Integrand size = 333, antiderivative size = 27 \[ \int \left (e^{32 x^4-64 e^{-2+x} x^4+48 e^{-4+2 x} x^4-16 e^{-6+3 x} x^4+2 e^{-8+4 x} x^4} \left (128 x^3+e^{-2+x} \left (-256 x^3-64 x^4\right )+e^{-6+3 x} \left (-64 x^3-48 x^4\right )+e^{-8+4 x} \left (8 x^3+8 x^4\right )+e^{-4+2 x} \left (192 x^3+96 x^4\right )\right )+e^{16 x^4-32 e^{-2+x} x^4+24 e^{-4+2 x} x^4-8 e^{-6+3 x} x^4+e^{-8+4 x} x^4} \left (2048 x^3-128 x^3 \log (2)+e^{-4+2 x} \left (3072 x^3+1536 x^4+\left (-192 x^3-96 x^4\right ) \log (2)\right )+e^{-8+4 x} \left (128 x^3+128 x^4+\left (-8 x^3-8 x^4\right ) \log (2)\right )+e^{-6+3 x} \left (-1024 x^3-768 x^4+\left (64 x^3+48 x^4\right ) \log (2)\right )+e^{-2+x} \left (-4096 x^3-1024 x^4+\left (256 x^3+64 x^4\right ) \log (2)\right )\right )\right ) \, dx=\left (16+e^{\left (-3 x+\left (5-e^{-2+x}\right ) x\right )^4}-\log (2)\right )^2 \]
Time = 0.49 (sec) , antiderivative size = 47, normalized size of antiderivative = 1.74 \[ \int \left (e^{32 x^4-64 e^{-2+x} x^4+48 e^{-4+2 x} x^4-16 e^{-6+3 x} x^4+2 e^{-8+4 x} x^4} \left (128 x^3+e^{-2+x} \left (-256 x^3-64 x^4\right )+e^{-6+3 x} \left (-64 x^3-48 x^4\right )+e^{-8+4 x} \left (8 x^3+8 x^4\right )+e^{-4+2 x} \left (192 x^3+96 x^4\right )\right )+e^{16 x^4-32 e^{-2+x} x^4+24 e^{-4+2 x} x^4-8 e^{-6+3 x} x^4+e^{-8+4 x} x^4} \left (2048 x^3-128 x^3 \log (2)+e^{-4+2 x} \left (3072 x^3+1536 x^4+\left (-192 x^3-96 x^4\right ) \log (2)\right )+e^{-8+4 x} \left (128 x^3+128 x^4+\left (-8 x^3-8 x^4\right ) \log (2)\right )+e^{-6+3 x} \left (-1024 x^3-768 x^4+\left (64 x^3+48 x^4\right ) \log (2)\right )+e^{-2+x} \left (-4096 x^3-1024 x^4+\left (256 x^3+64 x^4\right ) \log (2)\right )\right )\right ) \, dx=e^{\frac {\left (-2 e^2+e^x\right )^4 x^4}{e^8}} \left (32+e^{\frac {\left (-2 e^2+e^x\right )^4 x^4}{e^8}}-\log (4)\right ) \]
Integrate[E^(32*x^4 - 64*E^(-2 + x)*x^4 + 48*E^(-4 + 2*x)*x^4 - 16*E^(-6 + 3*x)*x^4 + 2*E^(-8 + 4*x)*x^4)*(128*x^3 + E^(-2 + x)*(-256*x^3 - 64*x^4) + E^(-6 + 3*x)*(-64*x^3 - 48*x^4) + E^(-8 + 4*x)*(8*x^3 + 8*x^4) + E^(-4 + 2*x)*(192*x^3 + 96*x^4)) + E^(16*x^4 - 32*E^(-2 + x)*x^4 + 24*E^(-4 + 2*x )*x^4 - 8*E^(-6 + 3*x)*x^4 + E^(-8 + 4*x)*x^4)*(2048*x^3 - 128*x^3*Log[2] + E^(-4 + 2*x)*(3072*x^3 + 1536*x^4 + (-192*x^3 - 96*x^4)*Log[2]) + E^(-8 + 4*x)*(128*x^3 + 128*x^4 + (-8*x^3 - 8*x^4)*Log[2]) + E^(-6 + 3*x)*(-1024 *x^3 - 768*x^4 + (64*x^3 + 48*x^4)*Log[2]) + E^(-2 + x)*(-4096*x^3 - 1024* x^4 + (256*x^3 + 64*x^4)*Log[2])),x]
Time = 5.42 (sec) , antiderivative size = 54, normalized size of antiderivative = 2.00, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.003, Rules used = {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.
