3.82.56 \(\int \frac {-64 e^6+224 e^4 x-243 e^2 x^2+81 x^3+e^{2 e^x} (-4 e^6+12 e^4 x-12 e^2 x^2+4 x^3+e^x (-8 e^6 x+24 e^4 x^2-24 e^2 x^3+8 x^4))+e^{e^x} (-32 e^6+104 e^4 x-108 e^2 x^2+36 x^3+e^x (-32 e^6 x+100 e^4 x^2-104 e^2 x^3+36 x^4))}{4 e^6-12 e^4 x+12 e^2 x^2-4 x^3} \, dx\)

Optimal. Leaf size=30 \[ \frac {70}{9}-x \left (4+e^{e^x}+\frac {x}{2 \left (-e^2+x\right )}\right )^2 \]

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Rubi [F]  time = 6.30, 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 {-64 e^6+224 e^4 x-243 e^2 x^2+81 x^3+e^{2 e^x} \left (-4 e^6+12 e^4 x-12 e^2 x^2+4 x^3+e^x \left (-8 e^6 x+24 e^4 x^2-24 e^2 x^3+8 x^4\right )\right )+e^{e^x} \left (-32 e^6+104 e^4 x-108 e^2 x^2+36 x^3+e^x \left (-32 e^6 x+100 e^4 x^2-104 e^2 x^3+36 x^4\right )\right )}{4 e^6-12 e^4 x+12 e^2 x^2-4 x^3} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(-64*E^6 + 224*E^4*x - 243*E^2*x^2 + 81*x^3 + E^(2*E^x)*(-4*E^6 + 12*E^4*x - 12*E^2*x^2 + 4*x^3 + E^x*(-8*
E^6*x + 24*E^4*x^2 - 24*E^2*x^3 + 8*x^4)) + E^E^x*(-32*E^6 + 104*E^4*x - 108*E^2*x^2 + 36*x^3 + E^x*(-32*E^6*x
+ 100*E^4*x^2 - 104*E^2*x^3 + 36*x^4)))/(4*E^6 - 12*E^4*x + 12*E^2*x^2 - 4*x^3),x]

[Out]

