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3.14.75 \(\int \frac {e^{-8+e^{e^{\frac {4 x^6+e^4 (2500 x^3-200 x^6+36 x^7+4 x^9)+e^8 (390625-62500 x^3+11250 x^4+3750 x^6-900 x^7+81 x^8-100 x^9+18 x^{10}+x^{12})}{e^8 x^8}}}+e^{\frac {4 x^6+e^4 (2500 x^3-200 x^6+36 x^7+4 x^9)+e^8 (390625-62500 x^3+11250 x^4+3750 x^6-900 x^7+81 x^8-100 x^9+18 x^{10}+x^{12})}{e^8 x^8}}+\frac {4 x^6+e^4 (2500 x^3-200 x^6+36 x^7+4 x^9)+e^8 (390625-62500 x^3+11250 x^4+3750 x^6-900 x^7+81 x^8-100 x^9+18 x^{10}+x^{12})}{e^8 x^8}} (-8 x^6+e^4 (-12500 x^3+400 x^6-36 x^7+4 x^9)+e^8 (-3125000+312500 x^3-45000 x^4-7500 x^6+900 x^7-100 x^9+36 x^{10}+4 x^{12}))}{x^9} \, dx\)

Optimal. Leaf size=31 \[ -2+e^{e^{e^{\left (9+\left (\frac {25}{x^2}-x\right )^2+\frac {2}{e^4 x}\right )^2}}} \]

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Rubi [F]  time = 102.92, 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 {\exp \left (-8+\exp \left (\exp \left (\frac {4 x^6+e^4 \left (2500 x^3-200 x^6+36 x^7+4 x^9\right )+e^8 \left (390625-62500 x^3+11250 x^4+3750 x^6-900 x^7+81 x^8-100 x^9+18 x^{10}+x^{12}\right )}{e^8 x^8}\right )\right )+\exp \left (\frac {4 x^6+e^4 \left (2500 x^3-200 x^6+36 x^7+4 x^9\right )+e^8 \left (390625-62500 x^3+11250 x^4+3750 x^6-900 x^7+81 x^8-100 x^9+18 x^{10}+x^{12}\right )}{e^8 x^8}\right )+\frac {4 x^6+e^4 \left (2500 x^3-200 x^6+36 x^7+4 x^9\right )+e^8 \left (390625-62500 x^3+11250 x^4+3750 x^6-900 x^7+81 x^8-100 x^9+18 x^{10}+x^{12}\right )}{e^8 x^8}\right ) \left (-8 x^6+e^4 \left (-12500 x^3+400 x^6-36 x^7+4 x^9\right )+e^8 \left (-3125000+312500 x^3-45000 x^4-7500 x^6+900 x^7-100 x^9+36 x^{10}+4 x^{12}\right )\right )}{x^9} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(E^(-8 + E^E^((4*x^6 + E^4*(2500*x^3 - 200*x^6 + 36*x^7 + 4*x^9) + E^8*(390625 - 62500*x^3 + 11250*x^4 + 3
750*x^6 - 900*x^7 + 81*x^8 - 100*x^9 + 18*x^10 + x^12))/(E^8*x^8)) + E^((4*x^6 + E^4*(2500*x^3 - 200*x^6 + 36*
x^7 + 4*x^9) + E^8*(390625 - 62500*x^3 + 11250*x^4 + 3750*x^6 - 900*x^7 + 81*x^8 - 100*x^9 + 18*x^10 + x^12))/
(E^8*x^8)) + (4*x^6 + E^4*(2500*x^3 - 200*x^6 + 36*x^7 + 4*x^9) + E^8*(390625 - 62500*x^3 + 11250*x^4 + 3750*x
^6 - 900*x^7 + 81*x^8 - 100*x^9 + 18*x^10 + x^12))/(E^8*x^8))*(-8*x^6 + E^4*(-12500*x^3 + 400*x^6 - 36*x^7 + 4
*x^9) + E^8*(-3125000 + 312500*x^3 - 45000*x^4 - 7500*x^6 + 900*x^7 - 100*x^9 + 36*x^10 + 4*x^12)))/x^9,x]

[Out]

