3.12.50 \(\int \frac {e^{e^{\frac {900+3960 x+1476 x^2+144 x^3+e^x (480 x^3+216 x^4+24 x^5)+e^{2 x} (16 x^5+8 x^6+x^7)}{225+90 x+9 x^2}}+\frac {900+3960 x+1476 x^2+144 x^3+e^x (480 x^3+216 x^4+24 x^5)+e^{2 x} (16 x^5+8 x^6+x^7)}{225+90 x+9 x^2}} (18000+10800 x+2160 x^2+144 x^3+e^x (7200 x^2+7200 x^3+2592 x^4+408 x^5+24 x^6)+e^{2 x} (400 x^4+448 x^5+179 x^6+31 x^7+2 x^8))}{1125+675 x+135 x^2+9 x^3} \, dx\)

Optimal. Leaf size=30 \[ e^{e^{4+x \left (4+\frac {e^x x^2}{3+\frac {3}{4+x}}\right )^2}} \]

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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^((900 + 3960*x + 1476*x^2 + 144*x^3 + E^x*(480*x^3 + 216*x^4 + 24*x^5) + E^(2*x)*(16*x^5 + 8*x^6 + x
^7))/(225 + 90*x + 9*x^2)) + (900 + 3960*x + 1476*x^2 + 144*x^3 + E^x*(480*x^3 + 216*x^4 + 24*x^5) + E^(2*x)*(
16*x^5 + 8*x^6 + x^7))/(225 + 90*x + 9*x^2))*(18000 + 10800*x + 2160*x^2 + 144*x^3 + E^x*(7200*x^2 + 7200*x^3
+ 2592*x^4 + 408*x^5 + 24*x^6) + E^(2*x)*(400*x^4 + 448*x^5 + 179*x^6 + 31*x^7 + 2*x^8)))/(1125 + 675*x + 135*
x^2 + 9*x^3),x]

[Out]

$Aborted

Rubi steps

Aborted

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Mathematica [A]  time = 1.93, size = 49, normalized size = 1.63 \begin {gather*} e^{e^{4+16 x+\frac {e^{2 x} x^5 (4+x)^2}{9 (5+x)^2}+\frac {8 e^x x^3 (4+x)}{3 (5+x)}}} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^(E^((900 + 3960*x + 1476*x^2 + 144*x^3 + E^x*(480*x^3 + 216*x^4 + 24*x^5) + E^(2*x)*(16*x^5 + 8*x
^6 + x^7))/(225 + 90*x + 9*x^2)) + (900 + 3960*x + 1476*x^2 + 144*x^3 + E^x*(480*x^3 + 216*x^4 + 24*x^5) + E^(
2*x)*(16*x^5 + 8*x^6 + x^7))/(225 + 90*x + 9*x^2))*(18000 + 10800*x + 2160*x^2 + 144*x^3 + E^x*(7200*x^2 + 720
0*x^3 + 2592*x^4 + 408*x^5 + 24*x^6) + E^(2*x)*(400*x^4 + 448*x^5 + 179*x^6 + 31*x^7 + 2*x^8)))/(1125 + 675*x
+ 135*x^2 + 9*x^3),x]

[Out]

E^E^(4 + 16*x + (E^(2*x)*x^5*(4 + x)^2)/(9*(5 + x)^2) + (8*E^x*x^3*(4 + x))/(3*(5 + x)))

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fricas [B]  time = 0.56, size = 205, normalized size = 6.83 \begin {gather*} e^{\left (\frac {144 \, x^{3} + 1476 \, x^{2} + {\left (x^{7} + 8 \, x^{6} + 16 \, x^{5}\right )} e^{\left (2 \, x\right )} + 24 \, {\left (x^{5} + 9 \, x^{4} + 20 \, x^{3}\right )} e^{x} + 9 \, {\left (x^{2} + 10 \, x + 25\right )} e^{\left (\frac {144 \, x^{3} + 1476 \, x^{2} + {\left (x^{7} + 8 \, x^{6} + 16 \, x^{5}\right )} e^{\left (2 \, x\right )} + 24 \, {\left (x^{5} + 9 \, x^{4} + 20 \, x^{3}\right )} e^{x} + 3960 \, x + 900}{9 \, {\left (x^{2} + 10 \, x + 25\right )}}\right )} + 3960 \, x + 900}{9 \, {\left (x^{2} + 10 \, x + 25\right )}} - \frac {144 \, x^{3} + 1476 \, x^{2} + {\left (x^{7} + 8 \, x^{6} + 16 \, x^{5}\right )} e^{\left (2 \, x\right )} + 24 \, {\left (x^{5} + 9 \, x^{4} + 20 \, x^{3}\right )} e^{x} + 3960 \, x + 900}{9 \, {\left (x^{2} + 10 \, x + 25\right )}}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((2*x^8+31*x^7+179*x^6+448*x^5+400*x^4)*exp(x)^2+(24*x^6+408*x^5+2592*x^4+7200*x^3+7200*x^2)*exp(x)+
144*x^3+2160*x^2+10800*x+18000)*exp(((x^7+8*x^6+16*x^5)*exp(x)^2+(24*x^5+216*x^4+480*x^3)*exp(x)+144*x^3+1476*
x^2+3960*x+900)/(9*x^2+90*x+225))*exp(exp(((x^7+8*x^6+16*x^5)*exp(x)^2+(24*x^5+216*x^4+480*x^3)*exp(x)+144*x^3
+1476*x^2+3960*x+900)/(9*x^2+90*x+225)))/(9*x^3+135*x^2+675*x+1125),x, algorithm="fricas")

