3.11.14 \(\int \frac {e^{\frac {4 (e^4 x+x^2)}{e^3}} (4 e^4+8 x)+e^{\frac {3 (e^4 x+x^2)}{e^3}} (-4 e^3+e^4 (-12-12 x)-24 x-24 x^2)+e^3 (4+12 x+12 x^2+4 x^3)+e^{\frac {2 (e^4 x+x^2)}{e^3}} (24 x+48 x^2+24 x^3+e^3 (12+12 x)+e^4 (12+24 x+12 x^2))+e^{\frac {e^4 x+x^2}{e^3}} (-8 x-24 x^2-24 x^3-8 x^4+e^3 (-12-24 x-12 x^2)+e^4 (-4-12 x-12 x^2-4 x^3))}{e^3} \, dx\)

Optimal. Leaf size=19 \[ \left (1-e^{\frac {x \left (e^4+x\right )}{e^3}}+x\right )^4 \]

________________________________________________________________________________________

Rubi [B]  time = 0.51, antiderivative size = 190, normalized size of antiderivative = 10.00, number of steps used = 8, number of rules used = 4, integrand size = 212, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.019, Rules used = {12, 2244, 2236, 2288} \begin {gather*} x^4+4 x^3+6 x^2+e^{\frac {4 x^2}{e^3}+4 e x}-\frac {4 e^{\frac {3 \left (x^2+e^4 x\right )}{e^3}} \left (2 x^2+2 x+e^4 (x+1)\right )}{2 x+e^4}+\frac {6 e^{\frac {2 \left (x^2+e^4 x\right )}{e^3}} \left (2 x^3+4 x^2+e^4 \left (x^2+2 x+1\right )+2 x\right )}{2 x+e^4}-\frac {4 e^{\frac {x^2+e^4 x}{e^3}} \left (2 x^4+6 x^3+6 x^2+e^4 \left (x^3+3 x^2+3 x+1\right )+2 x\right )}{2 x+e^4}+4 x \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(E^((4*(E^4*x + x^2))/E^3)*(4*E^4 + 8*x) + E^((3*(E^4*x + x^2))/E^3)*(-4*E^3 + E^4*(-12 - 12*x) - 24*x - 2
4*x^2) + E^3*(4 + 12*x + 12*x^2 + 4*x^3) + E^((2*(E^4*x + x^2))/E^3)*(24*x + 48*x^2 + 24*x^3 + E^3*(12 + 12*x)
+ E^4*(12 + 24*x + 12*x^2)) + E^((E^4*x + x^2)/E^3)*(-8*x - 24*x^2 - 24*x^3 - 8*x^4 + E^3*(-12 - 24*x - 12*x^
2) + E^4*(-4 - 12*x - 12*x^2 - 4*x^3)))/E^3,x]

[Out]

E^(4*E*x + (4*x^2)/E^3) + 4*x + 6*x^2 + 4*x^3 + x^4 - (4*E^((3*(E^4*x + x^2))/E^3)*(2*x + 2*x^2 + E^4*(1 + x))
)/(E^4 + 2*x) + (6*E^((2*(E^4*x + x^2))/E^3)*(2*x + 4*x^2 + 2*x^3 + E^4*(1 + 2*x + x^2)))/(E^4 + 2*x) - (4*E^(
(E^4*x + x^2)/E^3)*(2*x + 6*x^2 + 6*x^3 + 2*x^4 + E^4*(1 + 3*x + 3*x^2 + x^3)))/(E^4 + 2*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 2236

Int[(F_)^((a_.) + (b_.)*(x_) + (c_.)*(x_)^2)*((d_.) + (e_.)*(x_)), x_Symbol] :> Simp[(e*F^(a + b*x + c*x^2))/(
2*c*Log[F]), x] /; FreeQ[{F, a, b, c, d, e}, x] && EqQ[b*e - 2*c*d, 0]

Rule 2244

Int[(F_)^(v_)*(u_)^(m_.), x_Symbol] :> Int[ExpandToSum[u, x]^m*F^ExpandToSum[v, x], x] /; FreeQ[{F, m}, x] &&
LinearQ[u, x] && QuadraticQ[v, x] &&  !(LinearMatchQ[u, x] && QuadraticMatchQ[v, x])

