3.54.7 \(\int \frac {e^{e^{\frac {3}{81+108 e+54 e^2+12 e^3+e^4+(-12-4 e) e^{12+3 x^2}+e^{16+4 x^2}+e^{8+2 x^2} (54+36 e+6 e^2)+e^{4+x^2} (-108-108 e-36 e^2-4 e^3)}}} (-243-405 e-270 e^2-90 e^3-15 e^4-e^5+(-15-5 e) e^{16+4 x^2}+e^{20+5 x^2}+e^{12+3 x^2} (90+60 e+10 e^2)+e^{8+2 x^2} (-270-270 e-90 e^2-10 e^3)+e^{4+x^2} (405+540 e+270 e^2+60 e^3+5 e^4)-24 e^{4+\frac {3}{81+108 e+54 e^2+12 e^3+e^4+(-12-4 e) e^{12+3 x^2}+e^{16+4 x^2}+e^{8+2 x^2} (54+36 e+6 e^2)+e^{4+x^2} (-108-108 e-36 e^2-4 e^3)}+x^2} x^2)}{-243-405 e-270 e^2-90 e^3-15 e^4-e^5+(-15-5 e) e^{16+4 x^2}+e^{20+5 x^2}+e^{12+3 x^2} (90+60 e+10 e^2)+e^{8+2 x^2} (-270-270 e-90 e^2-10 e^3)+e^{4+x^2} (405+540 e+270 e^2+60 e^3+5 e^4)} \, dx\)

Optimal. Leaf size=22 \[ e^{e^{\frac {3}{\left (-3-e+e^{4+x^2}\right )^4}}} x \]

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Rubi [B]  time = 3.14, antiderivative size = 277, normalized size of antiderivative = 12.59, number of steps used = 1, number of rules used = 1, integrand size = 441, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.002, Rules used = {2288} \begin {gather*} \frac {\left (e^{4 x^2+16}-4 (3+e) e^{3 x^2+12}+6 (3+e)^2 e^{2 x^2+8}-4 (3+e)^3 e^{x^2+4}+(3+e)^4\right )^2 x^2 \exp \left (\exp \left (\frac {3}{e^{4 x^2+16}-4 (3+e) e^{3 x^2+12}+6 (3+e)^2 e^{2 x^2+8}-4 (3+e)^3 e^{x^2+4}+(3+e)^4}\right )+x^2+4\right )}{\left (e^{5 x^2+20}-5 (3+e) e^{4 x^2+16}+10 (3+e)^2 e^{3 x^2+12}-10 (3+e)^3 e^{2 x^2+8}+5 (3+e)^4 e^{x^2+4}-(3+e)^5\right ) \left (e^{4 x^2+16} x-(3+e)^3 e^{x^2+4} x+3 (3+e)^2 e^{2 x^2+8} x-3 (3+e) e^{3 x^2+12} x\right )} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(E^E^(3/(81 + 108*E + 54*E^2 + 12*E^3 + E^4 + (-12 - 4*E)*E^(12 + 3*x^2) + E^(16 + 4*x^2) + E^(8 + 2*x^2)*
(54 + 36*E + 6*E^2) + E^(4 + x^2)*(-108 - 108*E - 36*E^2 - 4*E^3)))*(-243 - 405*E - 270*E^2 - 90*E^3 - 15*E^4
- E^5 + (-15 - 5*E)*E^(16 + 4*x^2) + E^(20 + 5*x^2) + E^(12 + 3*x^2)*(90 + 60*E + 10*E^2) + E^(8 + 2*x^2)*(-27
0 - 270*E - 90*E^2 - 10*E^3) + E^(4 + x^2)*(405 + 540*E + 270*E^2 + 60*E^3 + 5*E^4) - 24*E^(4 + 3/(81 + 108*E
+ 54*E^2 + 12*E^3 + E^4 + (-12 - 4*E)*E^(12 + 3*x^2) + E^(16 + 4*x^2) + E^(8 + 2*x^2)*(54 + 36*E + 6*E^2) + E^
(4 + x^2)*(-108 - 108*E - 36*E^2 - 4*E^3)) + x^2)*x^2))/(-243 - 405*E - 270*E^2 - 90*E^3 - 15*E^4 - E^5 + (-15
- 5*E)*E^(16 + 4*x^2) + E^(20 + 5*x^2) + E^(12 + 3*x^2)*(90 + 60*E + 10*E^2) + E^(8 + 2*x^2)*(-270 - 270*E -
90*E^2 - 10*E^3) + E^(4 + x^2)*(405 + 540*E + 270*E^2 + 60*E^3 + 5*E^4)),x]

