Integrand size = 240, antiderivative size = 31 \[ \int \frac {-7-e^{12}+36 x-111 x^2+66 x^3+12 x^4-24 x^5+53 x^6-42 x^7+20 x^9-15 x^{10}+6 x^{11}-x^{12}+e^8 \left (-9-3 x^2+6 x^3-3 x^4\right )+e^4 \left (-15-6 x^2+3 x^4+12 x^5-18 x^6+12 x^7-3 x^8\right )}{1+e^{12}+3 x^2-6 x^3+6 x^4-12 x^5+19 x^6-18 x^7+18 x^8-20 x^9+15 x^{10}-6 x^{11}+x^{12}+e^8 \left (3+3 x^2-6 x^3+3 x^4\right )+e^4 \left (3+6 x^2-12 x^3+9 x^4-12 x^5+18 x^6-12 x^7+3 x^8\right )} \, dx=-x+x^2-\left (x+\frac {3}{1+e^4+\left (-x+x^2\right )^2}\right )^2 \] Output:
x^2-(x+3/(1+exp(4)+(x^2-x)^2))^2-x
Time = 0.03 (sec) , antiderivative size = 45, normalized size of antiderivative = 1.45 \[ \int \frac {-7-e^{12}+36 x-111 x^2+66 x^3+12 x^4-24 x^5+53 x^6-42 x^7+20 x^9-15 x^{10}+6 x^{11}-x^{12}+e^8 \left (-9-3 x^2+6 x^3-3 x^4\right )+e^4 \left (-15-6 x^2+3 x^4+12 x^5-18 x^6+12 x^7-3 x^8\right )}{1+e^{12}+3 x^2-6 x^3+6 x^4-12 x^5+19 x^6-18 x^7+18 x^8-20 x^9+15 x^{10}-6 x^{11}+x^{12}+e^8 \left (3+3 x^2-6 x^3+3 x^4\right )+e^4 \left (3+6 x^2-12 x^3+9 x^4-12 x^5+18 x^6-12 x^7+3 x^8\right )} \, dx=-x-\frac {9}{\left (1+e^4+x^2-2 x^3+x^4\right )^2}-\frac {6 x}{1+e^4+x^2-2 x^3+x^4} \] Input:
Integrate[(-7 - E^12 + 36*x - 111*x^2 + 66*x^3 + 12*x^4 - 24*x^5 + 53*x^6 - 42*x^7 + 20*x^9 - 15*x^10 + 6*x^11 - x^12 + E^8*(-9 - 3*x^2 + 6*x^3 - 3* x^4) + E^4*(-15 - 6*x^2 + 3*x^4 + 12*x^5 - 18*x^6 + 12*x^7 - 3*x^8))/(1 + E^12 + 3*x^2 - 6*x^3 + 6*x^4 - 12*x^5 + 19*x^6 - 18*x^7 + 18*x^8 - 20*x^9 + 15*x^10 - 6*x^11 + x^12 + E^8*(3 + 3*x^2 - 6*x^3 + 3*x^4) + E^4*(3 + 6*x ^2 - 12*x^3 + 9*x^4 - 12*x^5 + 18*x^6 - 12*x^7 + 3*x^8)),x]
Output:
-x - 9/(1 + E^4 + x^2 - 2*x^3 + x^4)^2 - (6*x)/(1 + E^4 + x^2 - 2*x^3 + x^ 4)
Leaf count is larger than twice the leaf count of optimal. \(83\) vs. \(2(31)=62\).
Time = 1.86 (sec) , antiderivative size = 83, normalized size of antiderivative = 2.68, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.008, Rules used = {2462, 2009}
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.
