3.89.54 \(\int (3+e^{e^{e^{e^{2 e} x^4+2 e^e x^5+x^6}}+x} (-2 e^x+e^{e^{e^{2 e} x^4+2 e^e x^5+x^6}+e^{2 e} x^4+2 e^e x^5+x^6} (-4 e^{2 e+x} x^3-10 e^{e+x} x^4-6 e^x x^5))) \, dx\)

Optimal. Leaf size=28 \[ 3-e^{e^{e^{x^4 \left (e^e+x\right )^2}}+2 x}+3 x \]

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Rubi [F]  time = 10.16, 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 \left (3+e^{e^{e^{e^{2 e} x^4+2 e^e x^5+x^6}}+x} \left (-2 e^x+\exp \left (e^{e^{2 e} x^4+2 e^e x^5+x^6}+e^{2 e} x^4+2 e^e x^5+x^6\right ) \left (-4 e^{2 e+x} x^3-10 e^{e+x} x^4-6 e^x x^5\right )\right )\right ) \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[3 + E^(E^E^(E^(2*E)*x^4 + 2*E^E*x^5 + x^6) + x)*(-2*E^x + E^(E^(E^(2*E)*x^4 + 2*E^E*x^5 + x^6) + E^(2*E)*x
^4 + 2*E^E*x^5 + x^6)*(-4*E^(2*E + x)*x^3 - 10*E^(E + x)*x^4 - 6*E^x*x^5)),x]

[Out]

3*x - 2*Defer[Int][E^(E^E^(x^4*(E^E + x)^2) + 2*x), x] - 4*Defer[Int][E^(2*E + E^E^(E^(2*E)*x^4 + 2*E^E*x^5 +
x^6) + E^(x^4*(E^E + x)^2) + 2*x + E^(2*E)*x^4 + 2*E^E*x^5 + x^6)*x^3, x] - 10*Defer[Int][E^(E + E^E^(E^(2*E)*
x^4 + 2*E^E*x^5 + x^6) + E^(x^4*(E^E + x)^2) + 2*x + E^(2*E)*x^4 + 2*E^E*x^5 + x^6)*x^4, x] - 6*Defer[Int][E^(
E^E^(E^(2*E)*x^4 + 2*E^E*x^5 + x^6) + E^(x^4*(E^E + x)^2) + 2*x + E^(2*E)*x^4 + 2*E^E*x^5 + x^6)*x^5, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=3 x+\int e^{e^{e^{e^{2 e} x^4+2 e^e x^5+x^6}}+x} \left (-2 e^x+\exp \left (e^{e^{2 e} x^4+2 e^e x^5+x^6}+e^{2 e} x^4+2 e^e x^5+x^6\right ) \left (-4 e^{2 e+x} x^3-10 e^{e+x} x^4-6 e^x x^5\right )\right ) \, dx\\ &=3 x+\int \left (-2 e^{e^{e^{e^{2 e} x^4+2 e^e x^5+x^6}}+2 x}-2 \exp \left (e^{e^{e^{2 e} x^4+2 e^e x^5+x^6}}+e^{x^4 \left (e^e+x\right )^2}+2 x+e^{2 e} x^4+2 e^e x^5+x^6\right ) x^3 \left (2 e^{2 e}+5 e^e x+3 x^2\right )\right ) \, dx\\ &=3 x-2 \int e^{e^{e^{e^{2 e} x^4+2 e^e x^5+x^6}}+2 x} \, dx-2 \int \exp \left (e^{e^{e^{2 e} x^4+2 e^e x^5+x^6}}+e^{x^4 \left (e^e+x\right )^2}+2 x+e^{2 e} x^4+2 e^e x^5+x^6\right ) x^3 \left (2 e^{2 e}+5 e^e x+3 x^2\right ) \, dx\\ &=3 x-2 \int e^{e^{e^{x^4 \left (e^e+x\right )^2}}+2 x} \, dx-2 \int \left (2 \exp \left (2 e+e^{e^{e^{2 e} x^4+2 e^e x^5+x^6}}+e^{x^4 \left (e^e+x\right )^2}+2 x+e^{2 e} x^4+2 e^e x^5+x^6\right ) x^3+5 \exp \left (e+e^{e^{e^{2 e} x^4+2 e^e x^5+x^6}}+e^{x^4 \left (e^e+x\right )^2}+2 x+e^{2 e} x^4+2 e^e x^5+x^6\right ) x^4+3 \exp \left (e^{e^{e^{2 e} x^4+2 e^e x^5+x^6}}+e^{x^4 \left (e^e+x\right )^2}+2 x+e^{2 e} x^4+2 e^e x^5+x^6\right ) x^5\right ) \, dx\\ &=3 x-2 \int e^{e^{e^{x^4 \left (e^e+x\right )^2}}+2 x} \, dx-4 \int \exp \left (2 e+e^{e^{e^{2 e} x^4+2 e^e x^5+x^6}}+e^{x^4 \left (e^e+x\right )^2}+2 x+e^{2 e} x^4+2 e^e x^5+x^6\right ) x^3 \, dx-6 \int \exp \left (e^{e^{e^{2 e} x^4+2 e^e x^5+x^6}}+e^{x^4 \left (e^e+x\right )^2}+2 x+e^{2 e} x^4+2 e^e x^5+x^6\right ) x^5 \, dx-10 \int \exp \left (e+e^{e^{e^{2 e} x^4+2 e^e x^5+x^6}}+e^{x^4 \left (e^e+x\right )^2}+2 x+e^{2 e} x^4+2 e^e x^5+x^6\right ) x^4 \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.27, size = 37, normalized size = 1.32 \begin {gather*} -e^{e^{e^{e^{2 e} x^4+2 e^e x^5+x^6}}+2 x}+3 x \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[3 + E^(E^E^(E^(2*E)*x^4 + 2*E^E*x^5 + x^6) + x)*(-2*E^x + E^(E^(E^(2*E)*x^4 + 2*E^E*x^5 + x^6) + E^(
2*E)*x^4 + 2*E^E*x^5 + x^6)*(-4*E^(2*E + x)*x^3 - 10*E^(E + x)*x^4 - 6*E^x*x^5)),x]