4*(1 - 25*E^4)*Defer[Int][E^(77 + E^E^((2*x^3 + E^4*(625 - 50*x^3 + 9*x^4 + x^6))^2/(E^8*x^8)) + E^((2*x^3 + E
^4*(625 - 50*x^3 + 9*x^4 + x^6))^2/(E^8*x^8)) + 390625/x^8 - 62500/x^5 + 11250/x^4 + (3750*(1 + 2/(1875*E^8)))
/x^2 - 900/x - 100*x + 18*x^2 + x^4 + (4*(625 - 50*x^3 + 9*x^4 + x^6))/(E^4*x^5)), x] - 3125000*Defer[Int][E^(
81 + E^E^((2*x^3 + E^4*(625 - 50*x^3 + 9*x^4 + x^6))^2/(E^8*x^8)) + E^((2*x^3 + E^4*(625 - 50*x^3 + 9*x^4 + x^
6))^2/(E^8*x^8)) + 390625/x^8 - 62500/x^5 + 11250/x^4 + (3750*(1 + 2/(1875*E^8)))/x^2 - 900/x - 100*x + 18*x^2
 + x^4 + (4*(625 - 50*x^3 + 9*x^4 + x^6))/(E^4*x^5))/x^9, x] - 12500*(1 - 25*E^4)*Defer[Int][E^(77 + E^E^((2*x
^3 + E^4*(625 - 50*x^3 + 9*x^4 + x^6))^2/(E^8*x^8)) + E^((2*x^3 + E^4*(625 - 50*x^3 + 9*x^4 + x^6))^2/(E^8*x^8
)) + 390625/x^8 - 62500/x^5 + 11250/x^4 + (3750*(1 + 2/(1875*E^8)))/x^2 - 900/x - 100*x + 18*x^2 + x^4 + (4*(6
25 - 50*x^3 + 9*x^4 + x^6))/(E^4*x^5))/x^6, x] - 45000*Defer[Int][E^(81 + E^E^((2*x^3 + E^4*(625 - 50*x^3 + 9*
x^4 + x^6))^2/(E^8*x^8)) + E^((2*x^3 + E^4*(625 - 50*x^3 + 9*x^4 + x^6))^2/(E^8*x^8)) + 390625/x^8 - 62500/x^5
 + 11250/x^4 + (3750*(1 + 2/(1875*E^8)))/x^2 - 900/x - 100*x + 18*x^2 + x^4 + (4*(625 - 50*x^3 + 9*x^4 + x^6))
/(E^4*x^5))/x^5, x] - 4*(2 - 100*E^4 + 1875*E^8)*Defer[Int][E^(73 + E^E^((2*x^3 + E^4*(625 - 50*x^3 + 9*x^4 +
x^6))^2/(E^8*x^8)) + E^((2*x^3 + E^4*(625 - 50*x^3 + 9*x^4 + x^6))^2/(E^8*x^8)) + 390625/x^8 - 62500/x^5 + 112
50/x^4 + (3750*(1 + 2/(1875*E^8)))/x^2 - 900/x - 100*x + 18*x^2 + x^4 + (4*(625 - 50*x^3 + 9*x^4 + x^6))/(E^4*
x^5))/x^3, x] - 36*(1 - 25*E^4)*Defer[Int][E^(77 + E^E^((2*x^3 + E^4*(625 - 50*x^3 + 9*x^4 + x^6))^2/(E^8*x^8)
) + E^((2*x^3 + E^4*(625 - 50*x^3 + 9*x^4 + x^6))^2/(E^8*x^8)) + 390625/x^8 - 62500/x^5 + 11250/x^4 + (3750*(1
 + 2/(1875*E^8)))/x^2 - 900/x - 100*x + 18*x^2 + x^4 + (4*(625 - 50*x^3 + 9*x^4 + x^6))/(E^4*x^5))/x^2, x] + 3
6*Defer[Int][E^(81 + E^E^((2*x^3 + E^4*(625 - 50*x^3 + 9*x^4 + x^6))^2/(E^8*x^8)) + E^((2*x^3 + E^4*(625 - 50*
x^3 + 9*x^4 + x^6))^2/(E^8*x^8)) + 390625/x^8 - 62500/x^5 + 11250/x^4 + (3750*(1 + 2/(1875*E^8)))/x^2 - 900/x
- 100*x + 18*x^2 + x^4 + (4*(625 - 50*x^3 + 9*x^4 + x^6))/(E^4*x^5))*x, x] + 4*Defer[Int][E^(81 + E^E^((2*x^3
+ E^4*(625 - 50*x^3 + 9*x^4 + x^6))^2/(E^8*x^8)) + E^((2*x^3 + E^4*(625 - 50*x^3 + 9*x^4 + x^6))^2/(E^8*x^8))
