3.20.44 \(\int \frac {e^{e^{\frac {2 e^{-2 x} (-100+40 x+76 x^2-16 x^3-16 x^4+e^{2+2 x} (x+4 x^2+4 x^3))}{1+4 x+4 x^2}}-2 x+\frac {2 e^{-2 x} (-100+40 x+76 x^2-16 x^3-16 x^4+e^{2+2 x} (x+4 x^2+4 x^3))}{1+4 x+4 x^2}} (1280+784 x-720 x^2-736 x^3+64 x^4+128 x^5+e^{2+2 x} (2+12 x+24 x^2+16 x^3))}{1+6 x+12 x^2+8 x^3} \, dx\)

Optimal. Leaf size=31 \[ e^{e^{2 e^2 x-8 e^{-2 x} \left (x-\frac {5}{1+2 x}\right )^2}} \]

________________________________________________________________________________________

Rubi [F]  time = 180.00, 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*} \text {\$Aborted} \end {gather*}

Verification is not applicable to the result.

[In]

Int[(E^(E^((2*(-100 + 40*x + 76*x^2 - 16*x^3 - 16*x^4 + E^(2 + 2*x)*(x + 4*x^2 + 4*x^3)))/(E^(2*x)*(1 + 4*x +
4*x^2))) - 2*x + (2*(-100 + 40*x + 76*x^2 - 16*x^3 - 16*x^4 + E^(2 + 2*x)*(x + 4*x^2 + 4*x^3)))/(E^(2*x)*(1 +
4*x + 4*x^2)))*(1280 + 784*x - 720*x^2 - 736*x^3 + 64*x^4 + 128*x^5 + E^(2 + 2*x)*(2 + 12*x + 24*x^2 + 16*x^3)
))/(1 + 6*x + 12*x^2 + 8*x^3),x]

[Out]

$Aborted

Rubi steps

Aborted

________________________________________________________________________________________

Mathematica [B]  time = 1.66, size = 64, normalized size = 2.06 \begin {gather*} e^{e^{\frac {e^{-2 x} \left (-200+2 \left (40+e^{2+2 x}\right ) x+8 \left (19+e^{2+2 x}\right ) x^2+8 \left (-4+e^{2+2 x}\right ) x^3-32 x^4\right )}{(1+2 x)^2}}} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^(E^((2*(-100 + 40*x + 76*x^2 - 16*x^3 - 16*x^4 + E^(2 + 2*x)*(x + 4*x^2 + 4*x^3)))/(E^(2*x)*(1 +
4*x + 4*x^2))) - 2*x + (2*(-100 + 40*x + 76*x^2 - 16*x^3 - 16*x^4 + E^(2 + 2*x)*(x + 4*x^2 + 4*x^3)))/(E^(2*x)
*(1 + 4*x + 4*x^2)))*(1280 + 784*x - 720*x^2 - 736*x^3 + 64*x^4 + 128*x^5 + E^(2 + 2*x)*(2 + 12*x + 24*x^2 + 1
6*x^3)))/(1 + 6*x + 12*x^2 + 8*x^3),x]

[Out]

E^E^((-200 + 2*(40 + E^(2 + 2*x))*x + 8*(19 + E^(2 + 2*x))*x^2 + 8*(-4 + E^(2 + 2*x))*x^3 - 32*x^4)/(E^(2*x)*(
1 + 2*x)^2))