\(\displaystyle \int \left (\left (128 x^3+e^{x-2} \left (-64 x^4-256 x^3\right )+e^{3 x-6} \left (-48 x^4-64 x^3\right )+e^{4 x-8} \left (8 x^4+8 x^3\right )+e^{2 x-4} \left (96 x^4+192 x^3\right )\right ) \exp \left (-64 e^{x-2} x^4+48 e^{2 x-4} x^4-16 e^{3 x-6} x^4+2 e^{4 x-8} x^4+32 x^4\right )+\exp \left (-32 e^{x-2} x^4+24 e^{2 x-4} x^4-8 e^{3 x-6} x^4+e^{4 x-8} x^4+16 x^4\right ) \left (2048 x^3-128 x^3 \log (2)+e^{2 x-4} \left (1536 x^4+3072 x^3+\left (-96 x^4-192 x^3\right ) \log (2)\right )+e^{4 x-8} \left (128 x^4+128 x^3+\left (-8 x^4-8 x^3\right ) \log (2)\right )+e^{3 x-6} \left (-768 x^4-1024 x^3+\left (48 x^4+64 x^3\right ) \log (2)\right )+e^{x-2} \left (-1024 x^4-4096 x^3+\left (64 x^4+256 x^3\right ) \log (2)\right )\right )\right ) \, dx\) |
\(\Big \downarrow \) 2009 |
\(\displaystyle e^{\frac {2 \left (2 e^2-e^x\right )^4 x^4}{e^8}}+2 e^{\frac {\left (2 e^2-e^x\right )^4 x^4}{e^8}} (16-\log (2))\) |
Int[E^(32*x^4 - 64*E^(-2 + x)*x^4 + 48*E^(-4 + 2*x)*x^4 - 16*E^(-6 + 3*x)* x^4 + 2*E^(-8 + 4*x)*x^4)*(128*x^3 + E^(-2 + x)*(-256*x^3 - 64*x^4) + E^(- 6 + 3*x)*(-64*x^3 - 48*x^4) + E^(-8 + 4*x)*(8*x^3 + 8*x^4) + E^(-4 + 2*x)* (192*x^3 + 96*x^4)) + E^(16*x^4 - 32*E^(-2 + x)*x^4 + 24*E^(-4 + 2*x)*x^4 - 8*E^(-6 + 3*x)*x^4 + E^(-8 + 4*x)*x^4)*(2048*x^3 - 128*x^3*Log[2] + E^(- 4 + 2*x)*(3072*x^3 + 1536*x^4 + (-192*x^3 - 96*x^4)*Log[2]) + E^(-8 + 4*x) *(128*x^3 + 128*x^4 + (-8*x^3 - 8*x^4)*Log[2]) + E^(-6 + 3*x)*(-1024*x^3 - 768*x^4 + (64*x^3 + 48*x^4)*Log[2]) + E^(-2 + x)*(-4096*x^3 - 1024*x^4 + (256*x^3 + 64*x^4)*Log[2])),x]
3.2.77.3.1 Defintions of rubi rules used
Leaf count of result is larger than twice the leaf count of optimal. \(114\) vs. \(2(25)=50\).