[Out]

(E^(4 + E^(3/(E^(16 + 4*x^2) - 4*E^(12 + 3*x^2)*(3 + E) + 6*E^(8 + 2*x^2)*(3 + E)^2 - 4*E^(4 + x^2)*(3 + E)^3
+ (3 + E)^4)) + x^2)*(E^(16 + 4*x^2) - 4*E^(12 + 3*x^2)*(3 + E) + 6*E^(8 + 2*x^2)*(3 + E)^2 - 4*E^(4 + x^2)*(3
+ E)^3 + (3 + E)^4)^2*x^2)/((E^(20 + 5*x^2) - 5*E^(16 + 4*x^2)*(3 + E) + 10*E^(12 + 3*x^2)*(3 + E)^2 - 10*E^(
8 + 2*x^2)*(3 + E)^3 + 5*E^(4 + x^2)*(3 + E)^4 - (3 + E)^5)*(E^(16 + 4*x^2)*x - 3*E^(12 + 3*x^2)*(3 + E)*x + 3
*E^(8 + 2*x^2)*(3 + E)^2*x - E^(4 + x^2)*(3 + E)^3*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 {\exp \left (4+\exp \left (\frac {3}{e^{16+4 x^2}-4 e^{12+3 x^2} (3+e)+6 e^{8+2 x^2} (3+e)^2-4 e^{4+x^2} (3+e)^3+(3+e)^4}\right )+x^2\right ) \left (e^{16+4 x^2}-4 e^{12+3 x^2} (3+e)+6 e^{8+2 x^2} (3+e)^2-4 e^{4+x^2} (3+e)^3+(3+e)^4\right )^2 x^2}{\left (e^{20+5 x^2}-5 e^{16+4 x^2} (3+e)+10 e^{12+3 x^2} (3+e)^2-10 e^{8+2 x^2} (3+e)^3+5 e^{4+x^2} (3+e)^4-(3+e)^5\right ) \left (e^{16+4 x^2} x-3 e^{12+3 x^2} (3+e) x+3 e^{8+2 x^2} (3+e)^2 x-e^{4+x^2} (3+e)^3 x\right )}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 1.11, size = 22, normalized size = 1.00 \begin {gather*} e^{e^{\frac {3}{\left (-3-e+e^{4+x^2}\right )^4}}} x \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^E^(3/(81 + 108*E + 54*E^2 + 12*E^3 + E^4 + (-12 - 4*E)*E^(12 + 3*x^2) + E^(16 + 4*x^2) + E^(8 + 2
*x^2)*(54 + 36*E + 6*E^2) + E^(4 + x^2)*(-108 - 108*E - 36*E^2 - 4*E^3)))*(-243 - 405*E - 270*E^2 - 90*E^3 - 1
5*E^4 - E^5 + (-15 - 5*E)*E^(16 + 4*x^2) + E^(20 + 5*x^2) + E^(12 + 3*x^2)*(90 + 60*E + 10*E^2) + E^(8 + 2*x^2
)*(-270 - 270*E - 90*E^2 - 10*E^3) + E^(4 + x^2)*(405 + 540*E + 270*E^2 + 60*E^3 + 5*E^4) - 24*E^(4 + 3/(81 +
108*E + 54*E^2 + 12*E^3 + E^4 + (-12 - 4*E)*E^(12 + 3*x^2) + E^(16 + 4*x^2) + E^(8 + 2*x^2)*(54 + 36*E + 6*E^2
) + E^(4 + x^2)*(-108 - 108*E - 36*E^2 - 4*E^3)) + x^2)*x^2))/(-243 - 405*E - 270*E^2 - 90*E^3 - 15*E^4 - E^5
+ (-15 - 5*E)*E^(16 + 4*x^2) + E^(20 + 5*x^2) + E^(12 + 3*x^2)*(90 + 60*E + 10*E^2) + E^(8 + 2*x^2)*(-270 - 27
0*E - 90*E^2 - 10*E^3) + E^(4 + x^2)*(405 + 540*E + 270*E^2 + 60*E^3 + 5*E^4)),x]

