Integrand size = 215, antiderivative size = 29 \[ \int \frac {e^{84+2 x} \left (4 x^4-2 x^5\right )+e^{42+x} \left (4 x^6-2 x^7\right )+e^{x^2} \left (2 x^7-4 x^9+e^{126+3 x} \left (2 x-4 x^3\right )+e^{84+2 x} \left (6 x^3-12 x^5\right )+e^{42+x} \left (6 x^5-12 x^7\right )\right )}{-x^9+e^{3 x^2} \left (e^{126+3 x}+3 e^{84+2 x} x^2+3 e^{42+x} x^4+x^6\right )+e^{2 x^2} \left (-3 e^{84+2 x} x^3-6 e^{42+x} x^5-3 x^7\right )+e^{x^2} \left (3 e^{42+x} x^6+3 x^8\right )} \, dx=\frac {x^2}{\left (-e^{x^2}+\frac {x^3}{e^{42+x}+x^2}\right )^2} \] Output:
x^2/(x^3/(x^2+exp(x+42))-exp(x^2))^2
Time = 5.95 (sec) , antiderivative size = 40, normalized size of antiderivative = 1.38 \[ \int \frac {e^{84+2 x} \left (4 x^4-2 x^5\right )+e^{42+x} \left (4 x^6-2 x^7\right )+e^{x^2} \left (2 x^7-4 x^9+e^{126+3 x} \left (2 x-4 x^3\right )+e^{84+2 x} \left (6 x^3-12 x^5\right )+e^{42+x} \left (6 x^5-12 x^7\right )\right )}{-x^9+e^{3 x^2} \left (e^{126+3 x}+3 e^{84+2 x} x^2+3 e^{42+x} x^4+x^6\right )+e^{2 x^2} \left (-3 e^{84+2 x} x^3-6 e^{42+x} x^5-3 x^7\right )+e^{x^2} \left (3 e^{42+x} x^6+3 x^8\right )} \, dx=\frac {x^2 \left (e^{42+x}+x^2\right )^2}{\left (e^{42+x+x^2}+e^{x^2} x^2-x^3\right )^2} \] Input:
Integrate[(E^(84 + 2*x)*(4*x^4 - 2*x^5) + E^(42 + x)*(4*x^6 - 2*x^7) + E^x ^2*(2*x^7 - 4*x^9 + E^(126 + 3*x)*(2*x - 4*x^3) + E^(84 + 2*x)*(6*x^3 - 12 *x^5) + E^(42 + x)*(6*x^5 - 12*x^7)))/(-x^9 + E^(3*x^2)*(E^(126 + 3*x) + 3 *E^(84 + 2*x)*x^2 + 3*E^(42 + x)*x^4 + x^6) + E^(2*x^2)*(-3*E^(84 + 2*x)*x ^3 - 6*E^(42 + x)*x^5 - 3*x^7) + E^x^2*(3*E^(42 + x)*x^6 + 3*x^8)),x]
Output:
(x^2*(E^(42 + x) + x^2)^2)/(E^(42 + x + x^2) + E^x^2*x^2 - x^3)^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.