________________________________________________________________________________________

fricas [B]  time = 0.90, size = 234, normalized size = 7.55 \begin {gather*} e^{\left (2 \, x - \frac {{\left (8 \, {\left (4 \, x^{4} + 4 \, x^{3} - 19 \, x^{2} - 10 \, x + 25\right )} e^{2} - {\left (4 \, x^{2} + 4 \, x + 1\right )} e^{\left (2 \, x - \frac {2 \, {\left (4 \, {\left (4 \, x^{4} + 4 \, x^{3} - 19 \, x^{2} - 10 \, x + 25\right )} e^{2} - {\left (4 \, x^{3} + 4 \, x^{2} + x\right )} e^{\left (2 \, x + 4\right )}\right )} e^{\left (-2 \, x - 2\right )}}{4 \, x^{2} + 4 \, x + 1} + 2\right )} + 2 \, {\left (4 \, x^{3} + 4 \, x^{2} - {\left (4 \, x^{3} + 4 \, x^{2} + x\right )} e^{2} + x\right )} e^{\left (2 \, x + 2\right )}\right )} e^{\left (-2 \, x - 2\right )}}{4 \, x^{2} + 4 \, x + 1} + \frac {2 \, {\left (4 \, {\left (4 \, x^{4} + 4 \, x^{3} - 19 \, x^{2} - 10 \, x + 25\right )} e^{2} - {\left (4 \, x^{3} + 4 \, x^{2} + x\right )} e^{\left (2 \, x + 4\right )}\right )} e^{\left (-2 \, x - 2\right )}}{4 \, x^{2} + 4 \, x + 1}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((16*x^3+24*x^2+12*x+2)*exp(2)*exp(x)^2+128*x^5+64*x^4-736*x^3-720*x^2+784*x+1280)*exp(((4*x^3+4*x^2
+x)*exp(2)*exp(x)^2-16*x^4-16*x^3+76*x^2+40*x-100)/(4*x^2+4*x+1)/exp(x)^2)^2*exp(exp(((4*x^3+4*x^2+x)*exp(2)*e
xp(x)^2-16*x^4-16*x^3+76*x^2+40*x-100)/(4*x^2+4*x+1)/exp(x)^2)^2)/(8*x^3+12*x^2+6*x+1)/exp(x)^2,x, algorithm="
fricas")

[Out]

e^(2*x - (8*(4*x^4 + 4*x^3 - 19*x^2 - 10*x + 25)*e^2 - (4*x^2 + 4*x + 1)*e^(2*x - 2*(4*(4*x^4 + 4*x^3 - 19*x^2
- 10*x + 25)*e^2 - (4*x^3 + 4*x^2 + x)*e^(2*x + 4))*e^(-2*x - 2)/(4*x^2 + 4*x + 1) + 2) + 2*(4*x^3 + 4*x^2 -
(4*x^3 + 4*x^2 + x)*e^2 + x)*e^(2*x + 2))*e^(-2*x - 2)/(4*x^2 + 4*x + 1) + 2*(4*(4*x^4 + 4*x^3 - 19*x^2 - 10*x
+ 25)*e^2 - (4*x^3 + 4*x^2 + x)*e^(2*x + 4))*e^(-2*x - 2)/(4*x^2 + 4*x + 1))

________________________________________________________________________________________

giac [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {2 \, {\left (64 \, x^{5} + 32 \, x^{4} - 368 \, x^{3} - 360 \, x^{2} + {\left (8 \, x^{3} + 12 \, x^{2} + 6 \, x + 1\right )} e^{\left (2 \, x + 2\right )} + 392 \, x + 640\right )} e^{\left (-2 \, x - \frac {2 \, {\left (16 \, x^{4} + 16 \, x^{3} - 76 \, x^{2} - {\left (4 \, x^{3} + 4 \, x^{2} + x\right )} e^{\left (2 \, x + 2\right )} - 40 \, x + 100\right )} e^{\left (-2 \, x\right )}}{4 \, x^{2} + 4 \, x + 1} + e^{\left (-\frac {2 \, {\left (16 \, x^{4} + 16 \, x^{3} - 76 \, x^{2} - {\left (4 \, x^{3} + 4 \, x^{2} + x\right )} e^{\left (2 \, x + 2\right )} - 40 \, x + 100\right )} e^{\left (-2 \, x\right )}}{4 \, x^{2} + 4 \, x + 1}\right )}\right )}}{8 \, x^{3} + 12 \, x^{2} + 6 \, x + 1}\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((16*x^3+24*x^2+12*x+2)*exp(2)*exp(x)^2+128*x^5+64*x^4-736*x^3-720*x^2+784*x+1280)*exp(((4*x^3+4*x^2
+x)*exp(2)*exp(x)^2-16*x^4-16*x^3+76*x^2+40*x-100)/(4*x^2+4*x+1)/exp(x)^2)^2*exp(exp(((4*x^3+4*x^2+x)*exp(2)*e
xp(x)^2-16*x^4-16*x^3+76*x^2+40*x-100)/(4*x^2+4*x+1)/exp(x)^2)^2)/(8*x^3+12*x^2+6*x+1)/exp(x)^2,x, algorithm="
giac")