[Out]

E^E^(3/(-3 - E + E^(4 + x^2))^4)*x

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fricas [B]  time = 1.20, size = 251, normalized size = 11.41 \begin {gather*} x e^{\left (e^{\left (-x^{2} - \frac {81 \, x^{2} + {\left (x^{2} + 4\right )} e^{4} + 12 \, {\left (x^{2} + 4\right )} e^{3} + 54 \, {\left (x^{2} + 4\right )} e^{2} + 108 \, {\left (x^{2} + 4\right )} e + {\left (x^{2} + 4\right )} e^{\left (4 \, x^{2} + 16\right )} - 4 \, {\left (3 \, x^{2} + {\left (x^{2} + 4\right )} e + 12\right )} e^{\left (3 \, x^{2} + 12\right )} + 6 \, {\left (9 \, x^{2} + {\left (x^{2} + 4\right )} e^{2} + 6 \, {\left (x^{2} + 4\right )} e + 36\right )} e^{\left (2 \, x^{2} + 8\right )} - 4 \, {\left (27 \, x^{2} + {\left (x^{2} + 4\right )} e^{3} + 9 \, {\left (x^{2} + 4\right )} e^{2} + 27 \, {\left (x^{2} + 4\right )} e + 108\right )} e^{\left (x^{2} + 4\right )} + 327}{4 \, {\left (e + 3\right )} e^{\left (3 \, x^{2} + 12\right )} - 6 \, {\left (e^{2} + 6 \, e + 9\right )} e^{\left (2 \, x^{2} + 8\right )} + 4 \, {\left (e^{3} + 9 \, e^{2} + 27 \, e + 27\right )} e^{\left (x^{2} + 4\right )} - e^{4} - 12 \, e^{3} - 54 \, e^{2} - 108 \, e - e^{\left (4 \, x^{2} + 16\right )} - 81} - 4\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-24*x^2*exp(x^2+4)*exp(3/(exp(x^2+4)^4+(-4*exp(1)-12)*exp(x^2+4)^3+(6*exp(1)^2+36*exp(1)+54)*exp(x^
2+4)^2+(-4*exp(1)^3-36*exp(1)^2-108*exp(1)-108)*exp(x^2+4)+exp(1)^4+12*exp(1)^3+54*exp(1)^2+108*exp(1)+81))+ex
p(x^2+4)^5+(-5*exp(1)-15)*exp(x^2+4)^4+(10*exp(1)^2+60*exp(1)+90)*exp(x^2+4)^3+(-10*exp(1)^3-90*exp(1)^2-270*e
xp(1)-270)*exp(x^2+4)^2+(5*exp(1)^4+60*exp(1)^3+270*exp(1)^2+540*exp(1)+405)*exp(x^2+4)-exp(1)^5-15*exp(1)^4-9
0*exp(1)^3-270*exp(1)^2-405*exp(1)-243)*exp(exp(3/(exp(x^2+4)^4+(-4*exp(1)-12)*exp(x^2+4)^3+(6*exp(1)^2+36*exp
(1)+54)*exp(x^2+4)^2+(-4*exp(1)^3-36*exp(1)^2-108*exp(1)-108)*exp(x^2+4)+exp(1)^4+12*exp(1)^3+54*exp(1)^2+108*
exp(1)+81)))/(exp(x^2+4)^5+(-5*exp(1)-15)*exp(x^2+4)^4+(10*exp(1)^2+60*exp(1)+90)*exp(x^2+4)^3+(-10*exp(1)^3-9
0*exp(1)^2-270*exp(1)-270)*exp(x^2+4)^2+(5*exp(1)^4+60*exp(1)^3+270*exp(1)^2+540*exp(1)+405)*exp(x^2+4)-exp(1)
^5-15*exp(1)^4-90*exp(1)^3-270*exp(1)^2-405*exp(1)-243),x, algorithm="fricas")