| \(\displaystyle \int \frac {e^{x+42} \left (4 x^6-2 x^7\right )+e^{2 x+84} \left (4 x^4-2 x^5\right )+e^{x^2} \left (-4 x^9+2 x^7+e^{3 x+126} \left (2 x-4 x^3\right )+e^{x+42} \left (6 x^5-12 x^7\right )+e^{2 x+84} \left (6 x^3-12 x^5\right )\right )}{-x^9+e^{x^2} \left (3 x^8+3 e^{x+42} x^6\right )+e^{3 x^2} \left (x^6+3 e^{x+42} x^4+3 e^{2 x+84} x^2+e^{3 x+126}\right )+e^{2 x^2} \left (-3 x^7-6 e^{x+42} x^5-3 e^{2 x+84} x^3\right )} \, dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {2 x \left (x^2+e^{x+42}\right ) \left (-e^{x+42} (x-2) x^3-2 e^{x^2+x+42} \left (2 x^2-1\right ) x^2-e^{x^2+2 x+84} \left (2 x^2-1\right )-e^{x^2} \left (2 x^2-1\right ) x^4\right )}{\left (-x^3+e^{x^2} x^2+e^{x^2+x+42}\right )^3}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle 2 \int \frac {x \left (x^2+e^{x+42}\right ) \left (e^{x^2} \left (1-2 x^2\right ) x^4+e^{x+42} (2-x) x^3+2 e^{x^2+x+42} \left (1-2 x^2\right ) x^2+e^{x^2+2 x+84} \left (1-2 x^2\right )\right )}{\left (-x^3+e^{x^2} x^2+e^{x^2+x+42}\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 2 \int \left (\frac {x^4 \left (2 x^6+4 e^{x+42} x^4-x^4+e^{x+42} x^3-4 e^{x+42} x^2+2 e^{2 x+84} x^2+e^{2 x+84} x-3 e^{2 x+84}\right )}{\left (x^3-e^{x^2} x^2-e^{x^2+x+42}\right )^3}-\frac {x \left (x^2+e^{x+42}\right )^2 \left (2 x^2-1\right )}{\left (x^3-e^{x^2} x^2-e^{x^2+x+42}\right )^2}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle 2 \left (\int \frac {e^{2 x+84} x}{\left (-x^3+e^{x^2} x^2+e^{x^2+x+42}\right )^2}dx+2 \int \frac {e^{x+42} x^3}{\left (-x^3+e^{x^2} x^2+e^{x^2+x+42}\right )^2}dx-2 \int \frac {e^{2 x+84} x^3}{\left (-x^3+e^{x^2} x^2+e^{x^2+x+42}\right )^2}dx+2 \int \frac {x^{10}}{\left (x^3-e^{x^2} x^2-e^{x^2+x+42}\right )^3}dx-4 \int \frac {e^{x+42} x^8}{\left (-x^3+e^{x^2} x^2+e^{x^2+x+42}\right )^3}dx-\int \frac {x^8}{\left (x^3-e^{x^2} x^2-e^{x^2+x+42}\right )^3}dx-\int \frac {e^{x+42} x^7}{\left (-x^3+e^{x^2} x^2+e^{x^2+x+42}\right )^3}dx-2 \int \frac {x^7}{\left (x^3-e^{x^2} x^2-e^{x^2+x+42}\right )^2}dx+4 \int \frac {e^{x+42} x^6}{\left (-x^3+e^{x^2} x^2+e^{x^2+x+42}\right )^3}dx-2 \int \frac {e^{2 x+84} x^6}{\left (-x^3+e^{x^2} x^2+e^{x^2+x+42}\right )^3}dx-\int \frac {e^{2 x+84} x^5}{\left (-x^3+e^{x^2} x^2+e^{x^2+x+42}\right )^3}dx-4 \int \frac {e^{x+42} x^5}{\left (-x^3+e^{x^2} x^2+e^{x^2+x+42}\right )^2}dx+\int \frac {x^5}{\left (x^3-e^{x^2} x^2-e^{x^2+x+42}\right )^2}dx+3 \int \frac {e^{2 x+84} x^4}{\left (-x^3+e^{x^2} x^2+e^{x^2+x+42}\right )^3}dx\right )\) |
Input:
Int[(E^(84 + 2*x)*(4*x^4 - 2*x^5) + E^(42 + x)*(4*x^6 - 2*x^7) + E^x^2*(2* x^7 - 4*x^9 + E^(126 + 3*x)*(2*x - 4*x^3) + E^(84 + 2*x)*(6*x^3 - 12*x^5) + E^(42 + x)*(6*x^5 - 12*x^7)))/(-x^9 + E^(3*x^2)*(E^(126 + 3*x) + 3*E^(84 + 2*x)*x^2 + 3*E^(42 + x)*x^4 + x^6) + E^(2*x^2)*(-3*E^(84 + 2*x)*x^3 - 6 *E^(42 + x)*x^5 - 3*x^7) + E^x^2*(3*E^(42 + x)*x^6 + 3*x^8)),x]
Output:
$Aborted
Leaf count of result is larger than twice the leaf count of optimal. \(68\) vs. \(2(27)=54\).
