^x\right )^3}-\frac {3375 x^9}{\left (15 x^3-15 x^2+e^x\right )^3}+\frac {10125 x^8}{\left (15 x^3-15 x^2+e^x\right )^3}-\frac {10125 x^7}{\left (15 x^3-15 x^2+e^x\right )^3}+\frac {3375 x^6}{\left (15 x^3-15 x^2+e^x\right )^3}-\frac {675 e^x (x-1)^2 x^4}{\left (15 x^3-15 x^2+e^x\right )^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {32 \left (15 x (3 x-2)+e^x\right ) \exp \left (-\frac {2 \left (225 x^6-450 x^5+225 x^4+30 e^x (x-1) x^2+e^{2 x}-8\right )}{\left (15 (x-1) x^2+e^x\right )^2}\right )-3375 x^9+10125 x^8-10125 x^7+3375 x^6-675 e^x (x-1)^2 x^4-45 e^{2 x} (x-1) x^2-e^{3 x}}{\left (15 (x-1) x^2+e^x\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {32 \left (45 x^2-30 x+e^x\right ) \exp \left (-\frac {2 \left (225 x^6-450 x^5+225 x^4+30 e^x x^3-30 e^x x^2+e^{2 x}-8\right )}{\left (15 x^3-15 x^2+e^x\right )^2}\right )}{\left (15 x^3-15 x^2+e^x\right )^3}-\frac {45 e^{2 x} (x-1) x^2}{\left (15 x^3-15 x^2+e^x\right )^3}-\frac {e^{3 x}}{\left (15 x^3-15 x^2+e^x\right )^3}-\frac {3375 x^9}{\left (15 x^3-15 x^2+e^x\right )^3}+\frac {10125 x^8}{\left (15 x^3-15 x^2+e^x\right )^3}-\frac {10125 x^7}{\left (15 x^3-15 x^2+e^x\right )^3}+\frac {3375 x^6}{\left (15 x^3-15 x^2+e^x\right )^3}-\frac {675 e^x (x-1)^2 x^4}{\left (15 x^3-15 x^2+e^x\right )^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {32 \left (15 x (3 x-2)+e^x\right ) \exp \left (-\frac {2 \left (225 x^6-450 x^5+225 x^4+30 e^x (x-1) x^2+e^{2 x}-8\right )}{\left (15 (x-1) x^2+e^x\right )^2}\right )-3375 x^9+10125 x^8-10125 x^7+3375 x^6-675 e^x (x-1)^2 x^4-45 e^{2 x} (x-1) x^2-e^{3 x}}{\left (15 (x-1) x^2+e^x\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {32 \left (45 x^2-30 x+e^x\right ) \exp \left (-\frac {2 \left (225 x^6-450 x^5+225 x^4+30 e^x x^3-30 e^x x^2+e^{2 x}-8\right )}{\left (15 x^3-15 x^2+e^x\right )^2}\right )}{\left (15 x^3-15 x^2+e^x\right )^3}-\frac {45 e^{2 x} (x-1) x^2}{\left (15 x^3-15 x^2+e^x\right )^3}-\frac {e^{3 x}}{\left (15 x^3-15 x^2+e^x\right )^3}-\frac {3375 x^9}{\left (15 x^3-15 x^2+e^x\right )^3}+\frac {10125 x^8}{\left (15 x^3-15 x^2+e^x\right )^3}-\frac {10125 x^7}{\left (15 x^3-15 x^2+e^x\right )^3}+\frac {3375 x^6}{\left (15 x^3-15 x^2+e^x\right )^3}-\frac {675 e^x (x-1)^2 x^4}{\left (15 x^3-15 x^2+e^x\right )^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {32 \left (15 x (3 x-2)+e^x\right ) \exp \left (-\frac {2 \left (225 x^6-450 x^5+225 x^4+30 e^x (x-1) x^2+e^{2 x}-8\right )}{\left (15 (x-1) x^2+e^x\right )^2}\right )-3375 x^9+10125 x^8-10125 x^7+3375 x^6-675 e^x (x-1)^2 x^4-45 e^{2 x} (x-1) x^2-e^{3 x}}{\left (15 (x-1) x^2+e^x\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {32 \left (45 x^2-30 x+e^x\right ) \exp \left (-\frac {2 \left (225 x^6-450 x^5+225 x^4+30 e^x x^3-30 e^x x^2+e^{2 x}-8\right )}{\left (15 x^3-15 x^2+e^x\right )^2}\right )}{\left (15 x^3-15 x^2+e^x\right )^3}-\frac {45 e^{2 x} (x-1) x^2}{\left (15 x^3-15 x^2+e^x\right )^3}-\frac {e^{3 x}}{\left (15 x^3-15 x^2+e^x\right )^3}-\frac {3375 x^9}{\left (15 x^3-15 x^2+e^x\right )^3}+\frac {10125 x^8}{\left (15 x^3-15 x^2+e^x\right )^3}-\frac {10125 x^7}{\left (15 x^3-15 x^2+e^x\right )^3}+\frac {3375 x^6}{\left (15 x^3-15 x^2+e^x\right )^3}-\frac {675 e^x (x-1)^2 x^4}{\left (15 x^3-15 x^2+e^x\right )^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {32 \left (15 x (3 x-2)+e^x\right ) \exp \left (-\frac {2 \left (225 x^6-450 x^5+225 x^4+30 e^x (x-1) x^2+e^{2 x}-8\right )}{\left (15 (x-1) x^2+e^x\right )^2}\right )-3375 x^9+10125 x^8-10125 x^7+3375 x^6-675 e^x (x-1)^2 x^4-45 e^{2 x} (x-1) x^2-e^{3 x}}{\left (15 (x-1) x^2+e^x\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {32 \left (45 x^2-30 x+e^x\right ) \exp \left (-\frac {2 \left (225 x^6-450 x^5+225 x^4+30 e^x x^3-30 e^x x^2+e^{2 x}-8\right )}{\left (15 x^3-15 x^2+e^x\right )^2}\right )}{\left (15 x^3-15 x^2+e^x\right )^3}-\frac {45 e^{2 x} (x-1) x^2}{\left (15 x^3-15 x^2+e^x\right )^3}-\frac {e^{3 x}}{\left (15 x^3-15 x^2+e^x\right )^3}-\frac {3375 x^9}{\left (15 x^3-15 x^2+e^x\right )^3}+\frac {10125 x^8}{\left (15 x^3-15 x^2+e^x\right )^3}-\frac {10125 x^7}{\left (15 x^3-15 x^2+e^x\right )^3}+\frac {3375 x^6}{\left (15 x^3-15 x^2+e^x\right )^3}-\frac {675 e^x (x-1)^2 x^4}{\left (15 x^3-15 x^2+e^x\right )^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {32 \left (15 x (3 x-2)+e^x\right ) \exp \left (-\frac {2 \left (225 x^6-450 x^5+225 x^4+30 e^x (x-1) x^2+e^{2 x}-8\right )}{\left (15 (x-1) x^2+e^x\right )^2}\right )-3375 x^9+10125 x^8-10125 x^7+3375 x^6-675 e^x (x-1)^2 x^4-45 e^{2 x} (x-1) x^2-e^{3 x}}{\left (15 (x-1) x^2+e^x\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {32 \left (45 x^2-30 x+e^x\right ) \exp \left (-\frac {2 \left (225 x^6-450 x^5+225 x^4+30 e^x x^3-30 e^x x^2+e^{2 x}-8\right )}{\left (15 x^3-15 x^2+e^x\right )^2}\right )}{\left (15 x^3-15 x^2+e^x\right )^3}-\frac {45 e^{2 x} (x-1) x^2}{\left (15 x^3-15 x^2+e^x\right )^3}-\frac {e^{3 x}}{\left (15 x^3-15 x^2+e^x\right )^3}-\frac {3375 x^9}{\left (15 x^3-15 x^2+e^x\right )^3}+\frac {10125 x^8}{\left (15 x^3-15 x^2+e^x\right )^3}-\frac {10125 x^7}{\left (15 x^3-15 x^2+e^x\right )^3}+\frac {3375 x^6}{\left (15 x^3-15 x^2+e^x\right )^3}-\frac {675 e^x (x-1)^2 x^4}{\left (15 x^3-15 x^2+e^x\right )^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {32 \left (15 x (3 x-2)+e^x\right ) \exp \left (-\frac {2 \left (225 x^6-450 x^5+225 x^4+30 e^x (x-1) x^2+e^{2 x}-8\right )}{\left (15 (x-1) x^2+e^x\right )^2}\right )-3375 x^9+10125 x^8-10125 x^7+3375 x^6-675 e^x (x-1)^2 x^4-45 e^{2 x} (x-1) x^2-e^{3 x}}{\left (15 (x-1) x^2+e^x\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {32 \left (45 x^2-30 x+e^x\right ) \exp \left (-\frac {2 \left (225 x^6-450 x^5+225 x^4+30 e^x x^3-30 e^x x^2+e^{2 x}-8\right )}{\left (15 x^3-15 x^2+e^x\right )^2}\right )}{\left (15 x^3-15 x^2+e^x\right )^3}-\frac {45 e^{2 x} (x-1) x^2}{\left (15 x^3-15 x^2+e^x\right )^3}-\frac {e^{3 x}}{\left (15 x^3-15 x^2+e^x\right )^3}-\frac {3375 x^9}{\left (15 x^3-15 x^2+e^x\right )^3}+\frac {10125 x^8}{\left (15 x^3-15 x^2+e^x\right )^3}-\frac {10125 x^7}{\left (15 x^3-15 x^2+e^x\right )^3}+\frac {3375 x^6}{\left (15 x^3-15 x^2+e^x\right )^3}-\frac {675 e^x (x-1)^2 x^4}{\left (15 x^3-15 x^2+e^x\right )^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {32 \left (15 x (3 x-2)+e^x\right ) \exp \left (-\frac {2 \left (225 x^6-450 x^5+225 x^4+30 e^x (x-1) x^2+e^{2 x}-8\right )}{\left (15 (x-1) x^2+e^x\right )^2}\right )-3375 x^9+10125 x^8-10125 x^7+3375 x^6-675 e^x (x-1)^2 x^4-45 e^{2 x} (x-1) x^2-e^{3 