[Out]

x*e^(e^(-x^2 - (81*x^2 + (x^2 + 4)*e^4 + 12*(x^2 + 4)*e^3 + 54*(x^2 + 4)*e^2 + 108*(x^2 + 4)*e + (x^2 + 4)*e^(
4*x^2 + 16) - 4*(3*x^2 + (x^2 + 4)*e + 12)*e^(3*x^2 + 12) + 6*(9*x^2 + (x^2 + 4)*e^2 + 6*(x^2 + 4)*e + 36)*e^(
2*x^2 + 8) - 4*(27*x^2 + (x^2 + 4)*e^3 + 9*(x^2 + 4)*e^2 + 27*(x^2 + 4)*e + 108)*e^(x^2 + 4) + 327)/(4*(e + 3)
*e^(3*x^2 + 12) - 6*(e^2 + 6*e + 9)*e^(2*x^2 + 8) + 4*(e^3 + 9*e^2 + 27*e + 27)*e^(x^2 + 4) - e^4 - 12*e^3 - 5
4*e^2 - 108*e - e^(4*x^2 + 16) - 81) - 4))

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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((-24*x^2*exp(x^2+4)*exp(3/(exp(x^2+4)^4+(-4*exp(1)-12)*exp(x^2+4)^3+(6*exp(1)^2+36*exp(1)+54)*exp(x^
2+4)^2+(-4*exp(1)^3-36*exp(1)^2-108*exp(1)-108)*exp(x^2+4)+exp(1)^4+12*exp(1)^3+54*exp(1)^2+108*exp(1)+81))+ex
p(x^2+4)^5+(-5*exp(1)-15)*exp(x^2+4)^4+(10*exp(1)^2+60*exp(1)+90)*exp(x^2+4)^3+(-10*exp(1)^3-90*exp(1)^2-270*e
xp(1)-270)*exp(x^2+4)^2+(5*exp(1)^4+60*exp(1)^3+270*exp(1)^2+540*exp(1)+405)*exp(x^2+4)-exp(1)^5-15*exp(1)^4-9
0*exp(1)^3-270*exp(1)^2-405*exp(1)-243)*exp(exp(3/(exp(x^2+4)^4+(-4*exp(1)-12)*exp(x^2+4)^3+(6*exp(1)^2+36*exp
(1)+54)*exp(x^2+4)^2+(-4*exp(1)^3-36*exp(1)^2-108*exp(1)-108)*exp(x^2+4)+exp(1)^4+12*exp(1)^3+54*exp(1)^2+108*
exp(1)+81)))/(exp(x^2+4)^5+(-5*exp(1)-15)*exp(x^2+4)^4+(10*exp(1)^2+60*exp(1)+90)*exp(x^2+4)^3+(-10*exp(1)^3-9
0*exp(1)^2-270*exp(1)-270)*exp(x^2+4)^2+(5*exp(1)^4+60*exp(1)^3+270*exp(1)^2+540*exp(1)+405)*exp(x^2+4)-exp(1)
^5-15*exp(1)^4-90*exp(1)^3-270*exp(1)^2-405*exp(1)-243),x, algorithm="giac")

[Out]