Rule 2288

Int[(y_.)*(F_)^(u_)*((v_) + (w_)), x_Symbol] :> With[{z = (v*y)/(Log[F]*D[u, x])}, Simp[F^u*z, x] /; EqQ[D[z,
x], w*y]] /; FreeQ[F, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int \left (e^{\frac {4 \left (e^4 x+x^2\right )}{e^3}} \left (4 e^4+8 x\right )+e^{\frac {3 \left (e^4 x+x^2\right )}{e^3}} \left (-4 e^3+e^4 (-12-12 x)-24 x-24 x^2\right )+e^3 \left (4+12 x+12 x^2+4 x^3\right )+e^{\frac {2 \left (e^4 x+x^2\right )}{e^3}} \left (24 x+48 x^2+24 x^3+e^3 (12+12 x)+e^4 \left (12+24 x+12 x^2\right )\right )+e^{\frac {e^4 x+x^2}{e^3}} \left (-8 x-24 x^2-24 x^3-8 x^4+e^3 \left (-12-24 x-12 x^2\right )+e^4 \left (-4-12 x-12 x^2-4 x^3\right )\right )\right ) \, dx}{e^3}\\ &=\frac {\int e^{\frac {4 \left (e^4 x+x^2\right )}{e^3}} \left (4 e^4+8 x\right ) \, dx}{e^3}+\frac {\int e^{\frac {3 \left (e^4 x+x^2\right )}{e^3}} \left (-4 e^3+e^4 (-12-12 x)-24 x-24 x^2\right ) \, dx}{e^3}+\frac {\int e^{\frac {2 \left (e^4 x+x^2\right )}{e^3}} \left (24 x+48 x^2+24 x^3+e^3 (12+12 x)+e^4 \left (12+24 x+12 x^2\right )\right ) \, dx}{e^3}+\frac {\int e^{\frac {e^4 x+x^2}{e^3}} \left (-8 x-24 x^2-24 x^3-8 x^4+e^3 \left (-12-24 x-12 x^2\right )+e^4 \left (-4-12 x-12 x^2-4 x^3\right )\right ) \, dx}{e^3}+\int \left (4+12 x+12 x^2+4 x^3\right ) \, dx\\ &=4 x+6 x^2+4 x^3+x^4-\frac {4 e^{\frac {3 \left (e^4 x+x^2\right )}{e^3}} \left (2 x+2 x^2+e^4 (1+x)\right )}{e^4+2 x}+\frac {6 e^{\frac {2 \left (e^4 x+x^2\right )}{e^3}} \left (2 x+4 x^2+2 x^3+e^4 \left (1+2 x+x^2\right )\right )}{e^4+2 x}-\frac {4 e^{\frac {e^4 x+x^2}{e^3}} \left (2 x+6 x^2+6 x^3+2 x^4+e^4 \left (1+3 x+3 x^2+x^3\right )\right )}{e^4+2 x}+\frac {\int e^{4 e x+\frac {4 x^2}{e^3}} \left (4 e^4+8 x\right ) \, dx}{e^3}\\ &=e^{4 e x+\frac {4 x^2}{e^3}}+4 x+6 x^2+4 x^3+x^4-\frac {4 e^{\frac {3 \left (e^4 x+x^2\right )}{e^3}} \left (2 x+2 x^2+e^4 (1+x)\right )}{e^4+2 x}+\frac {6 e^{\frac {2 \left (e^4 x+x^2\right )}{e^3}} \left (2 x+4 x^2+2 x^3+e^4 \left (1+2 x+x^2\right )\right )}{e^4+2 x}-\frac {4 e^{\frac {e^4 x+x^2}{e^3}} \left (2 x+6 x^2+6 x^3+2 x^4+e^4 \left (1+3 x+3 x^2+x^3\right )\right )}{e^4+2 x}\\ \end {aligned} \end {gather*}