x}}{\left (15 (x-1) x^2+e^x\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {32 \left (45 x^2-30 x+e^x\right ) \exp \left (-\frac {2 \left (225 x^6-450 x^5+225 x^4+30 e^x x^3-30 e^x x^2+e^{2 x}-8\right )}{\left (15 x^3-15 x^2+e^x\right )^2}\right )}{\left (15 x^3-15 x^2+e^x\right )^3}-\frac {45 e^{2 x} (x-1) x^2}{\left (15 x^3-15 x^2+e^x\right )^3}-\frac {e^{3 x}}{\left (15 x^3-15 x^2+e^x\right )^3}-\frac {3375 x^9}{\left (15 x^3-15 x^2+e^x\right )^3}+\frac {10125 x^8}{\left (15 x^3-15 x^2+e^x\right )^3}-\frac {10125 x^7}{\left (15 x^3-15 x^2+e^x\right )^3}+\frac {3375 x^6}{\left (15 x^3-15 x^2+e^x\right )^3}-\frac {675 e^x (x-1)^2 x^4}{\left (15 x^3-15 x^2+e^x\right )^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {32 \left (15 x (3 x-2)+e^x\right ) \exp \left (-\frac {2 \left (225 x^6-450 x^5+225 x^4+30 e^x (x-1) x^2+e^{2 x}-8\right )}{\left (15 (x-1) x^2+e^x\right )^2}\right )-3375 x^9+10125 x^8-10125 x^7+3375 x^6-675 e^x (x-1)^2 x^4-45 e^{2 x} (x-1) x^2-e^{3 x}}{\left (15 (x-1) x^2+e^x\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {32 \left (45 x^2-30 x+e^x\right ) \exp \left (-\frac {2 \left (225 x^6-450 x^5+225 x^4+30 e^x x^3-30 e^x x^2+e^{2 x}-8\right )}{\left (15 x^3-15 x^2+e^x\right )^2}\right )}{\left (15 x^3-15 x^2+e^x\right )^3}-\frac {45 e^{2 x} (x-1) x^2}{\left (15 x^3-15 x^2+e^x\right )^3}-\frac {e^{3 x}}{\left (15 x^3-15 x^2+e^x\right )^3}-\frac {3375 x^9}{\left (15 x^3-15 x^2+e^x\right )^3}+\frac {10125 x^8}{\left (15 x^3-15 x^2+e^x\right )^3}-\frac {10125 x^7}{\left (15 x^3-15 x^2+e^x\right )^3}+\frac {3375 x^6}{\left (15 x^3-15 x^2+e^x\right )^3}-\frac {675 e^x (x-1)^2 x^4}{\left (15 x^3-15 x^2+e^x\right )^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {32 \left (15 x (3 x-2)+e^x\right ) \exp \left (-\frac {2 \left (225 x^6-450 x^5+225 x^4+30 e^x (x-1) x^2+e^{2 x}-8\right )}{\left (15 (x-1) x^2+e^x\right )^2}\right )-3375 x^9+10125 x^8-10125 x^7+3375 x^6-675 e^x (x-1)^2 x^4-45 e^{2 x} (x-1) x^2-e^{3 x}}{\left (15 (x-1) x^2+e^x\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {32 \left (45 x^2-30 x+e^x\right ) \exp \left (-\frac {2 \left (225 x^6-450 x^5+225 x^4+30 e^x x^3-30 e^x x^2+e^{2 x}-8\right )}{\left (15 x^3-15 x^2+e^x\right )^2}\right )}{\left (15 x^3-15 x^2+e^x\right )^3}-\frac {45 e^{2 x} (x-1) x^2}{\left (15 x^3-15 x^2+e^x\right )^3}-\frac {e^{3 x}}{\left (15 x^3-15 x^2+e^x\right )^3}-\frac {3375 x^9}{\left (15 x^3-15 x^2+e^x\right )^3}+\frac {10125 x^8}{\left (15 x^3-15 x^2+e^x\right )^3}-\frac {10125 x^7}{\left (15 x^3-15 x^2+e^x\right )^3}+\frac {3375 x^6}{\left (15 x^3-15 x^2+e^x\right )^3}-\frac {675 e^x (x-1)^2 x^4}{\left (15 x^3-15 x^2+e^x\right )^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {32 \left (15 x (3 x-2)+e^x\right ) \exp \left (-\frac {2 \left (225 x^6-450 x^5+225 x^4+30 e^x (x-1) x^2+e^{2 x}-8\right )}{\left (15 (x-1) x^2+e^x\right )^2}\right )-3375 x^9+10125 x^8-10125 x^7+3375 x^6-675 e^x (x-1)^2 x^4-45 e^{2 x} (x-1) x^2-e^{3 x}}{\left (15 (x-1) x^2+e^x\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {32 \left (45 x^2-30 x+e^x\right ) \exp \left (-\frac {2 \left (225 x^6-450 x^5+225 x^4+30 e^x x^3-30 e^x x^2+e^{2 x}-8\right )}{\left (15 x^3-15 x^2+e^x\right )^2}\right )}{\left (15 x^3-15 x^2+e^x\right )^3}-\frac {45 e^{2 x} (x-1) x^2}{\left (15 x^3-15 x^2+e^x\right )^3}-\frac {e^{3 x}}{\left (15 x^3-15 x^2+e^x\right )^3}-\frac {3375 x^9}{\left (15 x^3-15 x^2+e^x\right )^3}+\frac {10125 x^8}{\left (15 x^3-15 x^2+e^x\right )^3}-\frac {10125 x^7}{\left (15 x^3-15 x^2+e^x\right )^3}+\frac {3375 x^6}{\left (15 x^3-15 x^2+e^x\right )^3}-\frac {675 e^x (x-1)^2 x^4}{\left (15 x^3-15 x^2+e^x\right )^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {32 \left (15 x (3 x-2)+e^x\right ) \exp \left (-\frac {2 \left (225 x^6-450 x^5+225 x^4+30 e^x (x-1) x^2+e^{2 x}-8\right )}{\left (15 (x-1) x^2+e^x\right )^2}\right )-3375 x^9+10125 x^8-10125 x^7+3375 x^6-675 e^x (x-1)^2 x^4-45 e^{2 x} (x-1) x^2-e^{3 x}}{\left (15 (x-1) x^2+e^x\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {32 \left (45 x^2-30 x+e^x\right ) \exp \left (-\frac {2 \left (225 x^6-450 x^5+225 x^4+30 e^x x^3-30 e^x x^2+e^{2 x}-8\right )}{\left (15 x^3-15 x^2+e^x\right )^2}\right )}{\left (15 x^3-15 x^2+e^x\right )^3}-\frac {45 e^{2 x} (x-1) x^2}{\left (15 x^3-15 x^2+e^x\right )^3}-\frac {e^{3 x}}{\left (15 x^3-15 x^2+e^x\right )^3}-\frac {3375 x^9}{\left (15 x^3-15 x^2+e^x\right )^3}+\frac {10125 x^8}{\left (15 x^3-15 x^2+e^x\right )^3}-\frac {10125 x^7}{\left (15 x^3-15 x^2+e^x\right )^3}+\frac {3375 x^6}{\left (15 x^3-15 x^2+e^x\right )^3}-\frac {675 e^x (x-1)^2 x^4}{\left (15 x^3-15 x^2+e^x\right )^3}\right )dx\) |
Input:
Int[(-E^(3*x) + 3375*x^6 - 10125*x^7 + 10125*x^8 - 3375*x^9 + E^((16 - 2*E ^(2*x) - 450*x^4 + 900*x^5 - 450*x^6 + E^x*(60*x^2 - 60*x^3))/(E^(2*x) + 2 25*x^4 - 450*x^5 + 225*x^6 + E^x*(-30*x^2 + 30*x^3)))*(32*E^x - 960*x + 14 40*x^2) + E^(2*x)*(45*x^2 - 45*x^3) + E^x*(-675*x^4 + 1350*x^5 - 675*x^6)) /(E^(3*x) - 3375*x^6 + 10125*x^7 - 10125*x^8 + 3375*x^9 + E^(2*x)*(-45*x^2 + 45*x^3) + E^x*(675*x^4 - 1350*x^5 + 675*x^6)),x]
Output:
$Aborted
Leaf count of result is larger than twice the leaf count of optimal. \(80\) vs. \(2(26)=52\).
Time = 17.04 (sec) , antiderivative size = 81, normalized size of antiderivative = 2.89
| method | result | size |
| risch | \(-x -{\mathrm e}^{-\frac {2 \left (225 x^{6}-450 x^{5}+30 \,{\mathrm e}^{x} x^{3}+225 x^{4}-30 \,{\mathrm e}^{x} x^{2}+{\mathrm e}^{2 x}-8\right )}{225 x^{6}-450 x^{5}+30 \,{\mathrm e}^{x} x^{3}+225 x^{4}-30 \,{\mathrm e}^{x} x^{2}+{\mathrm e}^{2 x}}}\) | \(81\) |
| parallelrisch | \(-x -{\mathrm e}^{\frac {-2 \,{\mathrm e}^{2 x}+\left (-60 x^{3}+60 x^{2}\right ) {\mathrm e}^{x}-450 x^{6}+900 x^{5}-450 x^{4}+16}{225 x^{6}-450 x^{5}+30 \,{\mathrm e}^{x} x^{3}+225 x^{4}-30 \,{\mathrm e}^{x} x^{2}+{\mathrm e}^{2 x}}}-\frac {5}{2}\) | \(83\) |
Input:
int(((32*exp(x)+1440*x^2-960*x)*exp((-2*exp(x)^2+(-60*x^3+60*x^2)*exp(x)-4 50*x^6+900*x^5-450*x^4+16)/(exp(x)^2+(30*x^3-30*x^2)*exp(x)+225*x^6-450*x^ 5+225*x^4))-exp(x)^3+(-45*x^3+45*x^2)*exp(x)^2+(-675*x^6+1350*x^5-675*x^4) *exp(x)-3375*x^9+10125*x^8-10125*x^7+3375*x^6)/(exp(x)^3+(45*x^3-45*x^2)*e xp(x)^2+(675*x^6-1350*x^5+675*x^4)*exp(x)+3375*x^9-10125*x^8+10125*x^7-337 5*x^6),x,method=_RETURNVERBOSE)
Output:
-x-exp(-2*(225*x^6-450*x^5+30*exp(x)*x^3+225*x^4-30*exp(x)*x^2+exp(2*x)-8) /(225*x^6-450*x^5+30*exp(x)*x^3+225*x^4-30*exp(x)*x^2+exp(2*x)))
Leaf count of result is larger than twice the leaf count of optimal. 78 vs. \(2 (24) = 48\).