\(\displaystyle \int \frac {-x^{12}+6 x^{11}-15 x^{10}+20 x^9-42 x^7+53 x^6-24 x^5+12 x^4+66 x^3-111 x^2+e^8 \left (-3 x^4+6 x^3-3 x^2-9\right )+e^4 \left (-3 x^8+12 x^7-18 x^6+12 x^5+3 x^4-6 x^2-15\right )+36 x-e^{12}-7}{x^{12}-6 x^{11}+15 x^{10}-20 x^9+18 x^8-18 x^7+19 x^6-12 x^5+6 x^4-6 x^3+3 x^2+e^8 \left (3 x^4-6 x^3+3 x^2+3\right )+e^4 \left (3 x^8-12 x^7+18 x^6-12 x^5+9 x^4-12 x^3+6 x^2+3\right )+e^{12}+1} \, dx\) |
\(\Big \downarrow \) 2462 |
\(\displaystyle \int \left (\frac {36 x \left (2 x^2-3 x+1\right )}{\left (x^4-2 x^3+x^2+e^4+1\right )^3}+\frac {18}{x^4-2 x^3+x^2+e^4+1}+\frac {12 \left (x^3-x^2-2 \left (1+e^4\right )\right )}{\left (x^4-2 x^3+x^2+e^4+1\right )^2}-1\right )dx\) |
\(\Big \downarrow \) 2009 |
\(\displaystyle -\frac {9}{\left (x^4-2 x^3+x^2+e^4+1\right )^2}+\frac {48 (1-2 x)}{(2 x-1)^4-2 (1-2 x)^2+16 e^4+17}-x-\frac {48}{(2 x-1)^4-2 (1-2 x)^2+16 e^4+17}\) |
Input:
Int[(-7 - E^12 + 36*x - 111*x^2 + 66*x^3 + 12*x^4 - 24*x^5 + 53*x^6 - 42*x ^7 + 20*x^9 - 15*x^10 + 6*x^11 - x^12 + E^8*(-9 - 3*x^2 + 6*x^3 - 3*x^4) + E^4*(-15 - 6*x^2 + 3*x^4 + 12*x^5 - 18*x^6 + 12*x^7 - 3*x^8))/(1 + E^12 + 3*x^2 - 6*x^3 + 6*x^4 - 12*x^5 + 19*x^6 - 18*x^7 + 18*x^8 - 20*x^9 + 15*x ^10 - 6*x^11 + x^12 + E^8*(3 + 3*x^2 - 6*x^3 + 3*x^4) + E^4*(3 + 6*x^2 - 1 2*x^3 + 9*x^4 - 12*x^5 + 18*x^6 - 12*x^7 + 3*x^8)),x]
Output:
-x - 9/(1 + E^4 + x^2 - 2*x^3 + x^4)^2 - 48/(17 + 16*E^4 - 2*(1 - 2*x)^2 + (-1 + 2*x)^4) + (48*(1 - 2*x))/(17 + 16*E^4 - 2*(1 - 2*x)^2 + (-1 + 2*x)^ 4)
Int[(u_.)*(Px_)^(p_), x_Symbol] :> With[{Qx = Factor[Px]}, Int[ExpandIntegr and[u*Qx^p, x], x] /; !SumQ[NonfreeFactors[Qx, x]]] /; PolyQ[Px, x] && GtQ [Expon[Px, x], 2] && !BinomialQ[Px, x] && !TrinomialQ[Px, x] && ILtQ[p, 0 ] && RationalFunctionQ[u, x]
Leaf count of result is larger than twice the leaf count of optimal. \(94\) vs. \(2(30)=60\).
