∫ 18+6x−22x2−6x3+6x4+2x5+e8(2+2x)+e4(12+8x−8x2−4x3)+e2ex (2x2+2x3)+eex (12x+8x2−8x3−4x4+e4(4x+4x2))+e 1 _________________________ 3+e4−x+eexx−x2 (−9−e8+5x+3x2−e2ex x2−2x3−x4+e4(−6+2x+2x2)+eex (−5x−2e4x+2x2+exx2+2x3))___________________________________________________________________________________________________________________________________________________________________ 9+e8−6x−5x2+e2exx2+2x3+x4+e4(6−2x−2x2)+eex(6x+2e4x−2x2−2x3) dx

3.43.22 \(\int \frac {18+6 x-22 x^2-6 x^3+6 x^4+2 x^5+e^8 (2+2 x)+e^4 (12+8 x-8 x^2-4 x^3)+e^{2 e^x} (2 x^2+2 x^3)+e^{e^x} (12 x+8 x^2-8 x^3-4 x^4+e^4 (4 x+4 x^2))+e^{\frac {1}{3+e^4-x+e^{e^x} x-x^2}} (-9-e^8+5 x+3 x^2-e^{2 e^x} x^2-2 x^3-x^4+e^4 (-6+2 x+2 x^2)+e^{e^x} (-5 x-2 e^4 x+2 x^2+e^x x^2+2 x^3))}{9+e^8-6 x-5 x^2+e^{2 e^x} x^2+2 x^3+x^4+e^4 (6-2 x-2 x^2)+e^{e^x} (6 x+2 e^4 x-2 x^2-2 x^3)} \, dx\)

Optimal. Leaf size=31 \[ x \left (2-e^{\frac {1}{3+e^4-x+e^{e^x} x-x^2}}+x\right ) \]

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Rubi [F] time = 106.69, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int \frac {18+6 x-22 x^2-6 x^3+6 x^4+2 x^5+e^8 (2+2 x)+e^4 \left (12+8 x-8 x^2-4 x^3\right )+e^{2 e^x} \left (2 x^2+2 x^3\right )+e^{e^x} \left (12 x+8 x^2-8 x^3-4 x^4+e^4 \left (4 x+4 x^2\right )\right )+e^{\frac {1}{3+e^4-x+e^{e^x} x-x^2}} \left (-9-e^8+5 x+3 x^2-e^{2 e^x} x^2-2 x^3-x^4+e^4 \left (-6+2 x+2 x^2\right )+e^{e^x} \left (-5 x-2 e^4 x+2 x^2+e^x x^2+2 x^3\right )\right )}{9+e^8-6 x-5 x^2+e^{2 e^x} x^2+2 x^3+x^4+e^4 \left (6-2 x-2 x^2\right )+e^{e^x} \left (6 x+2 e^4 x-2 x^2-2 x^3\right )} \, dx \end {gather*}

Veriﬁcation is not applicable to the result.

[In]

Int[(18 + 6*x - 22*x^2 - 6*x^3 + 6*x^4 + 2*x^5 + E^8*(2 + 2*x) + E^4*(12 + 8*x - 8*x^2 - 4*x^3) + E^(2*E^x)*(2

*x^2 + 2*x^3) + E^E^x*(12*x + 8*x^2 - 8*x^3 - 4*x^4 + E^4*(4*x + 4*x^2)) + E^(3 + E^4 - x + E^E^x*x - x^2)^(-1

)*(-9 - E^8 + 5*x + 3*x^2 - E^(2*E^x)*x^2 - 2*x^3 - x^4 + E^4*(-6 + 2*x + 2*x^2) + E^E^x*(-5*x - 2*E^4*x + 2*x

^2 + E^x*x^2 + 2*x^3)))/(9 + E^8 - 6*x - 5*x^2 + E^(2*E^x)*x^2 + 2*x^3 + x^4 + E^4*(6 - 2*x - 2*x^2) + E^E^x*(

6*x + 2*E^4*x - 2*x^2 - 2*x^3)),x]

[Out]

18*Defer[Int][(3*(1 + E^4/3) - x + E^E^x*x - x^2)^(-2), x] + 12*E^4*Defer[Int][(3*(1 + E^4/3) - x + E^E^x*x -

x^2)^(-2), x] + 2*E^8*Defer[Int][(3*(1 + E^4/3) - x + E^E^x*x - x^2)^(-2), x] - (3 + E^4)^2*Defer[Int][E^(3*(1