Time = 0.07 (sec) , antiderivative size = 78, normalized size of antiderivative = 2.79 \[ \int \frac {-e^{3 x}+3375 x^6-10125 x^7+10125 x^8-3375 x^9+e^{\frac {16-2 e^{2 x}-450 x^4+900 x^5-450 x^6+e^x \left (60 x^2-60 x^3\right )}{e^{2 x}+225 x^4-450 x^5+225 x^6+e^x \left (-30 x^2+30 x^3\right )}} \left (32 e^x-960 x+1440 x^2\right )+e^{2 x} \left (45 x^2-45 x^3\right )+e^x \left (-675 x^4+1350 x^5-675 x^6\right )}{e^{3 x}-3375 x^6+10125 x^7-10125 x^8+3375 x^9+e^{2 x} \left (-45 x^2+45 x^3\right )+e^x \left (675 x^4-1350 x^5+675 x^6\right )} \, dx=-x - e^{\left (-\frac {2 \, {\left (225 \, x^{6} - 450 \, x^{5} + 225 \, x^{4} + 30 \, {\left (x^{3} - x^{2}\right )} e^{x} + e^{\left (2 \, x\right )} - 8\right )}}{225 \, x^{6} - 450 \, x^{5} + 225 \, x^{4} + 30 \, {\left (x^{3} - x^{2}\right )} e^{x} + e^{\left (2 \, x\right )}}\right )} \] Input:
integrate(((32*exp(x)+1440*x^2-960*x)*exp((-2*exp(x)^2+(-60*x^3+60*x^2)*ex p(x)-450*x^6+900*x^5-450*x^4+16)/(exp(x)^2+(30*x^3-30*x^2)*exp(x)+225*x^6- 450*x^5+225*x^4))-exp(x)^3+(-45*x^3+45*x^2)*exp(x)^2+(-675*x^6+1350*x^5-67 5*x^4)*exp(x)-3375*x^9+10125*x^8-10125*x^7+3375*x^6)/(exp(x)^3+(45*x^3-45* x^2)*exp(x)^2+(675*x^6-1350*x^5+675*x^4)*exp(x)+3375*x^9-10125*x^8+10125*x ^7-3375*x^6),x, algorithm="fricas")
Output:
-x - e^(-2*(225*x^6 - 450*x^5 + 225*x^4 + 30*(x^3 - x^2)*e^x + e^(2*x) - 8 )/(225*x^6 - 450*x^5 + 225*x^4 + 30*(x^3 - x^2)*e^x + e^(2*x)))
Leaf count of result is larger than twice the leaf count of optimal. 75 vs. \(2 (22) = 44\).
Time = 0.40 (sec) , antiderivative size = 75, normalized size of antiderivative = 2.68 \[ \int \frac {-e^{3 x}+3375 x^6-10125 x^7+10125 x^8-3375 x^9+e^{\frac {16-2 e^{2 x}-450 x^4+900 x^5-450 x^6+e^x \left (60 x^2-60 x^3\right )}{e^{2 x}+225 x^4-450 x^5+225 x^6+e^x \left (-30 x^2+30 x^3\right )}} \left (32 e^x-960 x+1440 x^2\right )+e^{2 x} \left (45 x^2-45 x^3\right )+e^x \left (-675 x^4+1350 x^5-675 x^6\right )}{e^{3 x}-3375 x^6+10125 x^7-10125 x^8+3375 x^9+e^{2 x} \left (-45 x^2+45 x^3\right )+e^x \left (675 x^4-1350 x^5+675 x^6\right )} \, dx=- x - e^{\frac {- 450 x^{6} + 900 x^{5} - 450 x^{4} + \left (- 60 x^{3} + 60 x^{2}\right ) e^{x} - 2 e^{2 x} + 16}{225 x^{6} - 450 x^{5} + 225 x^{4} + \left (30 x^{3} - 30 x^{2}\right ) e^{x} + e^{2 x}}} \] Input:
integrate(((32*exp(x)+1440*x**2-960*x)*exp((-2*exp(x)**2+(-60*x**3+60*x**2 )*exp(x)-450*x**6+900*x**5-450*x**4+16)/(exp(x)**2+(30*x**3-30*x**2)*exp(x )+225*x**6-450*x**5+225*x**4))-exp(x)**3+(-45*x**3+45*x**2)*exp(x)**2+(-67 5*x**6+1350*x**5-675*x**4)*exp(x)-3375*x**9+10125*x**8-10125*x**7+3375*x** 6)/(exp(x)**3+(45*x**3-45*x**2)*exp(x)**2+(675*x**6-1350*x**5+675*x**4)*ex p(x)+3375*x**9-10125*x**8+10125*x**7-3375*x**6),x)
Output:
-x - exp((-450*x**6 + 900*x**5 - 450*x**4 + (-60*x**3 + 60*x**2)*exp(x) - 2*exp(2*x) + 16)/(225*x**6 - 450*x**5 + 225*x**4 + (30*x**3 - 30*x**2)*exp (x) + exp(2*x)))
Leaf count of result is larger than twice the leaf count of optimal. 173 vs. \(2 (24) = 48\).