-E^(2 + E^x) - (5*E^6)/(4*(E^2 - x)^2) + (E^2*(8*E^2 - 9*x)^2)/(E^2 - x)^2 + (91*E^4)/(4*(E^2 - x)) - (81*x)/4
- 9*ExpIntegralEi[E^x] - ExpIntegralEi[2*E^x] - 4*E^4*Defer[Int][E^E^x/(E^2 - x)^2, x] + (19*E^2*Defer[Int][E
^(2 + E^x)/(E^2 - x)^2, x])/2 - (9*Defer[Int][E^(4 + E^x)/(E^2 - x)^2, x])/2 + 2*Defer[Int][E^(2*(1 + E^x))/(E
^2 - x), x] + (19*Defer[Int][E^(2 + E^x)/(E^2 - x), x])/2 + Defer[Int][E^(4 + E^x + x)/(E^2 - x), x] - 9*Defer
[Int][E^(E^x + x)*x, x] - 2*Defer[Int][E^(2*E^x + x)*x, x] + (19*E^2*Defer[Int][E^E^x/(-E^2 + x), x])/2 + 2*De
fer[Int][E^(2*(1 + E^x))/(-E^2 + x), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {\left (8 e^2+2 e^{2+e^x}-9 x-2 e^{e^x} x\right ) \left (-8 e^4-2 e^{4+e^x}+19 e^2 x+4 e^{2+e^x} x-4 e^{4+e^x+x} x-9 x^2-2 e^{e^x} x^2+8 e^{2+e^x+x} x^2-4 e^{e^x+x} x^3\right )}{4 \left (e^2-x\right )^3} \, dx\\ &=\frac {1}{4} \int \frac {\left (8 e^2+2 e^{2+e^x}-9 x-2 e^{e^x} x\right ) \left (-8 e^4-2 e^{4+e^x}+19 e^2 x+4 e^{2+e^x} x-4 e^{4+e^x+x} x-9 x^2-2 e^{e^x} x^2+8 e^{2+e^x+x} x^2-4 e^{e^x+x} x^3\right )}{\left (e^2-x\right )^3} \, dx\\ &=\frac {1}{4} \int \left (-\frac {8 e^4 \left (8 e^2+2 e^{2+e^x}-9 x-2 e^{e^x} x\right )}{\left (e^2-x\right )^3}-\frac {2 e^{4+e^x} \left (8 e^2+2 e^{2+e^x}-9 x-2 e^{e^x} x\right )}{\left (e^2-x\right )^3}+\frac {19 e^2 x \left (8 e^2+2 e^{2+e^x}-9 x-2 e^{e^x} x\right )}{\left (e^2-x\right )^3}+\frac {4 e^{2+e^x} x \left (8 e^2+2 e^{2+e^x}-9 x-2 e^{e^x} x\right )}{\left (e^2-x\right )^3}-\frac {4 e^{e^x+x} x \left (8 e^2+2 e^{2+e^x}-9 x-2 e^{e^x} x\right )}{e^2-x}-\frac {9 x^2 \left (8 e^2+2 e^{2+e^x}-9 x-2 e^{e^x} x\right )}{\left (e^2-x\right )^3}-\frac {2 e^{e^x} x^2 \left (8 e^2+2 e^{2+e^x}-9 x-2 e^{e^x} x\right )}{\left (e^2-x\right )^3}\right ) \, dx\\ &=-\left (\frac {1}{2} \int \frac {e^{4+e^x} \left (8 e^2+2 e^{2+e^x}-9 x-2 e^{e^x} x\right )}{\left (e^2-x\right )^3} \, dx\right )-\frac {1}{2} \int \frac {e^{e^x} x^2 \left (8 e^2+2 e^{2+e^x}-9 x-2 e^{e^x} x\right )}{\left (e^2-x\right )^3} \, dx-\frac {9}{4} \int \frac {x^2 \left (8 e^2+2 e^{2+e^x}-9 x-2 e^{e^x} x\right )}{\left (e^2-x\right )^3} \, dx+\frac {1}{4} \left (19 e^2\right ) \int \frac {x \left (8 e^2+2 e^{2+e^x}-9 x-2 e^{e^x} x\right )}{\left (e^2-x\right )^3} \, dx-\left (2 e^4\right ) \int \frac {8 e^2+2 e^{2+e^x}-9 x-2 e^{e^x} x}{\left (e^2-x\right )^3} \, dx+\int \frac {e^{2+e^x} x \left (8 e^2+2 e^{2+e^x}-9 x-2 e^{e^x} x\right )}{\left (e^2-x\right )^3} \, dx-\int \frac {e^{e^x+x} x \left (8 e^2+2 e^{2+e^x}-9 x-2 e^{e^x} x\right )}{e^2-x} \, dx\\ &=-\left (\frac {1}{2} \int \left (\frac {e^{4+e^x} \left (8 e^2-9 x\right )}{\left (e^2-x\right )^3}+\frac {2 e^{4+2 e^x}}{\left (e^2-x\right )^2}\right ) \, dx\right )-\frac {1}{2} \int \left (\frac {e^{e^x} \left (8 e^2-9 x\right ) x^2}{\left (e^2-x\right )^3}+\frac {2 e^{2 e^x} x^2}{\left (e^2-x\right )^2}\right ) \, dx-\frac {9}{4} \int \left (\frac {\left (8 e^2-9 x\right ) x^2}{\left (e^2-x\right )^3}+\frac {2 e^{e^x} x^2}{\left (e^2-x\right )^2}\right ) \, dx+\frac {1}{4} \left (19 e^2\right ) \int \left (\frac {\left (8 e^2-9 x\right ) x}{\left (e^2-x\right )^3}+\frac {2 e^{e^x} x}{\left (e^2-x\right )^2}\right ) \, dx-\left (2 e^4\right ) \int \left (\frac {8 e^2-9 x}{\left (e^2-x\right )^3}+\frac {2 e^{e^x}}{\left (e^2-x\right )^2}\right ) \, dx+\int \left (\frac {e^{2+e^x} \left (8 e^2-9 x\right ) x}{\left (e^2-x\right )^3}+\frac {2 e^{2+2 e^x} x}{\left (e^2-x\right )^2}\right ) \, dx-\int \left (2 e^{2 e^x+x} x+\frac {e^{e^x+x} \left (8 e^2-9 x\right ) x}{e^2-x}\right ) \, dx\\ &=-\left (\frac {1}{2} \int \frac {e^{4+e^x} \left (8 e^2-9 x\right )}{\left (e^2-x\right )^3} \, dx\right )-\frac {1}{2} \int \frac {e^{e^x} \left (8 e^2-9 x\right ) x^2}{\left (e^2-x\right )^3} \, dx-2 \int e^{2 e^x+x} x \, dx+2 \int \frac {e^{2+2 e^x} x}{\left (e^2-x\right )^2} \, dx-\frac {9}{4} \int \frac {\left (8 e^2-9 x\right ) x^2}{\left (e^2-x\right )^3} \, dx-\frac {9}{2} \int \frac {e^{e^x} x^2}{\left (e^2-x\right )^2} \, dx+\frac {1}{4} \left (19 e^2\right ) \int \frac {\left (8 e^2-9 x\right ) x}{\left (e^2-x\right )^3} \, dx+\frac {1}{2} \left (19 e^2\right ) \int \frac {e^{e^x} x}{\left (e^2-x\right )^2} \, dx-\left (2 e^4\right ) \int \frac {8 e^2-9 x}{\left (e^2-x\right )^3} \, dx-\left (4 e^4\right ) \int \frac {e^{e^x}}{\left (e^2-x\right )^2} \, dx-\int \frac {e^{4+2 e^x}}{\left (e^2-x\right )^2} \, dx+\int \frac {e^{2+e^x} \left (8 e^2-9 x\right ) x}{\left (e^2-x\right )^3} \, dx-\int \frac {e^{e^x+x} \left (8 e^2-9 x\right ) x}{e^2-x} \, dx-\int \frac {e^{2 e^x} x^2}{\left (e^2-x\right )^2} \, dx\\ &=\frac {e^2 \left (8 e^2-9 x\right )^2}{\left (e^2-x\right )^2}-\frac {1}{2} \int \left (-\frac {e^{6+e^x}}{\left (e^2-x\right )^3}+\frac {9 e^{4+e^x}}{\left (e^2-x\right )^2}\right ) \, dx-\frac {1}{2} \int \left (9 e^{e^x}-\frac {e^{6+e^x}}{\left (e^2-x\right )^3}+\frac {11 e^{4+e^x}}{\left (e^2-x\right )^2}-\frac {19 e^{2+e^x}}{e^2-x}\right ) \, dx-2 \int e^{2 e^x+x} x \, dx+2 \int \frac {e^{2 \left (1+e^x\right )} x}{\left (e^2-x\right )^2} \, dx-\frac {9}{4} \int \left (9-\frac {e^6}{\left (e^2-x\right )^3}+\frac {11 e^4}{\left (e^2-x\right )^2}-\frac {19 e^2}{e^2-x}\right ) \, dx-\frac {9}{2} \int \left (e^{e^x}+\frac {e^{4+e^x}}{\left (e^2-x\right )^2}-\frac {2 e^{2+e^x}}{e^2-x}\right ) \, dx+\frac {1}{4} \left (19 e^2\right ) \int \left (-\frac {e^4}{\left (e^2-x\right )^3}+\frac {10 e^2}{\left (e^2-x\right )^2}-\frac {9}{e^2-x}\right ) \, dx+\frac {1}{2} \left (19 e^2\right ) \int \left (\frac {e^{2+e^x}}{\left (e^2-x\right )^2}+\frac {e^{e^x}}{-e^2+x}\right ) \, dx-\left (4 e^4\right ) \int \frac {e^{e^x}}{\left (e^2-x\right )^2} \, dx+\int \left (-\frac {e^{6+e^x}}{\left (e^2-x\right )^3}+\frac {10 e^{4+e^x}}{\left (e^2-x\right )^2}-\frac {9 e^{2+e^x}}{e^2-x}\right ) \, dx-\int \left (e^{2 e^x}+\frac {e^{4+2 e^x}}{\left (e^2-x\right )^2}-\frac {2 e^{2+2 e^x}}{e^2-x}\right ) \, dx-\int \frac {e^{2 \left (2+e^x\right )}}{\left (e^2-x\right )^2} \, dx-\int \left (e^{2+e^x+x}-\frac {e^{4+e^x+x}}{e^2-x}+9 e^{e^x+x} x\right ) \, dx\\ &=-\frac {5 e^6}{4 \left (e^2-x\right )^2}+\frac {e^2 \left (8 e^2-9 x\right )^2}{\left (e^2-x\right )^2}+\frac {91 e^4}{4 \left (e^2-x\right )}-\frac {81 x}{4}+2 \left (\frac {1}{2} \int \frac {e^{6+e^x}}{\left (e^2-x\right )^3} \, dx\right )+2 \int \frac {e^{2+2 e^x}}{e^2-x} \, dx-2 \int e^{2 e^x+x} x \, dx+2 \int \left (\frac {e^{2+2 \left (1+e^x\right )}}{\left (e^2-x\right )^2}+\frac {e^{2 \left (1+e^x\right )}}{-e^2+x}\right ) \, dx-2 \left (\frac {9}{2} \int e^{e^x} \, dx\right )-2 \left (\frac {9}{2} \int \frac {e^{4+e^x}}{\left (e^2-x\right )^2} \, dx\right )-\frac {11}{2} \int \frac {e^{4+e^x}}{\left (e^2-x\right )^2} \, dx-9 \int e^{e^x+x} x \, dx+\frac {19}{2} \int \frac {e^{2+e^x}}{e^2-x} \, dx+10 \int \frac {e^{4+e^x}}{\left (e^2-x\right )^2} \, dx+\frac {1}{2} \left (19 e^2\right ) \int \frac {e^{2+e^x}}{\left (e^2-x\right )^2} \, dx+\frac {1}{2} \left (19 e^2\right ) \int \frac {e^{e^x}}{-e^2+x} \, dx-\left (4 e^4\right ) \int \frac {e^{e^x}}{\left (e^2-x\right )^2} \, dx-\int e^{2 e^x} \, dx-\int e^{2+e^x+x} \, dx-\int \frac {e^{6+e^x}}{\left (e^2-x\right )^3} \, dx-\int \frac {e^{2 \left (2+e^x\right )}}{\left (e^2-x\right )^2} \, dx-\int \frac {e^{4+2 e^x}}{\left (e^2-x\right )^2} \, dx+\int \frac {e^{4+e^x+x}}{e^2-x} \, dx\\ &=-\frac {5 e^6}{4 \left (e^2-x\right )^2}+\frac {e^2 \left (8 e^2-9 x\right )^2}{\left (e^2-x\right )^2}+\frac {91 e^4}{4 \left (e^2-x\right )}-\frac {81 x}{4}+2 \left (\frac {1}{2} \int \frac {e^{6+e^x}}{\left (e^2-x\right )^3} \, dx\right )+2 \int \frac {e^{2+2 \left (1+e^x\right )}}{\left (e^2-x\right )^2} \, dx+2 \int \frac {e^{2 \left (1+e^x\right )}}{e^2-x} \, dx-2 \int e^{2 e^x+x} x \, dx+2 \int \frac {e^{2 \left (1+e^x\right )}}{-e^2+x} \, dx-2 \left (\frac {9}{2} \int \frac {e^{4+e^x}}{\left (e^2-x\right )^2} \, dx\right )-2 \left (\frac {9}{2} \operatorname {Subst}\left (\int \frac {e^x}{x} \, dx,x,e^x\right )\right )-\frac {11}{2} \int \frac {e^{4+e^x}}{\left (e^2-x\right )^2} \, dx-9 \int e^{e^x+x} x \, dx+\frac {19}{2} \int \frac {e^{2+e^x}}{e^2-x} \, dx+10 \int \frac {e^{4+e^x}}{\left (e^2-x\right )^2} \, dx+\frac {1}{2} \left (19 e^2\right ) \int \frac {e^{2+e^x}}{\left (e^2-x\right )^2} \, dx+\frac {1}{2} \left (19 e^2\right ) \int \frac {e^{e^x}}{-e^2+x} \, dx-\left (4 e^4\right ) \int \frac {e^{e^x}}{\left (e^2-x\right )^2} \, dx-\int \frac {e^{6+e^x}}{\left (e^2-x\right )^3} \, dx-2 \int \frac {e^{2 \left (2+e^x\right )}}{\left (e^2-x\right )^2} \, dx+\int \frac {e^{4+e^x+x}}{e^2-x} \, dx-\operatorname {Subst}\left (\int e^{2+x} \, dx,x,e^x\right )-\operatorname {Subst}\left (\int \frac {e^{2 x}}{x} \, dx,x,e^x\right )\\ &=-e^{2+e^x}-\frac {5 e^6}{4 \left (e^2-x\right )^2}+\frac {e^2 \left (8 e^2-9 x\right )^2}{\left (e^2-x\right )^2}+\frac {91 e^4}{4 \left (e^2-x\right )}-\frac {81 x}{4}-9 \text {Ei}\left (e^x\right )-\text {Ei}\left (2 e^x\right )+2 \left (\frac {1}{2} \int \frac {e^{6+e^x}}{\left (e^2-x\right )^3} \, dx\right )+2 \int \frac {e^{2 \left (2+e^x\right )}}{\left (e^2-x\right )^2} \, dx+2 \int \frac {e^{2 \left (1+e^x\right )}}{e^2-x} \, dx-2 \int e^{2 e^x+x} x \, dx+2 \int \frac {e^{2 \left (1+e^x\right )}}{-e^2+x} \, dx-2 \left (\frac {9}{2} \int \frac {e^{4+e^x}}{\left (e^2-x\right )^2} \, dx\right )-\frac {11}{2} \int \frac {e^{4+e^x}}{\left (e^2-x\right )^2} \, dx-9 \int e^{e^x+x} x \, dx+\frac {19}{2} \int \frac {e^{2+e^x}}{e^2-x} \, dx+10 \int \frac {e^{4+e^x}}{\left (e^2-x\right )^2} \, dx+\frac {1}{2} \left (19 e^2\right ) \int \frac {e^{2+e^x}}{\left (e^2-x\right )^2} \, dx+\frac {1}{2} \left (19 e^2\right ) \int \frac {e^{e^x}}{-e^2+x} \, dx-\left (4 e^4\right ) \int \frac {e^{e^x}}{\left (e^2-x\right )^2} \, dx-\int \frac {e^{6+e^x}}{\left (e^2-x\right )^3} \, dx-2 \int \frac {e^{2 \left (2+e^x\right )}}{\left (e^2-x\right )^2} \, dx+\int \frac {e^{4+e^x+x}}{e^2-x} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [B]  time = 0.12, size = 72, normalized size = 2.40 \begin {gather*} \frac {1}{4} \left (-\frac {e^6}{\left (e^2-x\right )^2}-81 x-4 e^{2 e^x} x-\frac {4 e^{e^x} \left (8 e^2-9 x\right ) x}{e^2-x}-\frac {19 e^4}{-e^2+x}\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-64*E^6 + 224*E^4*x - 243*E^2*x^2 + 81*x^3 + E^(2*E^x)*(-4*E^6 + 12*E^4*x - 12*E^2*x^2 + 4*x^3 + E^
x*(-8*E^6*x + 24*E^4*x^2 - 24*E^2*x^3 + 8*x^4)) + E^E^x*(-32*E^6 + 104*E^4*x - 108*E^2*x^2 + 36*x^3 + E^x*(-32
*E^6*x + 100*E^4*x^2 - 104*E^2*x^3 + 36*x^4)))/(4*E^6 - 12*E^4*x + 12*E^2*x^2 - 4*x^3),x]

