3.56.50 \(\int \frac {e^3+e^{3 e^x}+3 e^{2+e^x}+3 e^{1+2 e^x}+e^{\frac {75-30 e+3 e^2+3 e^{2 e^x}+(-30+6 e) \log (5)+3 \log ^2(5)+e^{e^x} (-30+6 e+6 \log (5))}{e^2+e^{2 e^x}+2 e^{1+e^x}}} (e^{2 e^x+x} (30-6 \log (5))+e^{e^x+x} (-150+30 e+(60-6 e) \log (5)-6 \log ^2(5)))}{e^3+e^{3 e^x}+3 e^{2+e^x}+3 e^{1+2 e^x}} \, dx\)

Optimal. Leaf size=24 \[ e^{3 \left (1+\frac {-5+\log (5)}{e+e^{e^x}}\right )^2}+x \]

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Rubi [F]  time = 12.82, 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 {e^3+e^{3 e^x}+3 e^{2+e^x}+3 e^{1+2 e^x}+\exp \left (\frac {75-30 e+3 e^2+3 e^{2 e^x}+(-30+6 e) \log (5)+3 \log ^2(5)+e^{e^x} (-30+6 e+6 \log (5))}{e^2+e^{2 e^x}+2 e^{1+e^x}}\right ) \left (e^{2 e^x+x} (30-6 \log (5))+e^{e^x+x} \left (-150+30 e+(60-6 e) \log (5)-6 \log ^2(5)\right )\right )}{e^3+e^{3 e^x}+3 e^{2+e^x}+3 e^{1+2 e^x}} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(E^3 + E^(3*E^x) + 3*E^(2 + E^x) + 3*E^(1 + 2*E^x) + E^((75 - 30*E + 3*E^2 + 3*E^(2*E^x) + (-30 + 6*E)*Log
[5] + 3*Log[5]^2 + E^E^x*(-30 + 6*E + 6*Log[5]))/(E^2 + E^(2*E^x) + 2*E^(1 + E^x)))*(E^(2*E^x + x)*(30 - 6*Log
[5]) + E^(E^x + x)*(-150 + 30*E + (60 - 6*E)*Log[5] - 6*Log[5]^2)))/(E^3 + E^(3*E^x) + 3*E^(2 + E^x) + 3*E^(1
+ 2*E^x)),x]

[Out]

