Integrand size = 101, antiderivative size = 30 \begin {dmath*} \int \frac {1}{4} \left (12 e^{8+3 x}+e^{2 x} \left (e^4 (-32+32 x)+e^8 \left (16+32 x+48 x^2\right )\right )+e^x \left (-12-16 x+16 x^2+e^4 \left (12-128 x+56 x^2+48 x^3\right )+e^8 \left (-3+68 x-32 x^2+120 x^3+36 x^4\right )\right )\right ) \, dx=e^x \left (-3+2 x+e^4 \left (\frac {3}{2}+e^x-x+3 x^2\right )\right )^2 \end {dmath*}
Time = 2.51 (sec) , antiderivative size = 35, normalized size of antiderivative = 1.17 \begin {dmath*} \int \frac {1}{4} \left (12 e^{8+3 x}+e^{2 x} \left (e^4 (-32+32 x)+e^8 \left (16+32 x+48 x^2\right )\right )+e^x \left (-12-16 x+16 x^2+e^4 \left (12-128 x+56 x^2+48 x^3\right )+e^8 \left (-3+68 x-32 x^2+120 x^3+36 x^4\right )\right )\right ) \, dx=\frac {1}{4} e^x \left (-6+2 e^{4+x}+4 x+e^4 \left (3-2 x+6 x^2\right )\right )^2 \end {dmath*}
Integrate[(12*E^(8 + 3*x) + E^(2*x)*(E^4*(-32 + 32*x) + E^8*(16 + 32*x + 4 8*x^2)) + E^x*(-12 - 16*x + 16*x^2 + E^4*(12 - 128*x + 56*x^2 + 48*x^3) + E^8*(-3 + 68*x - 32*x^2 + 120*x^3 + 36*x^4)))/4,x]
Leaf count is larger than twice the leaf count of optimal. \(167\) vs. \(2(30)=60\).
Time = 0.57 (sec) , antiderivative size = 167, normalized size of antiderivative = 5.57, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.020, Rules used = {27, 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.
| \(\displaystyle \int \frac {1}{4} \left (e^{2 x} \left (e^8 \left (48 x^2+32 x+16\right )+e^4 (32 x-32)\right )+e^x \left (16 x^2+e^4 \left (48 x^3+56 x^2-128 x+12\right )+e^8 \left (36 x^4+120 x^3-32 x^2+68 x-3\right )-16 x-12\right )+12 e^{3 x+8}\right ) \, dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {1}{4} \int \left (-16 e^{2 x} \left (2 e^4 (1-x)-e^8 \left (3 x^2+2 x+1\right )\right )+12 e^{3 x+8}-e^x \left (-16 x^2+16 x-4 e^4 \left (12 x^3+14 x^2-32 x+3\right )+e^8 \left (-36 x^4-120 x^3+32 x^2-68 x+3\right )+12\right )\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle \frac {1}{4} \left (36 e^{x+8} x^4+48 e^{x+4} x^3-24 e^{x+8} x^3+16 e^x x^2-88 e^{x+4} x^2+40 e^{x+8} x^2+24 e^{2 x+8} x^2-48 e^x x+48 e^{x+4} x-12 e^{x+8} x-8 e^{2 x+8} x+36 e^x-36 e^{x+4}+9 e^{x+8}-8 e^{2 x+4}+12 e^{2 x+8}+4 e^{3 x+8}-16 e^{2 x+4} (1-x)\right )\) |
Int[(12*E^(8 + 3*x) + E^(2*x)*(E^4*(-32 + 32*x) + E^8*(16 + 32*x + 48*x^2) ) + E^x*(-12 - 16*x + 16*x^2 + E^4*(12 - 128*x + 56*x^2 + 48*x^3) + E^8*(- 3 + 68*x - 32*x^2 + 120*x^3 + 36*x^4)))/4,x]
(36*E^x - 36*E^(4 + x) + 9*E^(8 + x) - 8*E^(4 + 2*x) + 12*E^(8 + 2*x) + 4* E^(8 + 3*x) - 16*E^(4 + 2*x)*(1 - x) - 48*E^x*x + 48*E^(4 + x)*x - 12*E^(8 + x)*x - 8*E^(8 + 2*x)*x + 16*E^x*x^2 - 88*E^(4 + x)*x^2 + 40*E^(8 + x)*x ^2 + 24*E^(8 + 2*x)*x^2 + 48*E^(4 + x)*x^3 - 24*E^(8 + x)*x^3 + 36*E^(8 + x)*x^4)/4
3.14.17.3.1 Defintions of rubi rules used
Int[(a_)*(Fx_), x_Symbol] :> Simp[a Int[Fx, x], x] /; FreeQ[a, x] && !Ma tchQ[Fx, (b_)*(Gx_) /; FreeQ[b, x]]
Leaf count of result is larger than twice the leaf count of optimal. \(106\) vs. \(2(25)=50\).