+ 390625/x^8 - 62500/x^5 + 11250/x^4 + (3750*(1 + 2/(1875*E^8)))/x^2 - 900/x - 100*x + 18*x^2 + x^4 + (4*(625
- 50*x^3 + 9*x^4 + x^6))/(E^4*x^5))*x^3, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {4 \exp \left (73+\exp \left (\exp \left (\frac {\left (2 x^3+e^4 \left (625-50 x^3+9 x^4+x^6\right )\right )^2}{e^8 x^8}\right )\right )+\exp \left (\frac {\left (2 x^3+e^4 \left (625-50 x^3+9 x^4+x^6\right )\right )^2}{e^8 x^8}\right )+\frac {390625}{x^8}-\frac {62500}{x^5}+\frac {11250}{x^4}+\frac {3750 \left (1+\frac {2}{1875 e^8}\right )}{x^2}-\frac {900}{x}-100 x+18 x^2+x^4+\frac {4 \left (625-50 x^3+9 x^4+x^6\right )}{e^4 x^5}\right ) \left (-2 x^6+e^4 x^3 \left (-3125+100 x^3-9 x^4+x^6\right )+e^8 \left (-781250+78125 x^3-11250 x^4-1875 x^6+225 x^7-25 x^9+9 x^{10}+x^{12}\right )\right )}{x^9} \, dx\\ &=4 \int \frac {\exp \left (73+\exp \left (\exp \left (\frac {\left (2 x^3+e^4 \left (625-50 x^3+9 x^4+x^6\right )\right )^2}{e^8 x^8}\right )\right )+\exp \left (\frac {\left (2 x^3+e^4 \left (625-50 x^3+9 x^4+x^6\right )\right )^2}{e^8 x^8}\right )+\frac {390625}{x^8}-\frac {62500}{x^5}+\frac {11250}{x^4}+\frac {3750 \left (1+\frac {2}{1875 e^8}\right )}{x^2}-\frac {900}{x}-100 x+18 x^2+x^4+\frac {4 \left (625-50 x^3+9 x^4+x^6\right )}{e^4 x^5}\right ) \left (-2 x^6+e^4 x^3 \left (-3125+100 x^3-9 x^4+x^6\right )+e^8 \left (-781250+78125 x^3-11250 x^4-1875 x^6+225 x^7-25 x^9+9 x^{10}+x^{12}\right )\right )}{x^9} \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.68, size = 40, normalized size = 1.29 \begin {gather*} e^{e^{e^{\frac {\left (2 x^3+e^4 \left (625-50 x^3+9 x^4+x^6\right )\right )^2}{e^8 x^8}}}} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^(-8 + E^E^((4*x^6 + E^4*(2500*x^3 - 200*x^6 + 36*x^7 + 4*x^9) + E^8*(390625 - 62500*x^3 + 11250*x
^4 + 3750*x^6 - 900*x^7 + 81*x^8 - 100*x^9 + 18*x^10 + x^12))/(E^8*x^8)) + E^((4*x^6 + E^4*(2500*x^3 - 200*x^6
 + 36*x^7 + 4*x^9) + E^8*(390625 - 62500*x^3 + 11250*x^4 + 3750*x^6 - 900*x^7 + 81*x^8 - 100*x^9 + 18*x^10 + x
^12))/(E^8*x^8)) + (4*x^6 + E^4*(2500*x^3 - 200*x^6 + 36*x^7 + 4*x^9) + E^8*(390625 - 62500*x^3 + 11250*x^4 +
3750*x^6 - 900*x^7 + 81*x^8 - 100*x^9 + 18*x^10 + x^12))/(E^8*x^8))*(-8*x^6 + E^4*(-12500*x^3 + 400*x^6 - 36*x
^7 + 4*x^9) + E^8*(-3125000 + 312500*x^3 - 45000*x^4 - 7500*x^6 + 900*x^7 - 100*x^9 + 36*x^10 + 4*x^12)))/x^9,
x]