Timed out

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maple [B]  time = 0.32, size = 115, normalized size = 5.23

method	result	size
risch	\(x \,{\mathrm e}^{{\mathrm e}^{\frac {3}{-36 \,{\mathrm e}^{x^{2}+6}+6 \,{\mathrm e}^{2 x^{2}+10}-108 \,{\mathrm e}^{x^{2}+5}-4 \,{\mathrm e}^{3 x^{2}+13}+36 \,{\mathrm e}^{2 x^{2}+9}-4 \,{\mathrm e}^{x^{2}+7}+54 \,{\mathrm e}^{2}+{\mathrm e}^{4}+108 \,{\mathrm e}+12 \,{\mathrm e}^{3}-108 \,{\mathrm e}^{x^{2}+4}+{\mathrm e}^{4 x^{2}+16}-12 \,{\mathrm e}^{3 x^{2}+12}+54 \,{\mathrm e}^{2 x^{2}+8}+81}}}\)	\(115\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((-24*x^2*exp(x^2+4)*exp(3/(exp(x^2+4)^4+(-4*exp(1)-12)*exp(x^2+4)^3+(6*exp(1)^2+36*exp(1)+54)*exp(x^2+4)^2
+(-4*exp(1)^3-36*exp(1)^2-108*exp(1)-108)*exp(x^2+4)+exp(1)^4+12*exp(1)^3+54*exp(1)^2+108*exp(1)+81))+exp(x^2+
4)^5+(-5*exp(1)-15)*exp(x^2+4)^4+(10*exp(1)^2+60*exp(1)+90)*exp(x^2+4)^3+(-10*exp(1)^3-90*exp(1)^2-270*exp(1)-
270)*exp(x^2+4)^2+(5*exp(1)^4+60*exp(1)^3+270*exp(1)^2+540*exp(1)+405)*exp(x^2+4)-exp(1)^5-15*exp(1)^4-90*exp(
1)^3-270*exp(1)^2-405*exp(1)-243)*exp(exp(3/(exp(x^2+4)^4+(-4*exp(1)-12)*exp(x^2+4)^3+(6*exp(1)^2+36*exp(1)+54
)*exp(x^2+4)^2+(-4*exp(1)^3-36*exp(1)^2-108*exp(1)-108)*exp(x^2+4)+exp(1)^4+12*exp(1)^3+54*exp(1)^2+108*exp(1)
+81)))/(exp(x^2+4)^5+(-5*exp(1)-15)*exp(x^2+4)^4+(10*exp(1)^2+60*exp(1)+90)*exp(x^2+4)^3+(-10*exp(1)^3-90*exp(
1)^2-270*exp(1)-270)*exp(x^2+4)^2+(5*exp(1)^4+60*exp(1)^3+270*exp(1)^2+540*exp(1)+405)*exp(x^2+4)-exp(1)^5-15*
exp(1)^4-90*exp(1)^3-270*exp(1)^2-405*exp(1)-243),x,method=_RETURNVERBOSE)

[Out]

x*exp(exp(3/(-36*exp(x^2+6)+6*exp(2*x^2+10)-108*exp(x^2+5)-4*exp(3*x^2+13)+36*exp(2*x^2+9)-4*exp(x^2+7)+54*exp
(2)+exp(4)+108*exp(1)+12*exp(3)-108*exp(x^2+4)+exp(4*x^2+16)-12*exp(3*x^2+12)+54*exp(2*x^2+8)+81)))