[Out]

(-(E^6/(E^2 - x)^2) - 81*x - 4*E^(2*E^x)*x - (4*E^E^x*(8*E^2 - 9*x)*x)/(E^2 - x) - (19*E^4)/(-E^2 + x))/4

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fricas [B]  time = 0.84, size = 82, normalized size = 2.73 \begin {gather*} -\frac {81 \, x^{3} - 162 \, x^{2} e^{2} + 100 \, x e^{4} + 4 \, {\left (x^{3} - 2 \, x^{2} e^{2} + x e^{4}\right )} e^{\left (2 \, e^{x}\right )} + 4 \, {\left (9 \, x^{3} - 17 \, x^{2} e^{2} + 8 \, x e^{4}\right )} e^{\left (e^{x}\right )} - 18 \, e^{6}}{4 \, {\left (x^{2} - 2 \, x e^{2} + e^{4}\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-8*x*exp(2)^3+24*x^2*exp(2)^2-24*x^3*exp(2)+8*x^4)*exp(x)-4*exp(2)^3+12*x*exp(2)^2-12*x^2*exp(2)+
4*x^3)*exp(exp(x))^2+((-32*x*exp(2)^3+100*x^2*exp(2)^2-104*x^3*exp(2)+36*x^4)*exp(x)-32*exp(2)^3+104*x*exp(2)^
2-108*x^2*exp(2)+36*x^3)*exp(exp(x))-64*exp(2)^3+224*x*exp(2)^2-243*x^2*exp(2)+81*x^3)/(4*exp(2)^3-12*x*exp(2)
^2+12*x^2*exp(2)-4*x^3),x, algorithm="fricas")