+ E^4/3) - x + E^E^x*x - x^2)^(-1)/(3*(1 + E^4/3) - x + E^E^x*x - x^2)^2, x] + 6*Defer[Int][x/(3*(1 + E^4/3)

- x + E^E^x*x - x^2)^2, x] + 8*E^4*Defer[Int][x/(3*(1 + E^4/3) - x + E^E^x*x - x^2)^2, x] + 2*E^8*Defer[Int][x

/(3*(1 + E^4/3) - x + E^E^x*x - x^2)^2, x] + 4*(3 + E^4)*Defer[Int][(E^E^x*x)/(3*(1 + E^4/3) - x + E^E^x*x - x

^2)^2, x] + (5 + 2*E^4)*Defer[Int][(E^(3*(1 + E^4/3) - x + E^E^x*x - x^2)^(-1)*x)/(3*(1 + E^4/3) - x + E^E^x*x

- x^2)^2, x] - (5 + 2*E^4)*Defer[Int][(E^(E^x + (3*(1 + E^4/3) - x + E^E^x*x - x^2)^(-1))*x)/(3*(1 + E^4/3) -

x + E^E^x*x - x^2)^2, x] - 22*Defer[Int][x^2/(3*(1 + E^4/3) - x + E^E^x*x - x^2)^2, x] - 8*E^4*Defer[Int][x^2

/(3*(1 + E^4/3) - x + E^E^x*x - x^2)^2, x] + 4*(2 + E^4)*Defer[Int][(E^E^x*x^2)/(3*(1 + E^4/3) - x + E^E^x*x -

x^2)^2, x] + 2*Defer[Int][(E^(2*E^x)*x^2)/(3*(1 + E^4/3) - x + E^E^x*x - x^2)^2, x] + (3 + 2*E^4)*Defer[Int][

(E^(3*(1 + E^4/3) - x + E^E^x*x - x^2)^(-1)*x^2)/(3*(1 + E^4/3) - x + E^E^x*x - x^2)^2, x] + 2*Defer[Int][(E^(

E^x + (3*(1 + E^4/3) - x + E^E^x*x - x^2)^(-1))*x^2)/(3*(1 + E^4/3) - x + E^E^x*x - x^2)^2, x] - Defer[Int][(E

^(2*E^x + (3*(1 + E^4/3) - x + E^E^x*x - x^2)^(-1))*x^2)/(3*(1 + E^4/3) - x + E^E^x*x - x^2)^2, x] + Defer[Int

][(E^(E^x + x + (3*(1 + E^4/3) - x + E^E^x*x - x^2)^(-1))*x^2)/(3*(1 + E^4/3) - x + E^E^x*x - x^2)^2, x] - 6*D

efer[Int][x^3/(3*(1 + E^4/3) - x + E^E^x*x - x^2)^2, x] - 4*E^4*Defer[Int][x^3/(3*(1 + E^4/3) - x + E^E^x*x -

x^2)^2, x] - 8*Defer[Int][(E^E^x*x^3)/(3*(1 + E^4/3) - x + E^E^x*x - x^2)^2, x] + 2*Defer[Int][(E^(2*E^x)*x^3)

/(3*(1 + E^4/3) - x + E^E^x*x - x^2)^2, x] - 2*Defer[Int][(E^(3*(1 + E^4/3) - x + E^E^x*x - x^2)^(-1)*x^3)/(3*

(1 + E^4/3) - x + E^E^x*x - x^2)^2, x] + 2*Defer[Int][(E^(E^x + (3*(1 + E^4/3) - x + E^E^x*x - x^2)^(-1))*x^3)

/(3*(1 + E^4/3) - x + E^E^x*x - x^2)^2, x] + 6*Defer[Int][x^4/(3*(1 + E^4/3) - x + E^E^x*x - x^2)^2, x] - 4*De

fer[Int][(E^E^x*x^4)/(3*(1 + E^4/3) - x + E^E^x*x - x^2)^2, x] - Defer[Int][(E^(3*(1 + E^4/3) - x + E^E^x*x -

x^2)^(-1)*x^4)/(3*(1 + E^4/3) - x + E^E^x*x - x^2)^2, x] + 2*Defer[Int][x^5/(3*(1 + E^4/3) - x + E^E^x*x - x^2