[Out]

E^E^E^((2*x^3 + E^4*(625 - 50*x^3 + 9*x^4 + x^6))^2/(E^8*x^8))

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fricas [B]  time = 0.66, size = 412, normalized size = 13.29 \begin {gather*} e^{\left (\frac {{\left (x^{8} e^{\left (\frac {{\left (4 \, x^{6} + {\left (x^{12} + 18 \, x^{10} - 100 \, x^{9} + 81 \, x^{8} - 900 \, x^{7} + 3750 \, x^{6} + 11250 \, x^{4} - 62500 \, x^{3} + 390625\right )} e^{8} + 4 \, {\left (x^{9} + 9 \, x^{7} - 50 \, x^{6} + 625 \, x^{3}\right )} e^{4}\right )} e^{\left (-8\right )}}{x^{8}} + 8\right )} + x^{8} e^{\left (e^{\left (\frac {{\left (4 \, x^{6} + {\left (x^{12} + 18 \, x^{10} - 100 \, x^{9} + 81 \, x^{8} - 900 \, x^{7} + 3750 \, x^{6} + 11250 \, x^{4} - 62500 \, x^{3} + 390625\right )} e^{8} + 4 \, {\left (x^{9} + 9 \, x^{7} - 50 \, x^{6} + 625 \, x^{3}\right )} e^{4}\right )} e^{\left (-8\right )}}{x^{8}}\right )} + 8\right )} + 4 \, x^{6} + {\left (x^{12} + 18 \, x^{10} - 100 \, x^{9} + 73 \, x^{8} - 900 \, x^{7} + 3750 \, x^{6} + 11250 \, x^{4} - 62500 \, x^{3} + 390625\right )} e^{8} + 4 \, {\left (x^{9} + 9 \, x^{7} - 50 \, x^{6} + 625 \, x^{3}\right )} e^{4}\right )} e^{\left (-8\right )}}{x^{8}} - \frac {{\left (4 \, x^{6} + {\left (x^{12} + 18 \, x^{10} - 100 \, x^{9} + 81 \, x^{8} - 900 \, x^{7} + 3750 \, x^{6} + 11250 \, x^{4} - 62500 \, x^{3} + 390625\right )} e^{8} + 4 \, {\left (x^{9} + 9 \, x^{7} - 50 \, x^{6} + 625 \, x^{3}\right )} e^{4}\right )} e^{\left (-8\right )}}{x^{8}} - e^{\left (\frac {{\left (4 \, x^{6} + {\left (x^{12} + 18 \, x^{10} - 100 \, x^{9} + 81 \, x^{8} - 900 \, x^{7} + 3750 \, x^{6} + 11250 \, x^{4} - 62500 \, x^{3} + 390625\right )} e^{8} + 4 \, {\left (x^{9} + 9 \, x^{7} - 50 \, x^{6} + 625 \, x^{3}\right )} e^{4}\right )} e^{\left (-8\right )}}{x^{8}}\right )} + 8\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((4*x^12+36*x^10-100*x^9+900*x^7-7500*x^6-45000*x^4+312500*x^3-3125000)*exp(4)^2+(4*x^9-36*x^7+400*x
^6-12500*x^3)*exp(4)-8*x^6)*exp(((x^12+18*x^10-100*x^9+81*x^8-900*x^7+3750*x^6+11250*x^4-62500*x^3+390625)*exp
(4)^2+(4*x^9+36*x^7-200*x^6+2500*x^3)*exp(4)+4*x^6)/x^8/exp(4)^2)*exp(exp(((x^12+18*x^10-100*x^9+81*x^8-900*x^
7+3750*x^6+11250*x^4-62500*x^3+390625)*exp(4)^2+(4*x^9+36*x^7-200*x^6+2500*x^3)*exp(4)+4*x^6)/x^8/exp(4)^2))*e
xp(exp(exp(((x^12+18*x^10-100*x^9+81*x^8-900*x^7+3750*x^6+11250*x^4-62500*x^3+390625)*exp(4)^2+(4*x^9+36*x^7-2
00*x^6+2500*x^3)*exp(4)+4*x^6)/x^8/exp(4)^2)))/x^9/exp(4)^2,x, algorithm="fricas")