[Out]

-1/4*(81*x^3 - 162*x^2*e^2 + 100*x*e^4 + 4*(x^3 - 2*x^2*e^2 + x*e^4)*e^(2*e^x) + 4*(9*x^3 - 17*x^2*e^2 + 8*x*e
^4)*e^(e^x) - 18*e^6)/(x^2 - 2*x*e^2 + e^4)

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giac [B]  time = 0.18, size = 95, normalized size = 3.17 \begin {gather*} -\frac {4 \, x^{3} e^{\left (2 \, e^{x}\right )} + 36 \, x^{3} e^{\left (e^{x}\right )} + 81 \, x^{3} - 162 \, x^{2} e^{2} - 8 \, x^{2} e^{\left (2 \, e^{x} + 2\right )} - 68 \, x^{2} e^{\left (e^{x} + 2\right )} + 100 \, x e^{4} + 4 \, x e^{\left (2 \, e^{x} + 4\right )} + 32 \, x e^{\left (e^{x} + 4\right )} - 18 \, e^{6}}{4 \, {\left (x^{2} - 2 \, x e^{2} + e^{4}\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-8*x*exp(2)^3+24*x^2*exp(2)^2-24*x^3*exp(2)+8*x^4)*exp(x)-4*exp(2)^3+12*x*exp(2)^2-12*x^2*exp(2)+
4*x^3)*exp(exp(x))^2+((-32*x*exp(2)^3+100*x^2*exp(2)^2-104*x^3*exp(2)+36*x^4)*exp(x)-32*exp(2)^3+104*x*exp(2)^
2-108*x^2*exp(2)+36*x^3)*exp(exp(x))-64*exp(2)^3+224*x*exp(2)^2-243*x^2*exp(2)+81*x^3)/(4*exp(2)^3-12*x*exp(2)
^2+12*x^2*exp(2)-4*x^3),x, algorithm="giac")

[Out]

-1/4*(4*x^3*e^(2*e^x) + 36*x^3*e^(e^x) + 81*x^3 - 162*x^2*e^2 - 8*x^2*e^(2*e^x + 2) - 68*x^2*e^(e^x + 2) + 100
*x*e^4 + 4*x*e^(2*e^x + 4) + 32*x*e^(e^x + 4) - 18*e^6)/(x^2 - 2*x*e^2 + e^4)