________________________________________________________________________________________

Mathematica [A]  time = 0.09, size = 19, normalized size = 1.00 \begin {gather*} \left (-1+e^{\frac {x \left (e^4+x\right )}{e^3}}-x\right )^4 \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^((4*(E^4*x + x^2))/E^3)*(4*E^4 + 8*x) + E^((3*(E^4*x + x^2))/E^3)*(-4*E^3 + E^4*(-12 - 12*x) - 24
*x - 24*x^2) + E^3*(4 + 12*x + 12*x^2 + 4*x^3) + E^((2*(E^4*x + x^2))/E^3)*(24*x + 48*x^2 + 24*x^3 + E^3*(12 +
12*x) + E^4*(12 + 24*x + 12*x^2)) + E^((E^4*x + x^2)/E^3)*(-8*x - 24*x^2 - 24*x^3 - 8*x^4 + E^3*(-12 - 24*x -
12*x^2) + E^4*(-4 - 12*x - 12*x^2 - 4*x^3)))/E^3,x]

[Out]

(-1 + E^((x*(E^4 + x))/E^3) - x)^4

________________________________________________________________________________________

fricas [B]  time = 1.09, size = 98, normalized size = 5.16 \begin {gather*} x^{4} + 4 \, x^{3} + 6 \, x^{2} - 4 \, {\left (x + 1\right )} e^{\left (3 \, {\left (x^{2} + x e^{4}\right )} e^{\left (-3\right )}\right )} + 6 \, {\left (x^{2} + 2 \, x + 1\right )} e^{\left (2 \, {\left (x^{2} + x e^{4}\right )} e^{\left (-3\right )}\right )} - 4 \, {\left (x^{3} + 3 \, x^{2} + 3 \, x + 1\right )} e^{\left ({\left (x^{2} + x e^{4}\right )} e^{\left (-3\right )}\right )} + 4 \, x + e^{\left (4 \, {\left (x^{2} + x e^{4}\right )} e^{\left (-3\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((4*exp(4)+8*x)*exp((x*exp(4)+x^2)/exp(3))^4+((-12*x-12)*exp(4)-4*exp(3)-24*x^2-24*x)*exp((x*exp(4)+
x^2)/exp(3))^3+((12*x^2+24*x+12)*exp(4)+(12*x+12)*exp(3)+24*x^3+48*x^2+24*x)*exp((x*exp(4)+x^2)/exp(3))^2+((-4
*x^3-12*x^2-12*x-4)*exp(4)+(-12*x^2-24*x-12)*exp(3)-8*x^4-24*x^3-24*x^2-8*x)*exp((x*exp(4)+x^2)/exp(3))+(4*x^3
+12*x^2+12*x+4)*exp(3))/exp(3),x, algorithm="fricas")

[Out]

x^4 + 4*x^3 + 6*x^2 - 4*(x + 1)*e^(3*(x^2 + x*e^4)*e^(-3)) + 6*(x^2 + 2*x + 1)*e^(2*(x^2 + x*e^4)*e^(-3)) - 4*
(x^3 + 3*x^2 + 3*x + 1)*e^((x^2 + x*e^4)*e^(-3)) + 4*x + e^(4*(x^2 + x*e^4)*e^(-3))

________________________________________________________________________________________

giac [C]  time = 0.50, size = 796, normalized size = 41.89 result too large to display

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((4*exp(4)+8*x)*exp((x*exp(4)+x^2)/exp(3))^4+((-12*x-12)*exp(4)-4*exp(3)-24*x^2-24*x)*exp((x*exp(4)+
x^2)/exp(3))^3+((12*x^2+24*x+12)*exp(4)+(12*x+12)*exp(3)+24*x^3+48*x^2+24*x)*exp((x*exp(4)+x^2)/exp(3))^2+((-4
*x^3-12*x^2-12*x-4)*exp(4)+(-12*x^2-24*x-12)*exp(3)-8*x^4-24*x^3-24*x^2-8*x)*exp((x*exp(4)+x^2)/exp(3))+(4*x^3
+12*x^2+12*x+4)*exp(3))/exp(3),x, algorithm="giac")