[Out]

e^((x^8*e^((4*x^6 + (x^12 + 18*x^10 - 100*x^9 + 81*x^8 - 900*x^7 + 3750*x^6 + 11250*x^4 - 62500*x^3 + 390625)*
e^8 + 4*(x^9 + 9*x^7 - 50*x^6 + 625*x^3)*e^4)*e^(-8)/x^8 + 8) + x^8*e^(e^((4*x^6 + (x^12 + 18*x^10 - 100*x^9 +
 81*x^8 - 900*x^7 + 3750*x^6 + 11250*x^4 - 62500*x^3 + 390625)*e^8 + 4*(x^9 + 9*x^7 - 50*x^6 + 625*x^3)*e^4)*e
^(-8)/x^8) + 8) + 4*x^6 + (x^12 + 18*x^10 - 100*x^9 + 73*x^8 - 900*x^7 + 3750*x^6 + 11250*x^4 - 62500*x^3 + 39
0625)*e^8 + 4*(x^9 + 9*x^7 - 50*x^6 + 625*x^3)*e^4)*e^(-8)/x^8 - (4*x^6 + (x^12 + 18*x^10 - 100*x^9 + 81*x^8 -
 900*x^7 + 3750*x^6 + 11250*x^4 - 62500*x^3 + 390625)*e^8 + 4*(x^9 + 9*x^7 - 50*x^6 + 625*x^3)*e^4)*e^(-8)/x^8
 - e^((4*x^6 + (x^12 + 18*x^10 - 100*x^9 + 81*x^8 - 900*x^7 + 3750*x^6 + 11250*x^4 - 62500*x^3 + 390625)*e^8 +
 4*(x^9 + 9*x^7 - 50*x^6 + 625*x^3)*e^4)*e^(-8)/x^8) + 8)

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giac [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int -\frac {4 \, {\left (2 \, x^{6} - {\left (x^{12} + 9 \, x^{10} - 25 \, x^{9} + 225 \, x^{7} - 1875 \, x^{6} - 11250 \, x^{4} + 78125 \, x^{3} - 781250\right )} e^{8} - {\left (x^{9} - 9 \, x^{7} + 100 \, x^{6} - 3125 \, x^{3}\right )} e^{4}\right )} e^{\left (\frac {{\left (4 \, x^{6} + {\left (x^{12} + 18 \, x^{10} - 100 \, x^{9} + 81 \, x^{8} - 900 \, x^{7} + 3750 \, x^{6} + 11250 \, x^{4} - 62500 \, x^{3} + 390625\right )} e^{8} + 4 \, {\left (x^{9} + 9 \, x^{7} - 50 \, x^{6} + 625 \, x^{3}\right )} e^{4}\right )} e^{\left (-8\right )}}{x^{8}} + e^{\left (\frac {{\left (4 \, x^{6} + {\left (x^{12} + 18 \, x^{10} - 100 \, x^{9} + 81 \, x^{8} - 900 \, x^{7} + 3750 \, x^{6} + 11250 \, x^{4} - 62500 \, x^{3} + 390625\right )} e^{8} + 4 \, {\left (x^{9} + 9 \, x^{7} - 50 \, x^{6} + 625 \, x^{3}\right )} e^{4}\right )} e^{\left (-8\right )}}{x^{8}}\right )} + e^{\left (e^{\left (\frac {{\left (4 \, x^{6} + {\left (x^{12} + 18 \, x^{10} - 100 \, x^{9} + 81 \, x^{8} - 900 \, x^{7} + 3750 \, x^{6} + 11250 \, x^{4} - 62500 \, x^{3} + 390625\right )} e^{8} + 4 \, {\left (x^{9} + 9 \, x^{7} - 50 \, x^{6} + 625 \, x^{3}\right )} e^{4}\right )} e^{\left (-8\right )}}{x^{8}}\right )}\right )} - 8\right )}}{x^{9}}\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((4*x^12+36*x^10-100*x^9+900*x^7-7500*x^6-45000*x^4+312500*x^3-3125000)*exp(4)^2+(4*x^9-36*x^7+400*x
^6-12500*x^3)*exp(4)-8*x^6)*exp(((x^12+18*x^10-100*x^9+81*x^8-900*x^7+3750*x^6+11250*x^4-62500*x^3+390625)*exp
(4)^2+(4*x^9+36*x^7-200*x^6+2500*x^3)*exp(4)+4*x^6)/x^8/exp(4)^2)*exp(exp(((x^12+18*x^10-100*x^9+81*x^8-900*x^
7+3750*x^6+11250*x^4-62500*x^3+390625)*exp(4)^2+(4*x^9+36*x^7-200*x^6+2500*x^3)*exp(4)+4*x^6)/x^8/exp(4)^2))*e
xp(exp(exp(((x^12+18*x^10-100*x^9+81*x^8-900*x^7+3750*x^6+11250*x^4-62500*x^3+390625)*exp(4)^2+(4*x^9+36*x^7-2
00*x^6+2500*x^3)*exp(4)+4*x^6)/x^8/exp(4)^2)))/x^9/exp(4)^2,x, algorithm="giac")

