3.84.38 \(\int \frac {1}{-2+e^3} \, dx\)

Optimal. Leaf size=9 \[ \frac {x}{-2+e^3} \]

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Rubi [A]  time = 0.00, antiderivative size = 12, normalized size of antiderivative = 1.33, number of steps used = 1, number of rules used = 1, integrand size = 7, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.143, Rules used = {8} \begin {gather*} -\frac {x}{2-e^3} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(-2 + E^3)^(-1),x]

[Out]

-(x/(2 - E^3))

Rule 8

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

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=-\frac {x}{2-e^3}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 9, normalized size = 1.00 \begin {gather*} \frac {x}{-2+e^3} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-2 + E^3)^(-1),x]

[Out]

x/(-2 + E^3)

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fricas [A]  time = 0.57, size = 8, normalized size = 0.89 \begin {gather*} \frac {x}{e^{3} - 2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(exp(3)-2),x, algorithm="fricas")

[Out]

x/(e^3 - 2)

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giac [A]  time = 0.18, size = 8, normalized size = 0.89 \begin {gather*} \frac {x}{e^{3} - 2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(exp(3)-2),x, algorithm="giac")

[Out]

x/(e^3 - 2)

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maple [A]  time = 0.02, size = 9, normalized size = 1.00

method	result	size
default	\(\frac {x}{{\mathrm e}^{3}-2}\)	\(9\)
norman	\(\frac {x}{{\mathrm e}^{3}-2}\)	\(9\)
risch	\(\frac {x}{{\mathrm e}^{3}-2}\)	\(9\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/(exp(3)-2),x,method=_RETURNVERBOSE)

[Out]

x/(exp(3)-2)

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maxima [A]  time = 0.39, size = 8, normalized size = 0.89 \begin {gather*} \frac {x}{e^{3} - 2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(exp(3)-2),x, algorithm="maxima")

[Out]

x/(e^3 - 2)

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mupad [B]  time = 0.00, size = 8, normalized size = 0.89 \begin {gather*} \frac {x}{{\mathrm {e}}^3-2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/(exp(3) - 2),x)

[Out]

x/(exp(3) - 2)

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sympy [A]  time = 0.05, size = 5, normalized size = 0.56 \begin {gather*} \frac {x}{-2 + e^{3}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(exp(3)-2),x)

[Out]

x/(-2 + exp(3))

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