[Out]

-1/12*(-9*I*sqrt(2)*sqrt(pi)*(e^8 - 4*e^4 - e^3 + 4)*erf(-1/2*I*sqrt(2)*(2*x + e^4)*e^(-3/2))*e^(-1/2*e^5 + 11
/2) + 18*I*sqrt(2)*sqrt(pi)*(e^4 - 2)*erf(-1/2*I*sqrt(2)*(2*x + e^4)*e^(-3/2))*e^(-1/2*e^5 + 9/2) + 9*I*sqrt(2
)*sqrt(pi)*(e^12 - 4*e^8 - 3*e^7 + 4*e^4 + 4*e^3)*erf(-1/2*I*sqrt(2)*(2*x + e^4)*e^(-3/2))*e^(-1/2*e^5 + 3/2)
- 12*I*sqrt(3)*sqrt(pi)*(e^4 - 2)*erf(-1/2*I*sqrt(3)*(2*x + e^4)*e^(-3/2))*e^(-3/4*e^5 + 11/2) + 4*I*sqrt(3)*s
qrt(pi)*(3*e^8 - 6*e^4 - 2*e^3)*erf(-1/2*I*sqrt(3)*(2*x + e^4)*e^(-3/2))*e^(-3/4*e^5 + 3/2) - 3*I*sqrt(pi)*(e^
12 - 6*e^8 - 6*e^7 + 12*e^4 + 12*e^3 - 8)*erf(-1/2*I*(2*x + e^4)*e^(-3/2))*e^(-1/4*e^5 + 11/2) + 18*I*sqrt(pi)
*(e^8 - 4*e^4 - 2*e^3 + 4)*erf(-1/2*I*(2*x + e^4)*e^(-3/2))*e^(-1/4*e^5 + 9/2) + 3*I*sqrt(pi)*(e^16 - 6*e^12 -
12*e^11 + 12*e^8 + 36*e^7 + 12*e^6 - 8*e^4 - 24*e^3)*erf(-1/2*I*(2*x + e^4)*e^(-3/2))*e^(-1/4*e^5 + 3/2) + 8*
I*sqrt(3)*sqrt(pi)*erf(-1/2*I*sqrt(3)*(2*x + e^4)*e^(-3/2))*e^(-3/4*e^5 + 9/2) - 12*(x^4 + 4*x^3 + 6*x^2 + 4*x
)*e^3 + 6*((2*x + e^4)^2*e^3 - 3*(2*x + e^4)*e^7 + 6*(2*x + e^4)*e^3 + 3*e^11 - 12*e^7 - 4*e^6 + 12*e^3)*e^((x
^2 + x*e^4 + 4*e^3)*e^(-3)) + 36*((2*x + e^4)*e^3 - 2*e^7 + 4*e^3)*e^((x^2 + x*e^4 + 3*e^3)*e^(-3)) - 18*((2*x
+ e^4)*e^3 - 2*e^7 + 4*e^3)*e^(2*(x^2 + x*e^4 + 2*e^3)*e^(-3)) + 24*((2*x + e^4)*e^3 - 2*e^7 + 2*e^3)*e^(3*(x
^2 + x*e^4)*e^(-3)) - 18*((2*x + e^4)^2*e^3 - 3*(2*x + e^4)*e^7 + 4*(2*x + e^4)*e^3 + 3*e^11 - 8*e^7 - 2*e^6 +
4*e^3)*e^(2*(x^2 + x*e^4)*e^(-3)) + 6*((2*x + e^4)^3*e^3 - 4*(2*x + e^4)^2*e^7 + 6*(2*x + e^4)^2*e^3 + 6*(2*x
+ e^4)*e^11 - 18*(2*x + e^4)*e^7 - 6*(2*x + e^4)*e^6 + 12*(2*x + e^4)*e^3 - 4*e^15 + 18*e^11 + 16*e^10 - 24*e
^7 - 24*e^6 + 8*e^3)*e^((x^2 + x*e^4)*e^(-3)) - 12*e^(4*x^2*e^(-3) + 4*x*e + 3) + 24*e^((3*x^2 + 3*x*e^4 + 4*e
^3)*e^(-3) + 3) - 36*e^((2*x^2 + 2*x*e^4 + 3*e^3)*e^(-3) + 3))*e^(-3)