[Out]

-E^(E^E^(E^(2*E)*x^4 + 2*E^E*x^5 + x^6) + 2*x) + 3*x

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fricas [B]  time = 0.59, size = 119, normalized size = 4.25 \begin {gather*} {\left (3 \, x e^{\left (2 \, e\right )} - e^{\left ({\left (x e^{\left (x^{6} + 2 \, x^{5} e^{e} + x^{4} e^{\left (2 \, e\right )}\right )} + e^{\left (x^{6} + 2 \, x^{5} e^{e} + x^{4} e^{\left (2 \, e\right )} + e^{\left (x^{6} + 2 \, x^{5} e^{e} + x^{4} e^{\left (2 \, e\right )}\right )}\right )}\right )} e^{\left (-x^{6} - 2 \, x^{5} e^{e} - x^{4} e^{\left (2 \, e\right )}\right )} + x + 2 \, e\right )}\right )} e^{\left (-2 \, e\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-4*x^3*exp(x)*exp(exp(1))^2-10*x^4*exp(x)*exp(exp(1))-6*x^5*exp(x))*exp(x^4*exp(exp(1))^2+2*x^5*ex
p(exp(1))+x^6)*exp(exp(x^4*exp(exp(1))^2+2*x^5*exp(exp(1))+x^6))-2*exp(x))*exp(exp(exp(x^4*exp(exp(1))^2+2*x^5
*exp(exp(1))+x^6))+x)+3,x, algorithm="fricas")

[Out]

(3*x*e^(2*e) - e^((x*e^(x^6 + 2*x^5*e^e + x^4*e^(2*e)) + e^(x^6 + 2*x^5*e^e + x^4*e^(2*e) + e^(x^6 + 2*x^5*e^e
+ x^4*e^(2*e))))*e^(-x^6 - 2*x^5*e^e - x^4*e^(2*e)) + x + 2*e))*e^(-2*e)

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giac [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int -2 \, {\left ({\left (3 \, x^{5} e^{x} + 5 \, x^{4} e^{\left (x + e\right )} + 2 \, x^{3} e^{\left (x + 2 \, e\right )}\right )} e^{\left (x^{6} + 2 \, x^{5} e^{e} + x^{4} e^{\left (2 \, e\right )} + e^{\left (x^{6} + 2 \, x^{5} e^{e} + x^{4} e^{\left (2 \, e\right )}\right )}\right )} + e^{x}\right )} e^{\left (x + e^{\left (e^{\left (x^{6} + 2 \, x^{5} e^{e} + x^{4} e^{\left (2 \, e\right )}\right )}\right )}\right )} + 3\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-4*x^3*exp(x)*exp(exp(1))^2-10*x^4*exp(x)*exp(exp(1))-6*x^5*exp(x))*exp(x^4*exp(exp(1))^2+2*x^5*ex
p(exp(1))+x^6)*exp(exp(x^4*exp(exp(1))^2+2*x^5*exp(exp(1))+x^6))-2*exp(x))*exp(exp(exp(x^4*exp(exp(1))^2+2*x^5
*exp(exp(1))+x^6))+x)+3,x, algorithm="giac")