Time = 0.10 (sec) , antiderivative size = 107, normalized size of antiderivative = 3.57
| method | result | size |
| risch | \({\mathrm e}^{8+3 x}+\frac {\left (24 x^{2} {\mathrm e}^{8}-8 x \,{\mathrm e}^{8}+12 \,{\mathrm e}^{8}+16 x \,{\mathrm e}^{4}-24 \,{\mathrm e}^{4}\right ) {\mathrm e}^{2 x}}{4}+\frac {\left (36 x^{4} {\mathrm e}^{8}-24 x^{3} {\mathrm e}^{8}+40 x^{2} {\mathrm e}^{8}+48 x^{3} {\mathrm e}^{4}-12 x \,{\mathrm e}^{8}-88 x^{2} {\mathrm e}^{4}+9 \,{\mathrm e}^{8}+48 x \,{\mathrm e}^{4}+16 x^{2}-36 \,{\mathrm e}^{4}-48 x +36\right ) {\mathrm e}^{x}}{4}\) | \(107\) |
| norman | \(\left (3 \,{\mathrm e}^{8}-6 \,{\mathrm e}^{4}\right ) {\mathrm e}^{2 x}+\left (9+\frac {9 \,{\mathrm e}^{8}}{4}-9 \,{\mathrm e}^{4}\right ) {\mathrm e}^{x}+{\mathrm e}^{8} {\mathrm e}^{3 x}+\left (-6 \,{\mathrm e}^{8}+12 \,{\mathrm e}^{4}\right ) x^{3} {\mathrm e}^{x}+\left (-2 \,{\mathrm e}^{8}+4 \,{\mathrm e}^{4}\right ) x \,{\mathrm e}^{2 x}+\left (-3 \,{\mathrm e}^{8}+12 \,{\mathrm e}^{4}-12\right ) x \,{\mathrm e}^{x}+\left (10 \,{\mathrm e}^{8}-22 \,{\mathrm e}^{4}+4\right ) x^{2} {\mathrm e}^{x}+9 \,{\mathrm e}^{8} {\mathrm e}^{x} x^{4}+6 \,{\mathrm e}^{8} {\mathrm e}^{2 x} x^{2}\) | \(134\) |
| parallelrisch | \({\mathrm e}^{8} {\mathrm e}^{3 x}+6 \,{\mathrm e}^{8} {\mathrm e}^{2 x} x^{2}-2 \,{\mathrm e}^{8} {\mathrm e}^{2 x} x +3 \,{\mathrm e}^{8} {\mathrm e}^{2 x}+4 \,{\mathrm e}^{4} {\mathrm e}^{2 x} x -6 \,{\mathrm e}^{4} {\mathrm e}^{2 x}+9 \,{\mathrm e}^{8} {\mathrm e}^{x} x^{4}-6 x^{3} {\mathrm e}^{8} {\mathrm e}^{x}+10 \,{\mathrm e}^{8} {\mathrm e}^{x} x^{2}+12 \,{\mathrm e}^{4} {\mathrm e}^{x} x^{3}-3 \,{\mathrm e}^{8} {\mathrm e}^{x} x -22 x^{2} {\mathrm e}^{4} {\mathrm e}^{x}+\frac {9 \,{\mathrm e}^{8} {\mathrm e}^{x}}{4}+12 x \,{\mathrm e}^{4} {\mathrm e}^{x}+4 \,{\mathrm e}^{x} x^{2}-9 \,{\mathrm e}^{4} {\mathrm e}^{x}-12 \,{\mathrm e}^{x} x +9 \,{\mathrm e}^{x}\) | \(159\) |