[Out]

integrate(-4*(2*x^6 - (x^12 + 9*x^10 - 25*x^9 + 225*x^7 - 1875*x^6 - 11250*x^4 + 78125*x^3 - 781250)*e^8 - (x^
9 - 9*x^7 + 100*x^6 - 3125*x^3)*e^4)*e^((4*x^6 + (x^12 + 18*x^10 - 100*x^9 + 81*x^8 - 900*x^7 + 3750*x^6 + 112
50*x^4 - 62500*x^3 + 390625)*e^8 + 4*(x^9 + 9*x^7 - 50*x^6 + 625*x^3)*e^4)*e^(-8)/x^8 + e^((4*x^6 + (x^12 + 18
*x^10 - 100*x^9 + 81*x^8 - 900*x^7 + 3750*x^6 + 11250*x^4 - 62500*x^3 + 390625)*e^8 + 4*(x^9 + 9*x^7 - 50*x^6
+ 625*x^3)*e^4)*e^(-8)/x^8) + e^(e^((4*x^6 + (x^12 + 18*x^10 - 100*x^9 + 81*x^8 - 900*x^7 + 3750*x^6 + 11250*x
^4 - 62500*x^3 + 390625)*e^8 + 4*(x^9 + 9*x^7 - 50*x^6 + 625*x^3)*e^4)*e^(-8)/x^8)) - 8)/x^9, x)

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maple [B]  time = 35.21, size = 103, normalized size = 3.32

method result size
risch \({\mathrm e}^{{\mathrm e}^{{\mathrm e}^{\frac {\left ({\mathrm e}^{8} x^{12}+18 \,{\mathrm e}^{8} x^{10}+4 x^{9} {\mathrm e}^{4}-100 \,{\mathrm e}^{8} x^{9}+81 \,{\mathrm e}^{8} x^{8}+36 x^{7} {\mathrm e}^{4}-900 \,{\mathrm e}^{8} x^{7}-200 x^{6} {\mathrm e}^{4}+3750 \,{\mathrm e}^{8} x^{6}+4 x^{6}+11250 x^{4} {\mathrm e}^{8}+2500 x^{3} {\mathrm e}^{4}-62500 \,{\mathrm e}^{8} x^{3}+390625 \,{\mathrm e}^{8}\right ) {\mathrm e}^{-8}}{x^{8}}}}}\) \(103\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((4*x^12+36*x^10-100*x^9+900*x^7-7500*x^6-45000*x^4+312500*x^3-3125000)*exp(4)^2+(4*x^9-36*x^7+400*x^6-125
00*x^3)*exp(4)-8*x^6)*exp(((x^12+18*x^10-100*x^9+81*x^8-900*x^7+3750*x^6+11250*x^4-62500*x^3+390625)*exp(4)^2+
(4*x^9+36*x^7-200*x^6+2500*x^3)*exp(4)+4*x^6)/x^8/exp(4)^2)*exp(exp(((x^12+18*x^10-100*x^9+81*x^8-900*x^7+3750
*x^6+11250*x^4-62500*x^3+390625)*exp(4)^2+(4*x^9+36*x^7-200*x^6+2500*x^3)*exp(4)+4*x^6)/x^8/exp(4)^2))*exp(exp
(exp(((x^12+18*x^10-100*x^9+81*x^8-900*x^7+3750*x^6+11250*x^4-62500*x^3+390625)*exp(4)^2+(4*x^9+36*x^7-200*x^6
+2500*x^3)*exp(4)+4*x^6)/x^8/exp(4)^2)))/x^9/exp(4)^2,x,method=_RETURNVERBOSE)

