3.34.100 \(\int \frac {e^{2 e^x} (-4+12 x^2-4 x^3)+e^6 (12 x^2-4 x^3)+e^{e^x} (4 e^{3+x} x+e^3 (-4+24 x^2-8 x^3))}{e^{2 e^x} (4-20 x+49 x^2-64 x^3+46 x^4-12 x^5+x^6)+e^6 (25 x^2-60 x^3+46 x^4-12 x^5+x^6)+e^{3+e^x} (-20 x+74 x^2-124 x^3+92 x^4-24 x^5+2 x^6)} \, dx\)

Optimal. Leaf size=32 \[ \frac {2}{(-5+x) (-1+x)+\frac {2}{-x-e^{3-e^x} x}} \]

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Rubi [F]  time = 9.23, 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 {e^{2 e^x} \left (-4+12 x^2-4 x^3\right )+e^6 \left (12 x^2-4 x^3\right )+e^{e^x} \left (4 e^{3+x} x+e^3 \left (-4+24 x^2-8 x^3\right )\right )}{e^{2 e^x} \left (4-20 x+49 x^2-64 x^3+46 x^4-12 x^5+x^6\right )+e^6 \left (25 x^2-60 x^3+46 x^4-12 x^5+x^6\right )+e^{3+e^x} \left (-20 x+74 x^2-124 x^3+92 x^4-24 x^5+2 x^6\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(E^(2*E^x)*(-4 + 12*x^2 - 4*x^3) + E^6*(12*x^2 - 4*x^3) + E^E^x*(4*E^(3 + x)*x + E^3*(-4 + 24*x^2 - 8*x^3)
))/(E^(2*E^x)*(4 - 20*x + 49*x^2 - 64*x^3 + 46*x^4 - 12*x^5 + x^6) + E^6*(25*x^2 - 60*x^3 + 46*x^4 - 12*x^5 +
x^6) + E^(3 + E^x)*(-20*x + 74*x^2 - 124*x^3 + 92*x^4 - 24*x^5 + 2*x^6)),x]

[Out]

