3.10.34 \(\int e^{e^{-2 x+2 e^{16} x}+8 x} (8+e^{-2 x+2 e^{16} x} (-2+2 e^{16})) \, dx\)

Optimal. Leaf size=19 \[ e^{e^{2 \left (-x+e^{16} x\right )}+8 x} \]

________________________________________________________________________________________

Rubi [A]  time = 0.17, antiderivative size = 18, normalized size of antiderivative = 0.95, number of steps used = 1, number of rules used = 1, integrand size = 41, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.024, Rules used = {6706} \begin {gather*} e^{8 x+e^{-2 \left (1-e^{16}\right ) x}} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[E^(E^(-2*x + 2*E^16*x) + 8*x)*(8 + E^(-2*x + 2*E^16*x)*(-2 + 2*E^16)),x]

[Out]

E^(E^(-2*(1 - E^16)*x) + 8*x)

Rule 6706

Int[(F_)^(v_)*(u_), x_Symbol] :> With[{q = DerivativeDivides[v, u, x]}, Simp[(q*F^v)/Log[F], x] /;  !FalseQ[q]
] /; FreeQ[F, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=e^{e^{-2 \left (1-e^{16}\right ) x}+8 x}\\ \end {aligned} \end {gather*}

________________________________________________________________________________________

Mathematica [A]  time = 0.13, size = 16, normalized size = 0.84 \begin {gather*} e^{e^{2 \left (-1+e^{16}\right ) x}+8 x} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[E^(E^(-2*x + 2*E^16*x) + 8*x)*(8 + E^(-2*x + 2*E^16*x)*(-2 + 2*E^16)),x]

[Out]

E^(E^(2*(-1 + E^16)*x) + 8*x)

________________________________________________________________________________________

fricas [A]  time = 0.78, size = 15, normalized size = 0.79 \begin {gather*} e^{\left (8 \, x + e^{\left (2 \, x e^{16} - 2 \, x\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((2*exp(4)^4-2)*exp(2*x*exp(4)^4-2*x)+8)*exp(exp(2*x*exp(4)^4-2*x)+8*x),x, algorithm="fricas")

[Out]

e^(8*x + e^(2*x*e^16 - 2*x))

________________________________________________________________________________________

giac [A]  time = 0.35, size = 15, normalized size = 0.79 \begin {gather*} e^{\left (8 \, x + e^{\left (2 \, x e^{16} - 2 \, x\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((2*exp(4)^4-2)*exp(2*x*exp(4)^4-2*x)+8)*exp(exp(2*x*exp(4)^4-2*x)+8*x),x, algorithm="giac")

[Out]

e^(8*x + e^(2*x*e^16 - 2*x))

________________________________________________________________________________________

maple [A]  time = 0.03, size = 14, normalized size = 0.74

method	result	size
risch	\({\mathrm e}^{{\mathrm e}^{2 x \left (-1+{\mathrm e}^{16}\right )}+8 x}\)	\(14\)
derivativedivides	\({\mathrm e}^{{\mathrm e}^{2 x \,{\mathrm e}^{16}-2 x}+8 x}\)	\(18\)
default	\({\mathrm e}^{{\mathrm e}^{2 x \,{\mathrm e}^{16}-2 x}+8 x}\)	\(18\)
norman	\({\mathrm e}^{{\mathrm e}^{2 x \,{\mathrm e}^{16}-2 x}+8 x}\)	\(18\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((2*exp(4)^4-2)*exp(2*x*exp(4)^4-2*x)+8)*exp(exp(2*x*exp(4)^4-2*x)+8*x),x,method=_RETURNVERBOSE)

[Out]

exp(exp(2*x*(-1+exp(16)))+8*x)

________________________________________________________________________________________

maxima [A]  time = 0.53, size = 15, normalized size = 0.79 \begin {gather*} e^{\left (8 \, x + e^{\left (2 \, x e^{16} - 2 \, x\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((2*exp(4)^4-2)*exp(2*x*exp(4)^4-2*x)+8)*exp(exp(2*x*exp(4)^4-2*x)+8*x),x, algorithm="maxima")

[Out]

e^(8*x + e^(2*x*e^16 - 2*x))

________________________________________________________________________________________

mupad [B]  time = 0.12, size = 15, normalized size = 0.79 \begin {gather*} {\mathrm {e}}^{8\,x+{\mathrm {e}}^{2\,x\,{\mathrm {e}}^{16}-2\,x}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp(8*x + exp(2*x*exp(16) - 2*x))*(exp(2*x*exp(16) - 2*x)*(2*exp(16) - 2) + 8),x)

[Out]

exp(8*x + exp(2*x*exp(16) - 2*x))

________________________________________________________________________________________

sympy [A]  time = 0.19, size = 15, normalized size = 0.79 \begin {gather*} e^{8 x + e^{- 2 x + 2 x e^{16}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((2*exp(4)**4-2)*exp(2*x*exp(4)**4-2*x)+8)*exp(exp(2*x*exp(4)**4-2*x)+8*x),x)

[Out]

exp(8*x + exp(-2*x + 2*x*exp(16)))

________________________________________________________________________________________