[Out]

integrate(-2*((3*x^5*e^x + 5*x^4*e^(x + e) + 2*x^3*e^(x + 2*e))*e^(x^6 + 2*x^5*e^e + x^4*e^(2*e) + e^(x^6 + 2*
x^5*e^e + x^4*e^(2*e))) + e^x)*e^(x + e^(e^(x^6 + 2*x^5*e^e + x^4*e^(2*e)))) + 3, x)

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maple [A]  time = 0.26, size = 33, normalized size = 1.18

method	result	size
risch	\(-{\mathrm e}^{2 x +{\mathrm e}^{{\mathrm e}^{x^{4} \left (2 x \,{\mathrm e}^{{\mathrm e}}+x^{2}+{\mathrm e}^{2 \,{\mathrm e}}\right )}}}+3 x\)	\(33\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((-4*x^3*exp(x)*exp(exp(1))^2-10*x^4*exp(x)*exp(exp(1))-6*x^5*exp(x))*exp(x^4*exp(exp(1))^2+2*x^5*exp(exp(
1))+x^6)*exp(exp(x^4*exp(exp(1))^2+2*x^5*exp(exp(1))+x^6))-2*exp(x))*exp(exp(exp(x^4*exp(exp(1))^2+2*x^5*exp(e
xp(1))+x^6))+x)+3,x,method=_RETURNVERBOSE)

[Out]

-exp(2*x+exp(exp(x^4*(2*x*exp(exp(1))+x^2+exp(2*exp(1))))))+3*x

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maxima [A]  time = 0.60, size = 34, normalized size = 1.21 \begin {gather*} 3 \, x - e^{\left (2 \, x + e^{\left (e^{\left (x^{6} + 2 \, x^{5} e^{e} + x^{4} e^{\left (2 \, e\right )}\right )}\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-4*x^3*exp(x)*exp(exp(1))^2-10*x^4*exp(x)*exp(exp(1))-6*x^5*exp(x))*exp(x^4*exp(exp(1))^2+2*x^5*ex
p(exp(1))+x^6)*exp(exp(x^4*exp(exp(1))^2+2*x^5*exp(exp(1))+x^6))-2*exp(x))*exp(exp(exp(x^4*exp(exp(1))^2+2*x^5
*exp(exp(1))+x^6))+x)+3,x, algorithm="maxima")

[Out]

3*x - e^(2*x + e^(e^(x^6 + 2*x^5*e^e + x^4*e^(2*e))))

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mupad [B]  time = 5.53, size = 36, normalized size = 1.29 \begin {gather*} 3\,x-{\mathrm {e}}^{2\,x}\,{\mathrm {e}}^{{\mathrm {e}}^{{\mathrm {e}}^{x^6}\,{\mathrm {e}}^{2\,x^5\,{\mathrm {e}}^{\mathrm {e}}}\,{\mathrm {e}}^{x^4\,{\mathrm {e}}^{2\,\mathrm {e}}}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(3 - exp(x + exp(exp(2*x^5*exp(exp(1)) + x^4*exp(2*exp(1)) + x^6)))*(2*exp(x) + exp(exp(2*x^5*exp(exp(1)) +
x^4*exp(2*exp(1)) + x^6))*exp(2*x^5*exp(exp(1)) + x^4*exp(2*exp(1)) + x^6)*(6*x^5*exp(x) + 4*x^3*exp(2*exp(1)
)*exp(x) + 10*x^4*exp(exp(1))*exp(x))),x)

[Out]

3*x - exp(2*x)*exp(exp(exp(x^6)*exp(2*x^5*exp(exp(1)))*exp(x^4*exp(2*exp(1)))))

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sympy [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(((-4*x**3*exp(x)*exp(exp(1))**2-10*x**4*exp(x)*exp(exp(1))-6*x**5*exp(x))*exp(x**4*exp(exp(1))**2+2*
x**5*exp(exp(1))+x**6)*exp(exp(x**4*exp(exp(1))**2+2*x**5*exp(exp(1))+x**6))-2*exp(x))*exp(exp(exp(x**4*exp(ex
p(1))**2+2*x**5*exp(exp(1))+x**6))+x)+3,x)

[Out]

Timed out

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