3.2.77 \(\int (e^{32 x^4-64 e^{-2+x} x^4+48 e^{-4+2 x} x^4-16 e^{-6+3 x} x^4+2 e^{-8+4 x} x^4} (128 x^3+e^{-2+x} (-256 x^3-64 x^4)+e^{-6+3 x} (-64 x^3-48 x^4)+e^{-8+4 x} (8 x^3+8 x^4)+e^{-4+2 x} (192 x^3+96 x^4))+e^{16 x^4-32 e^{-2+x} x^4+24 e^{-4+2 x} x^4-8 e^{-6+3 x} x^4+e^{-8+4 x} x^4} (2048 x^3-128 x^3 \log (2)+e^{-4+2 x} (3072 x^3+1536 x^4+(-192 x^3-96 x^4) \log (2))+e^{-8+4 x} (128 x^3+128 x^4+(-8 x^3-8 x^4) \log (2))+e^{-6+3 x} (-1024 x^3-768 x^4+(64 x^3+48 x^4) \log (2))+e^{-2+x} (-4096 x^3-1024 x^4+(256 x^3+64 x^4) \log (2)))) \, dx\)

Optimal. Leaf size=27 \[ \left (16+e^{\left (-3 x+\left (5-e^{-2+x}\right ) x\right )^4}-\log (2)\right )^2 \]

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Rubi [A]  time = 8.49, antiderivative size = 54, normalized size of antiderivative = 2.00, number of steps used = 8, number of rules used = 4, integrand size = 333, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.012, Rules used = {6688, 12, 6706, 6} \begin {gather*} 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)) \end {gather*}

Antiderivative was successfully verified.

[In]

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]

[Out]

E^((2*(2*E^2 - E^x)^4*x^4)/E^8) + 2*E^(((2*E^2 - E^x)^4*x^4)/E^8)*(16 - Log[2])

Rule 6

Int[(u_.)*((w_.) + (a_.)*(v_) + (b_.)*(v_))^(p_.), x_Symbol] :> Int[u*((a + b)*v + w)^p, x] /; FreeQ[{a, b}, x
] &&  !FreeQ[v, x]

Rule 12

Int[(a_)*(u_), x_Symbol] :> Dist[a, Int[u, x], x] /; FreeQ[a, x] &&  !MatchQ[u, (b_)*(v_) /; FreeQ[b, x]]

Rule 6688

Int[u_, x_Symbol] :> With[{v = SimplifyIntegrand[u, x]}, Int[v, x] /; SimplerIntegrandQ[v, u, x]]

Rule 6706

Int[(F_)^(v_)*(u_), x_Symbol] :> With[{q = DerivativeDivides[v, u, x]}, Simp[(q*F^v)/Log[F], x] /;  !FalseQ[q]
] /; FreeQ[F, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \exp \left (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\right ) \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 ) \, dx+\int \exp \left (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\right ) \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 ) \, dx\\ &=\int 8 e^{-8+\frac {2 \left (-2 e^2+e^x\right )^4 x^4}{e^8}} \left (2 e^2-e^x\right )^3 x^3 \left (2 e^2-e^x (1+x)\right ) \, dx+\int \exp \left (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\right ) \left (x^3 (2048-128 \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 ) \, dx\\ &=8 \int e^{-8+\frac {2 \left (-2 e^2+e^x\right )^4 x^4}{e^8}} \left (2 e^2-e^x\right )^3 x^3 \left (2 e^2-e^x (1+x)\right ) \, dx+\int 8 e^{-8+\frac {\left (-2 e^2+e^x\right )^4 x^4}{e^8}} \left (2 e^2-e^x\right )^3 x^3 \left (2 e^2-e^x (1+x)\right ) (16-\log (2)) \, dx\\ &=e^{\frac {2 \left (2 e^2-e^x\right )^4 x^4}{e^8}}+(8 (16-\log (2))) \int e^{-8+\frac {\left (-2 e^2+e^x\right )^4 x^4}{e^8}} \left (2 e^2-e^x\right )^3 x^3 \left (2 e^2-e^x (1+x)\right ) \, dx\\ &=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))\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.48, size = 47, normalized size = 1.74 \begin {gather*} 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 ) \end {gather*}

Antiderivative was successfully verified.