)^2, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {18+6 x-22 x^2-6 x^3+6 x^4+2 x^5+e^8 (2+2 x)+e^4 \left (12+8 x-8 x^2-4 x^3\right )+e^{2 e^x} \left (2 x^2+2 x^3\right )+e^{e^x} \left (12 x+8 x^2-8 x^3-4 x^4+e^4 \left (4 x+4 x^2\right )\right )+e^{\frac {1}{3+e^4-x+e^{e^x} x-x^2}} \left (-9-e^8+5 x+3 x^2-e^{2 e^x} x^2-2 x^3-x^4+e^4 \left (-6+2 x+2 x^2\right )+e^{e^x} \left (-5 x-2 e^4 x+2 x^2+e^x x^2+2 x^3\right )\right )}{\left (3 \left (1+\frac {e^4}{3}\right )-x+e^{e^x} x-x^2\right )^2} \, dx\\ &=\int \left (\frac {18}{\left (3 \left (1+\frac {e^4}{3}\right )-x+e^{e^x} x-x^2\right )^2}+\frac {6 x}{\left (3 \left (1+\frac {e^4}{3}\right )-x+e^{e^x} x-x^2\right )^2}-\frac {22 x^2}{\left (3 \left (1+\frac {e^4}{3}\right )-x+e^{e^x} x-x^2\right )^2}-\frac {6 x^3}{\left (3 \left (1+\frac {e^4}{3}\right )-x+e^{e^x} x-x^2\right )^2}+\frac {6 x^4}{\left (3 \left (1+\frac {e^4}{3}\right )-x+e^{e^x} x-x^2\right )^2}+\frac {2 x^5}{\left (3 \left (1+\frac {e^4}{3}\right )-x+e^{e^x} x-x^2\right )^2}+\frac {2 e^8 (1+x)}{\left (3 \left (1+\frac {e^4}{3}\right )-x+e^{e^x} x-x^2\right )^2}+\frac {2 e^{2 e^x} x^2 (1+x)}{\left (3 \left (1+\frac {e^4}{3}\right )-x+e^{e^x} x-x^2\right )^2}+\frac {4 e^4 (1+x) \left (3-x-x^2\right )}{\left (3 \left (1+\frac {e^4}{3}\right )-x+e^{e^x} x-x^2\right )^2}+\frac {4 e^{e^x} x (1+x) \left (3+e^4-x-x^2\right )}{\left (3 \left (1+\frac {e^4}{3}\right )-x+e^{e^x} x-x^2\right )^2}+\frac {e^{\frac {1}{3 \left (1+\frac {e^4}{3}\right )-x+e^{e^x} x-x^2}} \left (-9 \left (1+\frac {1}{9} e^4 \left (6+e^4\right )\right )+5 \left (1+\frac {2 e^4}{5}\right ) x-5 e^{e^x} \left (1+\frac {2 e^4}{5}\right ) x+2 e^{e^x} x^2-e^{2 e^x} x^2+e^{e^x+x} x^2+3 \left (1+\frac {2 e^4}{3}\right ) x^2-2 x^3+2 e^{e^x} x^3-x^4\right )}{\left (3 \left (1+\frac {e^4}{3}\right )-x+e^{e^x} x-x^2\right )^2}\right ) \, dx\\ &=2 \int \frac {x^5}{\left (3 \left (1+\frac {e^4}{3}\right )-x+e^{e^x} x-x^2\right )^2} \, dx+2 \int \frac {e^{2 e^x} x^2 (1+x)}{\left (3 \left (1+\frac {e^4}{3}\right )-x+e^{e^x} x-x^2\right )^2} \, dx+4 \int \frac {e^{e^x} x (1+x) \left (3+e^4-x-x^2\right )}{\left (3 \left (1+\frac {e^4}{3}\right )-x+e^{e^x} x-x^2\right )^2} \, dx+6 \int \frac {x}{\left (3 \left (1+\frac {e^4}{3}\right )-x+e^{e^x} x-x^2\right )^2} \, dx-6 \int \frac {x^3}{\left (3 \left (1+\frac {e^4}{3}\right )-x+e^{e^x} x-x^2\right )^2} \, dx+6 \int \frac {x^4}{\left (3 \left (1+\frac {e^4}{3}\right )-x+e^{e^x} x-x^2\right )^2} \, dx+18 \int \frac {1}{\left (3 \left (1+\frac {e^4}{3}\right )-x+e^{e^x} x-x^2\right )^2} \, dx-22 \int \frac {x^2}{\left (3 \left (1+\frac {e^4}{3}\right )-x+e^{e^x} x-x^2\right )^2} \, dx+\left (4 e^4\right ) \int \frac {(1+x) \left (3-x-x^2\right )}{\left (3 \left (1+\frac {e^4}{3}\right )-x+e^{e^x} x-x^2\right )^2} \, dx+\left (2 e^8\right ) \int \frac {1+x}{\left (3 \left (1+\frac {e^4}{3}\right )-x+e^{e^x} x-x^2\right )^2} \, dx+\int \frac {e^{\frac {1}{3 \left (1+\frac {e^4}{3}\right )-x+e^{e^x} x-x^2}} \left (-9 \left (1+\frac {1}{9} e^4 \left (6+e^4\right )\right )+5 \left (1+\frac {2 e^4}{5}\right ) x-5 e^{e^x} \left (1+\frac {2 e^4}{5}\right ) x+2 e^{e^x} x^2-e^{2 e^x} x^2+e^{e^x+x} x^2+3 \left (1+\frac {2 e^4}{3}\right ) x^2-2 x^3+2 e^{e^x} x^3-x^4\right )}{\left (3 \left (1+\frac {e^4}{3}\right )-x+e^{e^x} x-x^2\right )^2} \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

