\(\int e \, dx\) [279]

Optimal result

Integrand size = 1, antiderivative size = 3 \[ \int e \, dx=e x \]

[Out]

x*exp(1)

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, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 1.000, Rules used = {8} \[ \int e \, dx=e x \]

[In]

Int[E,x]

[Out]

E*x

Rule 8

Int[a_, x_Symbol] :> Simp[a*x, x] /; FreeQ[a, 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 \[ \int e \, dx=e x \]

[In]

Integrate[E,x]

[Out]

E*x

Maple [A] (verified)

Time = 0.02 (sec) , antiderivative size = 9, normalized size of antiderivative = 3.00

method	result	size
parallelrisch	\(x^{\frac {1}{\ln \left (x \right )}} x\)	\(9\)

[In]

int(x^(1/ln(x)),x,method=_RETURNVERBOSE)

[Out]

x^(1/ln(x))*x

Fricas [A] (verification not implemented)

none

Time = 0.23 (sec) , antiderivative size = 4, normalized size of antiderivative = 1.33 \[ \int e \, dx=x e \]

[In]

integrate(x^(1/log(x)),x, algorithm="fricas")

[Out]

x*e

Sympy [A] (verification not implemented)

Time = 0.01 (sec) , antiderivative size = 3, normalized size of antiderivative = 1.00 \[ \int e \, dx=e x \]

[In]

integrate(x**(1/ln(x)),x)

[Out]

E*x

Maxima [A] (verification not implemented)

none

Time = 0.20 (sec) , antiderivative size = 4, normalized size of antiderivative = 1.33 \[ \int e \, dx=x e \]

[In]

integrate(x^(1/log(x)),x, algorithm="maxima")

[Out]

x*e

Giac [A] (verification not implemented)

none

Time = 0.25 (sec) , antiderivative size = 4, normalized size of antiderivative = 1.33 \[ \int e \, dx=x e \]

[In]

integrate(x^(1/log(x)),x, algorithm="giac")

[Out]

x*e

Mupad [B] (verification not implemented)

Time = 0.00 (sec) , antiderivative size = 4, normalized size of antiderivative = 1.33 \[ \int e \, dx=x\,\mathrm {e} \]

[In]

int(x^(1/log(x)),x)

[Out]

x*exp(1)