[Out]

integrate(2*(64*x^5 + 32*x^4 - 368*x^3 - 360*x^2 + (8*x^3 + 12*x^2 + 6*x + 1)*e^(2*x + 2) + 392*x + 640)*e^(-2
*x - 2*(16*x^4 + 16*x^3 - 76*x^2 - (4*x^3 + 4*x^2 + x)*e^(2*x + 2) - 40*x + 100)*e^(-2*x)/(4*x^2 + 4*x + 1) +
e^(-2*(16*x^4 + 16*x^3 - 76*x^2 - (4*x^3 + 4*x^2 + x)*e^(2*x + 2) - 40*x + 100)*e^(-2*x)/(4*x^2 + 4*x + 1)))/(
8*x^3 + 12*x^2 + 6*x + 1), x)

________________________________________________________________________________________

maple [B]  time = 0.32, size = 67, normalized size = 2.16

method	result	size
risch	\({\mathrm e}^{{\mathrm e}^{-\frac {2 \left (-4 x^{3} {\mathrm e}^{2 x +2}+16 x^{4}-4 x^{2} {\mathrm e}^{2 x +2}+16 x^{3}-x \,{\mathrm e}^{2 x +2}-76 x^{2}-40 x +100\right ) {\mathrm e}^{-2 x}}{\left (2 x +1\right )^{2}}}}\)	\(67\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((16*x^3+24*x^2+12*x+2)*exp(2)*exp(x)^2+128*x^5+64*x^4-736*x^3-720*x^2+784*x+1280)*exp(((4*x^3+4*x^2+x)*ex
p(2)*exp(x)^2-16*x^4-16*x^3+76*x^2+40*x-100)/(4*x^2+4*x+1)/exp(x)^2)^2*exp(exp(((4*x^3+4*x^2+x)*exp(2)*exp(x)^
2-16*x^4-16*x^3+76*x^2+40*x-100)/(4*x^2+4*x+1)/exp(x)^2)^2)/(8*x^3+12*x^2+6*x+1)/exp(x)^2,x,method=_RETURNVERB
OSE)

[Out]

exp(exp(-2*(-4*x^3*exp(2*x+2)+16*x^4-4*x^2*exp(2*x+2)+16*x^3-x*exp(2*x+2)-76*x^2-40*x+100)*exp(-2*x)/(2*x+1)^2
))

________________________________________________________________________________________

maxima [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(((16*x^3+24*x^2+12*x+2)*exp(2)*exp(x)^2+128*x^5+64*x^4-736*x^3-720*x^2+784*x+1280)*exp(((4*x^3+4*x^2
+x)*exp(2)*exp(x)^2-16*x^4-16*x^3+76*x^2+40*x-100)/(4*x^2+4*x+1)/exp(x)^2)^2*exp(exp(((4*x^3+4*x^2+x)*exp(2)*e
xp(x)^2-16*x^4-16*x^3+76*x^2+40*x-100)/(4*x^2+4*x+1)/exp(x)^2)^2)/(8*x^3+12*x^2+6*x+1)/exp(x)^2,x, algorithm="
maxima")

[Out]