[Out]

e^(1/9*(144*x^3 + 1476*x^2 + (x^7 + 8*x^6 + 16*x^5)*e^(2*x) + 24*(x^5 + 9*x^4 + 20*x^3)*e^x + 9*(x^2 + 10*x +
25)*e^(1/9*(144*x^3 + 1476*x^2 + (x^7 + 8*x^6 + 16*x^5)*e^(2*x) + 24*(x^5 + 9*x^4 + 20*x^3)*e^x + 3960*x + 900
)/(x^2 + 10*x + 25)) + 3960*x + 900)/(x^2 + 10*x + 25) - 1/9*(144*x^3 + 1476*x^2 + (x^7 + 8*x^6 + 16*x^5)*e^(2
*x) + 24*(x^5 + 9*x^4 + 20*x^3)*e^x + 3960*x + 900)/(x^2 + 10*x + 25))

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giac [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {{\left (144 \, x^{3} + 2160 \, x^{2} + {\left (2 \, x^{8} + 31 \, x^{7} + 179 \, x^{6} + 448 \, x^{5} + 400 \, x^{4}\right )} e^{\left (2 \, x\right )} + 24 \, {\left (x^{6} + 17 \, x^{5} + 108 \, x^{4} + 300 \, x^{3} + 300 \, x^{2}\right )} e^{x} + 10800 \, x + 18000\right )} e^{\left (\frac {144 \, x^{3} + 1476 \, x^{2} + {\left (x^{7} + 8 \, x^{6} + 16 \, x^{5}\right )} e^{\left (2 \, x\right )} + 24 \, {\left (x^{5} + 9 \, x^{4} + 20 \, x^{3}\right )} e^{x} + 3960 \, x + 900}{9 \, {\left (x^{2} + 10 \, x + 25\right )}} + e^{\left (\frac {144 \, x^{3} + 1476 \, x^{2} + {\left (x^{7} + 8 \, x^{6} + 16 \, x^{5}\right )} e^{\left (2 \, x\right )} + 24 \, {\left (x^{5} + 9 \, x^{4} + 20 \, x^{3}\right )} e^{x} + 3960 \, x + 900}{9 \, {\left (x^{2} + 10 \, x + 25\right )}}\right )}\right )}}{9 \, {\left (x^{3} + 15 \, x^{2} + 75 \, x + 125\right )}}\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((2*x^8+31*x^7+179*x^6+448*x^5+400*x^4)*exp(x)^2+(24*x^6+408*x^5+2592*x^4+7200*x^3+7200*x^2)*exp(x)+
144*x^3+2160*x^2+10800*x+18000)*exp(((x^7+8*x^6+16*x^5)*exp(x)^2+(24*x^5+216*x^4+480*x^3)*exp(x)+144*x^3+1476*
x^2+3960*x+900)/(9*x^2+90*x+225))*exp(exp(((x^7+8*x^6+16*x^5)*exp(x)^2+(24*x^5+216*x^4+480*x^3)*exp(x)+144*x^3
+1476*x^2+3960*x+900)/(9*x^2+90*x+225)))/(9*x^3+135*x^2+675*x+1125),x, algorithm="giac")

[Out]

integrate(1/9*(144*x^3 + 2160*x^2 + (2*x^8 + 31*x^7 + 179*x^6 + 448*x^5 + 400*x^4)*e^(2*x) + 24*(x^6 + 17*x^5
+ 108*x^4 + 300*x^3 + 300*x^2)*e^x + 10800*x + 18000)*e^(1/9*(144*x^3 + 1476*x^2 + (x^7 + 8*x^6 + 16*x^5)*e^(2
*x) + 24*(x^5 + 9*x^4 + 20*x^3)*e^x + 3960*x + 900)/(x^2 + 10*x + 25) + e^(1/9*(144*x^3 + 1476*x^2 + (x^7 + 8*
x^6 + 16*x^5)*e^(2*x) + 24*(x^5 + 9*x^4 + 20*x^3)*e^x + 3960*x + 900)/(x^2 + 10*x + 25)))/(x^3 + 15*x^2 + 75*x
+ 125), x)