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maple [B]  time = 0.30, size = 59, normalized size = 1.97

method	result	size
risch	\(-\frac {81 x}{4}+\frac {\frac {9 \,{\mathrm e}^{6}}{2}-\frac {19 x \,{\mathrm e}^{4}}{4}}{{\mathrm e}^{4}-2 \,{\mathrm e}^{2} x +x^{2}}-{\mathrm e}^{2 \,{\mathrm e}^{x}} x -\frac {\left (8 \,{\mathrm e}^{2}-9 x \right ) x \,{\mathrm e}^{{\mathrm e}^{x}}}{{\mathrm e}^{2}-x}\)	\(59\)
norman	\(\frac {56 x \,{\mathrm e}^{4}-\frac {81 x^{3}}{4}-9 x^{3} {\mathrm e}^{{\mathrm e}^{x}}-x^{3} {\mathrm e}^{2 \,{\mathrm e}^{x}}+17 \,{\mathrm e}^{2} {\mathrm e}^{{\mathrm e}^{x}} x^{2}+2 \,{\mathrm e}^{2} {\mathrm e}^{2 \,{\mathrm e}^{x}} x^{2}-8 \,{\mathrm e}^{4} {\mathrm e}^{{\mathrm e}^{x}} x -{\mathrm e}^{4} {\mathrm e}^{2 \,{\mathrm e}^{x}} x -36 \,{\mathrm e}^{6}}{\left ({\mathrm e}^{2}-x \right )^{2}}\)	\(91\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((-8*x*exp(2)^3+24*x^2*exp(2)^2-24*x^3*exp(2)+8*x^4)*exp(x)-4*exp(2)^3+12*x*exp(2)^2-12*x^2*exp(2)+4*x^3)
*exp(exp(x))^2+((-32*x*exp(2)^3+100*x^2*exp(2)^2-104*x^3*exp(2)+36*x^4)*exp(x)-32*exp(2)^3+104*x*exp(2)^2-108*
x^2*exp(2)+36*x^3)*exp(exp(x))-64*exp(2)^3+224*x*exp(2)^2-243*x^2*exp(2)+81*x^3)/(4*exp(2)^3-12*x*exp(2)^2+12*
x^2*exp(2)-4*x^3),x,method=_RETURNVERBOSE)

[Out]

-81/4*x+(9/2*exp(6)-19/4*x*exp(4))/(exp(4)-2*exp(2)*x+x^2)-exp(2*exp(x))*x-(8*exp(2)-9*x)*x/(exp(2)-x)*exp(exp
(x))

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maxima [B]  time = 0.44, size = 161, normalized size = 5.37 \begin {gather*} -\frac {243}{8} \, {\left (\frac {4 \, x e^{2} - 3 \, e^{4}}{x^{2} - 2 \, x e^{2} + e^{4}} - 2 \, \log \left (x - e^{2}\right )\right )} e^{2} - \frac {243}{4} \, e^{2} \log \left (x - e^{2}\right ) - \frac {81}{4} \, x + \frac {28 \, {\left (2 \, x - e^{2}\right )} e^{4}}{x^{2} - 2 \, x e^{2} + e^{4}} + \frac {81 \, {\left (6 \, x e^{4} - 5 \, e^{6}\right )}}{8 \, {\left (x^{2} - 2 \, x e^{2} + e^{4}\right )}} - \frac {{\left (x^{2} - x e^{2}\right )} e^{\left (2 \, e^{x}\right )} + {\left (9 \, x^{2} - 8 \, x e^{2}\right )} e^{\left (e^{x}\right )}}{x - e^{2}} - \frac {8 \, e^{6}}{x^{2} - 2 \, x e^{2} + e^{4}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-8*x*exp(2)^3+24*x^2*exp(2)^2-24*x^3*exp(2)+8*x^4)*exp(x)-4*exp(2)^3+12*x*exp(2)^2-12*x^2*exp(2)+
4*x^3)*exp(exp(x))^2+((-32*x*exp(2)^3+100*x^2*exp(2)^2-104*x^3*exp(2)+36*x^4)*exp(x)-32*exp(2)^3+104*x*exp(2)^
2-108*x^2*exp(2)+36*x^3)*exp(exp(x))-64*exp(2)^3+224*x*exp(2)^2-243*x^2*exp(2)+81*x^3)/(4*exp(2)^3-12*x*exp(2)
^2+12*x^2*exp(2)-4*x^3),x, algorithm="maxima")