[Out]

exp(exp(exp((exp(8)*x^12+18*exp(8)*x^10+4*x^9*exp(4)-100*exp(8)*x^9+81*exp(8)*x^8+36*x^7*exp(4)-900*exp(8)*x^7
-200*x^6*exp(4)+3750*exp(8)*x^6+4*x^6+11250*x^4*exp(8)+2500*x^3*exp(4)-62500*exp(8)*x^3+390625*exp(8))*exp(-8)
/x^8)))

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maxima [B]  time = 3.48, size = 74, normalized size = 2.39 \begin {gather*} e^{\left (e^{\left (e^{\left (x^{4} + 18 \, x^{2} + 4 \, x e^{\left (-4\right )} - 100 \, x + \frac {36 \, e^{\left (-4\right )}}{x} - \frac {900}{x} - \frac {200 \, e^{\left (-4\right )}}{x^{2}} + \frac {4 \, e^{\left (-8\right )}}{x^{2}} + \frac {3750}{x^{2}} + \frac {11250}{x^{4}} + \frac {2500 \, e^{\left (-4\right )}}{x^{5}} - \frac {62500}{x^{5}} + \frac {390625}{x^{8}} + 81\right )}\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((4*x^12+36*x^10-100*x^9+900*x^7-7500*x^6-45000*x^4+312500*x^3-3125000)*exp(4)^2+(4*x^9-36*x^7+400*x
^6-12500*x^3)*exp(4)-8*x^6)*exp(((x^12+18*x^10-100*x^9+81*x^8-900*x^7+3750*x^6+11250*x^4-62500*x^3+390625)*exp
(4)^2+(4*x^9+36*x^7-200*x^6+2500*x^3)*exp(4)+4*x^6)/x^8/exp(4)^2)*exp(exp(((x^12+18*x^10-100*x^9+81*x^8-900*x^
7+3750*x^6+11250*x^4-62500*x^3+390625)*exp(4)^2+(4*x^9+36*x^7-200*x^6+2500*x^3)*exp(4)+4*x^6)/x^8/exp(4)^2))*e
xp(exp(exp(((x^12+18*x^10-100*x^9+81*x^8-900*x^7+3750*x^6+11250*x^4-62500*x^3+390625)*exp(4)^2+(4*x^9+36*x^7-2
00*x^6+2500*x^3)*exp(4)+4*x^6)/x^8/exp(4)^2)))/x^9/exp(4)^2,x, algorithm="maxima")

[Out]

e^(e^(e^(x^4 + 18*x^2 + 4*x*e^(-4) - 100*x + 36*e^(-4)/x - 900/x - 200*e^(-4)/x^2 + 4*e^(-8)/x^2 + 3750/x^2 +
11250/x^4 + 2500*e^(-4)/x^5 - 62500/x^5 + 390625/x^8 + 81)))