| meijerg | \(-\frac {3 \,{\mathrm e}^{8} \left (2-\frac {\left (12 x^{2}-12 x +6\right ) {\mathrm e}^{2 x}}{3}\right )}{2}+2 \,{\mathrm e}^{4} \left ({\mathrm e}^{4}+1\right ) \left (1-\frac {\left (-4 x +2\right ) {\mathrm e}^{2 x}}{2}\right )-\left (-8 \,{\mathrm e}^{8}+14 \,{\mathrm e}^{4}+4\right ) \left (2-\frac {\left (3 x^{2}-6 x +6\right ) {\mathrm e}^{x}}{3}\right )-\left (-17 \,{\mathrm e}^{8}+32 \,{\mathrm e}^{4}+4\right ) \left (1-\frac {\left (2-2 x \right ) {\mathrm e}^{x}}{2}\right )-9 \,{\mathrm e}^{8} \left (24-\frac {\left (5 x^{4}-20 x^{3}+60 x^{2}-120 x +120\right ) {\mathrm e}^{x}}{5}\right )-\left (-30 \,{\mathrm e}^{8}-12 \,{\mathrm e}^{4}\right ) \left (6-\frac {\left (-4 x^{3}+12 x^{2}-24 x +24\right ) {\mathrm e}^{x}}{4}\right )-{\mathrm e}^{8} \left (1-{\mathrm e}^{3 x}\right )-2 \,{\mathrm e}^{4} \left ({\mathrm e}^{4}-2\right ) \left (1-{\mathrm e}^{2 x}\right )-\left (-3-\frac {3 \,{\mathrm e}^{8}}{4}+3 \,{\mathrm e}^{4}\right ) \left (1-{\mathrm e}^{x}\right )\) | \(204\) |
| default | \(-4 \,{\mathrm e}^{4} {\mathrm e}^{2 x}+2 \,{\mathrm e}^{8} {\mathrm e}^{2 x}+8 \,{\mathrm e}^{4} \left (\frac {x \,{\mathrm e}^{2 x}}{2}-\frac {{\mathrm e}^{2 x}}{4}\right )+8 \,{\mathrm e}^{8} \left (\frac {x \,{\mathrm e}^{2 x}}{2}-\frac {{\mathrm e}^{2 x}}{4}\right )+12 \,{\mathrm e}^{8} \left (\frac {{\mathrm e}^{2 x} x^{2}}{2}-\frac {x \,{\mathrm e}^{2 x}}{2}+\frac {{\mathrm e}^{2 x}}{4}\right )-12 \,{\mathrm e}^{x} x +9 \,{\mathrm e}^{x}+4 \,{\mathrm e}^{x} x^{2}+3 \,{\mathrm e}^{4} {\mathrm e}^{x}-\frac {3 \,{\mathrm e}^{8} {\mathrm e}^{x}}{4}-32 \,{\mathrm e}^{4} \left ({\mathrm e}^{x} x -{\mathrm e}^{x}\right )+14 \,{\mathrm e}^{4} \left ({\mathrm e}^{x} x^{2}-2 \,{\mathrm e}^{x} x +2 \,{\mathrm e}^{x}\right )+12 \,{\mathrm e}^{4} \left ({\mathrm e}^{x} x^{3}-3 \,{\mathrm e}^{x} x^{2}+6 \,{\mathrm e}^{x} x -6 \,{\mathrm e}^{x}\right )+17 \,{\mathrm e}^{8} \left ({\mathrm e}^{x} x -{\mathrm e}^{x}\right )-8 \,{\mathrm e}^{8} \left ({\mathrm e}^{x} x^{2}-2 \,{\mathrm e}^{x} x +2 \,{\mathrm e}^{x}\right )+30 \,{\mathrm e}^{8} \left ({\mathrm e}^{x} x^{3}-3 \,{\mathrm e}^{x} x^{2}+6 \,{\mathrm e}^{x} x -6 \,{\mathrm e}^{x}\right )+9 \,{\mathrm e}^{8} \left ({\mathrm e}^{x} x^{4}-4 \,{\mathrm e}^{x} x^{3}+12 \,{\mathrm e}^{x} x^{2}-24 \,{\mathrm e}^{x} x +24 \,{\mathrm e}^{x}\right )+{\mathrm e}^{8} {\mathrm e}^{3 x}\) | \(288\) |