Timed out

________________________________________________________________________________________

mupad [B]  time = 1.83, size = 165, normalized size = 5.32 \begin {gather*} {\mathrm {e}}^{{\mathrm {e}}^{\frac {80\,x\,{\mathrm {e}}^{-2\,x}}{4\,x^2+4\,x+1}}\,{\mathrm {e}}^{\frac {2\,x\,{\mathrm {e}}^2}{4\,x^2+4\,x+1}}\,{\mathrm {e}}^{-\frac {32\,x^3\,{\mathrm {e}}^{-2\,x}}{4\,x^2+4\,x+1}}\,{\mathrm {e}}^{-\frac {32\,x^4\,{\mathrm {e}}^{-2\,x}}{4\,x^2+4\,x+1}}\,{\mathrm {e}}^{\frac {152\,x^2\,{\mathrm {e}}^{-2\,x}}{4\,x^2+4\,x+1}}\,{\mathrm {e}}^{-\frac {200\,{\mathrm {e}}^{-2\,x}}{4\,x^2+4\,x+1}}\,{\mathrm {e}}^{\frac {8\,x^2\,{\mathrm {e}}^2}{4\,x^2+4\,x+1}}\,{\mathrm {e}}^{\frac {8\,x^3\,{\mathrm {e}}^2}{4\,x^2+4\,x+1}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(-2*x)*exp(exp((2*exp(-2*x)*(40*x + 76*x^2 - 16*x^3 - 16*x^4 + exp(2*x)*exp(2)*(x + 4*x^2 + 4*x^3) - 1
00))/(4*x + 4*x^2 + 1)))*exp((2*exp(-2*x)*(40*x + 76*x^2 - 16*x^3 - 16*x^4 + exp(2*x)*exp(2)*(x + 4*x^2 + 4*x^
3) - 100))/(4*x + 4*x^2 + 1))*(784*x - 720*x^2 - 736*x^3 + 64*x^4 + 128*x^5 + exp(2*x)*exp(2)*(12*x + 24*x^2 +
16*x^3 + 2) + 1280))/(6*x + 12*x^2 + 8*x^3 + 1),x)

[Out]

exp(exp((80*x*exp(-2*x))/(4*x + 4*x^2 + 1))*exp((2*x*exp(2))/(4*x + 4*x^2 + 1))*exp(-(32*x^3*exp(-2*x))/(4*x +
4*x^2 + 1))*exp(-(32*x^4*exp(-2*x))/(4*x + 4*x^2 + 1))*exp((152*x^2*exp(-2*x))/(4*x + 4*x^2 + 1))*exp(-(200*e
xp(-2*x))/(4*x + 4*x^2 + 1))*exp((8*x^2*exp(2))/(4*x + 4*x^2 + 1))*exp((8*x^3*exp(2))/(4*x + 4*x^2 + 1)))

________________________________________________________________________________________

sympy [B]  time = 3.82, size = 60, normalized size = 1.94 \begin {gather*} e^{e^{\frac {2 \left (- 16 x^{4} - 16 x^{3} + 76 x^{2} + 40 x + \left (4 x^{3} + 4 x^{2} + x\right ) e^{2} e^{2 x} - 100\right ) e^{- 2 x}}{4 x^{2} + 4 x + 1}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((16*x**3+24*x**2+12*x+2)*exp(2)*exp(x)**2+128*x**5+64*x**4-736*x**3-720*x**2+784*x+1280)*exp(((4*x*
*3+4*x**2+x)*exp(2)*exp(x)**2-16*x**4-16*x**3+76*x**2+40*x-100)/(4*x**2+4*x+1)/exp(x)**2)**2*exp(exp(((4*x**3+
4*x**2+x)*exp(2)*exp(x)**2-16*x**4-16*x**3+76*x**2+40*x-100)/(4*x**2+4*x+1)/exp(x)**2)**2)/(8*x**3+12*x**2+6*x
+1)/exp(x)**2,x)

[Out]

exp(exp(2*(-16*x**4 - 16*x**3 + 76*x**2 + 40*x + (4*x**3 + 4*x**2 + x)*exp(2)*exp(2*x) - 100)*exp(-2*x)/(4*x**
2 + 4*x + 1)))

________________________________________________________________________________________