[In]

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]

[Out]

E^(((-2*E^2 + E^x)^4*x^4)/E^8)*(32 + E^(((-2*E^2 + E^x)^4*x^4)/E^8) - Log[4])

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fricas [B]  time = 0.73, size = 104, normalized size = 3.85 \begin {gather*} -2 \, {\left (\log \relax (2) - 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 )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((8*x^4+8*x^3)*exp(x-2)^4+(-48*x^4-64*x^3)*exp(x-2)^3+(96*x^4+192*x^3)*exp(x-2)^2+(-64*x^4-256*x^3)*
exp(x-2)+128*x^3)*exp(x^4*exp(x-2)^4-8*x^4*exp(x-2)^3+24*x^4*exp(x-2)^2-32*x^4*exp(x-2)+16*x^4)^2+(((-8*x^4-8*
x^3)*log(2)+128*x^4+128*x^3)*exp(x-2)^4+((48*x^4+64*x^3)*log(2)-768*x^4-1024*x^3)*exp(x-2)^3+((-96*x^4-192*x^3
)*log(2)+1536*x^4+3072*x^3)*exp(x-2)^2+((64*x^4+256*x^3)*log(2)-1024*x^4-4096*x^3)*exp(x-2)-128*x^3*log(2)+204
8*x^3)*exp(x^4*exp(x-2)^4-8*x^4*exp(x-2)^3+24*x^4*exp(x-2)^2-32*x^4*exp(x-2)+16*x^4),x, algorithm="fricas")

[Out]

-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)

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giac [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \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 \relax (2) - 256 \, x^{3} - {\left (16 \, x^{4} + 16 \, x^{3} - {\left (x^{4} + x^{3}\right )} \log \relax (2)\right )} e^{\left (4 \, x - 8\right )} + 2 \, {\left (48 \, x^{4} + 64 \, x^{3} - {\left (3 \, x^{4} + 4 \, x^{3}\right )} \log \relax (2)\right )} e^{\left (3 \, x - 6\right )} - 12 \, {\left (16 \, x^{4} + 32 \, x^{3} - {\left (x^{4} + 2 \, x^{3}\right )} \log \relax (2)\right )} e^{\left (2 \, x - 4\right )} + 8 \, {\left (16 \, x^{4} + 64 \, x^{3} - {\left (x^{4} + 4 \, x^{3}\right )} \log \relax (2)\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} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((8*x^4+8*x^3)*exp(x-2)^4+(-48*x^4-64*x^3)*exp(x-2)^3+(96*x^4+192*x^3)*exp(x-2)^2+(-64*x^4-256*x^3)*
exp(x-2)+128*x^3)*exp(x^4*exp(x-2)^4-8*x^4*exp(x-2)^3+24*x^4*exp(x-2)^2-32*x^4*exp(x-2)+16*x^4)^2+(((-8*x^4-8*
x^3)*log(2)+128*x^4+128*x^3)*exp(x-2)^4+((48*x^4+64*x^3)*log(2)-768*x^4-1024*x^3)*exp(x-2)^3+((-96*x^4-192*x^3
)*log(2)+1536*x^4+3072*x^3)*exp(x-2)^2+((64*x^4+256*x^3)*log(2)-1024*x^4-4096*x^3)*exp(x-2)-128*x^3*log(2)+204
8*x^3)*exp(x^4*exp(x-2)^4-8*x^4*exp(x-2)^3+24*x^4*exp(x-2)^2-32*x^4*exp(x-2)+16*x^4),x, algorithm="giac")

[Out]

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
+ 64*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)

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maple [B]  time = 0.20, size = 114, normalized size = 4.22

method	result	size
risch	\({\mathrm e}^{2 x^{4} \left (-32 \,{\mathrm e}^{x -2}+{\mathrm e}^{4 x -8}-8 \,{\mathrm e}^{3 x -6}+24 \,{\mathrm e}^{2 x -4}+16\right )}-2 \,{\mathrm e}^{x^{4} \left (-32 \,{\mathrm e}^{x -2}+{\mathrm e}^{4 x -8}-8 \,{\mathrm e}^{3 x -6}+24 \,{\mathrm e}^{2 x -4}+16\right )} \ln \relax (2)+32 \,{\mathrm e}^{x^{4} \left (-32 \,{\mathrm e}^{x -2}+{\mathrm e}^{4 x -8}-8 \,{\mathrm e}^{3 x -6}+24 \,{\mathrm e}^{2 x -4}+16\right )}\)	\(114\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((8*x^4+8*x^3)*exp(x-2)^4+(-48*x^4-64*x^3)*exp(x-2)^3+(96*x^4+192*x^3)*exp(x-2)^2+(-64*x^4-256*x^3)*exp(x-
2)+128*x^3)*exp(x^4*exp(x-2)^4-8*x^4*exp(x-2)^3+24*x^4*exp(x-2)^2-32*x^4*exp(x-2)+16*x^4)^2+(((-8*x^4-8*x^3)*l
n(2)+128*x^4+128*x^3)*exp(x-2)^4+((48*x^4+64*x^3)*ln(2)-768*x^4-1024*x^3)*exp(x-2)^3+((-96*x^4-192*x^3)*ln(2)+
1536*x^4+3072*x^3)*exp(x-2)^2+((64*x^4+256*x^3)*ln(2)-1024*x^4-4096*x^3)*exp(x-2)-128*x^3*ln(2)+2048*x^3)*exp(
x^4*exp(x-2)^4-8*x^4*exp(x-2)^3+24*x^4*exp(x-2)^2-32*x^4*exp(x-2)+16*x^4),x,method=_RETURNVERBOSE)