| parts | \(-4 \,{\mathrm e}^{4} {\mathrm e}^{2 x}+2 \,{\mathrm e}^{8} {\mathrm e}^{2 x}+8 \,{\mathrm e}^{4} \left (\frac {x \,{\mathrm e}^{2 x}}{2}-\frac {{\mathrm e}^{2 x}}{4}\right )+8 \,{\mathrm e}^{8} \left (\frac {x \,{\mathrm e}^{2 x}}{2}-\frac {{\mathrm e}^{2 x}}{4}\right )+12 \,{\mathrm e}^{8} \left (\frac {{\mathrm e}^{2 x} x^{2}}{2}-\frac {x \,{\mathrm e}^{2 x}}{2}+\frac {{\mathrm e}^{2 x}}{4}\right )-12 \,{\mathrm e}^{x} x +9 \,{\mathrm e}^{x}+4 \,{\mathrm e}^{x} x^{2}+3 \,{\mathrm e}^{4} {\mathrm e}^{x}-\frac {3 \,{\mathrm e}^{8} {\mathrm e}^{x}}{4}-32 \,{\mathrm e}^{4} \left ({\mathrm e}^{x} x -{\mathrm e}^{x}\right )+14 \,{\mathrm e}^{4} \left ({\mathrm e}^{x} x^{2}-2 \,{\mathrm e}^{x} x +2 \,{\mathrm e}^{x}\right )+12 \,{\mathrm e}^{4} \left ({\mathrm e}^{x} x^{3}-3 \,{\mathrm e}^{x} x^{2}+6 \,{\mathrm e}^{x} x -6 \,{\mathrm e}^{x}\right )+17 \,{\mathrm e}^{8} \left ({\mathrm e}^{x} x -{\mathrm e}^{x}\right )-8 \,{\mathrm e}^{8} \left ({\mathrm e}^{x} x^{2}-2 \,{\mathrm e}^{x} x +2 \,{\mathrm e}^{x}\right )+30 \,{\mathrm e}^{8} \left ({\mathrm e}^{x} x^{3}-3 \,{\mathrm e}^{x} x^{2}+6 \,{\mathrm e}^{x} x -6 \,{\mathrm e}^{x}\right )+9 \,{\mathrm e}^{8} \left ({\mathrm e}^{x} x^{4}-4 \,{\mathrm e}^{x} x^{3}+12 \,{\mathrm e}^{x} x^{2}-24 \,{\mathrm e}^{x} x +24 \,{\mathrm e}^{x}\right )+{\mathrm e}^{8} {\mathrm e}^{3 x}\) | \(288\) |
int(3*exp(4)^2*exp(x)^3+1/4*((48*x^2+32*x+16)*exp(4)^2+(32*x-32)*exp(4))*e xp(x)^2+1/4*((36*x^4+120*x^3-32*x^2+68*x-3)*exp(4)^2+(48*x^3+56*x^2-128*x+ 12)*exp(4)+16*x^2-16*x-12)*exp(x),x,method=_RETURNVERBOSE)
exp(8+3*x)+1/4*(24*x^2*exp(8)-8*x*exp(8)+12*exp(8)+16*x*exp(4)-24*exp(4))* exp(2*x)+1/4*(36*x^4*exp(8)-24*x^3*exp(8)+40*x^2*exp(8)+48*x^3*exp(4)-12*x *exp(8)-88*x^2*exp(4)+9*exp(8)+48*x*exp(4)+16*x^2-36*exp(4)-48*x+36)*exp(x )
Leaf count of result is larger than twice the leaf count of optimal. 91 vs. \(2 (28) = 56\).