E^((3*(5 - E - E^E^x - Log[5])^2)/(E + E^E^x)^2) - (3*E^(2 - x))/(2*(E + E^E^x)^2) + x - (3*E^2*Defer[Subst][D
efer[Int][1/((E + E^x)^2*x^2), x], x, E^x])/2 + 3*Defer[Subst][Defer[Int][E^(1 + 2*x)/((E + E^x)^3*x), x], x,
E^x] + 3*E^2*Defer[Subst][Defer[Int][1/((E + E^x)^2*x), x], x, E^x] - 3*E*Defer[Subst][Defer[Int][1/((E + E^x)
*x), x], x, E^x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\operatorname {Subst}\left (\int \frac {e^3+e^{3 x}+3 e^{2+x}+3 e^{1+2 x}-6 e^{x+\frac {3 \left (-5+e+e^x+\log (5)\right )^2}{\left (e+e^x\right )^2}} x (-5+\log (5)) \left (-5+e+e^x+\log (5)\right )}{\left (e+e^x\right )^3 x} \, dx,x,e^x\right )\\ &=\operatorname {Subst}\left (\int \left (\frac {e^3}{\left (e+e^x\right )^3 x}+\frac {e^{3 x}}{\left (e+e^x\right )^3 x}+\frac {3 e^{2+x}}{\left (e+e^x\right )^3 x}+\frac {3 e^{1+2 x}}{\left (e+e^x\right )^3 x}+\frac {6 e^{x+\frac {3 \left (-5+e+e^x+\log (5)\right )^2}{\left (e+e^x\right )^2}} \left (e^x-5 \left (1+\frac {1}{5} (-e-\log (5))\right )\right ) (5-\log (5))}{\left (e+e^x\right )^3}\right ) \, dx,x,e^x\right )\\ &=3 \operatorname {Subst}\left (\int \frac {e^{2+x}}{\left (e+e^x\right )^3 x} \, dx,x,e^x\right )+3 \operatorname {Subst}\left (\int \frac {e^{1+2 x}}{\left (e+e^x\right )^3 x} \, dx,x,e^x\right )+e^3 \operatorname {Subst}\left (\int \frac {1}{\left (e+e^x\right )^3 x} \, dx,x,e^x\right )+(6 (5-\log (5))) \operatorname {Subst}\left (\int \frac {e^{x+\frac {3 \left (-5+e+e^x+\log (5)\right )^2}{\left (e+e^x\right )^2}} \left (e^x-5 \left (1+\frac {1}{5} (-e-\log (5))\right )\right )}{\left (e+e^x\right )^3} \, dx,x,e^x\right )+\operatorname {Subst}\left (\int \frac {e^{3 x}}{\left (e+e^x\right )^3 x} \, dx,x,e^x\right )\\ &=3 \operatorname {Subst}\left (\int \frac {e^{1+2 x}}{\left (e+e^x\right )^3 x} \, dx,x,e^x\right )+\left (3 e^2\right ) \operatorname {Subst}\left (\int \frac {e^x}{\left (e+e^x\right )^3 x} \, dx,x,e^x\right )+e^3 \operatorname {Subst}\left (\int \frac {1}{\left (e+e^x\right )^3 x} \, dx,x,e^x\right )+(6 (5-\log (5))) \operatorname {Subst}\left (\int \frac {e^{\frac {3 (-5+e+x+\log (5))^2}{(e+x)^2}} (-5+e+x+\log (5))}{(e+x)^3} \, dx,x,e^{e^x}\right )+\operatorname {Subst}\left (\int \left (\frac {1}{x}-\frac {e^3}{\left (e+e^x\right )^3 x}+\frac {3 e^2}{\left (e+e^x\right )^2 x}-\frac {3 e}{\left (e+e^x\right ) x}\right ) \, dx,x,e^x\right )\\ &=e^{\frac {3 \left (5-e-e^{e^x}-\log (5)\right )^2}{\left (e+e^{e^x}\right )^2}}-\frac {3 e^{2-x}}{2 \left (e+e^{e^x}\right )^2}+x+3 \operatorname {Subst}\left (\int \frac {e^{1+2 x}}{\left (e+e^x\right )^3 x} \, dx,x,e^x\right )-(3 e) \operatorname {Subst}\left (\int \frac {1}{\left (e+e^x\right ) x} \, dx,x,e^x\right )-\frac {1}{2} \left (3 e^2\right ) \operatorname {Subst}\left (\int \frac {1}{\left (e+e^x\right )^2 x^2} \, dx,x,e^x\right )+\left (3 e^2\right ) \operatorname {Subst}\left (\int \frac {1}{\left (e+e^x\right )^2 x} \, dx,x,e^x\right )\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 1.24, size = 27, normalized size = 1.12 \begin {gather*} e^{\frac {3 \left (-5+e+e^{e^x}+\log (5)\right )^2}{\left (e+e^{e^x}\right )^2}}+x \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^3 + E^(3*E^x) + 3*E^(2 + E^x) + 3*E^(1 + 2*E^x) + E^((75 - 30*E + 3*E^2 + 3*E^(2*E^x) + (-30 + 6*
E)*Log[5] + 3*Log[5]^2 + E^E^x*(-30 + 6*E + 6*Log[5]))/(E^2 + E^(2*E^x) + 2*E^(1 + E^x)))*(E^(2*E^x + x)*(30 -
6*Log[5]) + E^(E^x + x)*(-150 + 30*E + (60 - 6*E)*Log[5] - 6*Log[5]^2)))/(E^3 + E^(3*E^x) + 3*E^(2 + E^x) + 3
*E^(1 + 2*E^x)),x]

[Out]