Time = 2.13 (sec) , antiderivative size = 69, normalized size of antiderivative = 2.38
| method | result | size |
| risch | \(x^{2} {\mathrm e}^{-2 x^{2}}-\frac {\left (x^{3}-2 x^{2} {\mathrm e}^{x^{2}}-2 \,{\mathrm e}^{x^{2}+x +42}\right ) x^{5} {\mathrm e}^{-2 x^{2}}}{\left (x^{3}-x^{2} {\mathrm e}^{x^{2}}-{\mathrm e}^{x^{2}+x +42}\right )^{2}}\) | \(69\) |
| parallelrisch | \(-\frac {-2 x^{6}-4 x^{4} {\mathrm e}^{x +42}-2 x^{2} {\mathrm e}^{2 x +84}}{2 \left (x^{6}-2 \,{\mathrm e}^{x^{2}} x^{5}+x^{4} {\mathrm e}^{2 x^{2}}-2 x^{3} {\mathrm e}^{x^{2}} {\mathrm e}^{x +42}+2 \,{\mathrm e}^{x +42} {\mathrm e}^{2 x^{2}} x^{2}+{\mathrm e}^{2 x +84} {\mathrm e}^{2 x^{2}}\right )}\) | \(95\) |
Input:
int((((-4*x^3+2*x)*exp(x+42)^3+(-12*x^5+6*x^3)*exp(x+42)^2+(-12*x^7+6*x^5) *exp(x+42)-4*x^9+2*x^7)*exp(x^2)+(-2*x^5+4*x^4)*exp(x+42)^2+(-2*x^7+4*x^6) *exp(x+42))/((exp(x+42)^3+3*x^2*exp(x+42)^2+3*x^4*exp(x+42)+x^6)*exp(x^2)^ 3+(-3*x^3*exp(x+42)^2-6*x^5*exp(x+42)-3*x^7)*exp(x^2)^2+(3*x^6*exp(x+42)+3 *x^8)*exp(x^2)-x^9),x,method=_RETURNVERBOSE)
Output:
x^2*exp(-2*x^2)-(x^3-2*x^2*exp(x^2)-2*exp(x^2+x+42))*x^5/(x^3-x^2*exp(x^2) -exp(x^2+x+42))^2*exp(-2*x^2)
Leaf count of result is larger than twice the leaf count of optimal. 74 vs. \(2 (27) = 54\).
Time = 0.09 (sec) , antiderivative size = 74, normalized size of antiderivative = 2.55 \[ \int \frac {e^{84+2 x} \left (4 x^4-2 x^5\right )+e^{42+x} \left (4 x^6-2 x^7\right )+e^{x^2} \left (2 x^7-4 x^9+e^{126+3 x} \left (2 x-4 x^3\right )+e^{84+2 x} \left (6 x^3-12 x^5\right )+e^{42+x} \left (6 x^5-12 x^7\right )\right )}{-x^9+e^{3 x^2} \left (e^{126+3 x}+3 e^{84+2 x} x^2+3 e^{42+x} x^4+x^6\right )+e^{2 x^2} \left (-3 e^{84+2 x} x^3-6 e^{42+x} x^5-3 x^7\right )+e^{x^2} \left (3 e^{42+x} x^6+3 x^8\right )} \, dx=\frac {x^{6} + 2 \, x^{4} e^{\left (x + 42\right )} + x^{2} e^{\left (2 \, x + 84\right )}}{x^{6} + {\left (x^{4} + 2 \, x^{2} e^{\left (x + 42\right )} + e^{\left (2 \, x + 84\right )}\right )} e^{\left (2 \, x^{2}\right )} - 2 \, {\left (x^{5} + x^{3} e^{\left (x + 42\right )}\right )} e^{\left (x^{2}\right )}} \] Input:
integrate((((-4*x^3+2*x)*exp(x+42)^3+(-12*x^5+6*x^3)*exp(x+42)^2+(-12*x^7+ 6*x^5)*exp(x+42)-4*x^9+2*x^7)*exp(x^2)+(-2*x^5+4*x^4)*exp(x+42)^2+(-2*x^7+ 4*x^6)*exp(x+42))/((exp(x+42)^3+3*x^2*exp(x+42)^2+3*x^4*exp(x+42)+x^6)*exp (x^2)^3+(-3*x^3*exp(x+42)^2-6*x^5*exp(x+42)-3*x^7)*exp(x^2)^2+(3*x^6*exp(x +42)+3*x^8)*exp(x^2)-x^9),x, algorithm="fricas")
Output:
(x^6 + 2*x^4*e^(x + 42) + x^2*e^(2*x + 84))/(x^6 + (x^4 + 2*x^2*e^(x + 42) + e^(2*x + 84))*e^(2*x^2) - 2*(x^5 + x^3*e^(x + 42))*e^(x^2))
Leaf count of result is larger than twice the leaf count of optimal. 112 vs. \(2 (20) = 40\).
