3.3.6 \(\int e \, dx\) [206]

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

[Out]

exp(1)*x

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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*}

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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

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Maple [A]
time = 0.01, size = 9, normalized size = 3.00

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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Maxima [A]
time = 0.34, size = 4, normalized size = 1.33 \begin {gather*} x e \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

x*e

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Fricas [A]
time = 0.54, size = 4, normalized size = 1.33 \begin {gather*} x e \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

x*e

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

E*x

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Giac [A]
time = 0.48, size = 4, normalized size = 1.33 \begin {gather*} x e \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

x*e

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Mupad [B]
time = 0.01, 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(x^(1/log(x)),x)

[Out]

x*exp(1)

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Chatgpt [A] valid for real x
time = 1.00, size = 4, normalized size = 1.33 \begin {gather*} {\mathrm e} x \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

exp(1)*x

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