E^((3*(-5 + E + E^E^x + Log[5])^2)/(E + E^E^x)^2) + x

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fricas [B]  time = 0.72, size = 83, normalized size = 3.46 \begin {gather*} x + e^{\left (\frac {3 \, {\left ({\left (2 \, {\left (e - 5\right )} \log \relax (5) + \log \relax (5)^{2} + e^{2} - 10 \, e + 25\right )} e^{\left (2 \, x\right )} + 2 \, {\left (e + \log \relax (5) - 5\right )} e^{\left (2 \, x + e^{x}\right )} + e^{\left (2 \, x + 2 \, e^{x}\right )}\right )}}{e^{\left (2 \, x + 2 \, e^{x}\right )} + 2 \, e^{\left (2 \, x + e^{x} + 1\right )} + e^{\left (2 \, x + 2\right )}}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-6*log(5)+30)*exp(x)*exp(exp(x))^2+(-6*log(5)^2+(-6*exp(1)+60)*log(5)+30*exp(1)-150)*exp(x)*exp(e
xp(x)))*exp((3*exp(exp(x))^2+(6*log(5)+6*exp(1)-30)*exp(exp(x))+3*log(5)^2+(6*exp(1)-30)*log(5)+3*exp(1)^2-30*
exp(1)+75)/(exp(exp(x))^2+2*exp(1)*exp(exp(x))+exp(1)^2))+exp(exp(x))^3+3*exp(1)*exp(exp(x))^2+3*exp(1)^2*exp(
exp(x))+exp(1)^3)/(exp(exp(x))^3+3*exp(1)*exp(exp(x))^2+3*exp(1)^2*exp(exp(x))+exp(1)^3),x, algorithm="fricas"
)

[Out]

x + e^(3*((2*(e - 5)*log(5) + log(5)^2 + e^2 - 10*e + 25)*e^(2*x) + 2*(e + log(5) - 5)*e^(2*x + e^x) + e^(2*x
+ 2*e^x))/(e^(2*x + 2*e^x) + 2*e^(2*x + e^x + 1) + e^(2*x + 2)))

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giac [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int -\frac {6 \, {\left ({\left (\log \relax (5) - 5\right )} e^{\left (x + 2 \, e^{x}\right )} + {\left ({\left (e - 10\right )} \log \relax (5) + \log \relax (5)^{2} - 5 \, e + 25\right )} e^{\left (x + e^{x}\right )}\right )} e^{\left (\frac {3 \, {\left (2 \, {\left (e + \log \relax (5) - 5\right )} e^{\left (e^{x}\right )} + 2 \, {\left (e - 5\right )} \log \relax (5) + \log \relax (5)^{2} + e^{2} - 10 \, e + e^{\left (2 \, e^{x}\right )} + 25\right )}}{e^{2} + e^{\left (2 \, e^{x}\right )} + 2 \, e^{\left (e^{x} + 1\right )}}\right )} - e^{3} - e^{\left (3 \, e^{x}\right )} - 3 \, e^{\left (2 \, e^{x} + 1\right )} - 3 \, e^{\left (e^{x} + 2\right )}}{e^{3} + e^{\left (3 \, e^{x}\right )} + 3 \, e^{\left (2 \, e^{x} + 1\right )} + 3 \, e^{\left (e^{x} + 2\right )}}\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-6*log(5)+30)*exp(x)*exp(exp(x))^2+(-6*log(5)^2+(-6*exp(1)+60)*log(5)+30*exp(1)-150)*exp(x)*exp(e
xp(x)))*exp((3*exp(exp(x))^2+(6*log(5)+6*exp(1)-30)*exp(exp(x))+3*log(5)^2+(6*exp(1)-30)*log(5)+3*exp(1)^2-30*
exp(1)+75)/(exp(exp(x))^2+2*exp(1)*exp(exp(x))+exp(1)^2))+exp(exp(x))^3+3*exp(1)*exp(exp(x))^2+3*exp(1)^2*exp(
exp(x))+exp(1)^3)/(exp(exp(x))^3+3*exp(1)*exp(exp(x))^2+3*exp(1)^2*exp(exp(x))+exp(1)^3),x, algorithm="giac")

[Out]

integrate(-(6*((log(5) - 5)*e^(x + 2*e^x) + ((e - 10)*log(5) + log(5)^2 - 5*e + 25)*e^(x + e^x))*e^(3*(2*(e +
log(5) - 5)*e^(e^x) + 2*(e - 5)*log(5) + log(5)^2 + e^2 - 10*e + e^(2*e^x) + 25)/(e^2 + e^(2*e^x) + 2*e^(e^x +
1))) - e^3 - e^(3*e^x) - 3*e^(2*e^x + 1) - 3*e^(e^x + 2))/(e^3 + e^(3*e^x) + 3*e^(2*e^x + 1) + 3*e^(e^x + 2))
, x)