________________________________________________________________________________________

maple [B]  time = 0.17, size = 131, normalized size = 6.89

method	result	size
risch	\(x^{4}+4 x^{3}+6 x^{2}+4 x +{\mathrm e}^{4 x \left (x +{\mathrm e}^{4}\right ) {\mathrm e}^{-3}}+\left (-4 x \,{\mathrm e}^{3}-4 \,{\mathrm e}^{3}\right ) {\mathrm e}^{3 x \,{\mathrm e}^{-3} {\mathrm e}^{4}+3 \,{\mathrm e}^{-3} x^{2}-3}+\left (6 x^{2} {\mathrm e}^{3}+12 x \,{\mathrm e}^{3}+6 \,{\mathrm e}^{3}\right ) {\mathrm e}^{2 x \,{\mathrm e}^{-3} {\mathrm e}^{4}+2 \,{\mathrm e}^{-3} x^{2}-3}+\left (-4 x^{3} {\mathrm e}^{3}-12 x^{2} {\mathrm e}^{3}-12 x \,{\mathrm e}^{3}-4 \,{\mathrm e}^{3}\right ) {\mathrm e}^{x \,{\mathrm e}^{-3} {\mathrm e}^{4}+{\mathrm e}^{-3} x^{2}-3}\)	\(131\)
norman	\(x^{4}+{\mathrm e}^{4 \left (x \,{\mathrm e}^{4}+x^{2}\right ) {\mathrm e}^{-3}}+4 x +6 x^{2}+4 x^{3}+6 \,{\mathrm e}^{2 \left (x \,{\mathrm e}^{4}+x^{2}\right ) {\mathrm e}^{-3}}-4 \,{\mathrm e}^{3 \left (x \,{\mathrm e}^{4}+x^{2}\right ) {\mathrm e}^{-3}}-12 x \,{\mathrm e}^{\left (x \,{\mathrm e}^{4}+x^{2}\right ) {\mathrm e}^{-3}}+12 x \,{\mathrm e}^{2 \left (x \,{\mathrm e}^{4}+x^{2}\right ) {\mathrm e}^{-3}}-4 x \,{\mathrm e}^{3 \left (x \,{\mathrm e}^{4}+x^{2}\right ) {\mathrm e}^{-3}}-12 x^{2} {\mathrm e}^{\left (x \,{\mathrm e}^{4}+x^{2}\right ) {\mathrm e}^{-3}}+6 x^{2} {\mathrm e}^{2 \left (x \,{\mathrm e}^{4}+x^{2}\right ) {\mathrm e}^{-3}}-4 x^{3} {\mathrm e}^{\left (x \,{\mathrm e}^{4}+x^{2}\right ) {\mathrm e}^{-3}}-4 \,{\mathrm e}^{\left (x \,{\mathrm e}^{4}+x^{2}\right ) {\mathrm e}^{-3}}\)	\(200\)
default	\(\text {Expression too large to display}\)	\(2846\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((4*exp(4)+8*x)*exp((x*exp(4)+x^2)/exp(3))^4+((-12*x-12)*exp(4)-4*exp(3)-24*x^2-24*x)*exp((x*exp(4)+x^2)/e
xp(3))^3+((12*x^2+24*x+12)*exp(4)+(12*x+12)*exp(3)+24*x^3+48*x^2+24*x)*exp((x*exp(4)+x^2)/exp(3))^2+((-4*x^3-1
2*x^2-12*x-4)*exp(4)+(-12*x^2-24*x-12)*exp(3)-8*x^4-24*x^3-24*x^2-8*x)*exp((x*exp(4)+x^2)/exp(3))+(4*x^3+12*x^
2+12*x+4)*exp(3))/exp(3),x,method=_RETURNVERBOSE)