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maxima [B]  time = 0.64, size = 91, normalized size = 4.14 \begin {gather*} x e^{\left (e^{\left (-\frac {3}{4 \, {\left (e^{13} + 3 \, e^{12}\right )} e^{\left (3 \, x^{2}\right )} - 6 \, {\left (e^{10} + 6 \, e^{9} + 9 \, e^{8}\right )} e^{\left (2 \, x^{2}\right )} + 4 \, {\left (e^{7} + 9 \, e^{6} + 27 \, e^{5} + 27 \, e^{4}\right )} e^{\left (x^{2}\right )} - e^{4} - 12 \, e^{3} - 54 \, e^{2} - 108 \, e - e^{\left (4 \, x^{2} + 16\right )} - 81}\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-24*x^2*exp(x^2+4)*exp(3/(exp(x^2+4)^4+(-4*exp(1)-12)*exp(x^2+4)^3+(6*exp(1)^2+36*exp(1)+54)*exp(x^
2+4)^2+(-4*exp(1)^3-36*exp(1)^2-108*exp(1)-108)*exp(x^2+4)+exp(1)^4+12*exp(1)^3+54*exp(1)^2+108*exp(1)+81))+ex
p(x^2+4)^5+(-5*exp(1)-15)*exp(x^2+4)^4+(10*exp(1)^2+60*exp(1)+90)*exp(x^2+4)^3+(-10*exp(1)^3-90*exp(1)^2-270*e
xp(1)-270)*exp(x^2+4)^2+(5*exp(1)^4+60*exp(1)^3+270*exp(1)^2+540*exp(1)+405)*exp(x^2+4)-exp(1)^5-15*exp(1)^4-9
0*exp(1)^3-270*exp(1)^2-405*exp(1)-243)*exp(exp(3/(exp(x^2+4)^4+(-4*exp(1)-12)*exp(x^2+4)^3+(6*exp(1)^2+36*exp
(1)+54)*exp(x^2+4)^2+(-4*exp(1)^3-36*exp(1)^2-108*exp(1)-108)*exp(x^2+4)+exp(1)^4+12*exp(1)^3+54*exp(1)^2+108*
exp(1)+81)))/(exp(x^2+4)^5+(-5*exp(1)-15)*exp(x^2+4)^4+(10*exp(1)^2+60*exp(1)+90)*exp(x^2+4)^3+(-10*exp(1)^3-9
0*exp(1)^2-270*exp(1)-270)*exp(x^2+4)^2+(5*exp(1)^4+60*exp(1)^3+270*exp(1)^2+540*exp(1)+405)*exp(x^2+4)-exp(1)
^5-15*exp(1)^4-90*exp(1)^3-270*exp(1)^2-405*exp(1)-243),x, algorithm="maxima")

[Out]

x*e^(e^(-3/(4*(e^13 + 3*e^12)*e^(3*x^2) - 6*(e^10 + 6*e^9 + 9*e^8)*e^(2*x^2) + 4*(e^7 + 9*e^6 + 27*e^5 + 27*e^
4)*e^(x^2) - e^4 - 12*e^3 - 54*e^2 - 108*e - e^(4*x^2 + 16) - 81)))

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mupad [B]  time = 4.72, size = 115, normalized size = 5.23 \begin {gather*} x\,{\mathrm {e}}^{{\mathrm {e}}^{\frac {3}{108\,\mathrm {e}+54\,{\mathrm {e}}^2+12\,{\mathrm {e}}^3+{\mathrm {e}}^4-108\,{\mathrm {e}}^{x^2}\,{\mathrm {e}}^4-108\,{\mathrm {e}}^{x^2}\,{\mathrm {e}}^5-36\,{\mathrm {e}}^{x^2}\,{\mathrm {e}}^6-4\,{\mathrm {e}}^{x^2}\,{\mathrm {e}}^7+54\,{\mathrm {e}}^8\,{\mathrm {e}}^{2\,x^2}+36\,{\mathrm {e}}^9\,{\mathrm {e}}^{2\,x^2}+6\,{\mathrm {e}}^{10}\,{\mathrm {e}}^{2\,x^2}-12\,{\mathrm {e}}^{12}\,{\mathrm {e}}^{3\,x^2}-4\,{\mathrm {e}}^{13}\,{\mathrm {e}}^{3\,x^2}+{\mathrm {e}}^{16}\,{\mathrm {e}}^{4\,x^2}+81}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(exp(3/(108*exp(1) + 54*exp(2) + 12*exp(3) + exp(4) + exp(4*x^2 + 16) + exp(2*x^2 + 8)*(36*exp(1) + 6*
exp(2) + 54) - exp(3*x^2 + 12)*(4*exp(1) + 12) - exp(x^2 + 4)*(108*exp(1) + 36*exp(2) + 4*exp(3) + 108) + 81))
)*(405*exp(1) + 270*exp(2) + 90*exp(3) + 15*exp(4) + exp(5) - exp(5*x^2 + 20) + exp(2*x^2 + 8)*(270*exp(1) + 9
0*exp(2) + 10*exp(3) + 270) - exp(3*x^2 + 12)*(60*exp(1) + 10*exp(2) + 90) - exp(x^2 + 4)*(540*exp(1) + 270*ex
p(2) + 60*exp(3) + 5*exp(4) + 405) + exp(4*x^2 + 16)*(5*exp(1) + 15) + 24*x^2*exp(x^2 + 4)*exp(3/(108*exp(1) +
54*exp(2) + 12*exp(3) + exp(4) + exp(4*x^2 + 16) + exp(2*x^2 + 8)*(36*exp(1) + 6*exp(2) + 54) - exp(3*x^2 + 1
2)*(4*exp(1) + 12) - exp(x^2 + 4)*(108*exp(1) + 36*exp(2) + 4*exp(3) + 108) + 81)) + 243))/(405*exp(1) + 270*e
xp(2) + 90*exp(3) + 15*exp(4) + exp(5) - exp(5*x^2 + 20) + exp(2*x^2 + 8)*(270*exp(1) + 90*exp(2) + 10*exp(3)
+ 270) - exp(3*x^2 + 12)*(60*exp(1) + 10*exp(2) + 90) - exp(x^2 + 4)*(540*exp(1) + 270*exp(2) + 60*exp(3) + 5*
exp(4) + 405) + exp(4*x^2 + 16)*(5*exp(1) + 15) + 243),x)