[Out]

exp(2*x^4*(-32*exp(x-2)+exp(4*x-8)-8*exp(3*x-6)+24*exp(2*x-4)+16))-2*exp(x^4*(-32*exp(x-2)+exp(4*x-8)-8*exp(3*
x-6)+24*exp(2*x-4)+16))*ln(2)+32*exp(x^4*(-32*exp(x-2)+exp(4*x-8)-8*exp(3*x-6)+24*exp(2*x-4)+16))

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maxima [B]  time = 0.83, size = 104, normalized size = 3.85 \begin {gather*} -2 \, {\left (\log \relax (2) - 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 )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((8*x^4+8*x^3)*exp(x-2)^4+(-48*x^4-64*x^3)*exp(x-2)^3+(96*x^4+192*x^3)*exp(x-2)^2+(-64*x^4-256*x^3)*
exp(x-2)+128*x^3)*exp(x^4*exp(x-2)^4-8*x^4*exp(x-2)^3+24*x^4*exp(x-2)^2-32*x^4*exp(x-2)+16*x^4)^2+(((-8*x^4-8*
x^3)*log(2)+128*x^4+128*x^3)*exp(x-2)^4+((48*x^4+64*x^3)*log(2)-768*x^4-1024*x^3)*exp(x-2)^3+((-96*x^4-192*x^3
)*log(2)+1536*x^4+3072*x^3)*exp(x-2)^2+((64*x^4+256*x^3)*log(2)-1024*x^4-4096*x^3)*exp(x-2)-128*x^3*log(2)+204
8*x^3)*exp(x^4*exp(x-2)^4-8*x^4*exp(x-2)^3+24*x^4*exp(x-2)^2-32*x^4*exp(x-2)+16*x^4),x, algorithm="maxima")

[Out]

-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)

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mupad [F]  time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \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 \relax (2)\,\left (64\,x^4+256\,x^3\right )+1024\,x^4\right )-{\mathrm {e}}^{4\,x-8}\,\left (128\,x^3-\ln \relax (2)\,\left (8\,x^4+8\,x^3\right )+128\,x^4\right )+{\mathrm {e}}^{3\,x-6}\,\left (1024\,x^3-\ln \relax (2)\,\left (48\,x^4+64\,x^3\right )+768\,x^4\right )-{\mathrm {e}}^{2\,x-4}\,\left (3072\,x^3-\ln \relax (2)\,\left (96\,x^4+192\,x^3\right )+1536\,x^4\right )+128\,x^3\,\ln \relax (2)-2048\,x^3\right ) \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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*exp(3*x - 6) + x^4*exp(4*x - 8) + 1
6*x^4)*(exp(x - 2)*(4096*x^3 - log(2)*(256*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 - l
og(2)*(192*x^3 + 96*x^4) + 1536*x^4) + 128*x^3*log(2) - 2048*x^3),x)

[Out]

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*exp(3*x - 6) + x^4*exp(4*x - 8) + 1
6*x^4)*(exp(x - 2)*(4096*x^3 - log(2)*(256*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 - l
og(2)*(192*x^3 + 96*x^4) + 1536*x^4) + 128*x^3*log(2) - 2048*x^3), x)

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sympy [B]  time = 0.76, size = 109, normalized size = 4.04 \begin {gather*} 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 {\relax (2 )}\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}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((8*x**4+8*x**3)*exp(x-2)**4+(-48*x**4-64*x**3)*exp(x-2)**3+(96*x**4+192*x**3)*exp(x-2)**2+(-64*x**4
-256*x**3)*exp(x-2)+128*x**3)*exp(x**4*exp(x-2)**4-8*x**4*exp(x-2)**3+24*x**4*exp(x-2)**2-32*x**4*exp(x-2)+16*
x**4)**2+(((-8*x**4-8*x**3)*ln(2)+128*x**4+128*x**3)*exp(x-2)**4+((48*x**4+64*x**3)*ln(2)-768*x**4-1024*x**3)*
exp(x-2)**3+((-96*x**4-192*x**3)*ln(2)+1536*x**4+3072*x**3)*exp(x-2)**2+((64*x**4+256*x**3)*ln(2)-1024*x**4-40
96*x**3)*exp(x-2)-128*x**3*ln(2)+2048*x**3)*exp(x**4*exp(x-2)**4-8*x**4*exp(x-2)**3+24*x**4*exp(x-2)**2-32*x**
4*exp(x-2)+16*x**4),x)

[Out]

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) + 24*x**4*exp(2*x - 4) - 8*x**4*exp(3*x - 6) + x**4*exp(4*x - 8) + 16*x**4)

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