3.53.55 \(\int \frac {e^{e^{\frac {153-24 x+x^2-120 x^3+10 x^4+25 x^6+e^{10} (17-16 x+4 x^2)+e^5 (-102+56 x-4 x^2+40 x^3-20 x^4)}{9 x-6 e^5 x+e^{10} x}}+\frac {153-24 x+x^2-120 x^3+10 x^4+25 x^6+e^{10} (17-16 x+4 x^2)+e^5 (-102+56 x-4 x^2+40 x^3-20 x^4)}{9 x-6 e^5 x+e^{10} x}} (-153+x^2-240 x^3+30 x^4+125 x^6+e^{10} (-17+4 x^2)+e^5 (102-4 x^2+80 x^3-60 x^4))}{9 x^2-6 e^5 x^2+e^{10} x^2} \, dx\)

Optimal. Leaf size=33 \[ e^{e^{\frac {1+\left (-4+2 x-\frac {5 \left (-x+x^3\right )}{-3+e^5}\right )^2}{x}}} \]

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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^((153 - 24*x + x^2 - 120*x^3 + 10*x^4 + 25*x^6 + E^10*(17 - 16*x + 4*x^2) + E^5*(-102 + 56*x - 4*x^2
+ 40*x^3 - 20*x^4))/(9*x - 6*E^5*x + E^10*x)) + (153 - 24*x + x^2 - 120*x^3 + 10*x^4 + 25*x^6 + E^10*(17 - 16
*x + 4*x^2) + E^5*(-102 + 56*x - 4*x^2 + 40*x^3 - 20*x^4))/(9*x - 6*E^5*x + E^10*x))*(-153 + x^2 - 240*x^3 + 3
0*x^4 + 125*x^6 + E^10*(-17 + 4*x^2) + E^5*(102 - 4*x^2 + 80*x^3 - 60*x^4)))/(9*x^2 - 6*E^5*x^2 + E^10*x^2),x]

[Out]

$Aborted

Rubi steps

Aborted

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Mathematica [B]  time = 1.83, size = 77, normalized size = 2.33 \begin {gather*} e^{e^{\frac {153-24 x+x^2-120 x^3+10 x^4+25 x^6+e^{10} \left (17-16 x+4 x^2\right )-2 e^5 \left (51-28 x+2 x^2-20 x^3+10 x^4\right )}{\left (-3+e^5\right )^2 x}}} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^(E^((153 - 24*x + x^2 - 120*x^3 + 10*x^4 + 25*x^6 + E^10*(17 - 16*x + 4*x^2) + E^5*(-102 + 56*x -
4*x^2 + 40*x^3 - 20*x^4))/(9*x - 6*E^5*x + E^10*x)) + (153 - 24*x + x^2 - 120*x^3 + 10*x^4 + 25*x^6 + E^10*(1
7 - 16*x + 4*x^2) + E^5*(-102 + 56*x - 4*x^2 + 40*x^3 - 20*x^4))/(9*x - 6*E^5*x + E^10*x))*(-153 + x^2 - 240*x
^3 + 30*x^4 + 125*x^6 + E^10*(-17 + 4*x^2) + E^5*(102 - 4*x^2 + 80*x^3 - 60*x^4)))/(9*x^2 - 6*E^5*x^2 + E^10*x
^2),x]

[Out]

E^E^((153 - 24*x + x^2 - 120*x^3 + 10*x^4 + 25*x^6 + E^10*(17 - 16*x + 4*x^2) - 2*E^5*(51 - 28*x + 2*x^2 - 20*
x^3 + 10*x^4))/((-3 + E^5)^2*x))