Time = 2.93 (sec) , antiderivative size = 115, normalized size of antiderivative = 4.26
method | result | size |
parallelrisch | \(-2 \,{\mathrm e}^{x^{4} \left ({\mathrm e}^{4 x -8}-8 \,{\mathrm e}^{-6+3 x}+24 \,{\mathrm e}^{2 x -4}-32 \,{\mathrm e}^{-2+x}+16\right )} \ln \left (2\right )+{\mathrm e}^{2 x^{4} \left ({\mathrm e}^{4 x -8}-8 \,{\mathrm e}^{-6+3 x}+24 \,{\mathrm e}^{2 x -4}-32 \,{\mathrm e}^{-2+x}+16\right )}+32 \,{\mathrm e}^{x^{4} \left ({\mathrm e}^{4 x -8}-8 \,{\mathrm e}^{-6+3 x}+24 \,{\mathrm e}^{2 x -4}-32 \,{\mathrm e}^{-2+x}+16\right )}\) | \(115\) |
risch | \(-2 \,{\mathrm e}^{-x^{4} \left (32 \,{\mathrm e}^{-2+x}-{\mathrm e}^{4 x -8}+8 \,{\mathrm e}^{-6+3 x}-24 \,{\mathrm e}^{2 x -4}-16\right )} \ln \left (2\right )+{\mathrm e}^{-2 x^{4} \left (32 \,{\mathrm e}^{-2+x}-{\mathrm e}^{4 x -8}+8 \,{\mathrm e}^{-6+3 x}-24 \,{\mathrm e}^{2 x -4}-16\right )}+32 \,{\mathrm e}^{-x^{4} \left (32 \,{\mathrm e}^{-2+x}-{\mathrm e}^{4 x -8}+8 \,{\mathrm e}^{-6+3 x}-24 \,{\mathrm e}^{2 x -4}-16\right )}\) | \(122\) |
int(((8*x^4+8*x^3)*exp(-2+x)^4+(-48*x^4-64*x^3)*exp(-2+x)^3+(96*x^4+192*x^ 3)*exp(-2+x)^2+(-64*x^4-256*x^3)*exp(-2+x)+128*x^3)*exp(x^4*exp(-2+x)^4-8* x^4*exp(-2+x)^3+24*x^4*exp(-2+x)^2-32*x^4*exp(-2+x)+16*x^4)^2+(((-8*x^4-8* x^3)*ln(2)+128*x^4+128*x^3)*exp(-2+x)^4+((48*x^4+64*x^3)*ln(2)-768*x^4-102 4*x^3)*exp(-2+x)^3+((-96*x^4-192*x^3)*ln(2)+1536*x^4+3072*x^3)*exp(-2+x)^2 +((64*x^4+256*x^3)*ln(2)-1024*x^4-4096*x^3)*exp(-2+x)-128*x^3*ln(2)+2048*x ^3)*exp(x^4*exp(-2+x)^4-8*x^4*exp(-2+x)^3+24*x^4*exp(-2+x)^2-32*x^4*exp(-2 +x)+16*x^4),x,method=_RETURNVERBOSE)
-2*exp(x^4*(exp(-2+x)^4-8*exp(-2+x)^3+24*exp(-2+x)^2-32*exp(-2+x)+16))*ln( 2)+exp(x^4*(exp(-2+x)^4-8*exp(-2+x)^3+24*exp(-2+x)^2-32*exp(-2+x)+16))^2+3 2*exp(x^4*(exp(-2+x)^4-8*exp(-2+x)^3+24*exp(-2+x)^2-32*exp(-2+x)+16))
Leaf count of result is larger than twice the leaf count of optimal. 104 vs. \(2 (23) = 46\).
Time = 0.27 (sec) , antiderivative size = 104, normalized size of antiderivative = 3.85 \[ \int \left (e^{32 x^4-64 e^{-2+x} x^4+48 e^{-4+2 x} x^4-16 e^{-6+3 x} x^4+2 e^{-8+4 x} x^4} \left (128 x^3+e^{-2+x} \left (-256 x^3-64 x^4\right )+e^{-6+3 x} \left (-64 x^3-48 x^4\right )+e^{-8+4 x} \left (8 x^3+8 x^4\right )+e^{-4+2 x} \left (192 x^3+96 x^4\right )\right )+e^{16 x^4-32 e^{-2+x} x^4+24 e^{-4+2 x} x^4-8 e^{-6+3 x} x^4+e^{-8+4 x} x^4} \left (2048 x^3-128 x^3 \log (2)+e^{-4+2 x} \left (3072 x^3+1536 x^4+\left (-192 x^3-96 x^4\right ) \log (2)\right )+e^{-8+4 x} \left (128 x^3+128 x^4+\left (-8 x^3-8 x^4\right ) \log (2)\right )+e^{-6+3 x} \left (-1024 x^3-768 x^4+\left (64 x^3+48 x^4\right ) \log (2)\right )+e^{-2+x} \left (-4096 x^3-1024 x^4+\left (256 x^3+64 x^4\right ) \log (2)\right )\right )\right ) \, dx=-2 \, {\left (\log \left (2\right ) - 16\right )} e^{\left (x^{4} e^{\left (4 \, x - 8\right )} - 8 \, x^{4} e^{\left (3 \, x - 6\right )} + 24 \, x^{4} e^{\left (2 \, x - 4\right )} - 32 \, x^{4} e^{\left (x - 2\right )} + 16 \, x^{4}\right )} + e^{\left (2 \, x^{4} e^{\left (4 \, x - 8\right )} - 16 \, x^{4} e^{\left (3 \, x - 6\right )} + 48 \, x^{4} e^{\left (2 \, x - 4\right )} - 64 \, x^{4} e^{\left (x - 2\right )} + 32 \, x^{4}\right )} \]
integrate(((8*x^4+8*x^3)*exp(-2+x)^4+(-48*x^4-64*x^3)*exp(-2+x)^3+(96*x^4+ 192*x^3)*exp(-2+x)^2+(-64*x^4-256*x^3)*exp(-2+x)+128*x^3)*exp(x^4*exp(-2+x )^4-8*x^4*exp(-2+x)^3+24*x^4*exp(-2+x)^2-32*x^4*exp(-2+x)+16*x^4)^2+(((-8* x^4-8*x^3)*log(2)+128*x^4+128*x^3)*exp(-2+x)^4+((48*x^4+64*x^3)*log(2)-768 *x^4-1024*x^3)*exp(-2+x)^3+((-96*x^4-192*x^3)*log(2)+1536*x^4+3072*x^3)*ex p(-2+x)^2+((64*x^4+256*x^3)*log(2)-1024*x^4-4096*x^3)*exp(-2+x)-128*x^3*lo g(2)+2048*x^3)*exp(x^4*exp(-2+x)^4-8*x^4*exp(-2+x)^3+24*x^4*exp(-2+x)^2-32 *x^4*exp(-2+x)+16*x^4),x, algorithm=\
-2*(log(2) - 16)*e^(x^4*e^(4*x - 8) - 8*x^4*e^(3*x - 6) + 24*x^4*e^(2*x - 4) - 32*x^4*e^(x - 2) + 16*x^4) + e^(2*x^4*e^(4*x - 8) - 16*x^4*e^(3*x - 6 ) + 48*x^4*e^(2*x - 4) - 64*x^4*e^(x - 2) + 32*x^4)
Leaf count of result is larger than twice the leaf count of optimal. 109 vs. \(2 (20) = 40\).
Time = 0.38 (sec) , antiderivative size = 109, normalized size of antiderivative = 4.04 \[ \int \left (e^{32 x^4-64 e^{-2+x} x^4+48 e^{-4+2 x} x^4-16 e^{-6+3 x} x^4+2 e^{-8+4 x} x^4} \left (128 x^3+e^{-2+x} \left (-256 x^3-64 x^4\right )+e^{-6+3 x} \left (-64 x^3-48 x^4\right )+e^{-8+4 x} \left (8 x^3+8 x^4\right )+e^{-4+2 x} \left (192 x^3+96 x^4\right )\right )+e^{16 x^4-32 e^{-2+x} x^4+24 e^{-4+2 x} x^4-8 e^{-6+3 x} x^4+e^{-8+4 x} x^4} \left (2048 x^3-128 x^3 \log (2)+e^{-4+2 x} \left (3072 x^3+1536 x^4+\left (-192 x^3-96 x^4\right ) \log (2)\right )+e^{-8+4 x} \left (128 x^3+128 x^4+\left (-8 x^3-8 x^4\right ) \log (2)\right )+e^{-6+3 x} \left (-1024 x^3-768 x^4+\left (64 x^3+48 x^4\right ) \log (2)\right )+e^{-2+x} \left (-4096 x^3-1024 x^4+\left (256 x^3+64 x^4\right ) \log (2)\right )\right )\right ) \, dx=e^{- 64 x^{4} e^{x - 2} + 48 x^{4} e^{2 x - 4} - 16 x^{4} e^{3 x - 6} + 2 x^{4} e^{4 x - 8} + 32 x^{4}} + \left (32 - 2 \log {\left (2 \right )}\right ) e^{- 32 x^{4} e^{x - 2} + 24 x^{4} e^{2 x - 4} - 8 x^{4} e^{3 x - 6} + x^{4} e^{4 x - 8} + 16 x^{4}} \]