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Mathematica [A] time = 0.38, size = 31, normalized size = 1.00 \begin {gather*} x \left (2-e^{\frac {1}{3+e^4-x+e^{e^x} x-x^2}}+x\right ) \end {gather*}

Antiderivative was successfully veriﬁed.

[In]

Integrate[(18 + 6*x - 22*x^2 - 6*x^3 + 6*x^4 + 2*x^5 + E^8*(2 + 2*x) + E^4*(12 + 8*x - 8*x^2 - 4*x^3) + E^(2*E

^x)*(2*x^2 + 2*x^3) + E^E^x*(12*x + 8*x^2 - 8*x^3 - 4*x^4 + E^4*(4*x + 4*x^2)) + E^(3 + E^4 - x + E^E^x*x - x^

2)^(-1)*(-9 - E^8 + 5*x + 3*x^2 - E^(2*E^x)*x^2 - 2*x^3 - x^4 + E^4*(-6 + 2*x + 2*x^2) + E^E^x*(-5*x - 2*E^4*x

+ 2*x^2 + E^x*x^2 + 2*x^3)))/(9 + E^8 - 6*x - 5*x^2 + E^(2*E^x)*x^2 + 2*x^3 + x^4 + E^4*(6 - 2*x - 2*x^2) + E

^E^x*(6*x + 2*E^4*x - 2*x^2 - 2*x^3)),x]

[Out]

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

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fricas [A] time = 2.04, size = 31, normalized size = 1.00 \begin {gather*} x^{2} - x e^{\left (-\frac {1}{x^{2} - x e^{\left (e^{x}\right )} + x - e^{4} - 3}\right )} + 2 \, x \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-x^2*exp(exp(x))^2+(exp(x)*x^2-2*x*exp(4)+2*x^3+2*x^2-5*x)*exp(exp(x))-exp(4)^2+(2*x^2+2*x-6)*exp(

4)-x^4-2*x^3+3*x^2+5*x-9)*exp(1/(x*exp(exp(x))+exp(4)-x^2-x+3))+(2*x^3+2*x^2)*exp(exp(x))^2+((4*x^2+4*x)*exp(4

)-4*x^4-8*x^3+8*x^2+12*x)*exp(exp(x))+(2*x+2)*exp(4)^2+(-4*x^3-8*x^2+8*x+12)*exp(4)+2*x^5+6*x^4-6*x^3-22*x^2+6