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fricas [B]  time = 0.60, size = 246, normalized size = 7.45 \begin {gather*} e^{\left (\frac {25 \, x^{6} + 10 \, x^{4} - 120 \, x^{3} + x^{2} + {\left (4 \, x^{2} - 16 \, x + 17\right )} e^{10} - 2 \, {\left (10 \, x^{4} - 20 \, x^{3} + 2 \, x^{2} - 28 \, x + 51\right )} e^{5} + {\left (x e^{10} - 6 \, x e^{5} + 9 \, x\right )} e^{\left (\frac {25 \, x^{6} + 10 \, x^{4} - 120 \, x^{3} + x^{2} + {\left (4 \, x^{2} - 16 \, x + 17\right )} e^{10} - 2 \, {\left (10 \, x^{4} - 20 \, x^{3} + 2 \, x^{2} - 28 \, x + 51\right )} e^{5} - 24 \, x + 153}{x e^{10} - 6 \, x e^{5} + 9 \, x}\right )} - 24 \, x + 153}{x e^{10} - 6 \, x e^{5} + 9 \, x} - \frac {25 \, x^{6} + 10 \, x^{4} - 120 \, x^{3} + x^{2} + {\left (4 \, x^{2} - 16 \, x + 17\right )} e^{10} - 2 \, {\left (10 \, x^{4} - 20 \, x^{3} + 2 \, x^{2} - 28 \, x + 51\right )} e^{5} - 24 \, x + 153}{x e^{10} - 6 \, x e^{5} + 9 \, x}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((4*x^2-17)*exp(5)^2+(-60*x^4+80*x^3-4*x^2+102)*exp(5)+125*x^6+30*x^4-240*x^3+x^2-153)*exp(((4*x^2-1
6*x+17)*exp(5)^2+(-20*x^4+40*x^3-4*x^2+56*x-102)*exp(5)+25*x^6+10*x^4-120*x^3+x^2-24*x+153)/(x*exp(5)^2-6*x*ex
p(5)+9*x))*exp(exp(((4*x^2-16*x+17)*exp(5)^2+(-20*x^4+40*x^3-4*x^2+56*x-102)*exp(5)+25*x^6+10*x^4-120*x^3+x^2-
24*x+153)/(x*exp(5)^2-6*x*exp(5)+9*x)))/(x^2*exp(5)^2-6*x^2*exp(5)+9*x^2),x, algorithm="fricas")

[Out]

e^((25*x^6 + 10*x^4 - 120*x^3 + x^2 + (4*x^2 - 16*x + 17)*e^10 - 2*(10*x^4 - 20*x^3 + 2*x^2 - 28*x + 51)*e^5 +
(x*e^10 - 6*x*e^5 + 9*x)*e^((25*x^6 + 10*x^4 - 120*x^3 + x^2 + (4*x^2 - 16*x + 17)*e^10 - 2*(10*x^4 - 20*x^3
+ 2*x^2 - 28*x + 51)*e^5 - 24*x + 153)/(x*e^10 - 6*x*e^5 + 9*x)) - 24*x + 153)/(x*e^10 - 6*x*e^5 + 9*x) - (25*
x^6 + 10*x^4 - 120*x^3 + x^2 + (4*x^2 - 16*x + 17)*e^10 - 2*(10*x^4 - 20*x^3 + 2*x^2 - 28*x + 51)*e^5 - 24*x +
153)/(x*e^10 - 6*x*e^5 + 9*x))

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giac [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {{\left (125 \, x^{6} + 30 \, x^{4} - 240 \, x^{3} + x^{2} + {\left (4 \, x^{2} - 17\right )} e^{10} - 2 \, {\left (30 \, x^{4} - 40 \, x^{3} + 2 \, x^{2} - 51\right )} e^{5} - 153\right )} e^{\left (\frac {25 \, x^{6} + 10 \, x^{4} - 120 \, x^{3} + x^{2} + {\left (4 \, x^{2} - 16 \, x + 17\right )} e^{10} - 2 \, {\left (10 \, x^{4} - 20 \, x^{3} + 2 \, x^{2} - 28 \, x + 51\right )} e^{5} - 24 \, x + 153}{x e^{10} - 6 \, x e^{5} + 9 \, x} + e^{\left (\frac {25 \, x^{6} + 10 \, x^{4} - 120 \, x^{3} + x^{2} + {\left (4 \, x^{2} - 16 \, x + 17\right )} e^{10} - 2 \, {\left (10 \, x^{4} - 20 \, x^{3} + 2 \, x^{2} - 28 \, x + 51\right )} e^{5} - 24 \, x + 153}{x e^{10} - 6 \, x e^{5} + 9 \, x}\right )}\right )}}{x^{2} e^{10} - 6 \, x^{2} e^{5} + 9 \, x^{2}}\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((4*x^2-17)*exp(5)^2+(-60*x^4+80*x^3-4*x^2+102)*exp(5)+125*x^6+30*x^4-240*x^3+x^2-153)*exp(((4*x^2-1
6*x+17)*exp(5)^2+(-20*x^4+40*x^3-4*x^2+56*x-102)*exp(5)+25*x^6+10*x^4-120*x^3+x^2-24*x+153)/(x*exp(5)^2-6*x*ex
p(5)+9*x))*exp(exp(((4*x^2-16*x+17)*exp(5)^2+(-20*x^4+40*x^3-4*x^2+56*x-102)*exp(5)+25*x^6+10*x^4-120*x^3+x^2-
24*x+153)/(x*exp(5)^2-6*x*exp(5)+9*x)))/(x^2*exp(5)^2-6*x^2*exp(5)+9*x^2),x, algorithm="giac")