Time = 0.43 (sec) , antiderivative size = 95, normalized size of antiderivative = 3.06
method | result | size |
risch | \(-x +\frac {-9-6 x^{5}+12 x^{4}-6 x^{3}+\left (-6 \,{\mathrm e}^{4}-6\right ) x}{x^{8}-4 x^{7}+6 x^{6}+2 x^{4} {\mathrm e}^{4}-4 x^{5}-4 x^{3} {\mathrm e}^{4}+3 x^{4}+2 x^{2} {\mathrm e}^{4}-4 x^{3}+{\mathrm e}^{8}+2 x^{2}+2 \,{\mathrm e}^{4}+1}\) | \(95\) |
norman | \(\frac {-20 x^{6}+10 x^{7}+\left (7-2 \,{\mathrm e}^{4}\right ) x^{5}+\left (-{\mathrm e}^{8}-8 \,{\mathrm e}^{4}-7\right ) x +\left (-8 \,{\mathrm e}^{4}-8\right ) x^{2}+\left (-4 \,{\mathrm e}^{4}+4\right ) x^{4}+\left (14 \,{\mathrm e}^{4}+8\right ) x^{3}-x^{9}-4 \,{\mathrm e}^{8}-8 \,{\mathrm e}^{4}-13}{\left (x^{4}-2 x^{3}+x^{2}+{\mathrm e}^{4}+1\right )^{2}}\) | \(100\) |
gosper | \(-\frac {x^{9}-10 x^{7}+2 x^{5} {\mathrm e}^{4}+20 x^{6}+4 x^{4} {\mathrm e}^{4}-7 x^{5}-14 x^{3} {\mathrm e}^{4}-4 x^{4}+x \,{\mathrm e}^{8}+8 x^{2} {\mathrm e}^{4}-8 x^{3}+4 \,{\mathrm e}^{8}+8 x \,{\mathrm e}^{4}+8 x^{2}+8 \,{\mathrm e}^{4}+7 x +13}{x^{8}-4 x^{7}+6 x^{6}+2 x^{4} {\mathrm e}^{4}-4 x^{5}-4 x^{3} {\mathrm e}^{4}+3 x^{4}+2 x^{2} {\mathrm e}^{4}-4 x^{3}+{\mathrm e}^{8}+2 x^{2}+2 \,{\mathrm e}^{4}+1}\) | \(156\) |
parallelrisch | \(-\frac {x^{9}-10 x^{7}+2 x^{5} {\mathrm e}^{4}+20 x^{6}+4 x^{4} {\mathrm e}^{4}-7 x^{5}-14 x^{3} {\mathrm e}^{4}-4 x^{4}+x \,{\mathrm e}^{8}+8 x^{2} {\mathrm e}^{4}-8 x^{3}+4 \,{\mathrm e}^{8}+8 x \,{\mathrm e}^{4}+8 x^{2}+8 \,{\mathrm e}^{4}+7 x +13}{x^{8}-4 x^{7}+6 x^{6}+2 x^{4} {\mathrm e}^{4}-4 x^{5}-4 x^{3} {\mathrm e}^{4}+3 x^{4}+2 x^{2} {\mathrm e}^{4}-4 x^{3}+{\mathrm e}^{8}+2 x^{2}+2 \,{\mathrm e}^{4}+1}\) | \(156\) |
Input:
int((-exp(4)^3+(-3*x^4+6*x^3-3*x^2-9)*exp(4)^2+(-3*x^8+12*x^7-18*x^6+12*x^ 5+3*x^4-6*x^2-15)*exp(4)-x^12+6*x^11-15*x^10+20*x^9-42*x^7+53*x^6-24*x^5+1 2*x^4+66*x^3-111*x^2+36*x-7)/(exp(4)^3+(3*x^4-6*x^3+3*x^2+3)*exp(4)^2+(3*x ^8-12*x^7+18*x^6-12*x^5+9*x^4-12*x^3+6*x^2+3)*exp(4)+x^12-6*x^11+15*x^10-2 0*x^9+18*x^8-18*x^7+19*x^6-12*x^5+6*x^4-6*x^3+3*x^2+1),x,method=_RETURNVER BOSE)
Output:
-x+(-9-6*x^5+12*x^4-6*x^3+(-6*exp(4)-6)*x)/(x^8-4*x^7+6*x^6+2*x^4*exp(4)-4 *x^5-4*x^3*exp(4)+3*x^4+2*x^2*exp(4)-4*x^3+exp(8)+2*x^2+2*exp(4)+1)
Leaf count of result is larger than twice the leaf count of optimal. 119 vs. \(2 (30) = 60\).