Time = 0.25 (sec) , antiderivative size = 91, normalized size of antiderivative = 3.03 \begin {dmath*} \int \frac {1}{4} \left (12 e^{8+3 x}+e^{2 x} \left (e^4 (-32+32 x)+e^8 \left (16+32 x+48 x^2\right )\right )+e^x \left (-12-16 x+16 x^2+e^4 \left (12-128 x+56 x^2+48 x^3\right )+e^8 \left (-3+68 x-32 x^2+120 x^3+36 x^4\right )\right )\right ) \, dx={\left ({\left (6 \, x^{2} - 2 \, x + 3\right )} e^{8} + 2 \, {\left (2 \, x - 3\right )} e^{4}\right )} e^{\left (2 \, x\right )} + \frac {1}{4} \, {\left (16 \, x^{2} + {\left (36 \, x^{4} - 24 \, x^{3} + 40 \, x^{2} - 12 \, x + 9\right )} e^{8} + 4 \, {\left (12 \, x^{3} - 22 \, x^{2} + 12 \, x - 9\right )} e^{4} - 48 \, x + 36\right )} e^{x} + e^{\left (3 \, x + 8\right )} \end {dmath*}
integrate(3*exp(4)^2*exp(x)^3+1/4*((48*x^2+32*x+16)*exp(4)^2+(32*x-32)*exp (4))*exp(x)^2+1/4*((36*x^4+120*x^3-32*x^2+68*x-3)*exp(4)^2+(48*x^3+56*x^2- 128*x+12)*exp(4)+16*x^2-16*x-12)*exp(x),x, algorithm=\
((6*x^2 - 2*x + 3)*e^8 + 2*(2*x - 3)*e^4)*e^(2*x) + 1/4*(16*x^2 + (36*x^4 - 24*x^3 + 40*x^2 - 12*x + 9)*e^8 + 4*(12*x^3 - 22*x^2 + 12*x - 9)*e^4 - 4 8*x + 36)*e^x + e^(3*x + 8)
Leaf count of result is larger than twice the leaf count of optimal. 128 vs. \(2 (26) = 52\).