[Out]

integrate((125*x^6 + 30*x^4 - 240*x^3 + x^2 + (4*x^2 - 17)*e^10 - 2*(30*x^4 - 40*x^3 + 2*x^2 - 51)*e^5 - 153)*
e^((25*x^6 + 10*x^4 - 120*x^3 + x^2 + (4*x^2 - 16*x + 17)*e^10 - 2*(10*x^4 - 20*x^3 + 2*x^2 - 28*x + 51)*e^5 -
24*x + 153)/(x*e^10 - 6*x*e^5 + 9*x) + e^((25*x^6 + 10*x^4 - 120*x^3 + x^2 + (4*x^2 - 16*x + 17)*e^10 - 2*(10
*x^4 - 20*x^3 + 2*x^2 - 28*x + 51)*e^5 - 24*x + 153)/(x*e^10 - 6*x*e^5 + 9*x)))/(x^2*e^10 - 6*x^2*e^5 + 9*x^2)
, x)

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maple [B]  time = 14.04, size = 82, normalized size = 2.48

method	result	size
norman	\({\mathrm e}^{{\mathrm e}^{\frac {\left (4 x^{2}-16 x +17\right ) {\mathrm e}^{10}+\left (-20 x^{4}+40 x^{3}-4 x^{2}+56 x -102\right ) {\mathrm e}^{5}+25 x^{6}+10 x^{4}-120 x^{3}+x^{2}-24 x +153}{x \,{\mathrm e}^{10}-6 x \,{\mathrm e}^{5}+9 x}}}\)	\(82\)
risch	\({\mathrm e}^{{\mathrm e}^{\frac {25 x^{6}-20 x^{4} {\mathrm e}^{5}+40 x^{3} {\mathrm e}^{5}+10 x^{4}-4 x^{2} {\mathrm e}^{5}+4 \,{\mathrm e}^{10} x^{2}-120 x^{3}+56 x \,{\mathrm e}^{5}-16 x \,{\mathrm e}^{10}+x^{2}-102 \,{\mathrm e}^{5}+17 \,{\mathrm e}^{10}-24 x +153}{x \left ({\mathrm e}^{10}-6 \,{\mathrm e}^{5}+9\right )}}}\)	\(86\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((4*x^2-17)*exp(5)^2+(-60*x^4+80*x^3-4*x^2+102)*exp(5)+125*x^6+30*x^4-240*x^3+x^2-153)*exp(((4*x^2-16*x+17
)*exp(5)^2+(-20*x^4+40*x^3-4*x^2+56*x-102)*exp(5)+25*x^6+10*x^4-120*x^3+x^2-24*x+153)/(x*exp(5)^2-6*x*exp(5)+9
*x))*exp(exp(((4*x^2-16*x+17)*exp(5)^2+(-20*x^4+40*x^3-4*x^2+56*x-102)*exp(5)+25*x^6+10*x^4-120*x^3+x^2-24*x+1
53)/(x*exp(5)^2-6*x*exp(5)+9*x)))/(x^2*exp(5)^2-6*x^2*exp(5)+9*x^2),x,method=_RETURNVERBOSE)

[Out]

exp(exp(((4*x^2-16*x+17)*exp(5)^2+(-20*x^4+40*x^3-4*x^2+56*x-102)*exp(5)+25*x^6+10*x^4-120*x^3+x^2-24*x+153)/(
x*exp(5)^2-6*x*exp(5)+9*x)))

