3.13.27 \(\int (-1+16 e^{2 e^{4 e^{2 x}}+4 e^{2 x}+2 x}) \, dx\)

Optimal. Leaf size=20 \[ e^5+e^{2 e^{4 e^{2 x}}}-x \]

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Rubi [F]  time = 0.06, 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 (-1+16 e^{2 e^{4 e^{2 x}}+4 e^{2 x}+2 x}\right ) \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[-1 + 16*E^(2*E^(4*E^(2*x)) + 4*E^(2*x) + 2*x),x]

[Out]

-x + 4*Defer[Subst][Defer[Int][E^(2*(E^(2*x) + x)), x], x, 2*E^(2*x)]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=-x+16 \int e^{2 e^{4 e^{2 x}}+4 e^{2 x}+2 x} \, dx\\ &=-x+8 \operatorname {Subst}\left (\int e^{2 \left (e^{4 x}+2 x\right )} \, dx,x,e^{2 x}\right )\\ &=-x+4 \operatorname {Subst}\left (\int e^{2 \left (e^{2 x}+x\right )} \, dx,x,2 e^{2 x}\right )\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.03, size = 17, normalized size = 0.85 \begin {gather*} e^{2 e^{4 e^{2 x}}}-x \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[-1 + 16*E^(2*E^(4*E^(2*x)) + 4*E^(2*x) + 2*x),x]

[Out]

E^(2*E^(4*E^(2*x))) - x

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fricas [B]  time = 0.51, size = 49, normalized size = 2.45 \begin {gather*} -{\left (x e^{\left (2 \, x + 4 \, e^{\left (2 \, x\right )}\right )} - e^{\left (2 \, x + 4 \, e^{\left (2 \, x\right )} + 2 \, e^{\left (4 \, e^{\left (2 \, x\right )}\right )}\right )}\right )} e^{\left (-2 \, x - 4 \, e^{\left (2 \, x\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(16*exp(x)^2*exp(4*exp(x)^2)*exp(2*exp(4*exp(x)^2))-1,x, algorithm="fricas")

[Out]

-(x*e^(2*x + 4*e^(2*x)) - e^(2*x + 4*e^(2*x) + 2*e^(4*e^(2*x))))*e^(-2*x - 4*e^(2*x))

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giac [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int 16 \, e^{\left (2 \, x + 4 \, e^{\left (2 \, x\right )} + 2 \, e^{\left (4 \, e^{\left (2 \, x\right )}\right )}\right )} - 1\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(16*exp(x)^2*exp(4*exp(x)^2)*exp(2*exp(4*exp(x)^2))-1,x, algorithm="giac")

[Out]

integrate(16*e^(2*x + 4*e^(2*x) + 2*e^(4*e^(2*x))) - 1, x)

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maple [A]  time = 0.03, size = 15, normalized size = 0.75

method	result	size
default	\(-x +{\mathrm e}^{2 \,{\mathrm e}^{4 \,{\mathrm e}^{2 x}}}\)	\(15\)
norman	\(-x +{\mathrm e}^{2 \,{\mathrm e}^{4 \,{\mathrm e}^{2 x}}}\)	\(15\)
risch	\(-x +{\mathrm e}^{2 \,{\mathrm e}^{4 \,{\mathrm e}^{2 x}}}\)	\(15\)
derivativedivides	\(-\ln \left ({\mathrm e}^{x}\right )+{\mathrm e}^{2 \,{\mathrm e}^{4 \,{\mathrm e}^{2 x}}}\)	\(17\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(16*exp(x)^2*exp(4*exp(x)^2)*exp(2*exp(4*exp(x)^2))-1,x,method=_RETURNVERBOSE)

[Out]

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

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maxima [A]  time = 0.40, size = 14, normalized size = 0.70 \begin {gather*} -x + e^{\left (2 \, e^{\left (4 \, e^{\left (2 \, x\right )}\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(16*exp(x)^2*exp(4*exp(x)^2)*exp(2*exp(4*exp(x)^2))-1,x, algorithm="maxima")

[Out]

-x + e^(2*e^(4*e^(2*x)))

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mupad [B]  time = 0.07, size = 14, normalized size = 0.70 \begin {gather*} {\mathrm {e}}^{2\,{\mathrm {e}}^{4\,{\mathrm {e}}^{2\,x}}}-x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(16*exp(4*exp(2*x))*exp(2*x)*exp(2*exp(4*exp(2*x))) - 1,x)

[Out]

exp(2*exp(4*exp(2*x))) - x

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sympy [A]  time = 0.19, size = 12, normalized size = 0.60 \begin {gather*} - x + e^{2 e^{4 e^{2 x}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(16*exp(x)**2*exp(4*exp(x)**2)*exp(2*exp(4*exp(x)**2))-1,x)

[Out]

-x + exp(2*exp(4*exp(2*x)))

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