-4*Defer[Int][E^(2*E^x)/(E^3*x*(5 - 6*x + x^2) + E^E^x*(-2 + 5*x - 6*x^2 + x^3))^2, x] - 4*Defer[Int][E^(3 + E
^x)/(E^3*x*(5 - 6*x + x^2) + E^E^x*(-2 + 5*x - 6*x^2 + x^3))^2, x] + 4*Defer[Int][(E^(3 + E^x + x)*x)/(E^3*x*(
5 - 6*x + x^2) + E^E^x*(-2 + 5*x - 6*x^2 + x^3))^2, x] + 12*E^6*Defer[Int][x^2/(E^3*x*(5 - 6*x + x^2) + E^E^x*
(-2 + 5*x - 6*x^2 + x^3))^2, x] + 12*Defer[Int][(E^(2*E^x)*x^2)/(E^3*x*(5 - 6*x + x^2) + E^E^x*(-2 + 5*x - 6*x
^2 + x^3))^2, x] + 24*Defer[Int][(E^(3 + E^x)*x^2)/(E^3*x*(5 - 6*x + x^2) + E^E^x*(-2 + 5*x - 6*x^2 + x^3))^2,
x] - 4*E^6*Defer[Int][x^3/(E^3*x*(5 - 6*x + x^2) + E^E^x*(-2 + 5*x - 6*x^2 + x^3))^2, x] - 4*Defer[Int][(E^(2
*E^x)*x^3)/(E^3*x*(5 - 6*x + x^2) + E^E^x*(-2 + 5*x - 6*x^2 + x^3))^2, x] - 8*Defer[Int][(E^(3 + E^x)*x^3)/(E^
3*x*(5 - 6*x + x^2) + E^E^x*(-2 + 5*x - 6*x^2 + x^3))^2, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {4 \left (e^{3+e^x+x} x-e^6 (-3+x) x^2-e^{2 e^x} \left (1-3 x^2+x^3\right )-e^{3+e^x} \left (1-6 x^2+2 x^3\right )\right )}{\left (e^3 x \left (5-6 x+x^2\right )+e^{e^x} \left (-2+5 x-6 x^2+x^3\right )\right )^2} \, dx\\ &=4 \int \frac {e^{3+e^x+x} x-e^6 (-3+x) x^2-e^{2 e^x} \left (1-3 x^2+x^3\right )-e^{3+e^x} \left (1-6 x^2+2 x^3\right )}{\left (e^3 x \left (5-6 x+x^2\right )+e^{e^x} \left (-2+5 x-6 x^2+x^3\right )\right )^2} \, dx\\ &=4 \int \left (\frac {e^{3+e^x+x} x}{\left (-2 e^{e^x}+5 e^3 x+5 e^{e^x} x-6 e^3 x^2-6 e^{e^x} x^2+e^3 x^3+e^{e^x} x^3\right )^2}-\frac {e^6 (-3+x) x^2}{\left (-2 e^{e^x}+5 e^3 x+5 e^{e^x} x-6 e^3 x^2-6 e^{e^x} x^2+e^3 x^3+e^{e^x} x^3\right )^2}-\frac {e^{2 e^x} \left (1-3 x^2+x^3\right )}{\left (-2 e^{e^x}+5 e^3 x+5 e^{e^x} x-6 e^3 x^2-6 e^{e^x} x^2+e^3 x^3+e^{e^x} x^3\right )^2}-\frac {e^{3+e^x} \left (1-6 x^2+2 x^3\right )}{\left (-2 e^{e^x}+5 e^3 x+5 e^{e^x} x-6 e^3 x^2-6 e^{e^x} x^2+e^3 x^3+e^{e^x} x^3\right )^2}\right ) \, dx\\ &=4 \int \frac {e^{3+e^x+x} x}{\left (-2 e^{e^x}+5 e^3 x+5 e^{e^x} x-6 e^3 x^2-6 e^{e^x} x^2+e^3 x^3+e^{e^x} x^3\right )^2} \, dx-4 \int \frac {e^{2 e^x} \left (1-3 x^2+x^3\right )}{\left (-2 e^{e^x}+5 e^3 x+5 e^{e^x} x-6 e^3 x^2-6 e^{e^x} x^2+e^3 x^3+e^{e^x} x^3\right )^2} \, dx-4 \int \frac {e^{3+e^x} \left (1-6 x^2+2 x^3\right )}{\left (-2 e^{e^x}+5 e^3 x+5 e^{e^x} x-6 e^3 x^2-6 e^{e^x} x^2+e^3 x^3+e^{e^x} x^3\right )^2} \, dx-\left (4 e^6\right ) \int \frac {(-3+x) x^2}{\left (-2 e^{e^x}+5 e^3 x+5 e^{e^x} x-6 e^3 x^2-6 e^{e^x} x^2+e^3 x^3+e^{e^x} x^3\right )^2} \, dx\\ &=4 \int \frac {e^{3+e^x+x} x}{\left (e^3 x \left (5-6 x+x^2\right )+e^{e^x} \left (-2+5 x-6 x^2+x^3\right )\right )^2} \, dx-4 \int \frac {e^{2 e^x} \left (1-3 x^2+x^3\right )}{\left (e^3 x \left (5-6 x+x^2\right )+e^{e^x} \left (-2+5 x-6 x^2+x^3\right )\right )^2} \, dx-4 \int \frac {e^{3+e^x} \left (1-6 x^2+2 x^3\right )}{\left (e^3 x \left (5-6 x+x^2\right )+e^{e^x} \left (-2+5 x-6 x^2+x^3\right )\right )^2} \, dx-\left (4 e^6\right ) \int \frac {(-3+x) x^2}{\left (e^3 x \left (5-6 x+x^2\right )+e^{e^x} \left (-2+5 x-6 x^2+x^3\right )\right )^2} \, dx\\ &=4 \int \frac {e^{3+e^x+x} x}{\left (e^3 x \left (5-6 x+x^2\right )+e^{e^x} \left (-2+5 x-6 x^2+x^3\right )\right )^2} \, dx-4 \int \left (\frac {e^{2 e^x}}{\left (-2 e^{e^x}+5 e^3 x+5 e^{e^x} x-6 e^3 x^2-6 e^{e^x} x^2+e^3 x^3+e^{e^x} x^3\right )^2}-\frac {3 e^{2 e^x} x^2}{\left (-2 e^{e^x}+5 e^3 x+5 e^{e^x} x-6 e^3 x^2-6 e^{e^x} x^2+e^3 x^3+e^{e^x} x^3\right )^2}+\frac {e^{2 e^x} x^3}{\left (-2 e^{e^x}+5 e^3 x+5 e^{e^x} x-6 e^3 x^2-6 e^{e^x} x^2+e^3 x^3+e^{e^x} x^3\right )^2}\right ) \, dx-4 \int \left (\frac {e^{3+e^x}}{\left (-2 e^{e^x}+5 e^3 x+5 e^{e^x} x-6 e^3 x^2-6 e^{e^x} x^2+e^3 x^3+e^{e^x} x^3\right )^2}-\frac {6 e^{3+e^x} x^2}{\left (-2 e^{e^x}+5 e^3 x+5 e^{e^x} x-6 e^3 x^2-6 e^{e^x} x^2+e^3 x^3+e^{e^x} x^3\right )^2}+\frac {2 e^{3+e^x} x^3}{\left (-2 e^{e^x}+5 e^3 x+5 e^{e^x} x-6 e^3 x^2-6 e^{e^x} x^2+e^3 x^3+e^{e^x} x^3\right )^2}\right ) \, dx-\left (4 e^6\right ) \int \left (-\frac {3 x^2}{\left (-2 e^{e^x}+5 e^3 x+5 e^{e^x} x-6 e^3 x^2-6 e^{e^x} x^2+e^3 x^3+e^{e^x} x^3\right )^2}+\frac {x^3}{\left (-2 e^{e^x}+5 e^3 x+5 e^{e^x} x-6 e^3 x^2-6 e^{e^x} x^2+e^3 x^3+e^{e^x} x^3\right )^2}\right ) \, dx\\ &=-\left (4 \int \frac {e^{2 e^x}}{\left (-2 e^{e^x}+5 e^3 x+5 e^{e^x} x-6 e^3 x^2-6 e^{e^x} x^2+e^3 x^3+e^{e^x} x^3\right )^2} \, dx\right )-4 \int \frac {e^{3+e^x}}{\left (-2 e^{e^x}+5 e^3 x+5 e^{e^x} x-6 e^3 x^2-6 e^{e^x} x^2+e^3 x^3+e^{e^x} x^3\right )^2} \, dx-4 \int \frac {e^{2 e^x} x^3}{\left (-2 e^{e^x}+5 e^3 x+5 e^{e^x} x-6 e^3 x^2-6 e^{e^x} x^2+e^3 x^3+e^{e^x} x^3\right )^2} \, dx+4 \int \frac {e^{3+e^x+x} x}{\left (e^3 x \left (5-6 x+x^2\right )+e^{e^x} \left (-2+5 x-6 x^2+x^3\right )\right )^2} \, dx-8 \int \frac {e^{3+e^x} x^3}{\left (-2 e^{e^x}+5 e^3 x+5 e^{e^x} x-6 e^3 x^2-6 e^{e^x} x^2+e^3 x^3+e^{e^x} x^3\right )^2} \, dx+12 \int \frac {e^{2 e^x} x^2}{\left (-2 e^{e^x}+5 e^3 x+5 e^{e^x} x-6 e^3 x^2-6 e^{e^x} x^2+e^3 x^3+e^{e^x} x^3\right )^2} \, dx+24 \int \frac {e^{3+e^x} x^2}{\left (-2 e^{e^x}+5 e^3 x+5 e^{e^x} x-6 e^3 x^2-6 e^{e^x} x^2+e^3 x^3+e^{e^x} x^3\right )^2} \, dx-\left (4 e^6\right ) \int \frac {x^3}{\left (-2 e^{e^x}+5 e^3 x+5 e^{e^x} x-6 e^3 x^2-6 e^{e^x} x^2+e^3 x^3+e^{e^x} x^3\right )^2} \, dx+\left (12 e^6\right ) \int \frac {x^2}{\left (-2 e^{e^x}+5 e^3 x+5 e^{e^x} x-6 e^3 x^2-6 e^{e^x} x^2+e^3 x^3+e^{e^x} x^3\right )^2} \, dx\\ &=-\left (4 \int \frac {e^{2 e^x}}{\left (e^3 x \left (5-6 x+x^2\right )+e^{e^x} \left (-2+5 x-6 x^2+x^3\right )\right )^2} \, dx\right )-4 \int \frac {e^{3+e^x}}{\left (e^3 x \left (5-6 x+x^2\right )+e^{e^x} \left (-2+5 x-6 x^2+x^3\right )\right )^2} \, dx+4 \int \frac {e^{3+e^x+x} x}{\left (e^3 x \left (5-6 x+x^2\right )+e^{e^x} \left (-2+5 x-6 x^2+x^3\right )\right )^2} \, dx-4 \int \frac {e^{2 e^x} x^3}{\left (e^3 x \left (5-6 x+x^2\right )+e^{e^x} \left (-2+5 x-6 x^2+x^3\right )\right )^2} \, dx-8 \int \frac {e^{3+e^x} x^3}{\left (e^3 x \left (5-6 x+x^2\right )+e^{e^x} \left (-2+5 x-6 x^2+x^3\right )\right )^2} \, dx+12 \int \frac {e^{2 e^x} x^2}{\left (e^3 x \left (5-6 x+x^2\right )+e^{e^x} \left (-2+5 x-6 x^2+x^3\right )\right )^2} \, dx+24 \int \frac {e^{3+e^x} x^2}{\left (e^3 x \left (5-6 x+x^2\right )+e^{e^x} \left (-2+5 x-6 x^2+x^3\right )\right )^2} \, dx-\left (4 e^6\right ) \int \frac {x^3}{\left (e^3 x \left (5-6 x+x^2\right )+e^{e^x} \left (-2+5 x-6 x^2+x^3\right )\right )^2} \, dx+\left (12 e^6\right ) \int \frac {x^2}{\left (e^3 x \left (5-6 x+x^2\right )+e^{e^x} \left (-2+5 x-6 x^2+x^3\right )\right )^2} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.11, size = 47, normalized size = 1.47 \begin {gather*} \frac {2 \left (e^3+e^{e^x}\right ) x}{e^3 x \left (5-6 x+x^2\right )+e^{e^x} \left (-2+5 x-6 x^2+x^3\right )} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^(2*E^x)*(-4 + 12*x^2 - 4*x^3) + E^6*(12*x^2 - 4*x^3) + E^E^x*(4*E^(3 + x)*x + E^3*(-4 + 24*x^2 -
8*x^3)))/(E^(2*E^x)*(4 - 20*x + 49*x^2 - 64*x^3 + 46*x^4 - 12*x^5 + x^6) + E^6*(25*x^2 - 60*x^3 + 46*x^4 - 12*
x^5 + x^6) + E^(3 + E^x)*(-20*x + 74*x^2 - 124*x^3 + 92*x^4 - 24*x^5 + 2*x^6)),x]