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maxima [B]  time = 2.37, size = 213, normalized size = 6.45 \begin {gather*} e^{\left (e^{\left (\frac {25 \, x^{5}}{e^{10} - 6 \, e^{5} + 9} - \frac {20 \, x^{3} e^{5}}{e^{10} - 6 \, e^{5} + 9} + \frac {10 \, x^{3}}{e^{10} - 6 \, e^{5} + 9} + \frac {40 \, x^{2} e^{5}}{e^{10} - 6 \, e^{5} + 9} - \frac {120 \, x^{2}}{e^{10} - 6 \, e^{5} + 9} + \frac {4 \, x e^{10}}{e^{10} - 6 \, e^{5} + 9} - \frac {4 \, x e^{5}}{e^{10} - 6 \, e^{5} + 9} + \frac {x}{e^{10} - 6 \, e^{5} + 9} - \frac {16 \, e^{10}}{e^{10} - 6 \, e^{5} + 9} + \frac {56 \, e^{5}}{e^{10} - 6 \, e^{5} + 9} - \frac {24}{e^{10} - 6 \, e^{5} + 9} + \frac {17 \, e^{10}}{x {\left (e^{10} - 6 \, e^{5} + 9\right )}} - \frac {102 \, e^{5}}{x {\left (e^{10} - 6 \, e^{5} + 9\right )}} + \frac {153}{x {\left (e^{10} - 6 \, e^{5} + 9\right )}}\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((4*x^2-17)*exp(5)^2+(-60*x^4+80*x^3-4*x^2+102)*exp(5)+125*x^6+30*x^4-240*x^3+x^2-153)*exp(((4*x^2-1
6*x+17)*exp(5)^2+(-20*x^4+40*x^3-4*x^2+56*x-102)*exp(5)+25*x^6+10*x^4-120*x^3+x^2-24*x+153)/(x*exp(5)^2-6*x*ex
p(5)+9*x))*exp(exp(((4*x^2-16*x+17)*exp(5)^2+(-20*x^4+40*x^3-4*x^2+56*x-102)*exp(5)+25*x^6+10*x^4-120*x^3+x^2-
24*x+153)/(x*exp(5)^2-6*x*exp(5)+9*x)))/(x^2*exp(5)^2-6*x^2*exp(5)+9*x^2),x, algorithm="maxima")

[Out]

e^(e^(25*x^5/(e^10 - 6*e^5 + 9) - 20*x^3*e^5/(e^10 - 6*e^5 + 9) + 10*x^3/(e^10 - 6*e^5 + 9) + 40*x^2*e^5/(e^10
- 6*e^5 + 9) - 120*x^2/(e^10 - 6*e^5 + 9) + 4*x*e^10/(e^10 - 6*e^5 + 9) - 4*x*e^5/(e^10 - 6*e^5 + 9) + x/(e^1
0 - 6*e^5 + 9) - 16*e^10/(e^10 - 6*e^5 + 9) + 56*e^5/(e^10 - 6*e^5 + 9) - 24/(e^10 - 6*e^5 + 9) + 17*e^10/(x*(
e^10 - 6*e^5 + 9)) - 102*e^5/(x*(e^10 - 6*e^5 + 9)) + 153/(x*(e^10 - 6*e^5 + 9))))

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mupad [B]  time = 5.23, size = 232, normalized size = 7.03 \begin {gather*} {\mathrm {e}}^{{\mathrm {e}}^{-\frac {16\,{\mathrm {e}}^{10}}{{\mathrm {e}}^{10}-6\,{\mathrm {e}}^5+9}}\,{\mathrm {e}}^{\frac {56\,{\mathrm {e}}^5}{{\mathrm {e}}^{10}-6\,{\mathrm {e}}^5+9}}\,{\mathrm {e}}^{\frac {x}{{\mathrm {e}}^{10}-6\,{\mathrm {e}}^5+9}}\,{\mathrm {e}}^{\frac {17\,{\mathrm {e}}^{10}}{9\,x-6\,x\,{\mathrm {e}}^5+x\,{\mathrm {e}}^{10}}}\,{\mathrm {e}}^{-\frac {102\,{\mathrm {e}}^5}{9\,x-6\,x\,{\mathrm {e}}^5+x\,{\mathrm {e}}^{10}}}\,{\mathrm {e}}^{\frac {10\,x^3}{{\mathrm {e}}^{10}-6\,{\mathrm {e}}^5+9}}\,{\mathrm {e}}^{\frac {25\,x^5}{{\mathrm {e}}^{10}-6\,{\mathrm {e}}^5+9}}\,{\mathrm {e}}^{-\frac {120\,x^2}{{\mathrm {e}}^{10}-6\,{\mathrm {e}}^5+9}}\,{\mathrm {e}}^{-\frac {4\,x\,{\mathrm {e}}^5}{{\mathrm {e}}^{10}-6\,{\mathrm {e}}^5+9}}\,{\mathrm {e}}^{\frac {4\,x\,{\mathrm {e}}^{10}}{{\mathrm {e}}^{10}-6\,{\mathrm {e}}^5+9}}\,{\mathrm {e}}^{-\frac {24}{{\mathrm {e}}^{10}-6\,{\mathrm {e}}^5+9}}\,{\mathrm {e}}^{\frac {153}{9\,x-6\,x\,{\mathrm {e}}^5+x\,{\mathrm {e}}^{10}}}\,{\mathrm {e}}^{-\frac {20\,x^3\,{\mathrm {e}}^5}{{\mathrm {e}}^{10}-6\,{\mathrm {e}}^5+9}}\,{\mathrm {e}}^{\frac {40\,x^2\,{\mathrm {e}}^5}{{\mathrm {e}}^{10}-6\,{\mathrm {e}}^5+9}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp((exp(10)*(4*x^2 - 16*x + 17) - 24*x - exp(5)*(4*x^2 - 56*x - 40*x^3 + 20*x^4 + 102) + x^2 - 120*x^3 +
10*x^4 + 25*x^6 + 153)/(9*x - 6*x*exp(5) + x*exp(10)))*exp(exp((exp(10)*(4*x^2 - 16*x + 17) - 24*x - exp(5)*(
4*x^2 - 56*x - 40*x^3 + 20*x^4 + 102) + x^2 - 120*x^3 + 10*x^4 + 25*x^6 + 153)/(9*x - 6*x*exp(5) + x*exp(10)))
)*(exp(10)*(4*x^2 - 17) - exp(5)*(4*x^2 - 80*x^3 + 60*x^4 - 102) + x^2 - 240*x^3 + 30*x^4 + 125*x^6 - 153))/(x
^2*exp(10) - 6*x^2*exp(5) + 9*x^2),x)