*x+18)/(x^2*exp(exp(x))^2+(2*x*exp(4)-2*x^3-2*x^2+6*x)*exp(exp(x))+exp(4)^2+(-2*x^2-2*x+6)*exp(4)+x^4+2*x^3-5*

x^2-6*x+9),x, algorithm="fricas")

[Out]

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

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giac [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-x^2*exp(exp(x))^2+(exp(x)*x^2-2*x*exp(4)+2*x^3+2*x^2-5*x)*exp(exp(x))-exp(4)^2+(2*x^2+2*x-6)*exp(

4)-x^4-2*x^3+3*x^2+5*x-9)*exp(1/(x*exp(exp(x))+exp(4)-x^2-x+3))+(2*x^3+2*x^2)*exp(exp(x))^2+((4*x^2+4*x)*exp(4

)-4*x^4-8*x^3+8*x^2+12*x)*exp(exp(x))+(2*x+2)*exp(4)^2+(-4*x^3-8*x^2+8*x+12)*exp(4)+2*x^5+6*x^4-6*x^3-22*x^2+6

*x+18)/(x^2*exp(exp(x))^2+(2*x*exp(4)-2*x^3-2*x^2+6*x)*exp(exp(x))+exp(4)^2+(-2*x^2-2*x+6)*exp(4)+x^4+2*x^3-5*

x^2-6*x+9),x, algorithm="giac")

[Out]

Timed out

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maple [A] time = 0.08, size = 31, normalized size = 1.00


method	result	size

risch	\(x^{2}-{\mathrm e}^{\frac {1}{x \,{\mathrm e}^{{\mathrm e}^{x}}+{\mathrm e}^{4}-x^{2}-x +3}} x +2 x\)	\(31\)

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

int(((-x^2*exp(exp(x))^2+(exp(x)*x^2-2*x*exp(4)+2*x^3+2*x^2-5*x)*exp(exp(x))-exp(4)^2+(2*x^2+2*x-6)*exp(4)-x^4

-2*x^3+3*x^2+5*x-9)*exp(1/(x*exp(exp(x))+exp(4)-x^2-x+3))+(2*x^3+2*x^2)*exp(exp(x))^2+((4*x^2+4*x)*exp(4)-4*x^

4-8*x^3+8*x^2+12*x)*exp(exp(x))+(2*x+2)*exp(4)^2+(-4*x^3-8*x^2+8*x+12)*exp(4)+2*x^5+6*x^4-6*x^3-22*x^2+6*x+18)

/(x^2*exp(exp(x))^2+(2*x*exp(4)-2*x^3-2*x^2+6*x)*exp(exp(x))+exp(4)^2+(-2*x^2-2*x+6)*exp(4)+x^4+2*x^3-5*x^2-6*

x+9),x,method=_RETURNVERBOSE)

[Out]

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

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maxima [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} x^{2} + 2 \, x - \int \frac {{\left (x^{4} + 2 \, x^{3} - x^{2} {\left (2 \, e^{4} + 3\right )} + x^{2} e^{\left (2 \, e^{x}\right )} - x {\left (2 \, e^{4} + 5\right )} - {\left (2 \, x^{3} + x^{2} e^{x} + 2 \, x^{2} - x {\left (2 \, e^{4} + 5\right )}\right )} e^{\left (e^{x}\right )} + e^{8} + 6 \, e^{4} + 9\right )} e^{\left (-\frac {1}{x^{2} - x e^{\left (e^{x}\right )} + x - e^{4} - 3}\right )}}{x^{4} + 2 \, x^{3} - x^{2} {\left (2 \, e^{4} + 5\right )} + x^{2} e^{\left (2 \, e^{x}\right )} - 2 \, x {\left (e^{4} + 3\right )} - 2 \, {\left (x^{3} + x^{2} - x {\left (e^{4} + 3\right )}\right )} e^{\left (e^{x}\right )} + e^{8} + 6 \, e^{4} + 9}\,{d x} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-x^2*exp(exp(x))^2+(exp(x)*x^2-2*x*exp(4)+2*x^3+2*x^2-5*x)*exp(exp(x))-exp(4)^2+(2*x^2+2*x-6)*exp(

4)-x^4-2*x^3+3*x^2+5*x-9)*exp(1/(x*exp(exp(x))+exp(4)-x^2-x+3))+(2*x^3+2*x^2)*exp(exp(x))^2+((4*x^2+4*x)*exp(4