Time = 0.58 (sec) , antiderivative size = 173, normalized size of antiderivative = 6.18 \[ \int \frac {-e^{3 x}+3375 x^6-10125 x^7+10125 x^8-3375 x^9+e^{\frac {16-2 e^{2 x}-450 x^4+900 x^5-450 x^6+e^x \left (60 x^2-60 x^3\right )}{e^{2 x}+225 x^4-450 x^5+225 x^6+e^x \left (-30 x^2+30 x^3\right )}} \left (32 e^x-960 x+1440 x^2\right )+e^{2 x} \left (45 x^2-45 x^3\right )+e^x \left (-675 x^4+1350 x^5-675 x^6\right )}{e^{3 x}-3375 x^6+10125 x^7-10125 x^8+3375 x^9+e^{2 x} \left (-45 x^2+45 x^3\right )+e^x \left (675 x^4-1350 x^5+675 x^6\right )} \, dx=-{\left (x e^{\left (\frac {2 \, e^{\left (2 \, x\right )}}{225 \, x^{6} - 450 \, x^{5} + 225 \, x^{4} + 30 \, {\left (x^{3} - x^{2}\right )} e^{x} + e^{\left (2 \, x\right )}} + 2\right )} + e^{\left (\frac {2 \, e^{\left (2 \, x\right )}}{225 \, x^{6} - 450 \, x^{5} + 225 \, x^{4} + 30 \, {\left (x^{3} - x^{2}\right )} e^{x} + e^{\left (2 \, x\right )}} + \frac {16}{225 \, x^{6} - 450 \, x^{5} + 225 \, x^{4} + 30 \, {\left (x^{3} - x^{2}\right )} e^{x} + e^{\left (2 \, x\right )}}\right )}\right )} e^{\left (-\frac {2 \, e^{\left (2 \, x\right )}}{225 \, x^{6} - 450 \, x^{5} + 225 \, x^{4} + 30 \, {\left (x^{3} - x^{2}\right )} e^{x} + e^{\left (2 \, x\right )}} - 2\right )} \] Input:
integrate(((32*exp(x)+1440*x^2-960*x)*exp((-2*exp(x)^2+(-60*x^3+60*x^2)*ex p(x)-450*x^6+900*x^5-450*x^4+16)/(exp(x)^2+(30*x^3-30*x^2)*exp(x)+225*x^6- 450*x^5+225*x^4))-exp(x)^3+(-45*x^3+45*x^2)*exp(x)^2+(-675*x^6+1350*x^5-67 5*x^4)*exp(x)-3375*x^9+10125*x^8-10125*x^7+3375*x^6)/(exp(x)^3+(45*x^3-45* x^2)*exp(x)^2+(675*x^6-1350*x^5+675*x^4)*exp(x)+3375*x^9-10125*x^8+10125*x ^7-3375*x^6),x, algorithm="maxima")
Output:
-(x*e^(2*e^(2*x)/(225*x^6 - 450*x^5 + 225*x^4 + 30*(x^3 - x^2)*e^x + e^(2* x)) + 2) + e^(2*e^(2*x)/(225*x^6 - 450*x^5 + 225*x^4 + 30*(x^3 - x^2)*e^x + e^(2*x)) + 16/(225*x^6 - 450*x^5 + 225*x^4 + 30*(x^3 - x^2)*e^x + e^(2*x ))))*e^(-2*e^(2*x)/(225*x^6 - 450*x^5 + 225*x^4 + 30*(x^3 - x^2)*e^x + e^( 2*x)) - 2)
\[ \int \frac {-e^{3 x}+3375 x^6-10125 x^7+10125 x^8-3375 x^9+e^{\frac {16-2 e^{2 x}-450 x^4+900 x^5-450 x^6+e^x \left (60 x^2-60 x^3\right )}{e^{2 x}+225 x^4-450 x^5+225 x^6+e^x \left (-30 x^2+30 x^3\right )}} \left (32 e^x-960 x+1440 x^2\right )+e^{2 x} \left (45 x^2-45 x^3\right )+e^x \left (-675 x^4+1350 x^5-675 x^6\right )}{e^{3 x}-3375 x^6+10125 x^7-10125 x^8+3375 x^9+e^{2 x} \left (-45 x^2+45 x^3\right )+e^x \left (675 x^4-1350 x^5+675 x^6\right )} \, dx=\int { -\frac {3375 \, x^{9} - 10125 \, x^{8} + 10125 \, x^{7} - 3375 \, x^{6} + 45 \, {\left (x^{3} - x^{2}\right )} e^{\left (2 \, x\right )} + 675 \, {\left (x^{6} - 2 \, x^{5} + x^{4}\right )} e^{x} - 32 \, {\left (45 \, x^{2} - 30 \, x + e^{x}\right )} e^{\left (-\frac {2 \, {\left (225 \, x^{6} - 450 \, x^{5} + 225 \, x^{4} + 30 \, {\left (x^{3} - x^{2}\right )} e^{x} + e^{\left (2 \, x\right )} - 8\right )}}{225 \, x^{6} - 450 \, x^{5} + 225 \, x^{4} + 30 \, {\left (x^{3} - x^{2}\right )} e^{x} + e^{\left (2 \, x\right )}}\right )} + e^{\left (3 \, x\right )}}{3375 \, x^{9} - 10125 \, x^{8} + 10125 \, x^{7} - 3375 \, x^{6} + 45 \, {\left (x^{3} - x^{2}\right )} e^{\left (2 \, x\right )} + 675 \, {\left (x^{6} - 2 \, x^{5} + x^{4}\right )} e^{x} + e^{\left (3 \, x\right )}} \,d x } \] Input:
integrate(((32*exp(x)+1440*x^2-960*x)*exp((-2*exp(x)^2+(-60*x^3+60*x^2)*ex p(x)-450*x^6+900*x^5-450*x^4+16)/(exp(x)^2+(30*x^3-30*x^2)*exp(x)+225*x^6- 450*x^5+225*x^4))-exp(x)^3+(-45*x^3+45*x^2)*exp(x)^2+(-675*x^6+1350*x^5-67 5*x^4)*exp(x)-3375*x^9+10125*x^8-10125*x^7+3375*x^6)/(exp(x)^3+(45*x^3-45* x^2)*exp(x)^2+(675*x^6-1350*x^5+675*x^4)*exp(x)+3375*x^9-10125*x^8+10125*x ^7-3375*x^6),x, algorithm="giac")
Output:
integrate(-(3375*x^9 - 10125*x^8 + 10125*x^7 - 3375*x^6 + 45*(x^3 - x^2)*e ^(2*x) + 675*(x^6 - 2*x^5 + x^4)*e^x - 32*(45*x^2 - 30*x + e^x)*e^(-2*(225 *x^6 - 450*x^5 + 225*x^4 + 30*(x^3 - x^2)*e^x + e^(2*x) - 8)/(225*x^6 - 45 0*x^5 + 225*x^4 + 30*(x^3 - x^2)*e^x + e^(2*x))) + e^(3*x))/(3375*x^9 - 10 125*x^8 + 10125*x^7 - 3375*x^6 + 45*(x^3 - x^2)*e^(2*x) + 675*(x^6 - 2*x^5 + x^4)*e^x + e^(3*x)), x)
Time = 2.04 (sec) , antiderivative size = 302, normalized size of antiderivative = 10.79 \[ \int \frac {-e^{3 x}+3375 x^6-10125 x^7+10125 x^8-3375 x^9+e^{\frac {16-2 e^{2 x}-450 x^4+900 x^5-450 x^6+e^x \left (60 x^2-60 x^3\right )}{e^{2 x}+225 x^4-450 x^5+225 x^6+e^x \left (-30 x^2+30 x^3\right )}} \left (32 e^x-960 x+1440 x^2\right )+e^{2 x} \left (45 x^2-45 x^3\right )+e^x \left (-675 x^4+1350 x^5-675 x^6\right )}{e^{3 x}-3375 x^6+10125 x^7-10125 x^8+3375 x^9+e^{2 x} \left (-45 x^2+45 x^3\right )+e^x \left (675 x^4-1350 x^5+675 x^6\right )} \, dx=-x-{\mathrm {e}}^{\frac {60\,x^2\,{\mathrm {e}}^x}{{\mathrm {e}}^{2\,x}-30\,x^2\,{\mathrm {e}}^x+30\,x^3\,{\mathrm {e}}^x+225\,x^4-450\,x^5+225\,x^6}}\,{\mathrm {e}}^{-\frac {60\,x^3\,{\mathrm {e}}^x}{{\mathrm {e}}^{2\,x}-30\,x^2\,{\mathrm {e}}^x+30\,x^3\,{\mathrm {e}}^x+225\,x^4-450\,x^5+225\,x^6}}\,{\mathrm {e}}^{-\frac {450\,x^4}{{\mathrm {e}}^{2\,x}-30\,x^2\,{\mathrm {e}}^x+30\,x^3\,{\mathrm {e}}^x+225\,x^4-450\,x^5+225\,x^6}}\,{\mathrm {e}}^{-\frac {450\,x^6}{{\mathrm {e}}^{2\,x}-30\,x^2\,{\mathrm {e}}^x+30\,x^3\,{\mathrm {e}}^x+225\,x^4-450\,x^5+225\,x^6}}\,{\mathrm {e}}^{\frac {900\,x^5}{{\mathrm {e}}^{2\,x}-30\,x^2\,{\mathrm {e}}^x+30\,x^3\,{\mathrm {e}}^x+225\,x^4-450\,x^5+225\,x^6}}\,{\mathrm {e}}^{\frac {16}{{\mathrm {e}}^{2\,x}-30\,x^2\,{\mathrm {e}}^x+30\,x^3\,{\mathrm {e}}^x+225\,x^4-450\,x^5+225\,x^6}}\,{\mathrm {e}}^{-\frac {2\,{\mathrm {e}}^{2\,x}}{{\mathrm {e}}^{2\,x}-30\,x^2\,{\mathrm {e}}^x+30\,x^3\,{\mathrm {e}}^x+225\,x^4-450\,x^5+225\,x^6}} \] Input:
