\(\int e^{2+x} \, dx\) [3398]

Optimal result

Integrand size = 5, antiderivative size = 5 \[ \int e^{2+x} \, dx=e^{2+x} \]

[Out]

exp(2+x)

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 5, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.200, Rules used = {2225} \[ \int e^{2+x} \, dx=e^{x+2} \]

[In]

Int[E^(2 + x),x]

[Out]

E^(2 + x)

Rule 2225

Int[((F_)^((c_.)*((a_.) + (b_.)*(x_))))^(n_.), x_Symbol] :> Simp[(F^(c*(a + b*x)))^n/(b*c*n*Log[F]), x] /; Fre
eQ[{F, a, b, c, n}, x]

Rubi steps \begin{align*} \text {integral}& = e^{2+x} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 5, normalized size of antiderivative = 1.00 \[ \int e^{2+x} \, dx=e^{2+x} \]

[In]

Integrate[E^(2 + x),x]

[Out]

E^(2 + x)

Maple [A] (verified)

Time = 0.42 (sec) , antiderivative size = 5, normalized size of antiderivative = 1.00

method	result	size
gosper	\({\mathrm e}^{2+x}\)	\(5\)
derivativedivides	\({\mathrm e}^{2+x}\)	\(5\)
default	\({\mathrm e}^{2+x}\)	\(5\)
norman	\({\mathrm e}^{2+x}\)	\(5\)
risch	\({\mathrm e}^{2+x}\)	\(5\)
parallelrisch	\({\mathrm e}^{2+x}\)	\(5\)
meijerg	\(-{\mathrm e}^{2} \left (1-{\mathrm e}^{x}\right )\)	\(11\)

[In]

int(exp(2+x),x,method=_RETURNVERBOSE)

[Out]

exp(2+x)

Fricas [A] (verification not implemented)

none

Time = 0.23 (sec) , antiderivative size = 4, normalized size of antiderivative = 0.80 \[ \int e^{2+x} \, dx=e^{\left (x + 2\right )} \]

[In]

integrate(exp(2+x),x, algorithm="fricas")

[Out]

e^(x + 2)

Sympy [A] (verification not implemented)

Time = 0.03 (sec) , antiderivative size = 3, normalized size of antiderivative = 0.60 \[ \int e^{2+x} \, dx=e^{x + 2} \]

[In]

integrate(exp(2+x),x)

[Out]

exp(x + 2)

Maxima [A] (verification not implemented)

none

Time = 0.18 (sec) , antiderivative size = 4, normalized size of antiderivative = 0.80 \[ \int e^{2+x} \, dx=e^{\left (x + 2\right )} \]

[In]

integrate(exp(2+x),x, algorithm="maxima")

[Out]

e^(x + 2)

Giac [A] (verification not implemented)

none

Time = 0.25 (sec) , antiderivative size = 4, normalized size of antiderivative = 0.80 \[ \int e^{2+x} \, dx=e^{\left (x + 2\right )} \]

[In]

integrate(exp(2+x),x, algorithm="giac")

[Out]

e^(x + 2)

Mupad [B] (verification not implemented)

Time = 0.02 (sec) , antiderivative size = 4, normalized size of antiderivative = 0.80 \[ \int e^{2+x} \, dx={\mathrm {e}}^{x+2} \]

[In]

int(exp(x + 2),x)

[Out]

exp(x + 2)