)-4*x^4-8*x^3+8*x^2+12*x)*exp(exp(x))+(2*x+2)*exp(4)^2+(-4*x^3-8*x^2+8*x+12)*exp(4)+2*x^5+6*x^4-6*x^3-22*x^2+6

*x+18)/(x^2*exp(exp(x))^2+(2*x*exp(4)-2*x^3-2*x^2+6*x)*exp(exp(x))+exp(4)^2+(-2*x^2-2*x+6)*exp(4)+x^4+2*x^3-5*

x^2-6*x+9),x, algorithm="maxima")

[Out]

x^2 + 2*x - integrate((x^4 + 2*x^3 - x^2*(2*e^4 + 3) + x^2*e^(2*e^x) - x*(2*e^4 + 5) - (2*x^3 + x^2*e^x + 2*x^

2 - x*(2*e^4 + 5))*e^(e^x) + e^8 + 6*e^4 + 9)*e^(-1/(x^2 - x*e^(e^x) + x - e^4 - 3))/(x^4 + 2*x^3 - x^2*(2*e^4

+ 5) + x^2*e^(2*e^x) - 2*x*(e^4 + 3) - 2*(x^3 + x^2 - x*(e^4 + 3))*e^(e^x) + e^8 + 6*e^4 + 9), x)

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mupad [B] time = 3.64, size = 27, normalized size = 0.87 \begin {gather*} x\,\left (x-{\mathrm {e}}^{\frac {1}{{\mathrm {e}}^4-x+x\,{\mathrm {e}}^{{\mathrm {e}}^x}-x^2+3}}+2\right ) \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

int((6*x + exp(4)*(8*x - 8*x^2 - 4*x^3 + 12) - exp(1/(exp(4) - x + x*exp(exp(x)) - x^2 + 3))*(exp(8) - 5*x - e

xp(4)*(2*x + 2*x^2 - 6) - exp(exp(x))*(x^2*exp(x) - 5*x - 2*x*exp(4) + 2*x^2 + 2*x^3) - 3*x^2 + 2*x^3 + x^4 +

x^2*exp(2*exp(x)) + 9) + exp(exp(x))*(12*x + exp(4)*(4*x + 4*x^2) + 8*x^2 - 8*x^3 - 4*x^4) + exp(2*exp(x))*(2*

x^2 + 2*x^3) - 22*x^2 - 6*x^3 + 6*x^4 + 2*x^5 + exp(8)*(2*x + 2) + 18)/(exp(8) - 6*x - exp(4)*(2*x + 2*x^2 - 6

) + exp(exp(x))*(6*x + 2*x*exp(4) - 2*x^2 - 2*x^3) - 5*x^2 + 2*x^3 + x^4 + x^2*exp(2*exp(x)) + 9),x)

[Out]

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

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sympy [A] time = 16.02, size = 27, normalized size = 0.87 \begin {gather*} x^{2} - x e^{\frac {1}{- x^{2} + x e^{e^{x}} - x + 3 + e^{4}}} + 2 x \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-x**2*exp(exp(x))**2+(exp(x)*x**2-2*x*exp(4)+2*x**3+2*x**2-5*x)*exp(exp(x))-exp(4)**2+(2*x**2+2*x-

6)*exp(4)-x**4-2*x**3+3*x**2+5*x-9)*exp(1/(x*exp(exp(x))+exp(4)-x**2-x+3))+(2*x**3+2*x**2)*exp(exp(x))**2+((4*

x**2+4*x)*exp(4)-4*x**4-8*x**3+8*x**2+12*x)*exp(exp(x))+(2*x+2)*exp(4)**2+(-4*x**3-8*x**2+8*x+12)*exp(4)+2*x**

5+6*x**4-6*x**3-22*x**2+6*x+18)/(x**2*exp(exp(x))**2+(2*x*exp(4)-2*x**3-2*x**2+6*x)*exp(exp(x))+exp(4)**2+(-2*

x**2-2*x+6)*exp(4)+x**4+2*x**3-5*x**2-6*x+9),x)

[Out]

x**2 - x*exp(1/(-x**2 + x*exp(exp(x)) - x + 3 + exp(4))) + 2*x

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