Time = 0.21 (sec) , antiderivative size = 112, normalized size of antiderivative = 3.86 \[ \int \frac {e^{84+2 x} \left (4 x^4-2 x^5\right )+e^{42+x} \left (4 x^6-2 x^7\right )+e^{x^2} \left (2 x^7-4 x^9+e^{126+3 x} \left (2 x-4 x^3\right )+e^{84+2 x} \left (6 x^3-12 x^5\right )+e^{42+x} \left (6 x^5-12 x^7\right )\right )}{-x^9+e^{3 x^2} \left (e^{126+3 x}+3 e^{84+2 x} x^2+3 e^{42+x} x^4+x^6\right )+e^{2 x^2} \left (-3 e^{84+2 x} x^3-6 e^{42+x} x^5-3 x^7\right )+e^{x^2} \left (3 e^{42+x} x^6+3 x^8\right )} \, dx=x^{2} e^{- 2 x^{2}} + \frac {- x^{8} + 2 x^{7} e^{x^{2}} + 2 x^{5} e^{x^{2}} e^{x + 42}}{x^{6} e^{2 x^{2}} - 2 x^{5} e^{3 x^{2}} + x^{4} e^{4 x^{2}} + \left (- 2 x^{3} e^{3 x^{2}} + 2 x^{2} e^{4 x^{2}}\right ) e^{x + 42} + e^{4 x^{2}} e^{2 x + 84}} \] Input:
integrate((((-4*x**3+2*x)*exp(x+42)**3+(-12*x**5+6*x**3)*exp(x+42)**2+(-12 *x**7+6*x**5)*exp(x+42)-4*x**9+2*x**7)*exp(x**2)+(-2*x**5+4*x**4)*exp(x+42 )**2+(-2*x**7+4*x**6)*exp(x+42))/((exp(x+42)**3+3*x**2*exp(x+42)**2+3*x**4 *exp(x+42)+x**6)*exp(x**2)**3+(-3*x**3*exp(x+42)**2-6*x**5*exp(x+42)-3*x** 7)*exp(x**2)**2+(3*x**6*exp(x+42)+3*x**8)*exp(x**2)-x**9),x)
Output:
x**2*exp(-2*x**2) + (-x**8 + 2*x**7*exp(x**2) + 2*x**5*exp(x**2)*exp(x + 4 2))/(x**6*exp(2*x**2) - 2*x**5*exp(3*x**2) + x**4*exp(4*x**2) + (-2*x**3*e xp(3*x**2) + 2*x**2*exp(4*x**2))*exp(x + 42) + exp(4*x**2)*exp(2*x + 84))
Leaf count of result is larger than twice the leaf count of optimal. 74 vs. \(2 (27) = 54\).