[Out]

x*exp(exp(3/(108*exp(1) + 54*exp(2) + 12*exp(3) + exp(4) - 108*exp(x^2)*exp(4) - 108*exp(x^2)*exp(5) - 36*exp(
x^2)*exp(6) - 4*exp(x^2)*exp(7) + 54*exp(8)*exp(2*x^2) + 36*exp(9)*exp(2*x^2) + 6*exp(10)*exp(2*x^2) - 12*exp(
12)*exp(3*x^2) - 4*exp(13)*exp(3*x^2) + exp(16)*exp(4*x^2) + 81)))

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sympy [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((-24*x**2*exp(x**2+4)*exp(3/(exp(x**2+4)**4+(-4*exp(1)-12)*exp(x**2+4)**3+(6*exp(1)**2+36*exp(1)+54)
*exp(x**2+4)**2+(-4*exp(1)**3-36*exp(1)**2-108*exp(1)-108)*exp(x**2+4)+exp(1)**4+12*exp(1)**3+54*exp(1)**2+108
*exp(1)+81))+exp(x**2+4)**5+(-5*exp(1)-15)*exp(x**2+4)**4+(10*exp(1)**2+60*exp(1)+90)*exp(x**2+4)**3+(-10*exp(
1)**3-90*exp(1)**2-270*exp(1)-270)*exp(x**2+4)**2+(5*exp(1)**4+60*exp(1)**3+270*exp(1)**2+540*exp(1)+405)*exp(
x**2+4)-exp(1)**5-15*exp(1)**4-90*exp(1)**3-270*exp(1)**2-405*exp(1)-243)*exp(exp(3/(exp(x**2+4)**4+(-4*exp(1)
-12)*exp(x**2+4)**3+(6*exp(1)**2+36*exp(1)+54)*exp(x**2+4)**2+(-4*exp(1)**3-36*exp(1)**2-108*exp(1)-108)*exp(x
**2+4)+exp(1)**4+12*exp(1)**3+54*exp(1)**2+108*exp(1)+81)))/(exp(x**2+4)**5+(-5*exp(1)-15)*exp(x**2+4)**4+(10*
exp(1)**2+60*exp(1)+90)*exp(x**2+4)**3+(-10*exp(1)**3-90*exp(1)**2-270*exp(1)-270)*exp(x**2+4)**2+(5*exp(1)**4
+60*exp(1)**3+270*exp(1)**2+540*exp(1)+405)*exp(x**2+4)-exp(1)**5-15*exp(1)**4-90*exp(1)**3-270*exp(1)**2-405*
exp(1)-243),x)

[Out]

Timed out

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