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maple [B]  time = 0.78, size = 69, normalized size = 2.88

method	result	size
risch	\(x +{\mathrm e}^{\frac {3 \ln \relax (5)^{2}+6 \,{\mathrm e} \ln \relax (5)+6 \,{\mathrm e}^{{\mathrm e}^{x}} \ln \relax (5)+6 \,{\mathrm e}^{{\mathrm e}^{x}+1}+3 \,{\mathrm e}^{2}-30 \ln \relax (5)-30 \,{\mathrm e}-30 \,{\mathrm e}^{{\mathrm e}^{x}}+3 \,{\mathrm e}^{2 \,{\mathrm e}^{x}}+75}{{\mathrm e}^{2 \,{\mathrm e}^{x}}+2 \,{\mathrm e}^{{\mathrm e}^{x}+1}+{\mathrm e}^{2}}}\)	\(69\)
norman	\(\frac {{\mathrm e}^{2} x +x \,{\mathrm e}^{2 \,{\mathrm e}^{x}}+{\mathrm e}^{2} {\mathrm e}^{\frac {3 \,{\mathrm e}^{2 \,{\mathrm e}^{x}}+\left (6 \ln \relax (5)+6 \,{\mathrm e}-30\right ) {\mathrm e}^{{\mathrm e}^{x}}+3 \ln \relax (5)^{2}+\left (6 \,{\mathrm e}-30\right ) \ln \relax (5)+3 \,{\mathrm e}^{2}-30 \,{\mathrm e}+75}{{\mathrm e}^{2 \,{\mathrm e}^{x}}+2 \,{\mathrm e} \,{\mathrm e}^{{\mathrm e}^{x}}+{\mathrm e}^{2}}}+{\mathrm e}^{2 \,{\mathrm e}^{x}} {\mathrm e}^{\frac {3 \,{\mathrm e}^{2 \,{\mathrm e}^{x}}+\left (6 \ln \relax (5)+6 \,{\mathrm e}-30\right ) {\mathrm e}^{{\mathrm e}^{x}}+3 \ln \relax (5)^{2}+\left (6 \,{\mathrm e}-30\right ) \ln \relax (5)+3 \,{\mathrm e}^{2}-30 \,{\mathrm e}+75}{{\mathrm e}^{2 \,{\mathrm e}^{x}}+2 \,{\mathrm e} \,{\mathrm e}^{{\mathrm e}^{x}}+{\mathrm e}^{2}}}+2 x \,{\mathrm e} \,{\mathrm e}^{{\mathrm e}^{x}}+2 \,{\mathrm e} \,{\mathrm e}^{{\mathrm e}^{x}} {\mathrm e}^{\frac {3 \,{\mathrm e}^{2 \,{\mathrm e}^{x}}+\left (6 \ln \relax (5)+6 \,{\mathrm e}-30\right ) {\mathrm e}^{{\mathrm e}^{x}}+3 \ln \relax (5)^{2}+\left (6 \,{\mathrm e}-30\right ) \ln \relax (5)+3 \,{\mathrm e}^{2}-30 \,{\mathrm e}+75}{{\mathrm e}^{2 \,{\mathrm e}^{x}}+2 \,{\mathrm e} \,{\mathrm e}^{{\mathrm e}^{x}}+{\mathrm e}^{2}}}}{\left ({\mathrm e}^{{\mathrm e}^{x}}+{\mathrm e}\right )^{2}}\)	\(257\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((-6*ln(5)+30)*exp(x)*exp(exp(x))^2+(-6*ln(5)^2+(-6*exp(1)+60)*ln(5)+30*exp(1)-150)*exp(x)*exp(exp(x)))*e
xp((3*exp(exp(x))^2+(6*ln(5)+6*exp(1)-30)*exp(exp(x))+3*ln(5)^2+(6*exp(1)-30)*ln(5)+3*exp(1)^2-30*exp(1)+75)/(
exp(exp(x))^2+2*exp(1)*exp(exp(x))+exp(1)^2))+exp(exp(x))^3+3*exp(1)*exp(exp(x))^2+3*exp(1)^2*exp(exp(x))+exp(
1)^3)/(exp(exp(x))^3+3*exp(1)*exp(exp(x))^2+3*exp(1)^2*exp(exp(x))+exp(1)^3),x,method=_RETURNVERBOSE)