Time = 0.16 (sec) , antiderivative size = 128, normalized size of antiderivative = 4.27 \begin {dmath*} \int \frac {1}{4} \left (12 e^{8+3 x}+e^{2 x} \left (e^4 (-32+32 x)+e^8 \left (16+32 x+48 x^2\right )\right )+e^x \left (-12-16 x+16 x^2+e^4 \left (12-128 x+56 x^2+48 x^3\right )+e^8 \left (-3+68 x-32 x^2+120 x^3+36 x^4\right )\right )\right ) \, dx=\frac {\left (24 x^{2} e^{8} - 8 x e^{8} + 16 x e^{4} - 24 e^{4} + 12 e^{8}\right ) e^{2 x}}{4} + \frac {\left (36 x^{4} e^{8} - 24 x^{3} e^{8} + 48 x^{3} e^{4} - 88 x^{2} e^{4} + 16 x^{2} + 40 x^{2} e^{8} - 12 x e^{8} - 48 x + 48 x e^{4} - 36 e^{4} + 36 + 9 e^{8}\right ) e^{x}}{4} + e^{8} e^{3 x} \end {dmath*}
integrate(3*exp(4)**2*exp(x)**3+1/4*((48*x**2+32*x+16)*exp(4)**2+(32*x-32) *exp(4))*exp(x)**2+1/4*((36*x**4+120*x**3-32*x**2+68*x-3)*exp(4)**2+(48*x* *3+56*x**2-128*x+12)*exp(4)+16*x**2-16*x-12)*exp(x),x)
(24*x**2*exp(8) - 8*x*exp(8) + 16*x*exp(4) - 24*exp(4) + 12*exp(8))*exp(2* x)/4 + (36*x**4*exp(8) - 24*x**3*exp(8) + 48*x**3*exp(4) - 88*x**2*exp(4) + 16*x**2 + 40*x**2*exp(8) - 12*x*exp(8) - 48*x + 48*x*exp(4) - 36*exp(4) + 36 + 9*exp(8))*exp(x)/4 + exp(8)*exp(3*x)
Leaf count of result is larger than twice the leaf count of optimal. 227 vs. \(2 (28) = 56\).
Time = 0.20 (sec) , antiderivative size = 227, normalized size of antiderivative = 7.57 \begin {dmath*} \int \frac {1}{4} \left (12 e^{8+3 x}+e^{2 x} \left (e^4 (-32+32 x)+e^8 \left (16+32 x+48 x^2\right )\right )+e^x \left (-12-16 x+16 x^2+e^4 \left (12-128 x+56 x^2+48 x^3\right )+e^8 \left (-3+68 x-32 x^2+120 x^3+36 x^4\right )\right )\right ) \, dx={\left (6 \, x^{2} e^{8} - 2 \, x {\left (e^{8} - 2 \, e^{4}\right )} + 3 \, e^{8} - 6 \, e^{4}\right )} e^{\left (2 \, x\right )} + 9 \, {\left (x^{4} e^{8} - 4 \, x^{3} e^{8} + 12 \, x^{2} e^{8} - 24 \, x e^{8} + 24 \, e^{8}\right )} e^{x} + 30 \, {\left (x^{3} e^{8} - 3 \, x^{2} e^{8} + 6 \, x e^{8} - 6 \, e^{8}\right )} e^{x} + 12 \, {\left (x^{3} e^{4} - 3 \, x^{2} e^{4} + 6 \, x e^{4} - 6 \, e^{4}\right )} e^{x} - 8 \, {\left (x^{2} e^{8} - 2 \, x e^{8} + 2 \, e^{8}\right )} e^{x} + 14 \, {\left (x^{2} e^{4} - 2 \, x e^{4} + 2 \, e^{4}\right )} e^{x} + 4 \, {\left (x^{2} - 2 \, x + 2\right )} e^{x} + 17 \, {\left (x e^{8} - e^{8}\right )} e^{x} - 32 \, {\left (x e^{4} - e^{4}\right )} e^{x} - 4 \, {\left (x - 1\right )} e^{x} + e^{\left (3 \, x + 8\right )} - \frac {3}{4} \, e^{\left (x + 8\right )} + 3 \, e^{\left (x + 4\right )} - 3 \, e^{x} \end {dmath*}
integrate(3*exp(4)^2*exp(x)^3+1/4*((48*x^2+32*x+16)*exp(4)^2+(32*x-32)*exp (4))*exp(x)^2+1/4*((36*x^4+120*x^3-32*x^2+68*x-3)*exp(4)^2+(48*x^3+56*x^2- 128*x+12)*exp(4)+16*x^2-16*x-12)*exp(x),x, algorithm=\
(6*x^2*e^8 - 2*x*(e^8 - 2*e^4) + 3*e^8 - 6*e^4)*e^(2*x) + 9*(x^4*e^8 - 4*x ^3*e^8 + 12*x^2*e^8 - 24*x*e^8 + 24*e^8)*e^x + 30*(x^3*e^8 - 3*x^2*e^8 + 6 *x*e^8 - 6*e^8)*e^x + 12*(x^3*e^4 - 3*x^2*e^4 + 6*x*e^4 - 6*e^4)*e^x - 8*( x^2*e^8 - 2*x*e^8 + 2*e^8)*e^x + 14*(x^2*e^4 - 2*x*e^4 + 2*e^4)*e^x + 4*(x ^2 - 2*x + 2)*e^x + 17*(x*e^8 - e^8)*e^x - 32*(x*e^4 - e^4)*e^x - 4*(x - 1 )*e^x + e^(3*x + 8) - 3/4*e^(x + 8) + 3*e^(x + 4) - 3*e^x
Leaf count of result is larger than twice the leaf count of optimal. 96 vs. \(2 (28) = 56\).