Time = 1.21 (sec) , antiderivative size = 74, normalized size of antiderivative = 2.55 \[ \int \frac {e^{84+2 x} \left (4 x^4-2 x^5\right )+e^{42+x} \left (4 x^6-2 x^7\right )+e^{x^2} \left (2 x^7-4 x^9+e^{126+3 x} \left (2 x-4 x^3\right )+e^{84+2 x} \left (6 x^3-12 x^5\right )+e^{42+x} \left (6 x^5-12 x^7\right )\right )}{-x^9+e^{3 x^2} \left (e^{126+3 x}+3 e^{84+2 x} x^2+3 e^{42+x} x^4+x^6\right )+e^{2 x^2} \left (-3 e^{84+2 x} x^3-6 e^{42+x} x^5-3 x^7\right )+e^{x^2} \left (3 e^{42+x} x^6+3 x^8\right )} \, dx=\frac {x^{6} + 2 \, x^{4} e^{\left (x + 42\right )} + x^{2} e^{\left (2 \, x + 84\right )}}{x^{6} + {\left (x^{4} + 2 \, x^{2} e^{\left (x + 42\right )} + e^{\left (2 \, x + 84\right )}\right )} e^{\left (2 \, x^{2}\right )} - 2 \, {\left (x^{5} + x^{3} e^{\left (x + 42\right )}\right )} e^{\left (x^{2}\right )}} \] Input:
integrate((((-4*x^3+2*x)*exp(x+42)^3+(-12*x^5+6*x^3)*exp(x+42)^2+(-12*x^7+ 6*x^5)*exp(x+42)-4*x^9+2*x^7)*exp(x^2)+(-2*x^5+4*x^4)*exp(x+42)^2+(-2*x^7+ 4*x^6)*exp(x+42))/((exp(x+42)^3+3*x^2*exp(x+42)^2+3*x^4*exp(x+42)+x^6)*exp (x^2)^3+(-3*x^3*exp(x+42)^2-6*x^5*exp(x+42)-3*x^7)*exp(x^2)^2+(3*x^6*exp(x +42)+3*x^8)*exp(x^2)-x^9),x, algorithm="maxima")
Output:
(x^6 + 2*x^4*e^(x + 42) + x^2*e^(2*x + 84))/(x^6 + (x^4 + 2*x^2*e^(x + 42) + e^(2*x + 84))*e^(2*x^2) - 2*(x^5 + x^3*e^(x + 42))*e^(x^2))
Leaf count of result is larger than twice the leaf count of optimal. 758 vs. \(2 (27) = 54\).
Time = 6.98 (sec) , antiderivative size = 758, normalized size of antiderivative = 26.14 \[ \int \frac {e^{84+2 x} \left (4 x^4-2 x^5\right )+e^{42+x} \left (4 x^6-2 x^7\right )+e^{x^2} \left (2 x^7-4 x^9+e^{126+3 x} \left (2 x-4 x^3\right )+e^{84+2 x} \left (6 x^3-12 x^5\right )+e^{42+x} \left (6 x^5-12 x^7\right )\right )}{-x^9+e^{3 x^2} \left (e^{126+3 x}+3 e^{84+2 x} x^2+3 e^{42+x} x^4+x^6\right )+e^{2 x^2} \left (-3 e^{84+2 x} x^3-6 e^{42+x} x^5-3 x^7\right )+e^{x^2} \left (3 e^{42+x} x^6+3 x^8\right )} \, dx=\text {Too large to display} \] Input:
integrate((((-4*x^3+2*x)*exp(x+42)^3+(-12*x^5+6*x^3)*exp(x+42)^2+(-12*x^7+ 6*x^5)*exp(x+42)-4*x^9+2*x^7)*exp(x^2)+(-2*x^5+4*x^4)*exp(x+42)^2+(-2*x^7+ 4*x^6)*exp(x+42))/((exp(x+42)^3+3*x^2*exp(x+42)^2+3*x^4*exp(x+42)+x^6)*exp (x^2)^3+(-3*x^3*exp(x+42)^2-6*x^5*exp(x+42)-3*x^7)*exp(x^2)^2+(3*x^6*exp(x +42)+3*x^8)*exp(x^2)-x^9),x, algorithm="giac")
Output:
((x + 42)^6*e^(2*(x + 42)^2 - 168*x - 7056) - 252*(x + 42)^5*e^(2*(x + 42) ^2 - 168*x - 7056) + 2*(x + 42)^4*e^(2*(x + 42)^2 - 167*x - 7014) + 26460* (x + 42)^4*e^(2*(x + 42)^2 - 168*x - 7056) - 336*(x + 42)^3*e^(2*(x + 42)^ 2 - 167*x - 7014) - 1481760*(x + 42)^3*e^(2*(x + 42)^2 - 168*x - 7056) + ( x + 42)^2*e^(2*(x + 42)^2 - 166*x - 6972) + 21168*(x + 42)^2*e^(2*(x + 42) ^2 - 167*x - 7014) + 46675440*(x + 42)^2*e^(2*(x + 42)^2 - 168*x - 7056) - 84*(x + 42)*e^(2*(x + 42)^2 - 166*x - 6972) - 592704*(x + 42)*e^(2*(x + 4 2)^2 - 167*x - 7014) - 784147392*(x + 42)*e^(2*(x + 42)^2 - 168*x - 7056) + 1764*e^(2*(x + 42)^2 - 166*x - 6972) + 6223392*e^(2*(x + 42)^2 - 167*x - 7014) + 5489031744*e^(2*(x + 42)^2 - 168*x - 7056))/((x + 42)^6*e^(2*(x + 42)^2 - 168*x - 7056) - 2*(x + 42)^5*e^(3*(x + 42)^2 - 252*x - 8820) - 25 2*(x + 42)^5*e^(2*(x + 42)^2 - 168*x - 7056) + (x + 42)^4*e^(4*(x + 42)^2 - 336*x - 10584) + 420*(x + 42)^4*e^(3*(x + 42)^2 - 252*x - 8820) + 26460* (x + 42)^4*e^(2*(x + 42)^2 - 168*x - 7056) - 168*(x + 42)^3*e^(4*(x + 42)^ 2 - 336*x - 10584) - 2*(x + 42)^3*e^(3*(x + 42)^2 - 251*x - 8778) - 35280* (x + 42)^3*e^(3*(x + 42)^2 - 252*x - 8820) - 1481760*(x + 42)^3*e^(2*(x + 42)^2 - 168*x - 7056) + 2*(x + 42)^2*e^(4*(x + 42)^2 - 335*x - 10542) + 10 584*(x + 42)^2*e^(4*(x + 42)^2 - 336*x - 10584) + 252*(x + 42)^2*e^(3*(x + 42)^2 - 251*x - 8778) + 1481760*(x + 42)^2*e^(3*(x + 42)^2 - 252*x - 8820 ) + 46675440*(x + 42)^2*e^(2*(x + 42)^2 - 168*x - 7056) - 168*(x + 42)*...
Time = 2.85 (sec) , antiderivative size = 175, normalized size of antiderivative = 6.03 \[ \int \frac {e^{84+2 x} \left (4 x^4-2 x^5\right )+e^{42+x} \left (4 x^6-2 x^7\right )+e^{x^2} \left (2 x^7-4 x^9+e^{126+3 x} \left (2 x-4 x^3\right )+e^{84+2 x} \left (6 x^3-12 x^5\right )+e^{42+x} \left (6 x^5-12 x^7\right )\right )}{-x^9+e^{3 x^2} \left (e^{126+3 x}+3 e^{84+2 x} x^2+3 e^{42+x} x^4+x^6\right )+e^{2 x^2} \left (-3 e^{84+2 x} x^3-6 e^{42+x} x^5-3 x^7\right )+e^{x^2} \left (3 e^{42+x} x^6+3 x^8\right )} \, dx=\frac {{\mathrm {e}}^{x+42}\,\left (6\,x^{10}+x^9-5\,x^8\right )-7\,x^6\,{\mathrm {e}}^{2\,x+84}+2\,x^7\,{\mathrm {e}}^{2\,x+84}+6\,x^8\,{\mathrm {e}}^{2\,x+84}-3\,x^4\,{\mathrm {e}}^{3\,x+126}+x^5\,{\mathrm {e}}^{3\,x+126}+2\,x^6\,{\mathrm {e}}^{3\,x+126}-x^{10}+2\,x^{12}}{\left ({\mathrm {e}}^{2\,x^2}\,{\left ({\mathrm {e}}^{x+42}+x^2\right )}^2+x^6-2\,x^3\,{\mathrm {e}}^{x^2}\,\left ({\mathrm {e}}^{x+42}+x^2\right )\right )\,\left (x^3\,{\mathrm {e}}^{x+42}-3\,x^2\,{\mathrm {e}}^{x+42}+2\,x^4\,{\mathrm {e}}^{x+42}-x^4+2\,x^6\right )} \] Input:
int((exp(x^2)*(exp(3*x + 126)*(2*x - 4*x^3) + exp(x + 42)*(6*x^5 - 12*x^7) + exp(2*x + 84)*(6*x^3 - 12*x^5) + 2*x^7 - 4*x^9) + exp(x + 42)*(4*x^6 - 2*x^7) + exp(2*x + 84)*(4*x^4 - 2*x^5))/(exp(3*x^2)*(exp(3*x + 126) + 3*x^ 4*exp(x + 42) + 3*x^2*exp(2*x + 84) + x^6) + exp(x^2)*(3*x^6*exp(x + 42) + 3*x^8) - x^9 - exp(2*x^2)*(6*x^5*exp(x + 42) + 3*x^3*exp(2*x + 84) + 3*x^ 7)),x)
Output:
(exp(x + 42)*(x^9 - 5*x^8 + 6*x^10) - 7*x^6*exp(2*x + 84) + 2*x^7*exp(2*x + 84) + 6*x^8*exp(2*x + 84) - 3*x^4*exp(3*x + 126) + x^5*exp(3*x + 126) + 2*x^6*exp(3*x + 126) - x^10 + 2*x^12)/((exp(2*x^2)*(exp(x + 42) + x^2)^2 + x^6 - 2*x^3*exp(x^2)*(exp(x + 42) + x^2))*(x^3*exp(x + 42) - 3*x^2*exp(x + 42) + 2*x^4*exp(x + 42) - x^4 + 2*x^6))
\[ \int \frac {e^{84+2 x} \left (4 x^4-2 x^5\right )+e^{42+x} \left (4 x^6-2 x^7\right )+e^{x^2} \left (2 x^7-4 x^9+e^{126+3 x} \left (2 x-4 x^3\right )+e^{84+2 x} \left (6 x^3-12 x^5\right )+e^{42+x} \left (6 x^5-12 x^7\right )\right )}{-x^9+e^{3 x^2} \left (e^{126+3 x}+3 e^{84+2 x} x^2+3 e^{42+x} x^4+x^6\right )+e^{2 x^2} \left (-3 e^{84+2 x} x^3-6 e^{42+x} x^5-3 x^7\right )+e^{x^2} \left (3 e^{42+x} x^6+3 x^8\right )} \, dx=\int \frac {\left (\left (-4 x^{3}+2 x \right ) \left ({\mathrm e}^{x +42}\right )^{3}+\left (-12 x^{5}+6 x^{3}\right ) \left ({\mathrm e}^{x +42}\right )^{2}+\left (-12 x^{7}+6 x^{5}\right ) {\mathrm e}^{x +42}-4 x^{9}+2 x^{7}\right ) {\mathrm e}^{x^{2}}+\left (-2 x^{5}+4 x^{4}\right ) \left ({\mathrm e}^{x +42}\right )^{2}+\left (-2 x^{7}+4 x^{6}\right ) {\mathrm e}^{x +42}}{\left (\left ({\mathrm e}^{x +42}\right )^{3}+3 x^{2} \left ({\mathrm e}^{x +42}\right )^{2}+3 x^{4} {\mathrm e}^{x +42}+x^{6}\right ) \left ({\mathrm e}^{x^{2}}\right )^{3}+\left (-3 x^{3} \left ({\mathrm e}^{x +42}\right )^{2}-6 x^{5} {\mathrm e}^{x +42}-3 x^{7}\right ) \left ({\mathrm e}^{x^{2}}\right )^{2}+\left (3 x^{6} {\mathrm e}^{x +42}+3 x^{8}\right ) {\mathrm e}^{x^{2}}-x^{9}}d x \] Input:
int((((-4*x^3+2*x)*exp(x+42)^3+(-12*x^5+6*x^3)*exp(x+42)^2+(-12*x^7+6*x^5) *exp(x+42)-4*x^9+2*x^7)*exp(x^2)+(-2*x^5+4*x^4)*exp(x+42)^2+(-2*x^7+4*x^6) *exp(x+42))/((exp(x+42)^3+3*x^2*exp(x+42)^2+3*x^4*exp(x+42)+x^6)*exp(x^2)^ 3+(-3*x^3*exp(x+42)^2-6*x^5*exp(x+42)-3*x^7)*exp(x^2)^2+(3*x^6*exp(x+42)+3 *x^8)*exp(x^2)-x^9),x)
Output:
int((((-4*x^3+2*x)*exp(x+42)^3+(-12*x^5+6*x^3)*exp(x+42)^2+(-12*x^7+6*x^5) *exp(x+42)-4*x^9+2*x^7)*exp(x^2)+(-2*x^5+4*x^4)*exp(x+42)^2+(-2*x^7+4*x^6) *exp(x+42))/((exp(x+42)^3+3*x^2*exp(x+42)^2+3*x^4*exp(x+42)+x^6)*exp(x^2)^ 3+(-3*x^3*exp(x+42)^2-6*x^5*exp(x+42)-3*x^7)*exp(x^2)^2+(3*x^6*exp(x+42)+3 *x^8)*exp(x^2)-x^9),x)