int(-(exp(3*x) - exp(-(2*exp(2*x) - exp(x)*(60*x^2 - 60*x^3) + 450*x^4 - 9 00*x^5 + 450*x^6 - 16)/(exp(2*x) - exp(x)*(30*x^2 - 30*x^3) + 225*x^4 - 45 0*x^5 + 225*x^6))*(32*exp(x) - 960*x + 1440*x^2) + exp(x)*(675*x^4 - 1350* x^5 + 675*x^6) - exp(2*x)*(45*x^2 - 45*x^3) - 3375*x^6 + 10125*x^7 - 10125 *x^8 + 3375*x^9)/(exp(3*x) + exp(x)*(675*x^4 - 1350*x^5 + 675*x^6) - exp(2 *x)*(45*x^2 - 45*x^3) - 3375*x^6 + 10125*x^7 - 10125*x^8 + 3375*x^9),x)
Output:
- x - exp((60*x^2*exp(x))/(exp(2*x) - 30*x^2*exp(x) + 30*x^3*exp(x) + 225* x^4 - 450*x^5 + 225*x^6))*exp(-(60*x^3*exp(x))/(exp(2*x) - 30*x^2*exp(x) + 30*x^3*exp(x) + 225*x^4 - 450*x^5 + 225*x^6))*exp(-(450*x^4)/(exp(2*x) - 30*x^2*exp(x) + 30*x^3*exp(x) + 225*x^4 - 450*x^5 + 225*x^6))*exp(-(450*x^ 6)/(exp(2*x) - 30*x^2*exp(x) + 30*x^3*exp(x) + 225*x^4 - 450*x^5 + 225*x^6 ))*exp((900*x^5)/(exp(2*x) - 30*x^2*exp(x) + 30*x^3*exp(x) + 225*x^4 - 450 *x^5 + 225*x^6))*exp(16/(exp(2*x) - 30*x^2*exp(x) + 30*x^3*exp(x) + 225*x^ 4 - 450*x^5 + 225*x^6))*exp(-(2*exp(2*x))/(exp(2*x) - 30*x^2*exp(x) + 30*x ^3*exp(x) + 225*x^4 - 450*x^5 + 225*x^6))
Time = 0.19 (sec) , antiderivative size = 56, normalized size of antiderivative = 2.00 \[ \int \frac {-e^{3 x}+3375 x^6-10125 x^7+10125 x^8-3375 x^9+e^{\frac {16-2 e^{2 x}-450 x^4+900 x^5-450 x^6+e^x \left (60 x^2-60 x^3\right )}{e^{2 x}+225 x^4-450 x^5+225 x^6+e^x \left (-30 x^2+30 x^3\right )}} \left (32 e^x-960 x+1440 x^2\right )+e^{2 x} \left (45 x^2-45 x^3\right )+e^x \left (-675 x^4+1350 x^5-675 x^6\right )}{e^{3 x}-3375 x^6+10125 x^7-10125 x^8+3375 x^9+e^{2 x} \left (-45 x^2+45 x^3\right )+e^x \left (675 x^4-1350 x^5+675 x^6\right )} \, dx=\frac {-e^{\frac {16}{e^{2 x}+30 e^{x} x^{3}-30 e^{x} x^{2}+225 x^{6}-450 x^{5}+225 x^{4}}}-e^{2} x}{e^{2}} \] Input:
int(((32*exp(x)+1440*x^2-960*x)*exp((-2*exp(x)^2+(-60*x^3+60*x^2)*exp(x)-4 50*x^6+900*x^5-450*x^4+16)/(exp(x)^2+(30*x^3-30*x^2)*exp(x)+225*x^6-450*x^ 5+225*x^4))-exp(x)^3+(-45*x^3+45*x^2)*exp(x)^2+(-675*x^6+1350*x^5-675*x^4) *exp(x)-3375*x^9+10125*x^8-10125*x^7+3375*x^6)/(exp(x)^3+(45*x^3-45*x^2)*e xp(x)^2+(675*x^6-1350*x^5+675*x^4)*exp(x)+3375*x^9-10125*x^8+10125*x^7-337 5*x^6),x)
Output:
( - (e**(16/(e**(2*x) + 30*e**x*x**3 - 30*e**x*x**2 + 225*x**6 - 450*x**5 + 225*x**4)) + e**2*x))/e**2