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mupad [B]  time = 2.35, size = 87, normalized size = 2.81 \begin {gather*} {\mathrm {e}}^{{\mathrm {e}}^{{\mathrm {e}}^{\frac {4\,{\mathrm {e}}^{-8}}{x^2}}\,{\mathrm {e}}^{\frac {36\,{\mathrm {e}}^{-4}}{x}}\,{\mathrm {e}}^{-\frac {200\,{\mathrm {e}}^{-4}}{x^2}}\,{\mathrm {e}}^{\frac {2500\,{\mathrm {e}}^{-4}}{x^5}}\,{\mathrm {e}}^{-100\,x}\,{\mathrm {e}}^{x^4}\,{\mathrm {e}}^{81}\,{\mathrm {e}}^{18\,x^2}\,{\mathrm {e}}^{-\frac {900}{x}}\,{\mathrm {e}}^{\frac {3750}{x^2}}\,{\mathrm {e}}^{\frac {11250}{x^4}}\,{\mathrm {e}}^{-\frac {62500}{x^5}}\,{\mathrm {e}}^{\frac {390625}{x^8}}\,{\mathrm {e}}^{4\,x\,{\mathrm {e}}^{-4}}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(exp((exp(-8)*(exp(8)*(11250*x^4 - 62500*x^3 + 3750*x^6 - 900*x^7 + 81*x^8 - 100*x^9 + 18*x^10 + x^12 + 3
90625) + 4*x^6 + exp(4)*(2500*x^3 - 200*x^6 + 36*x^7 + 4*x^9)))/x^8)*exp(-8)*exp(exp((exp(-8)*(exp(8)*(11250*x
^4 - 62500*x^3 + 3750*x^6 - 900*x^7 + 81*x^8 - 100*x^9 + 18*x^10 + x^12 + 390625) + 4*x^6 + exp(4)*(2500*x^3 -
 200*x^6 + 36*x^7 + 4*x^9)))/x^8))*exp(exp(exp((exp(-8)*(exp(8)*(11250*x^4 - 62500*x^3 + 3750*x^6 - 900*x^7 +
81*x^8 - 100*x^9 + 18*x^10 + x^12 + 390625) + 4*x^6 + exp(4)*(2500*x^3 - 200*x^6 + 36*x^7 + 4*x^9)))/x^8)))*(8
*x^6 - exp(8)*(312500*x^3 - 45000*x^4 - 7500*x^6 + 900*x^7 - 100*x^9 + 36*x^10 + 4*x^12 - 3125000) + exp(4)*(1
2500*x^3 - 400*x^6 + 36*x^7 - 4*x^9)))/x^9,x)

[Out]

exp(exp(exp((4*exp(-8))/x^2)*exp((36*exp(-4))/x)*exp(-(200*exp(-4))/x^2)*exp((2500*exp(-4))/x^5)*exp(-100*x)*e
xp(x^4)*exp(81)*exp(18*x^2)*exp(-900/x)*exp(3750/x^2)*exp(11250/x^4)*exp(-62500/x^5)*exp(390625/x^8)*exp(4*x*e
xp(-4))))

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sympy [B]  time = 5.85, size = 83, normalized size = 2.68 \begin {gather*} e^{e^{e^{\frac {4 x^{6} + \left (4 x^{9} + 36 x^{7} - 200 x^{6} + 2500 x^{3}\right ) e^{4} + \left (x^{12} + 18 x^{10} - 100 x^{9} + 81 x^{8} - 900 x^{7} + 3750 x^{6} + 11250 x^{4} - 62500 x^{3} + 390625\right ) e^{8}}{x^{8} e^{8}}}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((4*x**12+36*x**10-100*x**9+900*x**7-7500*x**6-45000*x**4+312500*x**3-3125000)*exp(4)**2+(4*x**9-36*
x**7+400*x**6-12500*x**3)*exp(4)-8*x**6)*exp(((x**12+18*x**10-100*x**9+81*x**8-900*x**7+3750*x**6+11250*x**4-6
2500*x**3+390625)*exp(4)**2+(4*x**9+36*x**7-200*x**6+2500*x**3)*exp(4)+4*x**6)/x**8/exp(4)**2)*exp(exp(((x**12
+18*x**10-100*x**9+81*x**8-900*x**7+3750*x**6+11250*x**4-62500*x**3+390625)*exp(4)**2+(4*x**9+36*x**7-200*x**6
+2500*x**3)*exp(4)+4*x**6)/x**8/exp(4)**2))*exp(exp(exp(((x**12+18*x**10-100*x**9+81*x**8-900*x**7+3750*x**6+1
1250*x**4-62500*x**3+390625)*exp(4)**2+(4*x**9+36*x**7-200*x**6+2500*x**3)*exp(4)+4*x**6)/x**8/exp(4)**2)))/x*
*9/exp(4)**2,x)

[Out]

exp(exp(exp((4*x**6 + (4*x**9 + 36*x**7 - 200*x**6 + 2500*x**3)*exp(4) + (x**12 + 18*x**10 - 100*x**9 + 81*x**
8 - 900*x**7 + 3750*x**6 + 11250*x**4 - 62500*x**3 + 390625)*exp(8))*exp(-8)/x**8)))

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