[Out]

-243/8*((4*x*e^2 - 3*e^4)/(x^2 - 2*x*e^2 + e^4) - 2*log(x - e^2))*e^2 - 243/4*e^2*log(x - e^2) - 81/4*x + 28*(
2*x - e^2)*e^4/(x^2 - 2*x*e^2 + e^4) + 81/8*(6*x*e^4 - 5*e^6)/(x^2 - 2*x*e^2 + e^4) - ((x^2 - x*e^2)*e^(2*e^x)
+ (9*x^2 - 8*x*e^2)*e^(e^x))/(x - e^2) - 8*e^6/(x^2 - 2*x*e^2 + e^4)

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mupad [B]  time = 5.59, size = 63, normalized size = 2.10 \begin {gather*} \frac {18\,{\mathrm {e}}^6-19\,x\,{\mathrm {e}}^4}{4\,x^2-8\,{\mathrm {e}}^2\,x+4\,{\mathrm {e}}^4}-x\,{\mathrm {e}}^{2\,{\mathrm {e}}^x}-\frac {81\,x}{4}+\frac {{\mathrm {e}}^{{\mathrm {e}}^x}\,\left (8\,x\,{\mathrm {e}}^2-9\,x^2\right )}{x-{\mathrm {e}}^2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(64*exp(6) + exp(exp(x))*(32*exp(6) - 104*x*exp(4) + exp(x)*(32*x*exp(6) + 104*x^3*exp(2) - 100*x^2*exp(4
) - 36*x^4) + 108*x^2*exp(2) - 36*x^3) - 224*x*exp(4) + exp(2*exp(x))*(4*exp(6) - 12*x*exp(4) + exp(x)*(8*x*ex
p(6) + 24*x^3*exp(2) - 24*x^2*exp(4) - 8*x^4) + 12*x^2*exp(2) - 4*x^3) + 243*x^2*exp(2) - 81*x^3)/(4*exp(6) -
12*x*exp(4) + 12*x^2*exp(2) - 4*x^3),x)

[Out]

(18*exp(6) - 19*x*exp(4))/(4*exp(4) - 8*x*exp(2) + 4*x^2) - x*exp(2*exp(x)) - (81*x)/4 + (exp(exp(x))*(8*x*exp
(2) - 9*x^2))/(x - exp(2))

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sympy [B]  time = 0.40, size = 70, normalized size = 2.33 \begin {gather*} - \frac {81 x}{4} - \frac {19 x e^{4} - 18 e^{6}}{4 x^{2} - 8 x e^{2} + 4 e^{4}} + \frac {\left (- 9 x^{2} + 8 x e^{2}\right ) e^{e^{x}} + \left (- x^{2} + x e^{2}\right ) e^{2 e^{x}}}{x - e^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-8*x*exp(2)**3+24*x**2*exp(2)**2-24*x**3*exp(2)+8*x**4)*exp(x)-4*exp(2)**3+12*x*exp(2)**2-12*x**2
*exp(2)+4*x**3)*exp(exp(x))**2+((-32*x*exp(2)**3+100*x**2*exp(2)**2-104*x**3*exp(2)+36*x**4)*exp(x)-32*exp(2)*
*3+104*x*exp(2)**2-108*x**2*exp(2)+36*x**3)*exp(exp(x))-64*exp(2)**3+224*x*exp(2)**2-243*x**2*exp(2)+81*x**3)/
(4*exp(2)**3-12*x*exp(2)**2+12*x**2*exp(2)-4*x**3),x)

[Out]

-81*x/4 - (19*x*exp(4) - 18*exp(6))/(4*x**2 - 8*x*exp(2) + 4*exp(4)) + ((-9*x**2 + 8*x*exp(2))*exp(exp(x)) + (
-x**2 + x*exp(2))*exp(2*exp(x)))/(x - exp(2))

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