[Out]

x+exp(3*(ln(5)^2+2*exp(1)*ln(5)+2*exp(exp(x))*ln(5)+2*exp(exp(x)+1)+exp(2)-10*ln(5)-10*exp(1)-10*exp(exp(x))+e
xp(2*exp(x))+25)/(exp(2*exp(x))+2*exp(exp(x)+1)+exp(2)))

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maxima [B]  time = 0.64, size = 296, normalized size = 12.33 \begin {gather*} {\left (x e^{\left (\frac {30 \, e}{e^{2} + e^{\left (2 \, e^{x}\right )} + 2 \, e^{\left (e^{x} + 1\right )}} + \frac {30 \, e^{\left (e^{x}\right )}}{e^{2} + e^{\left (2 \, e^{x}\right )} + 2 \, e^{\left (e^{x} + 1\right )}} + \frac {30 \, \log \relax (5)}{e^{2} + e^{\left (2 \, e^{x}\right )} + 2 \, e^{\left (e^{x} + 1\right )}}\right )} + e^{\left (\frac {6 \, e \log \relax (5)}{e^{2} + e^{\left (2 \, e^{x}\right )} + 2 \, e^{\left (e^{x} + 1\right )}} + \frac {6 \, e^{\left (e^{x}\right )} \log \relax (5)}{e^{2} + e^{\left (2 \, e^{x}\right )} + 2 \, e^{\left (e^{x} + 1\right )}} + \frac {3 \, \log \relax (5)^{2}}{e^{2} + e^{\left (2 \, e^{x}\right )} + 2 \, e^{\left (e^{x} + 1\right )}} + \frac {3 \, e^{2}}{e^{2} + e^{\left (2 \, e^{x}\right )} + 2 \, e^{\left (e^{x} + 1\right )}} + \frac {3 \, e^{\left (2 \, e^{x}\right )}}{e^{2} + e^{\left (2 \, e^{x}\right )} + 2 \, e^{\left (e^{x} + 1\right )}} + \frac {6 \, e^{\left (e^{x} + 1\right )}}{e^{2} + e^{\left (2 \, e^{x}\right )} + 2 \, e^{\left (e^{x} + 1\right )}} + \frac {75}{e^{2} + e^{\left (2 \, e^{x}\right )} + 2 \, e^{\left (e^{x} + 1\right )}}\right )}\right )} e^{\left (-\frac {30 \, e}{e^{2} + e^{\left (2 \, e^{x}\right )} + 2 \, e^{\left (e^{x} + 1\right )}} - \frac {30 \, e^{\left (e^{x}\right )}}{e^{2} + e^{\left (2 \, e^{x}\right )} + 2 \, e^{\left (e^{x} + 1\right )}} - \frac {30 \, \log \relax (5)}{e^{2} + e^{\left (2 \, e^{x}\right )} + 2 \, e^{\left (e^{x} + 1\right )}}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-6*log(5)+30)*exp(x)*exp(exp(x))^2+(-6*log(5)^2+(-6*exp(1)+60)*log(5)+30*exp(1)-150)*exp(x)*exp(e
xp(x)))*exp((3*exp(exp(x))^2+(6*log(5)+6*exp(1)-30)*exp(exp(x))+3*log(5)^2+(6*exp(1)-30)*log(5)+3*exp(1)^2-30*
exp(1)+75)/(exp(exp(x))^2+2*exp(1)*exp(exp(x))+exp(1)^2))+exp(exp(x))^3+3*exp(1)*exp(exp(x))^2+3*exp(1)^2*exp(
exp(x))+exp(1)^3)/(exp(exp(x))^3+3*exp(1)*exp(exp(x))^2+3*exp(1)^2*exp(exp(x))+exp(1)^3),x, algorithm="maxima"
)