[Out]

exp(exp(-(16*exp(10))/(exp(10) - 6*exp(5) + 9))*exp((56*exp(5))/(exp(10) - 6*exp(5) + 9))*exp(x/(exp(10) - 6*e
xp(5) + 9))*exp((17*exp(10))/(9*x - 6*x*exp(5) + x*exp(10)))*exp(-(102*exp(5))/(9*x - 6*x*exp(5) + x*exp(10)))
*exp((10*x^3)/(exp(10) - 6*exp(5) + 9))*exp((25*x^5)/(exp(10) - 6*exp(5) + 9))*exp(-(120*x^2)/(exp(10) - 6*exp
(5) + 9))*exp(-(4*x*exp(5))/(exp(10) - 6*exp(5) + 9))*exp((4*x*exp(10))/(exp(10) - 6*exp(5) + 9))*exp(-24/(exp
(10) - 6*exp(5) + 9))*exp(153/(9*x - 6*x*exp(5) + x*exp(10)))*exp(-(20*x^3*exp(5))/(exp(10) - 6*exp(5) + 9))*e
xp((40*x^2*exp(5))/(exp(10) - 6*exp(5) + 9)))

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sympy [B]  time = 1.34, size = 78, normalized size = 2.36 \begin {gather*} e^{e^{\frac {25 x^{6} + 10 x^{4} - 120 x^{3} + x^{2} - 24 x + \left (4 x^{2} - 16 x + 17\right ) e^{10} + \left (- 20 x^{4} + 40 x^{3} - 4 x^{2} + 56 x - 102\right ) e^{5} + 153}{- 6 x e^{5} + 9 x + x e^{10}}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((4*x**2-17)*exp(5)**2+(-60*x**4+80*x**3-4*x**2+102)*exp(5)+125*x**6+30*x**4-240*x**3+x**2-153)*exp(
((4*x**2-16*x+17)*exp(5)**2+(-20*x**4+40*x**3-4*x**2+56*x-102)*exp(5)+25*x**6+10*x**4-120*x**3+x**2-24*x+153)/
(x*exp(5)**2-6*x*exp(5)+9*x))*exp(exp(((4*x**2-16*x+17)*exp(5)**2+(-20*x**4+40*x**3-4*x**2+56*x-102)*exp(5)+25
*x**6+10*x**4-120*x**3+x**2-24*x+153)/(x*exp(5)**2-6*x*exp(5)+9*x)))/(x**2*exp(5)**2-6*x**2*exp(5)+9*x**2),x)

[Out]

exp(exp((25*x**6 + 10*x**4 - 120*x**3 + x**2 - 24*x + (4*x**2 - 16*x + 17)*exp(10) + (-20*x**4 + 40*x**3 - 4*x
**2 + 56*x - 102)*exp(5) + 153)/(-6*x*exp(5) + 9*x + x*exp(10))))

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