Time = 0.09 (sec) , antiderivative size = 119, normalized size of antiderivative = 3.84 \[ \int \frac {-7-e^{12}+36 x-111 x^2+66 x^3+12 x^4-24 x^5+53 x^6-42 x^7+20 x^9-15 x^{10}+6 x^{11}-x^{12}+e^8 \left (-9-3 x^2+6 x^3-3 x^4\right )+e^4 \left (-15-6 x^2+3 x^4+12 x^5-18 x^6+12 x^7-3 x^8\right )}{1+e^{12}+3 x^2-6 x^3+6 x^4-12 x^5+19 x^6-18 x^7+18 x^8-20 x^9+15 x^{10}-6 x^{11}+x^{12}+e^8 \left (3+3 x^2-6 x^3+3 x^4\right )+e^4 \left (3+6 x^2-12 x^3+9 x^4-12 x^5+18 x^6-12 x^7+3 x^8\right )} \, dx=-\frac {x^{9} - 4 \, x^{8} + 6 \, x^{7} - 4 \, x^{6} + 9 \, x^{5} - 16 \, x^{4} + 8 \, x^{3} + x e^{8} + 2 \, {\left (x^{5} - 2 \, x^{4} + x^{3} + 4 \, x\right )} e^{4} + 7 \, x + 9}{x^{8} - 4 \, x^{7} + 6 \, x^{6} - 4 \, x^{5} + 3 \, x^{4} - 4 \, x^{3} + 2 \, x^{2} + 2 \, {\left (x^{4} - 2 \, x^{3} + x^{2} + 1\right )} e^{4} + e^{8} + 1} \] Input:
integrate((-exp(4)^3+(-3*x^4+6*x^3-3*x^2-9)*exp(4)^2+(-3*x^8+12*x^7-18*x^6 +12*x^5+3*x^4-6*x^2-15)*exp(4)-x^12+6*x^11-15*x^10+20*x^9-42*x^7+53*x^6-24 *x^5+12*x^4+66*x^3-111*x^2+36*x-7)/(exp(4)^3+(3*x^4-6*x^3+3*x^2+3)*exp(4)^ 2+(3*x^8-12*x^7+18*x^6-12*x^5+9*x^4-12*x^3+6*x^2+3)*exp(4)+x^12-6*x^11+15* x^10-20*x^9+18*x^8-18*x^7+19*x^6-12*x^5+6*x^4-6*x^3+3*x^2+1),x, algorithm= "fricas")
Output:
-(x^9 - 4*x^8 + 6*x^7 - 4*x^6 + 9*x^5 - 16*x^4 + 8*x^3 + x*e^8 + 2*(x^5 - 2*x^4 + x^3 + 4*x)*e^4 + 7*x + 9)/(x^8 - 4*x^7 + 6*x^6 - 4*x^5 + 3*x^4 - 4 *x^3 + 2*x^2 + 2*(x^4 - 2*x^3 + x^2 + 1)*e^4 + e^8 + 1)
Leaf count of result is larger than twice the leaf count of optimal. 88 vs. \(2 (20) = 40\).
Time = 3.18 (sec) , antiderivative size = 88, normalized size of antiderivative = 2.84 \[ \int \frac {-7-e^{12}+36 x-111 x^2+66 x^3+12 x^4-24 x^5+53 x^6-42 x^7+20 x^9-15 x^{10}+6 x^{11}-x^{12}+e^8 \left (-9-3 x^2+6 x^3-3 x^4\right )+e^4 \left (-15-6 x^2+3 x^4+12 x^5-18 x^6+12 x^7-3 x^8\right )}{1+e^{12}+3 x^2-6 x^3+6 x^4-12 x^5+19 x^6-18 x^7+18 x^8-20 x^9+15 x^{10}-6 x^{11}+x^{12}+e^8 \left (3+3 x^2-6 x^3+3 x^4\right )+e^4 \left (3+6 x^2-12 x^3+9 x^4-12 x^5+18 x^6-12 x^7+3 x^8\right )} \, dx=- x - \frac {6 x^{5} - 12 x^{4} + 6 x^{3} + x \left (6 + 6 e^{4}\right ) + 9}{x^{8} - 4 x^{7} + 6 x^{6} - 4 x^{5} + x^{4} \cdot \left (3 + 2 e^{4}\right ) + x^{3} \left (- 4 e^{4} - 4\right ) + x^{2} \cdot \left (2 + 2 e^{4}\right ) + 1 + 2 e^{4} + e^{8}} \] Input:
integrate((-exp(4)**3+(-3*x**4+6*x**3-3*x**2-9)*exp(4)**2+(-3*x**8+12*x**7 -18*x**6+12*x**5+3*x**4-6*x**2-15)*exp(4)-x**12+6*x**11-15*x**10+20*x**9-4 2*x**7+53*x**6-24*x**5+12*x**4+66*x**3-111*x**2+36*x-7)/(exp(4)**3+(3*x**4 -6*x**3+3*x**2+3)*exp(4)**2+(3*x**8-12*x**7+18*x**6-12*x**5+9*x**4-12*x**3 +6*x**2+3)*exp(4)+x**12-6*x**11+15*x**10-20*x**9+18*x**8-18*x**7+19*x**6-1 2*x**5+6*x**4-6*x**3+3*x**2+1),x)
Output:
-x - (6*x**5 - 12*x**4 + 6*x**3 + x*(6 + 6*exp(4)) + 9)/(x**8 - 4*x**7 + 6 *x**6 - 4*x**5 + x**4*(3 + 2*exp(4)) + x**3*(-4*exp(4) - 4) + x**2*(2 + 2* exp(4)) + 1 + 2*exp(4) + exp(8))
Leaf count of result is larger than twice the leaf count of optimal. 86 vs. \(2 (30) = 60\).
Time = 0.04 (sec) , antiderivative size = 86, normalized size of antiderivative = 2.77 \[ \int \frac {-7-e^{12}+36 x-111 x^2+66 x^3+12 x^4-24 x^5+53 x^6-42 x^7+20 x^9-15 x^{10}+6 x^{11}-x^{12}+e^8 \left (-9-3 x^2+6 x^3-3 x^4\right )+e^4 \left (-15-6 x^2+3 x^4+12 x^5-18 x^6+12 x^7-3 x^8\right )}{1+e^{12}+3 x^2-6 x^3+6 x^4-12 x^5+19 x^6-18 x^7+18 x^8-20 x^9+15 x^{10}-6 x^{11}+x^{12}+e^8 \left (3+3 x^2-6 x^3+3 x^4\right )+e^4 \left (3+6 x^2-12 x^3+9 x^4-12 x^5+18 x^6-12 x^7+3 x^8\right )} \, dx=-x - \frac {3 \, {\left (2 \, x^{5} - 4 \, x^{4} + 2 \, x^{3} + 2 \, x {\left (e^{4} + 1\right )} + 3\right )}}{x^{8} - 4 \, x^{7} + 6 \, x^{6} - 4 \, x^{5} + x^{4} {\left (2 \, e^{4} + 3\right )} - 4 \, x^{3} {\left (e^{4} + 1\right )} + 2 \, x^{2} {\left (e^{4} + 1\right )} + e^{8} + 2 \, e^{4} + 1} \] Input:
integrate((-exp(4)^3+(-3*x^4+6*x^3-3*x^2-9)*exp(4)^2+(-3*x^8+12*x^7-18*x^6 +12*x^5+3*x^4-6*x^2-15)*exp(4)-x^12+6*x^11-15*x^10+20*x^9-42*x^7+53*x^6-24 *x^5+12*x^4+66*x^3-111*x^2+36*x-7)/(exp(4)^3+(3*x^4-6*x^3+3*x^2+3)*exp(4)^ 2+(3*x^8-12*x^7+18*x^6-12*x^5+9*x^4-12*x^3+6*x^2+3)*exp(4)+x^12-6*x^11+15* x^10-20*x^9+18*x^8-18*x^7+19*x^6-12*x^5+6*x^4-6*x^3+3*x^2+1),x, algorithm= "maxima")
