3.11.48 \(\int e \, dx\)

Optimal. Leaf size=3 \[ e x \]

________________________________________________________________________________________

Rubi [A]  time = 0.00, antiderivative size = 3, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 1.000, Rules used = {8} \begin {gather*} e x \end {gather*}

Antiderivative was successfully verified.

[In]

Int[E,x]

[Out]

E*x

Rule 8

Int[a_, x_Symbol] :> Simp[a*x, x] /; FreeQ[a, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=e x\\ \end {aligned} \end {gather*}

________________________________________________________________________________________

Mathematica [A]  time = 0.00, size = 3, normalized size = 1.00 \begin {gather*} e x \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[E,x]

[Out]

E*x

________________________________________________________________________________________

fricas [A]  time = 0.60, size = 4, normalized size = 1.33 \begin {gather*} x e \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(1),x, algorithm="fricas")

[Out]

x*e

________________________________________________________________________________________

giac [A]  time = 0.58, size = 4, normalized size = 1.33 \begin {gather*} x e \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(1),x, algorithm="giac")

[Out]

x*e

________________________________________________________________________________________

maple [A]  time = 0.01, size = 5, normalized size = 1.67

method	result	size
default	\(x \,{\mathrm e}\)	\(5\)
norman	\(x \,{\mathrm e}\)	\(5\)
risch	\(x \,{\mathrm e}\)	\(5\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp(1),x,method=_RETURNVERBOSE)

[Out]

x*exp(1)

________________________________________________________________________________________

maxima [A]  time = 0.47, size = 4, normalized size = 1.33 \begin {gather*} x e \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(1),x, algorithm="maxima")

[Out]

x*e

________________________________________________________________________________________

mupad [B]  time = 0.00, size = 4, normalized size = 1.33 \begin {gather*} x\,\mathrm {e} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp(1),x)

[Out]

x*exp(1)

________________________________________________________________________________________

sympy [A]  time = 0.01, size = 3, normalized size = 1.00 \begin {gather*} e x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(1),x)

[Out]

E*x

________________________________________________________________________________________