[Out]

(x*e^(30*e/(e^2 + e^(2*e^x) + 2*e^(e^x + 1)) + 30*e^(e^x)/(e^2 + e^(2*e^x) + 2*e^(e^x + 1)) + 30*log(5)/(e^2 +
e^(2*e^x) + 2*e^(e^x + 1))) + e^(6*e*log(5)/(e^2 + e^(2*e^x) + 2*e^(e^x + 1)) + 6*e^(e^x)*log(5)/(e^2 + e^(2*
e^x) + 2*e^(e^x + 1)) + 3*log(5)^2/(e^2 + e^(2*e^x) + 2*e^(e^x + 1)) + 3*e^2/(e^2 + e^(2*e^x) + 2*e^(e^x + 1))
+ 3*e^(2*e^x)/(e^2 + e^(2*e^x) + 2*e^(e^x + 1)) + 6*e^(e^x + 1)/(e^2 + e^(2*e^x) + 2*e^(e^x + 1)) + 75/(e^2 +
e^(2*e^x) + 2*e^(e^x + 1))))*e^(-30*e/(e^2 + e^(2*e^x) + 2*e^(e^x + 1)) - 30*e^(e^x)/(e^2 + e^(2*e^x) + 2*e^(
e^x + 1)) - 30*log(5)/(e^2 + e^(2*e^x) + 2*e^(e^x + 1)))

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mupad [B]  time = 4.12, size = 234, normalized size = 9.75 \begin {gather*} x+\frac {5^{\frac {6\,{\mathrm {e}}^{{\mathrm {e}}^x}}{{\mathrm {e}}^2+{\mathrm {e}}^{2\,{\mathrm {e}}^x}+2\,{\mathrm {e}}^{{\mathrm {e}}^x}\,\mathrm {e}}}\,5^{\frac {6\,\mathrm {e}}{{\mathrm {e}}^2+{\mathrm {e}}^{2\,{\mathrm {e}}^x}+2\,{\mathrm {e}}^{{\mathrm {e}}^x}\,\mathrm {e}}}\,{\mathrm {e}}^{\frac {3\,{\mathrm {e}}^{2\,{\mathrm {e}}^x}}{{\mathrm {e}}^2+{\mathrm {e}}^{2\,{\mathrm {e}}^x}+2\,{\mathrm {e}}^{{\mathrm {e}}^x}\,\mathrm {e}}}\,{\mathrm {e}}^{\frac {6\,{\mathrm {e}}^{{\mathrm {e}}^x}\,\mathrm {e}}{{\mathrm {e}}^2+{\mathrm {e}}^{2\,{\mathrm {e}}^x}+2\,{\mathrm {e}}^{{\mathrm {e}}^x}\,\mathrm {e}}}\,{\mathrm {e}}^{\frac {3\,{\ln \relax (5)}^2}{{\mathrm {e}}^2+{\mathrm {e}}^{2\,{\mathrm {e}}^x}+2\,{\mathrm {e}}^{{\mathrm {e}}^x}\,\mathrm {e}}}\,{\mathrm {e}}^{\frac {75}{{\mathrm {e}}^2+{\mathrm {e}}^{2\,{\mathrm {e}}^x}+2\,{\mathrm {e}}^{{\mathrm {e}}^x}\,\mathrm {e}}}\,{\mathrm {e}}^{-\frac {30\,{\mathrm {e}}^{{\mathrm {e}}^x}}{{\mathrm {e}}^2+{\mathrm {e}}^{2\,{\mathrm {e}}^x}+2\,{\mathrm {e}}^{{\mathrm {e}}^x}\,\mathrm {e}}}\,{\mathrm {e}}^{\frac {3\,{\mathrm {e}}^2}{{\mathrm {e}}^2+{\mathrm {e}}^{2\,{\mathrm {e}}^x}+2\,{\mathrm {e}}^{{\mathrm {e}}^x}\,\mathrm {e}}}\,{\mathrm {e}}^{-\frac {30\,\mathrm {e}}{{\mathrm {e}}^2+{\mathrm {e}}^{2\,{\mathrm {e}}^x}+2\,{\mathrm {e}}^{{\mathrm {e}}^x}\,\mathrm {e}}}}{5^{\frac {30}{{\mathrm {e}}^2+{\mathrm {e}}^{2\,{\mathrm {e}}^x}+2\,{\mathrm {e}}^{{\mathrm {e}}^x}\,\mathrm {e}}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(3) + exp(3*exp(x)) + 3*exp(exp(x))*exp(2) + 3*exp(1)*exp(2*exp(x)) - exp((3*exp(2) - 30*exp(1) + 3*ex
p(2*exp(x)) + exp(exp(x))*(6*exp(1) + 6*log(5) - 30) + 3*log(5)^2 + log(5)*(6*exp(1) - 30) + 75)/(exp(2) + exp
(2*exp(x)) + 2*exp(exp(x))*exp(1)))*(exp(2*exp(x))*exp(x)*(6*log(5) - 30) + exp(exp(x))*exp(x)*(6*log(5)^2 - 3
0*exp(1) + log(5)*(6*exp(1) - 60) + 150)))/(exp(3) + exp(3*exp(x)) + 3*exp(exp(x))*exp(2) + 3*exp(1)*exp(2*exp
(x))),x)