[Out]

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

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fricas [B]  time = 0.47, size = 67, normalized size = 2.09 \begin {gather*} \frac {2 \, {\left (x e^{6} + x e^{\left ({\left (3 \, e^{3} + e^{\left (x + 3\right )}\right )} e^{\left (-3\right )}\right )}\right )}}{{\left (x^{3} - 6 \, x^{2} + 5 \, x\right )} e^{6} + {\left (x^{3} - 6 \, x^{2} + 5 \, x - 2\right )} e^{\left ({\left (3 \, e^{3} + e^{\left (x + 3\right )}\right )} e^{\left (-3\right )}\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-4*x^3+12*x^2-4)*exp(exp(x))^2+(4*x*exp(3)*exp(x)+(-8*x^3+24*x^2-4)*exp(3))*exp(exp(x))+(-4*x^3+12
*x^2)*exp(3)^2)/((x^6-12*x^5+46*x^4-64*x^3+49*x^2-20*x+4)*exp(exp(x))^2+(2*x^6-24*x^5+92*x^4-124*x^3+74*x^2-20
*x)*exp(3)*exp(exp(x))+(x^6-12*x^5+46*x^4-60*x^3+25*x^2)*exp(3)^2),x, algorithm="fricas")

[Out]

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

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giac [B]  time = 0.57, size = 59, normalized size = 1.84 \begin {gather*} \frac {2 \, {\left (x e^{3} + x e^{\left (e^{x}\right )}\right )}}{x^{3} e^{3} + x^{3} e^{\left (e^{x}\right )} - 6 \, x^{2} e^{3} - 6 \, x^{2} e^{\left (e^{x}\right )} + 5 \, x e^{3} + 5 \, x e^{\left (e^{x}\right )} - 2 \, e^{\left (e^{x}\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-4*x^3+12*x^2-4)*exp(exp(x))^2+(4*x*exp(3)*exp(x)+(-8*x^3+24*x^2-4)*exp(3))*exp(exp(x))+(-4*x^3+12
*x^2)*exp(3)^2)/((x^6-12*x^5+46*x^4-64*x^3+49*x^2-20*x+4)*exp(exp(x))^2+(2*x^6-24*x^5+92*x^4-124*x^3+74*x^2-20
*x)*exp(3)*exp(exp(x))+(x^6-12*x^5+46*x^4-60*x^3+25*x^2)*exp(3)^2),x, algorithm="giac")

[Out]

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

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maple [B]  time = 0.07, size = 87, normalized size = 2.72

method	result	size
risch	\(\frac {2 x}{x^{3}-6 x^{2}+5 x -2}-\frac {4 x \,{\mathrm e}^{3}}{\left (x^{3}-6 x^{2}+5 x -2\right ) \left (x^{3} {\mathrm e}^{3}+x^{3} {\mathrm e}^{{\mathrm e}^{x}}-6 x^{2} {\mathrm e}^{3}-6 \,{\mathrm e}^{{\mathrm e}^{x}} x^{2}+5 x \,{\mathrm e}^{3}+5 x \,{\mathrm e}^{{\mathrm e}^{x}}-2 \,{\mathrm e}^{{\mathrm e}^{x}}\right )}\)	\(87\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((-4*x^3+12*x^2-4)*exp(exp(x))^2+(4*x*exp(3)*exp(x)+(-8*x^3+24*x^2-4)*exp(3))*exp(exp(x))+(-4*x^3+12*x^2)*
exp(3)^2)/((x^6-12*x^5+46*x^4-64*x^3+49*x^2-20*x+4)*exp(exp(x))^2+(2*x^6-24*x^5+92*x^4-124*x^3+74*x^2-20*x)*ex
p(3)*exp(exp(x))+(x^6-12*x^5+46*x^4-60*x^3+25*x^2)*exp(3)^2),x,method=_RETURNVERBOSE)

[Out]

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

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maxima [A]  time = 0.63, size = 50, normalized size = 1.56 \begin {gather*} \frac {2 \, {\left (x e^{3} + x e^{\left (e^{x}\right )}\right )}}{x^{3} e^{3} - 6 \, x^{2} e^{3} + 5 \, x e^{3} + {\left (x^{3} - 6 \, x^{2} + 5 \, x - 2\right )} e^{\left (e^{x}\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-4*x^3+12*x^2-4)*exp(exp(x))^2+(4*x*exp(3)*exp(x)+(-8*x^3+24*x^2-4)*exp(3))*exp(exp(x))+(-4*x^3+12
*x^2)*exp(3)^2)/((x^6-12*x^5+46*x^4-64*x^3+49*x^2-20*x+4)*exp(exp(x))^2+(2*x^6-24*x^5+92*x^4-124*x^3+74*x^2-20
*x)*exp(3)*exp(exp(x))+(x^6-12*x^5+46*x^4-60*x^3+25*x^2)*exp(3)^2),x, algorithm="maxima")

[Out]