[Out]

x^4+4*x^3+6*x^2+4*x+exp(4*x*(x+exp(4))*exp(-3))+(-4*x*exp(3)-4*exp(3))*exp(3*x*exp(-3)*exp(4)+3*exp(-3)*x^2-3)
+(6*x^2*exp(3)+12*x*exp(3)+6*exp(3))*exp(2*x*exp(-3)*exp(4)+2*exp(-3)*x^2-3)+(-4*x^3*exp(3)-12*x^2*exp(3)-12*x
*exp(3)-4*exp(3))*exp(x*exp(-3)*exp(4)+exp(-3)*x^2-3)

________________________________________________________________________________________

maxima [B]  time = 0.54, size = 127, normalized size = 6.68 \begin {gather*} {\left ({\left (x^{4} + 4 \, x^{3} + 6 \, x^{2} + 4 \, x\right )} e^{3} - 4 \, {\left (x e^{3} + e^{3}\right )} e^{\left (3 \, x^{2} e^{\left (-3\right )} + 3 \, x e\right )} + 6 \, {\left (x^{2} e^{3} + 2 \, x e^{3} + e^{3}\right )} e^{\left (2 \, x^{2} e^{\left (-3\right )} + 2 \, x e\right )} - 4 \, {\left (x^{3} e^{3} + 3 \, x^{2} e^{3} + 3 \, x e^{3} + e^{3}\right )} e^{\left (x^{2} e^{\left (-3\right )} + x e\right )} + e^{\left (4 \, {\left (x^{2} + x e^{4}\right )} e^{\left (-3\right )} + 3\right )}\right )} e^{\left (-3\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((4*exp(4)+8*x)*exp((x*exp(4)+x^2)/exp(3))^4+((-12*x-12)*exp(4)-4*exp(3)-24*x^2-24*x)*exp((x*exp(4)+
x^2)/exp(3))^3+((12*x^2+24*x+12)*exp(4)+(12*x+12)*exp(3)+24*x^3+48*x^2+24*x)*exp((x*exp(4)+x^2)/exp(3))^2+((-4
*x^3-12*x^2-12*x-4)*exp(4)+(-12*x^2-24*x-12)*exp(3)-8*x^4-24*x^3-24*x^2-8*x)*exp((x*exp(4)+x^2)/exp(3))+(4*x^3
+12*x^2+12*x+4)*exp(3))/exp(3),x, algorithm="maxima")

[Out]

((x^4 + 4*x^3 + 6*x^2 + 4*x)*e^3 - 4*(x*e^3 + e^3)*e^(3*x^2*e^(-3) + 3*x*e) + 6*(x^2*e^3 + 2*x*e^3 + e^3)*e^(2
*x^2*e^(-3) + 2*x*e) - 4*(x^3*e^3 + 3*x^2*e^3 + 3*x*e^3 + e^3)*e^(x^2*e^(-3) + x*e) + e^(4*(x^2 + x*e^4)*e^(-3
) + 3))*e^(-3)