[Out]

x + (5^((6*exp(exp(x)))/(exp(2) + exp(2*exp(x)) + 2*exp(exp(x))*exp(1)))*5^((6*exp(1))/(exp(2) + exp(2*exp(x))
+ 2*exp(exp(x))*exp(1)))*exp((3*exp(2*exp(x)))/(exp(2) + exp(2*exp(x)) + 2*exp(exp(x))*exp(1)))*exp((6*exp(ex
p(x))*exp(1))/(exp(2) + exp(2*exp(x)) + 2*exp(exp(x))*exp(1)))*exp((3*log(5)^2)/(exp(2) + exp(2*exp(x)) + 2*ex
p(exp(x))*exp(1)))*exp(75/(exp(2) + exp(2*exp(x)) + 2*exp(exp(x))*exp(1)))*exp(-(30*exp(exp(x)))/(exp(2) + exp
(2*exp(x)) + 2*exp(exp(x))*exp(1)))*exp((3*exp(2))/(exp(2) + exp(2*exp(x)) + 2*exp(exp(x))*exp(1)))*exp(-(30*e
xp(1))/(exp(2) + exp(2*exp(x)) + 2*exp(exp(x))*exp(1))))/5^(30/(exp(2) + exp(2*exp(x)) + 2*exp(exp(x))*exp(1))
)

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sympy [B]  time = 0.89, size = 76, normalized size = 3.17 \begin {gather*} x + e^{\frac {3 e^{2 e^{x}} + \left (-30 + 6 \log {\relax (5 )} + 6 e\right ) e^{e^{x}} - 30 e + \left (-30 + 6 e\right ) \log {\relax (5 )} + 3 \log {\relax (5 )}^{2} + 3 e^{2} + 75}{e^{2 e^{x}} + 2 e e^{e^{x}} + e^{2}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-6*ln(5)+30)*exp(x)*exp(exp(x))**2+(-6*ln(5)**2+(-6*exp(1)+60)*ln(5)+30*exp(1)-150)*exp(x)*exp(ex
p(x)))*exp((3*exp(exp(x))**2+(6*ln(5)+6*exp(1)-30)*exp(exp(x))+3*ln(5)**2+(6*exp(1)-30)*ln(5)+3*exp(1)**2-30*e
xp(1)+75)/(exp(exp(x))**2+2*exp(1)*exp(exp(x))+exp(1)**2))+exp(exp(x))**3+3*exp(1)*exp(exp(x))**2+3*exp(1)**2*
exp(exp(x))+exp(1)**3)/(exp(exp(x))**3+3*exp(1)*exp(exp(x))**2+3*exp(1)**2*exp(exp(x))+exp(1)**3),x)

[Out]

x + exp((3*exp(2*exp(x)) + (-30 + 6*log(5) + 6*E)*exp(exp(x)) - 30*E + (-30 + 6*E)*log(5) + 3*log(5)**2 + 3*ex
p(2) + 75)/(exp(2*exp(x)) + 2*E*exp(exp(x)) + exp(2)))

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