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maple [B]  time = 0.34, size = 72, normalized size = 2.40

method	result	size
risch	\({\mathrm e}^{{\mathrm e}^{\frac {{\mathrm e}^{2 x} x^{7}+8 \,{\mathrm e}^{2 x} x^{6}+16 x^{5} {\mathrm e}^{2 x}+24 x^{5} {\mathrm e}^{x}+216 \,{\mathrm e}^{x} x^{4}+480 \,{\mathrm e}^{x} x^{3}+144 x^{3}+1476 x^{2}+3960 x +900}{9 \left (5+x \right )^{2}}}}\)	\(72\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((2*x^8+31*x^7+179*x^6+448*x^5+400*x^4)*exp(x)^2+(24*x^6+408*x^5+2592*x^4+7200*x^3+7200*x^2)*exp(x)+144*x^
3+2160*x^2+10800*x+18000)*exp(((x^7+8*x^6+16*x^5)*exp(x)^2+(24*x^5+216*x^4+480*x^3)*exp(x)+144*x^3+1476*x^2+39
60*x+900)/(9*x^2+90*x+225))*exp(exp(((x^7+8*x^6+16*x^5)*exp(x)^2+(24*x^5+216*x^4+480*x^3)*exp(x)+144*x^3+1476*
x^2+3960*x+900)/(9*x^2+90*x+225)))/(9*x^3+135*x^2+675*x+1125),x,method=_RETURNVERBOSE)

[Out]

exp(exp(1/9*(exp(2*x)*x^7+8*exp(2*x)*x^6+16*x^5*exp(2*x)+24*x^5*exp(x)+216*exp(x)*x^4+480*exp(x)*x^3+144*x^3+1
476*x^2+3960*x+900)/(5+x)^2))

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maxima [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \frac {1}{9} \, \int \frac {{\left (144 \, x^{3} + 2160 \, x^{2} + {\left (2 \, x^{8} + 31 \, x^{7} + 179 \, x^{6} + 448 \, x^{5} + 400 \, x^{4}\right )} e^{\left (2 \, x\right )} + 24 \, {\left (x^{6} + 17 \, x^{5} + 108 \, x^{4} + 300 \, x^{3} + 300 \, x^{2}\right )} e^{x} + 10800 \, x + 18000\right )} e^{\left (\frac {144 \, x^{3} + 1476 \, x^{2} + {\left (x^{7} + 8 \, x^{6} + 16 \, x^{5}\right )} e^{\left (2 \, x\right )} + 24 \, {\left (x^{5} + 9 \, x^{4} + 20 \, x^{3}\right )} e^{x} + 3960 \, x + 900}{9 \, {\left (x^{2} + 10 \, x + 25\right )}} + e^{\left (\frac {144 \, x^{3} + 1476 \, x^{2} + {\left (x^{7} + 8 \, x^{6} + 16 \, x^{5}\right )} e^{\left (2 \, x\right )} + 24 \, {\left (x^{5} + 9 \, x^{4} + 20 \, x^{3}\right )} e^{x} + 3960 \, x + 900}{9 \, {\left (x^{2} + 10 \, x + 25\right )}}\right )}\right )}}{x^{3} + 15 \, x^{2} + 75 \, x + 125}\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((2*x^8+31*x^7+179*x^6+448*x^5+400*x^4)*exp(x)^2+(24*x^6+408*x^5+2592*x^4+7200*x^3+7200*x^2)*exp(x)+
144*x^3+2160*x^2+10800*x+18000)*exp(((x^7+8*x^6+16*x^5)*exp(x)^2+(24*x^5+216*x^4+480*x^3)*exp(x)+144*x^3+1476*
x^2+3960*x+900)/(9*x^2+90*x+225))*exp(exp(((x^7+8*x^6+16*x^5)*exp(x)^2+(24*x^5+216*x^4+480*x^3)*exp(x)+144*x^3
+1476*x^2+3960*x+900)/(9*x^2+90*x+225)))/(9*x^3+135*x^2+675*x+1125),x, algorithm="maxima")

[Out]

1/9*integrate((144*x^3 + 2160*x^2 + (2*x^8 + 31*x^7 + 179*x^6 + 448*x^5 + 400*x^4)*e^(2*x) + 24*(x^6 + 17*x^5
+ 108*x^4 + 300*x^3 + 300*x^2)*e^x + 10800*x + 18000)*e^(1/9*(144*x^3 + 1476*x^2 + (x^7 + 8*x^6 + 16*x^5)*e^(2
*x) + 24*(x^5 + 9*x^4 + 20*x^3)*e^x + 3960*x + 900)/(x^2 + 10*x + 25) + e^(1/9*(144*x^3 + 1476*x^2 + (x^7 + 8*
x^6 + 16*x^5)*e^(2*x) + 24*(x^5 + 9*x^4 + 20*x^3)*e^x + 3960*x + 900)/(x^2 + 10*x + 25)))/(x^3 + 15*x^2 + 75*x
+ 125), x)