________________________________________________________________________________________

mupad [B]  time = 0.99, size = 179, normalized size = 9.42 \begin {gather*} 4\,x-4\,{\mathrm {e}}^{{\mathrm {e}}^{-3}\,x^2+\mathrm {e}\,x}+6\,{\mathrm {e}}^{2\,{\mathrm {e}}^{-3}\,x^2+2\,\mathrm {e}\,x}-4\,{\mathrm {e}}^{3\,{\mathrm {e}}^{-3}\,x^2+3\,\mathrm {e}\,x}+{\mathrm {e}}^{4\,{\mathrm {e}}^{-3}\,x^2+4\,\mathrm {e}\,x}-12\,x\,{\mathrm {e}}^{{\mathrm {e}}^{-3}\,x^2+\mathrm {e}\,x}+12\,x\,{\mathrm {e}}^{2\,{\mathrm {e}}^{-3}\,x^2+2\,\mathrm {e}\,x}-4\,x\,{\mathrm {e}}^{3\,{\mathrm {e}}^{-3}\,x^2+3\,\mathrm {e}\,x}-12\,x^2\,{\mathrm {e}}^{{\mathrm {e}}^{-3}\,x^2+\mathrm {e}\,x}-4\,x^3\,{\mathrm {e}}^{{\mathrm {e}}^{-3}\,x^2+\mathrm {e}\,x}+6\,x^2\,{\mathrm {e}}^{2\,{\mathrm {e}}^{-3}\,x^2+2\,\mathrm {e}\,x}+6\,x^2+4\,x^3+x^4 \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp(-3)*(exp(3)*(12*x + 12*x^2 + 4*x^3 + 4) - exp(3*exp(-3)*(x*exp(4) + x^2))*(24*x + 4*exp(3) + 24*x^2 +
exp(4)*(12*x + 12)) - exp(exp(-3)*(x*exp(4) + x^2))*(8*x + exp(3)*(24*x + 12*x^2 + 12) + exp(4)*(12*x + 12*x^2
+ 4*x^3 + 4) + 24*x^2 + 24*x^3 + 8*x^4) + exp(2*exp(-3)*(x*exp(4) + x^2))*(24*x + exp(4)*(24*x + 12*x^2 + 12)
+ 48*x^2 + 24*x^3 + exp(3)*(12*x + 12)) + exp(4*exp(-3)*(x*exp(4) + x^2))*(8*x + 4*exp(4))),x)

[Out]

4*x - 4*exp(x*exp(1) + x^2*exp(-3)) + 6*exp(2*x*exp(1) + 2*x^2*exp(-3)) - 4*exp(3*x*exp(1) + 3*x^2*exp(-3)) +
exp(4*x*exp(1) + 4*x^2*exp(-3)) - 12*x*exp(x*exp(1) + x^2*exp(-3)) + 12*x*exp(2*x*exp(1) + 2*x^2*exp(-3)) - 4*
x*exp(3*x*exp(1) + 3*x^2*exp(-3)) - 12*x^2*exp(x*exp(1) + x^2*exp(-3)) - 4*x^3*exp(x*exp(1) + x^2*exp(-3)) + 6
*x^2*exp(2*x*exp(1) + 2*x^2*exp(-3)) + 6*x^2 + 4*x^3 + x^4

________________________________________________________________________________________

sympy [B]  time = 0.33, size = 114, normalized size = 6.00 \begin {gather*} x^{4} + 4 x^{3} + 6 x^{2} + 4 x + \left (- 4 x - 4\right ) e^{\frac {3 \left (x^{2} + x e^{4}\right )}{e^{3}}} + \left (6 x^{2} + 12 x + 6\right ) e^{\frac {2 \left (x^{2} + x e^{4}\right )}{e^{3}}} + \left (- 4 x^{3} - 12 x^{2} - 12 x - 4\right ) e^{\frac {x^{2} + x e^{4}}{e^{3}}} + e^{\frac {4 \left (x^{2} + x e^{4}\right )}{e^{3}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((4*exp(4)+8*x)*exp((x*exp(4)+x**2)/exp(3))**4+((-12*x-12)*exp(4)-4*exp(3)-24*x**2-24*x)*exp((x*exp(
4)+x**2)/exp(3))**3+((12*x**2+24*x+12)*exp(4)+(12*x+12)*exp(3)+24*x**3+48*x**2+24*x)*exp((x*exp(4)+x**2)/exp(3
))**2+((-4*x**3-12*x**2-12*x-4)*exp(4)+(-12*x**2-24*x-12)*exp(3)-8*x**4-24*x**3-24*x**2-8*x)*exp((x*exp(4)+x**
2)/exp(3))+(4*x**3+12*x**2+12*x+4)*exp(3))/exp(3),x)

[Out]

x**4 + 4*x**3 + 6*x**2 + 4*x + (-4*x - 4)*exp(3*(x**2 + x*exp(4))*exp(-3)) + (6*x**2 + 12*x + 6)*exp(2*(x**2 +
x*exp(4))*exp(-3)) + (-4*x**3 - 12*x**2 - 12*x - 4)*exp((x**2 + x*exp(4))*exp(-3)) + exp(4*(x**2 + x*exp(4))*
exp(-3))

________________________________________________________________________________________