\(\int e^x \, dx\) [76]

Optimal result

Integrand size = 3, antiderivative size = 3 \[ \int e^x \, dx=e^x \]

[Out]

exp(x)

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 3, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.333, Rules used = {2225} \[ \int e^x \, dx=e^x \]

[In]

Int[E^x,x]

[Out]

E^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^x \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 3, normalized size of antiderivative = 1.00 \[ \int e^x \, dx=e^x \]

[In]

Integrate[E^x,x]

[Out]

E^x

Maple [A] (verified)

Time = 0.01 (sec) , antiderivative size = 3, normalized size of antiderivative = 1.00

method	result	size
gosper	\({\mathrm e}^{x}\)	\(3\)
lookup	\({\mathrm e}^{x}\)	\(3\)
derivativedivides	\({\mathrm e}^{x}\)	\(3\)
default	\({\mathrm e}^{x}\)	\(3\)
norman	\({\mathrm e}^{x}\)	\(3\)
risch	\({\mathrm e}^{x}\)	\(3\)
parallelrisch	\({\mathrm e}^{x}\)	\(3\)
meijerg	\({\mathrm e}^{x}-1\)	\(5\)

[In]

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

[Out]

exp(x)

Fricas [A] (verification not implemented)

none

Time = 0.26 (sec) , antiderivative size = 2, normalized size of antiderivative = 0.67 \[ \int e^x \, dx=e^{x} \]

[In]

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

[Out]

e^x

Sympy [A] (verification not implemented)

Time = 0.02 (sec) , antiderivative size = 2, normalized size of antiderivative = 0.67 \[ \int e^x \, dx=e^{x} \]

[In]

integrate(exp(x),x)

[Out]

exp(x)

Maxima [A] (verification not implemented)

none

Time = 0.20 (sec) , antiderivative size = 2, normalized size of antiderivative = 0.67 \[ \int e^x \, dx=e^{x} \]

[In]

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

[Out]

e^x

Giac [A] (verification not implemented)

none

Time = 0.28 (sec) , antiderivative size = 2, normalized size of antiderivative = 0.67 \[ \int e^x \, dx=e^{x} \]

[In]

integrate(exp(x),x, algorithm="giac")

[Out]

e^x

Mupad [B] (verification not implemented)

Time = 0.01 (sec) , antiderivative size = 2, normalized size of antiderivative = 0.67 \[ \int e^x \, dx={\mathrm {e}}^x \]

[In]

int(exp(x),x)

[Out]

exp(x)