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

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mupad [F]  time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} \int -\frac {{\mathrm {e}}^{{\mathrm {e}}^x}\,\left ({\mathrm {e}}^3\,\left (8\,x^3-24\,x^2+4\right )-4\,x\,{\mathrm {e}}^3\,{\mathrm {e}}^x\right )-{\mathrm {e}}^6\,\left (12\,x^2-4\,x^3\right )+{\mathrm {e}}^{2\,{\mathrm {e}}^x}\,\left (4\,x^3-12\,x^2+4\right )}{{\mathrm {e}}^6\,\left (x^6-12\,x^5+46\,x^4-60\,x^3+25\,x^2\right )+{\mathrm {e}}^{2\,{\mathrm {e}}^x}\,\left (x^6-12\,x^5+46\,x^4-64\,x^3+49\,x^2-20\,x+4\right )-{\mathrm {e}}^{{\mathrm {e}}^x}\,{\mathrm {e}}^3\,\left (-2\,x^6+24\,x^5-92\,x^4+124\,x^3-74\,x^2+20\,x\right )} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(exp(exp(x))*(exp(3)*(8*x^3 - 24*x^2 + 4) - 4*x*exp(3)*exp(x)) - exp(6)*(12*x^2 - 4*x^3) + exp(2*exp(x))*
(4*x^3 - 12*x^2 + 4))/(exp(6)*(25*x^2 - 60*x^3 + 46*x^4 - 12*x^5 + x^6) + exp(2*exp(x))*(49*x^2 - 20*x - 64*x^
3 + 46*x^4 - 12*x^5 + x^6 + 4) - exp(exp(x))*exp(3)*(20*x - 74*x^2 + 124*x^3 - 92*x^4 + 24*x^5 - 2*x^6)),x)

[Out]

int(-(exp(exp(x))*(exp(3)*(8*x^3 - 24*x^2 + 4) - 4*x*exp(3)*exp(x)) - exp(6)*(12*x^2 - 4*x^3) + exp(2*exp(x))*
(4*x^3 - 12*x^2 + 4))/(exp(6)*(25*x^2 - 60*x^3 + 46*x^4 - 12*x^5 + x^6) + exp(2*exp(x))*(49*x^2 - 20*x - 64*x^
3 + 46*x^4 - 12*x^5 + x^6 + 4) - exp(exp(x))*exp(3)*(20*x - 74*x^2 + 124*x^3 - 92*x^4 + 24*x^5 - 2*x^6)), x)

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sympy [B]  time = 0.62, size = 104, normalized size = 3.25 \begin {gather*} - \frac {4 x e^{3}}{x^{6} e^{3} - 12 x^{5} e^{3} + 46 x^{4} e^{3} - 62 x^{3} e^{3} + 37 x^{2} e^{3} - 10 x e^{3} + \left (x^{6} - 12 x^{5} + 46 x^{4} - 64 x^{3} + 49 x^{2} - 20 x + 4\right ) e^{e^{x}}} + \frac {2 x}{x^{3} - 6 x^{2} + 5 x - 2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-4*x**3+12*x**2-4)*exp(exp(x))**2+(4*x*exp(3)*exp(x)+(-8*x**3+24*x**2-4)*exp(3))*exp(exp(x))+(-4*x
**3+12*x**2)*exp(3)**2)/((x**6-12*x**5+46*x**4-64*x**3+49*x**2-20*x+4)*exp(exp(x))**2+(2*x**6-24*x**5+92*x**4-
124*x**3+74*x**2-20*x)*exp(3)*exp(exp(x))+(x**6-12*x**5+46*x**4-60*x**3+25*x**2)*exp(3)**2),x)

[Out]

-4*x*exp(3)/(x**6*exp(3) - 12*x**5*exp(3) + 46*x**4*exp(3) - 62*x**3*exp(3) + 37*x**2*exp(3) - 10*x*exp(3) + (
x**6 - 12*x**5 + 46*x**4 - 64*x**3 + 49*x**2 - 20*x + 4)*exp(exp(x))) + 2*x/(x**3 - 6*x**2 + 5*x - 2)

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