integrate(((8*x**4+8*x**3)*exp(-2+x)**4+(-48*x**4-64*x**3)*exp(-2+x)**3+(9 6*x**4+192*x**3)*exp(-2+x)**2+(-64*x**4-256*x**3)*exp(-2+x)+128*x**3)*exp( x**4*exp(-2+x)**4-8*x**4*exp(-2+x)**3+24*x**4*exp(-2+x)**2-32*x**4*exp(-2+ x)+16*x**4)**2+(((-8*x**4-8*x**3)*ln(2)+128*x**4+128*x**3)*exp(-2+x)**4+(( 48*x**4+64*x**3)*ln(2)-768*x**4-1024*x**3)*exp(-2+x)**3+((-96*x**4-192*x** 3)*ln(2)+1536*x**4+3072*x**3)*exp(-2+x)**2+((64*x**4+256*x**3)*ln(2)-1024* x**4-4096*x**3)*exp(-2+x)-128*x**3*ln(2)+2048*x**3)*exp(x**4*exp(-2+x)**4- 8*x**4*exp(-2+x)**3+24*x**4*exp(-2+x)**2-32*x**4*exp(-2+x)+16*x**4),x)
exp(-64*x**4*exp(x - 2) + 48*x**4*exp(2*x - 4) - 16*x**4*exp(3*x - 6) + 2* x**4*exp(4*x - 8) + 32*x**4) + (32 - 2*log(2))*exp(-32*x**4*exp(x - 2) + 2 4*x**4*exp(2*x - 4) - 8*x**4*exp(3*x - 6) + x**4*exp(4*x - 8) + 16*x**4)
Leaf count of result is larger than twice the leaf count of optimal. 104 vs. \(2 (23) = 46\).
Time = 0.41 (sec) , antiderivative size = 104, normalized size of antiderivative = 3.85 \[ \int \left (e^{32 x^4-64 e^{-2+x} x^4+48 e^{-4+2 x} x^4-16 e^{-6+3 x} x^4+2 e^{-8+4 x} x^4} \left (128 x^3+e^{-2+x} \left (-256 x^3-64 x^4\right )+e^{-6+3 x} \left (-64 x^3-48 x^4\right )+e^{-8+4 x} \left (8 x^3+8 x^4\right )+e^{-4+2 x} \left (192 x^3+96 x^4\right )\right )+e^{16 x^4-32 e^{-2+x} x^4+24 e^{-4+2 x} x^4-8 e^{-6+3 x} x^4+e^{-8+4 x} x^4} \left (2048 x^3-128 x^3 \log (2)+e^{-4+2 x} \left (3072 x^3+1536 x^4+\left (-192 x^3-96 x^4\right ) \log (2)\right )+e^{-8+4 x} \left (128 x^3+128 x^4+\left (-8 x^3-8 x^4\right ) \log (2)\right )+e^{-6+3 x} \left (-1024 x^3-768 x^4+\left (64 x^3+48 x^4\right ) \log (2)\right )+e^{-2+x} \left (-4096 x^3-1024 x^4+\left (256 x^3+64 x^4\right ) \log (2)\right )\right )\right ) \, dx=-2 \, {\left (\log \left (2\right ) - 16\right )} e^{\left (x^{4} e^{\left (4 \, x - 8\right )} - 8 \, x^{4} e^{\left (3 \, x - 6\right )} + 24 \, x^{4} e^{\left (2 \, x - 4\right )} - 32 \, x^{4} e^{\left (x - 2\right )} + 16 \, x^{4}\right )} + e^{\left (2 \, x^{4} e^{\left (4 \, x - 8\right )} - 16 \, x^{4} e^{\left (3 \, x - 6\right )} + 48 \, x^{4} e^{\left (2 \, x - 4\right )} - 64 \, x^{4} e^{\left (x - 2\right )} + 32 \, x^{4}\right )} \]