Output:
-x - 3*(2*x^5 - 4*x^4 + 2*x^3 + 2*x*(e^4 + 1) + 3)/(x^8 - 4*x^7 + 6*x^6 - 4*x^5 + x^4*(2*e^4 + 3) - 4*x^3*(e^4 + 1) + 2*x^2*(e^4 + 1) + e^8 + 2*e^4 + 1)
Time = 0.18 (sec) , antiderivative size = 48, normalized size of antiderivative = 1.55 \[ \int \frac {-7-e^{12}+36 x-111 x^2+66 x^3+12 x^4-24 x^5+53 x^6-42 x^7+20 x^9-15 x^{10}+6 x^{11}-x^{12}+e^8 \left (-9-3 x^2+6 x^3-3 x^4\right )+e^4 \left (-15-6 x^2+3 x^4+12 x^5-18 x^6+12 x^7-3 x^8\right )}{1+e^{12}+3 x^2-6 x^3+6 x^4-12 x^5+19 x^6-18 x^7+18 x^8-20 x^9+15 x^{10}-6 x^{11}+x^{12}+e^8 \left (3+3 x^2-6 x^3+3 x^4\right )+e^4 \left (3+6 x^2-12 x^3+9 x^4-12 x^5+18 x^6-12 x^7+3 x^8\right )} \, dx=-x - \frac {3 \, {\left (2 \, x^{5} - 4 \, x^{4} + 2 \, x^{3} + 2 \, x e^{4} + 2 \, x + 3\right )}}{{\left (x^{4} - 2 \, x^{3} + x^{2} + e^{4} + 1\right )}^{2}} \] Input:
integrate((-exp(4)^3+(-3*x^4+6*x^3-3*x^2-9)*exp(4)^2+(-3*x^8+12*x^7-18*x^6 +12*x^5+3*x^4-6*x^2-15)*exp(4)-x^12+6*x^11-15*x^10+20*x^9-42*x^7+53*x^6-24 *x^5+12*x^4+66*x^3-111*x^2+36*x-7)/(exp(4)^3+(3*x^4-6*x^3+3*x^2+3)*exp(4)^ 2+(3*x^8-12*x^7+18*x^6-12*x^5+9*x^4-12*x^3+6*x^2+3)*exp(4)+x^12-6*x^11+15* x^10-20*x^9+18*x^8-18*x^7+19*x^6-12*x^5+6*x^4-6*x^3+3*x^2+1),x, algorithm= "giac")
Output:
-x - 3*(2*x^5 - 4*x^4 + 2*x^3 + 2*x*e^4 + 2*x + 3)/(x^4 - 2*x^3 + x^2 + e^ 4 + 1)^2
Time = 3.33 (sec) , antiderivative size = 58, normalized size of antiderivative = 1.87 \[ \int \frac {-7-e^{12}+36 x-111 x^2+66 x^3+12 x^4-24 x^5+53 x^6-42 x^7+20 x^9-15 x^{10}+6 x^{11}-x^{12}+e^8 \left (-9-3 x^2+6 x^3-3 x^4\right )+e^4 \left (-15-6 x^2+3 x^4+12 x^5-18 x^6+12 x^7-3 x^8\right )}{1+e^{12}+3 x^2-6 x^3+6 x^4-12 x^5+19 x^6-18 x^7+18 x^8-20 x^9+15 x^{10}-6 x^{11}+x^{12}+e^8 \left (3+3 x^2-6 x^3+3 x^4\right )+e^4 \left (3+6 x^2-12 x^3+9 x^4-12 x^5+18 x^6-12 x^7+3 x^8\right )} \, dx=-x-\frac {6\,x^5-12\,x^4+6\,x^3+\left (8\,{\mathrm {e}}^4+{\mathrm {e}}^8-{\left ({\mathrm {e}}^4+1\right )}^2+7\right )\,x+9}{{\left (x^4-2\,x^3+x^2+{\mathrm {e}}^4+1\right )}^2} \] Input:
int(-(exp(12) - 36*x + exp(4)*(6*x^2 - 3*x^4 - 12*x^5 + 18*x^6 - 12*x^7 + 3*x^8 + 15) + exp(8)*(3*x^2 - 6*x^3 + 3*x^4 + 9) + 111*x^2 - 66*x^3 - 12*x ^4 + 24*x^5 - 53*x^6 + 42*x^7 - 20*x^9 + 15*x^10 - 6*x^11 + x^12 + 7)/(exp (12) + exp(4)*(6*x^2 - 12*x^3 + 9*x^4 - 12*x^5 + 18*x^6 - 12*x^7 + 3*x^8 + 3) + exp(8)*(3*x^2 - 6*x^3 + 3*x^4 + 3) + 3*x^2 - 6*x^3 + 6*x^4 - 12*x^5 + 19*x^6 - 18*x^7 + 18*x^8 - 20*x^9 + 15*x^10 - 6*x^11 + x^12 + 1),x)
Output:
- x - (6*x^3 - 12*x^4 + 6*x^5 + x*(8*exp(4) + exp(8) - (exp(4) + 1)^2 + 7) + 9)/(exp(4) + x^2 - 2*x^3 + x^4 + 1)^2
Time = 0.15 (sec) , antiderivative size = 168, normalized size of antiderivative = 5.42 \[ \int \frac {-7-e^{12}+36 x-111 x^2+66 x^3+12 x^4-24 x^5+53 x^6-42 x^7+20 x^9-15 x^{10}+6 x^{11}-x^{12}+e^8 \left (-9-3 x^2+6 x^3-3 x^4\right )+e^4 \left (-15-6 x^2+3 x^4+12 x^5-18 x^6+12 x^7-3 x^8\right )}{1+e^{12}+3 x^2-6 x^3+6 x^4-12 x^5+19 x^6-18 x^7+18 x^8-20 x^9+15 x^{10}-6 x^{11}+x^{12}+e^8 \left (3+3 x^2-6 x^3+3 x^4\right )+e^4 \left (3+6 x^2-12 x^3+9 x^4-12 x^5+18 x^6-12 x^7+3 x^8\right )} \, dx=\frac {-2 e^{8} x -4 e^{4} x^{5}-2 x^{9}-3 e^{8}+2 e^{4} x^{4}+5 x^{8}+8 e^{4} x^{3}-6 e^{4} x^{2}-10 x^{6}-16 e^{4} x -6 x^{5}-6 e^{4}+23 x^{4}-4 x^{3}-6 x^{2}-14 x -21}{2 e^{8}+4 e^{4} x^{4}+2 x^{8}-8 e^{4} x^{3}-8 x^{7}+4 e^{4} x^{2}+12 x^{6}-8 x^{5}+4 e^{4}+6 x^{4}-8 x^{3}+4 x^{2}+2} \] Input:
int((-exp(4)^3+(-3*x^4+6*x^3-3*x^2-9)*exp(4)^2+(-3*x^8+12*x^7-18*x^6+12*x^ 5+3*x^4-6*x^2-15)*exp(4)-x^12+6*x^11-15*x^10+20*x^9-42*x^7+53*x^6-24*x^5+1 2*x^4+66*x^3-111*x^2+36*x-7)/(exp(4)^3+(3*x^4-6*x^3+3*x^2+3)*exp(4)^2+(3*x ^8-12*x^7+18*x^6-12*x^5+9*x^4-12*x^3+6*x^2+3)*exp(4)+x^12-6*x^11+15*x^10-2 0*x^9+18*x^8-18*x^7+19*x^6-12*x^5+6*x^4-6*x^3+3*x^2+1),x)
Output:
( - 2*e**8*x - 3*e**8 - 4*e**4*x**5 + 2*e**4*x**4 + 8*e**4*x**3 - 6*e**4*x **2 - 16*e**4*x - 6*e**4 - 2*x**9 + 5*x**8 - 10*x**6 - 6*x**5 + 23*x**4 - 4*x**3 - 6*x**2 - 14*x - 21)/(2*(e**8 + 2*e**4*x**4 - 4*e**4*x**3 + 2*e**4 *x**2 + 2*e**4 + x**8 - 4*x**7 + 6*x**6 - 4*x**5 + 3*x**4 - 4*x**3 + 2*x** 2 + 1))