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

Optimal. Leaf size=28 $$3-e^{e^{e^{x^4{(e^e+x)}^2}}+2x}+3x$$

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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 = {} $$\begin{array}{c}\int (3+e^{e^{e^{e^{2e}{x}^4+2e^e{x}^5+x^6}}+x}(-2e^x+\exp (e^{e^{2e}{x}^4+2e^e{x}^5+x^6}+e^{2e}{x}^4+2e^e{x}^5+x^6)(-4e^{2e+x}{x}^3-10e^{e+x}{x}^4-6e^x{x}^5)))dx\end{array}$$

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

$$\begin{array}{c}\begin{array}{rl}\text{integral}& =3x+\int e^{e^{e^{e^{2e}{x}^4+2e^e{x}^5+x^6}}+x}(-2e^x+\exp (e^{e^{2e}{x}^4+2e^e{x}^5+x^6}+e^{2e}{x}^4+2e^e{x}^5+x^6)(-4e^{2e+x}{x}^3-10e^{e+x}{x}^4-6e^x{x}^5))dx\\ & =3x+\int (-2e^{e^{e^{e^{2e}{x}^4+2e^e{x}^5+x^6}}+2x}-2\exp (e^{e^{e^{2e}{x}^4+2e^e{x}^5+x^6}}+e^{x^4{(e^e+x)}^2}+2x+e^{2e}{x}^4+2e^e{x}^5+x^6)x^3(2e^{2e}+5e^{e}x+3x^2))dx\\ & =3x-2\int e^{e^{e^{e^{2e}{x}^4+2e^e{x}^5+x^6}}+2x}dx-2\int \exp (e^{e^{e^{2e}{x}^4+2e^e{x}^5+x^6}}+e^{x^4{(e^e+x)}^2}+2x+e^{2e}{x}^4+2e^e{x}^5+x^6)x^3(2e^{2e}+5e^{e}x+3x^2)dx\\ & =3x-2\int e^{e^{e^{x^4{(e^e+x)}^2}}+2x}dx-2\int (2\exp (2e+e^{e^{e^{2e}{x}^4+2e^e{x}^5+x^6}}+e^{x^4{(e^e+x)}^2}+2x+e^{2e}{x}^4+2e^e{x}^5+x^6)x^3+5\exp (e+e^{e^{e^{2e}{x}^4+2e^e{x}^5+x^6}}+e^{x^4{(e^e+x)}^2}+2x+e^{2e}{x}^4+2e^e{x}^5+x^6)x^4+3\exp (e^{e^{e^{2e}{x}^4+2e^e{x}^5+x^6}}+e^{x^4{(e^e+x)}^2}+2x+e^{2e}{x}^4+2e^e{x}^5+x^6)x^5)dx\\ & =3x-2\int e^{e^{e^{x^4{(e^e+x)}^2}}+2x}dx-4\int \exp (2e+e^{e^{e^{2e}{x}^4+2e^e{x}^5+x^6}}+e^{x^4{(e^e+x)}^2}+2x+e^{2e}{x}^4+2e^e{x}^5+x^6)x^{3}dx-6\int \exp (e^{e^{e^{2e}{x}^4+2e^e{x}^5+x^6}}+e^{x^4{(e^e+x)}^2}+2x+e^{2e}{x}^4+2e^e{x}^5+x^6)x^{5}dx-10\int \exp (e+e^{e^{e^{2e}{x}^4+2e^e{x}^5+x^6}}+e^{x^4{(e^e+x)}^2}+2x+e^{2e}{x}^4+2e^e{x}^5+x^6)x^{4}dx\end{array}\end{array}$$

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

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 $$\begin{array}{c}(3x{e}^{\left(2e\right)}-e^{((x{e}^{(x^6+2x^5{e}^e+x^4{e}^{\left(2e\right)})}+e^{(x^6+2x^5{e}^e+x^4{e}^{\left(2e\right)}+e^{(x^6+2x^5{e}^e+x^4{e}^{\left(2e\right)})})})e^{(-x^6-2x^5{e}^e-x^4{e}^{\left(2e\right)})}+x+2e)})e^{(-2e)}\end{array}$$

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 $$\begin{array}{c}\int -2((3x^5{e}^x+5x^4{e}^{(x+e)}+2x^3{e}^{(x+2e)})e^{(x^6+2x^5{e}^e+x^4{e}^{\left(2e\right)}+e^{(x^6+2x^5{e}^e+x^4{e}^{\left(2e\right)})})}+e^x)e^{(x+e^{\left(e^{(x^6+2x^5{e}^e+x^4{e}^{\left(2e\right)})}\right)})}+3dx\end{array}$$

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	$-{\mathrm{e}}^{2x+{\mathrm{e}}^{{\mathrm{e}}^{x^4(2x{\mathrm{e}}^{\mathrm{e}}+x^2+{\mathrm{e}}^{2\mathrm{e}})}}}+3x$	$33$

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 $$\begin{array}{c}3x-e^{(2x+e^{\left(e^{(x^6+2x^5{e}^e+x^4{e}^{\left(2e\right)})}\right)})}\end{array}$$

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 $$\begin{array}{c}3x-{\mathrm{e}}^{2x}{\mathrm{e}}^{{\mathrm{e}}^{{\mathrm{e}}^{x^6}{\mathrm{e}}^{2x^5{\mathrm{e}}^{\mathrm{e}}}{\mathrm{e}}^{x^4{\mathrm{e}}^{2\mathrm{e}}}}}\end{array}$$

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 $$\begin{array}{c}\text{Timed out}\end{array}$$

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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