integrate(((8*x^4+8*x^3)*exp(-2+x)^4+(-48*x^4-64*x^3)*exp(-2+x)^3+(96*x^4+ 192*x^3)*exp(-2+x)^2+(-64*x^4-256*x^3)*exp(-2+x)+128*x^3)*exp(x^4*exp(-2+x )^4-8*x^4*exp(-2+x)^3+24*x^4*exp(-2+x)^2-32*x^4*exp(-2+x)+16*x^4)^2+(((-8* x^4-8*x^3)*log(2)+128*x^4+128*x^3)*exp(-2+x)^4+((48*x^4+64*x^3)*log(2)-768 *x^4-1024*x^3)*exp(-2+x)^3+((-96*x^4-192*x^3)*log(2)+1536*x^4+3072*x^3)*ex p(-2+x)^2+((64*x^4+256*x^3)*log(2)-1024*x^4-4096*x^3)*exp(-2+x)-128*x^3*lo g(2)+2048*x^3)*exp(x^4*exp(-2+x)^4-8*x^4*exp(-2+x)^3+24*x^4*exp(-2+x)^2-32 *x^4*exp(-2+x)+16*x^4),x, algorithm=\
-2*(log(2) - 16)*e^(x^4*e^(4*x - 8) - 8*x^4*e^(3*x - 6) + 24*x^4*e^(2*x - 4) - 32*x^4*e^(x - 2) + 16*x^4) + e^(2*x^4*e^(4*x - 8) - 16*x^4*e^(3*x - 6 ) + 48*x^4*e^(2*x - 4) - 64*x^4*e^(x - 2) + 32*x^4)
\[ \int \left (e^{32 x^4-64 e^{-2+x} x^4+48 e^{-4+2 x} x^4-16 e^{-6+3 x} x^4+2 e^{-8+4 x} x^4} \left (128 x^3+e^{-2+x} \left (-256 x^3-64 x^4\right )+e^{-6+3 x} \left (-64 x^3-48 x^4\right )+e^{-8+4 x} \left (8 x^3+8 x^4\right )+e^{-4+2 x} \left (192 x^3+96 x^4\right )\right )+e^{16 x^4-32 e^{-2+x} x^4+24 e^{-4+2 x} x^4-8 e^{-6+3 x} x^4+e^{-8+4 x} x^4} \left (2048 x^3-128 x^3 \log (2)+e^{-4+2 x} \left (3072 x^3+1536 x^4+\left (-192 x^3-96 x^4\right ) \log (2)\right )+e^{-8+4 x} \left (128 x^3+128 x^4+\left (-8 x^3-8 x^4\right ) \log (2)\right )+e^{-6+3 x} \left (-1024 x^3-768 x^4+\left (64 x^3+48 x^4\right ) \log (2)\right )+e^{-2+x} \left (-4096 x^3-1024 x^4+\left (256 x^3+64 x^4\right ) \log (2)\right )\right )\right ) \, dx=\int { 8 \, {\left (16 \, x^{3} + {\left (x^{4} + x^{3}\right )} e^{\left (4 \, x - 8\right )} - 2 \, {\left (3 \, x^{4} + 4 \, x^{3}\right )} e^{\left (3 \, x - 6\right )} + 12 \, {\left (x^{4} + 2 \, x^{3}\right )} e^{\left (2 \, x - 4\right )} - 8 \, {\left (x^{4} + 4 \, x^{3}\right )} e^{\left (x - 2\right )}\right )} e^{\left (2 \, x^{4} e^{\left (4 \, x - 8\right )} - 16 \, x^{4} e^{\left (3 \, x - 6\right )} + 48 \, x^{4} e^{\left (2 \, x - 4\right )} - 64 \, x^{4} e^{\left (x - 2\right )} + 32 \, x^{4}\right )} - 8 \, {\left (16 \, x^{3} \log \left (2\right ) - 256 \, x^{3} - {\left (16 \, x^{4} + 16 \, x^{3} - {\left (x^{4} + x^{3}\right )} \log \left (2\right )\right )} e^{\left (4 \, x - 8\right )} + 2 \, {\left (48 \, x^{4} + 64 \, x^{3} - {\left (3 \, x^{4} + 4 \, x^{3}\right )} \log \left (2\right )\right )} e^{\left (3 \, x - 6\right )} - 12 \, {\left (16 \, x^{4} + 32 \, x^{3} - {\left (x^{4} + 2 \, x^{3}\right )} \log \left (2\right )\right )} e^{\left (2 \, x - 4\right )} + 8 \, {\left (16 \, x^{4} + 64 \, x^{3} - {\left (x^{4} + 4 \, x^{3}\right )} \log \left (2\right )\right )} e^{\left (x - 2\right )}\right )} e^{\left (x^{4} e^{\left (4 \, x - 8\right )} - 8 \, x^{4} e^{\left (3 \, x - 6\right )} + 24 \, x^{4} e^{\left (2 \, x - 4\right )} - 32 \, x^{4} e^{\left (x - 2\right )} + 16 \, x^{4}\right )} \,d x } \]
integrate(((8*x^4+8*x^3)*exp(-2+x)^4+(-48*x^4-64*x^3)*exp(-2+x)^3+(96*x^4+ 192*x^3)*exp(-2+x)^2+(-64*x^4-256*x^3)*exp(-2+x)+128*x^3)*exp(x^4*exp(-2+x )^4-8*x^4*exp(-2+x)^3+24*x^4*exp(-2+x)^2-32*x^4*exp(-2+x)+16*x^4)^2+(((-8* x^4-8*x^3)*log(2)+128*x^4+128*x^3)*exp(-2+x)^4+((48*x^4+64*x^3)*log(2)-768 *x^4-1024*x^3)*exp(-2+x)^3+((-96*x^4-192*x^3)*log(2)+1536*x^4+3072*x^3)*ex p(-2+x)^2+((64*x^4+256*x^3)*log(2)-1024*x^4-4096*x^3)*exp(-2+x)-128*x^3*lo g(2)+2048*x^3)*exp(x^4*exp(-2+x)^4-8*x^4*exp(-2+x)^3+24*x^4*exp(-2+x)^2-32 *x^4*exp(-2+x)+16*x^4),x, algorithm=\
integrate(8*(16*x^3 + (x^4 + x^3)*e^(4*x - 8) - 2*(3*x^4 + 4*x^3)*e^(3*x - 6) + 12*(x^4 + 2*x^3)*e^(2*x - 4) - 8*(x^4 + 4*x^3)*e^(x - 2))*e^(2*x^4*e ^(4*x - 8) - 16*x^4*e^(3*x - 6) + 48*x^4*e^(2*x - 4) - 64*x^4*e^(x - 2) + 32*x^4) - 8*(16*x^3*log(2) - 256*x^3 - (16*x^4 + 16*x^3 - (x^4 + x^3)*log( 2))*e^(4*x - 8) + 2*(48*x^4 + 64*x^3 - (3*x^4 + 4*x^3)*log(2))*e^(3*x - 6) - 12*(16*x^4 + 32*x^3 - (x^4 + 2*x^3)*log(2))*e^(2*x - 4) + 8*(16*x^4 + 6 4*x^3 - (x^4 + 4*x^3)*log(2))*e^(x - 2))*e^(x^4*e^(4*x - 8) - 8*x^4*e^(3*x - 6) + 24*x^4*e^(2*x - 4) - 32*x^4*e^(x - 2) + 16*x^4), x)
Timed out. \[ \int \left (e^{32 x^4-64 e^{-2+x} x^4+48 e^{-4+2 x} x^4-16 e^{-6+3 x} x^4+2 e^{-8+4 x} x^4} \left (128 x^3+e^{-2+x} \left (-256 x^3-64 x^4\right )+e^{-6+3 x} \left (-64 x^3-48 x^4\right )+e^{-8+4 x} \left (8 x^3+8 x^4\right )+e^{-4+2 x} \left (192 x^3+96 x^4\right )\right )+e^{16 x^4-32 e^{-2+x} x^4+24 e^{-4+2 x} x^4-8 e^{-6+3 x} x^4+e^{-8+4 x} x^4} \left (2048 x^3-128 x^3 \log (2)+e^{-4+2 x} \left (3072 x^3+1536 x^4+\left (-192 x^3-96 x^4\right ) \log (2)\right )+e^{-8+4 x} \left (128 x^3+128 x^4+\left (-8 x^3-8 x^4\right ) \log (2)\right )+e^{-6+3 x} \left (-1024 x^3-768 x^4+\left (64 x^3+48 x^4\right ) \log (2)\right )+e^{-2+x} \left (-4096 x^3-1024 x^4+\left (256 x^3+64 x^4\right ) \log (2)\right )\right )\right ) \, dx=\int {\mathrm {e}}^{48\,x^4\,{\mathrm {e}}^{2\,x-4}-64\,x^4\,{\mathrm {e}}^{x-2}-16\,x^4\,{\mathrm {e}}^{3\,x-6}+2\,x^4\,{\mathrm {e}}^{4\,x-8}+32\,x^4}\,\left ({\mathrm {e}}^{4\,x-8}\,\left (8\,x^4+8\,x^3\right )-{\mathrm {e}}^{x-2}\,\left (64\,x^4+256\,x^3\right )-{\mathrm {e}}^{3\,x-6}\,\left (48\,x^4+64\,x^3\right )+{\mathrm {e}}^{2\,x-4}\,\left (96\,x^4+192\,x^3\right )+128\,x^3\right )-{\mathrm {e}}^{24\,x^4\,{\mathrm {e}}^{2\,x-4}-32\,x^4\,{\mathrm {e}}^{x-2}-8\,x^4\,{\mathrm {e}}^{3\,x-6}+x^4\,{\mathrm {e}}^{4\,x-8}+16\,x^4}\,\left ({\mathrm {e}}^{x-2}\,\left (4096\,x^3-\ln \left (2\right )\,\left (64\,x^4+256\,x^3\right )+1024\,x^4\right )-{\mathrm {e}}^{4\,x-8}\,\left (128\,x^3-\ln \left (2\right )\,\left (8\,x^4+8\,x^3\right )+128\,x^4\right )+{\mathrm {e}}^{3\,x-6}\,\left (1024\,x^3-\ln \left (2\right )\,\left (48\,x^4+64\,x^3\right )+768\,x^4\right )-{\mathrm {e}}^{2\,x-4}\,\left (3072\,x^3-\ln \left (2\right )\,\left (96\,x^4+192\,x^3\right )+1536\,x^4\right )+128\,x^3\,\ln \left (2\right )-2048\,x^3\right ) \,d x \]
int(exp(48*x^4*exp(2*x - 4) - 64*x^4*exp(x - 2) - 16*x^4*exp(3*x - 6) + 2* x^4*exp(4*x - 8) + 32*x^4)*(exp(4*x - 8)*(8*x^3 + 8*x^4) - exp(x - 2)*(256 *x^3 + 64*x^4) - exp(3*x - 6)*(64*x^3 + 48*x^4) + exp(2*x - 4)*(192*x^3 + 96*x^4) + 128*x^3) - exp(24*x^4*exp(2*x - 4) - 32*x^4*exp(x - 2) - 8*x^4*e xp(3*x - 6) + x^4*exp(4*x - 8) + 16*x^4)*(exp(x - 2)*(4096*x^3 - log(2)*(2 56*x^3 + 64*x^4) + 1024*x^4) - exp(4*x - 8)*(128*x^3 - log(2)*(8*x^3 + 8*x ^4) + 128*x^4) + exp(3*x - 6)*(1024*x^3 - log(2)*(64*x^3 + 48*x^4) + 768*x ^4) - exp(2*x - 4)*(3072*x^3 - log(2)*(192*x^3 + 96*x^4) + 1536*x^4) + 128 *x^3*log(2) - 2048*x^3),x)
int(exp(48*x^4*exp(2*x - 4) - 64*x^4*exp(x - 2) - 16*x^4*exp(3*x - 6) + 2* x^4*exp(4*x - 8) + 32*x^4)*(exp(4*x - 8)*(8*x^3 + 8*x^4) - exp(x - 2)*(256 *x^3 + 64*x^4) - exp(3*x - 6)*(64*x^3 + 48*x^4) + exp(2*x - 4)*(192*x^3 + 96*x^4) + 128*x^3) - exp(24*x^4*exp(2*x - 4) - 32*x^4*exp(x - 2) - 8*x^4*e xp(3*x - 6) + x^4*exp(4*x - 8) + 16*x^4)*(exp(x - 2)*(4096*x^3 - log(2)*(2 56*x^3 + 64*x^4) + 1024*x^4) - exp(4*x - 8)*(128*x^3 - log(2)*(8*x^3 + 8*x ^4) + 128*x^4) + exp(3*x - 6)*(1024*x^3 - log(2)*(64*x^3 + 48*x^4) + 768*x ^4) - exp(2*x - 4)*(3072*x^3 - log(2)*(192*x^3 + 96*x^4) + 1536*x^4) + 128 *x^3*log(2) - 2048*x^3), x)