Time = 0.26 (sec) , antiderivative size = 96, normalized size of antiderivative = 3.20 \begin {dmath*} \int \frac {1}{4} \left (12 e^{8+3 x}+e^{2 x} \left (e^4 (-32+32 x)+e^8 \left (16+32 x+48 x^2\right )\right )+e^x \left (-12-16 x+16 x^2+e^4 \left (12-128 x+56 x^2+48 x^3\right )+e^8 \left (-3+68 x-32 x^2+120 x^3+36 x^4\right )\right )\right ) \, dx={\left (6 \, x^{2} - 2 \, x + 3\right )} e^{\left (2 \, x + 8\right )} + 2 \, {\left (2 \, x - 3\right )} e^{\left (2 \, x + 4\right )} + \frac {1}{4} \, {\left (36 \, x^{4} - 24 \, x^{3} + 40 \, x^{2} - 12 \, x + 9\right )} e^{\left (x + 8\right )} + {\left (12 \, x^{3} - 22 \, x^{2} + 12 \, x - 9\right )} e^{\left (x + 4\right )} + {\left (4 \, x^{2} - 12 \, x + 9\right )} e^{x} + e^{\left (3 \, x + 8\right )} \end {dmath*}
integrate(3*exp(4)^2*exp(x)^3+1/4*((48*x^2+32*x+16)*exp(4)^2+(32*x-32)*exp (4))*exp(x)^2+1/4*((36*x^4+120*x^3-32*x^2+68*x-3)*exp(4)^2+(48*x^3+56*x^2- 128*x+12)*exp(4)+16*x^2-16*x-12)*exp(x),x, algorithm=\
(6*x^2 - 2*x + 3)*e^(2*x + 8) + 2*(2*x - 3)*e^(2*x + 4) + 1/4*(36*x^4 - 24 *x^3 + 40*x^2 - 12*x + 9)*e^(x + 8) + (12*x^3 - 22*x^2 + 12*x - 9)*e^(x + 4) + (4*x^2 - 12*x + 9)*e^x + e^(3*x + 8)
Time = 17.74 (sec) , antiderivative size = 33, normalized size of antiderivative = 1.10 \begin {dmath*} \int \frac {1}{4} \left (12 e^{8+3 x}+e^{2 x} \left (e^4 (-32+32 x)+e^8 \left (16+32 x+48 x^2\right )\right )+e^x \left (-12-16 x+16 x^2+e^4 \left (12-128 x+56 x^2+48 x^3\right )+e^8 \left (-3+68 x-32 x^2+120 x^3+36 x^4\right )\right )\right ) \, dx=\frac {{\mathrm {e}}^x\,{\left (4\,x+2\,{\mathrm {e}}^{x+4}+3\,{\mathrm {e}}^4-2\,x\,{\mathrm {e}}^4+6\,x^2\,{\mathrm {e}}^4-6\right )}^2}{4} \end {dmath*}