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mupad [B]  time = 0.92, size = 184, normalized size = 6.13 \begin {gather*} {\mathrm {e}}^{{\mathrm {e}}^{\frac {16\,x^3}{x^2+10\,x+25}}\,{\mathrm {e}}^{\frac {164\,x^2}{x^2+10\,x+25}}\,{\mathrm {e}}^{\frac {100}{x^2+10\,x+25}}\,{\mathrm {e}}^{\frac {8\,x^5\,{\mathrm {e}}^x}{3\,x^2+30\,x+75}}\,{\mathrm {e}}^{\frac {160\,x^3\,{\mathrm {e}}^x}{3\,x^2+30\,x+75}}\,{\mathrm {e}}^{\frac {x^7\,{\mathrm {e}}^{2\,x}}{9\,x^2+90\,x+225}}\,{\mathrm {e}}^{\frac {8\,x^6\,{\mathrm {e}}^{2\,x}}{9\,x^2+90\,x+225}}\,{\mathrm {e}}^{\frac {16\,x^5\,{\mathrm {e}}^{2\,x}}{9\,x^2+90\,x+225}}\,{\mathrm {e}}^{\frac {440\,x}{x^2+10\,x+25}}\,{\mathrm {e}}^{\frac {24\,x^4\,{\mathrm {e}}^x}{x^2+10\,x+25}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(exp((3960*x + exp(2*x)*(16*x^5 + 8*x^6 + x^7) + exp(x)*(480*x^3 + 216*x^4 + 24*x^5) + 1476*x^2 + 144*
x^3 + 900)/(90*x + 9*x^2 + 225)))*exp((3960*x + exp(2*x)*(16*x^5 + 8*x^6 + x^7) + exp(x)*(480*x^3 + 216*x^4 +
24*x^5) + 1476*x^2 + 144*x^3 + 900)/(90*x + 9*x^2 + 225))*(10800*x + exp(2*x)*(400*x^4 + 448*x^5 + 179*x^6 + 3
1*x^7 + 2*x^8) + exp(x)*(7200*x^2 + 7200*x^3 + 2592*x^4 + 408*x^5 + 24*x^6) + 2160*x^2 + 144*x^3 + 18000))/(67
5*x + 135*x^2 + 9*x^3 + 1125),x)

[Out]

exp(exp((16*x^3)/(10*x + x^2 + 25))*exp((164*x^2)/(10*x + x^2 + 25))*exp(100/(10*x + x^2 + 25))*exp((8*x^5*exp
(x))/(30*x + 3*x^2 + 75))*exp((160*x^3*exp(x))/(30*x + 3*x^2 + 75))*exp((x^7*exp(2*x))/(90*x + 9*x^2 + 225))*e
xp((8*x^6*exp(2*x))/(90*x + 9*x^2 + 225))*exp((16*x^5*exp(2*x))/(90*x + 9*x^2 + 225))*exp((440*x)/(10*x + x^2
+ 25))*exp((24*x^4*exp(x))/(10*x + x^2 + 25)))

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sympy [B]  time = 10.41, size = 65, normalized size = 2.17 \begin {gather*} e^{e^{\frac {144 x^{3} + 1476 x^{2} + 3960 x + \left (24 x^{5} + 216 x^{4} + 480 x^{3}\right ) e^{x} + \left (x^{7} + 8 x^{6} + 16 x^{5}\right ) e^{2 x} + 900}{9 x^{2} + 90 x + 225}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((2*x**8+31*x**7+179*x**6+448*x**5+400*x**4)*exp(x)**2+(24*x**6+408*x**5+2592*x**4+7200*x**3+7200*x*
*2)*exp(x)+144*x**3+2160*x**2+10800*x+18000)*exp(((x**7+8*x**6+16*x**5)*exp(x)**2+(24*x**5+216*x**4+480*x**3)*
exp(x)+144*x**3+1476*x**2+3960*x+900)/(9*x**2+90*x+225))*exp(exp(((x**7+8*x**6+16*x**5)*exp(x)**2+(24*x**5+216
*x**4+480*x**3)*exp(x)+144*x**3+1476*x**2+3960*x+900)/(9*x**2+90*x+225)))/(9*x**3+135*x**2+675*x+1125),x)

[Out]

exp(exp((144*x**3 + 1476*x**2 + 3960*x + (24*x**5 + 216*x**4 + 480*x**3)*exp(x) + (x**7 + 8*x**6 + 16*x**5)*ex
p(2*x) + 900)/(9*x**2 + 90*x + 225)))

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