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

Optimal. Leaf size=11 \[ \frac {x}{-\frac {1}{3}+e^2} \]

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Rubi [A]  time = 0.00, antiderivative size = 12, normalized size of antiderivative = 1.09, number of steps used = 1, number of rules used = 1, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {8} \begin {gather*} -\frac {3 x}{1-3 e^2} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[3/(-1 + 3*E^2),x]

[Out]

(-3*x)/(1 - 3*E^2)

Rule 8

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

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=-\frac {3 x}{1-3 e^2}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 12, normalized size = 1.09 \begin {gather*} \frac {3 x}{-1+3 e^2} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[3/(-1 + 3*E^2),x]

[Out]

(3*x)/(-1 + 3*E^2)

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fricas [A]  time = 0.81, size = 11, normalized size = 1.00 \begin {gather*} \frac {3 \, x}{3 \, e^{2} - 1} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

3*x/(3*e^2 - 1)

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giac [A]  time = 0.28, size = 11, normalized size = 1.00 \begin {gather*} \frac {3 \, x}{3 \, e^{2} - 1} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

3*x/(3*e^2 - 1)

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maple [A]  time = 0.02, size = 12, normalized size = 1.09

method	result	size
default	\(\frac {3 x}{3 \,{\mathrm e}^{2}-1}\)	\(12\)
norman	\(\frac {3 x}{3 \,{\mathrm e}^{2}-1}\)	\(12\)
risch	\(\frac {3 x}{3 \,{\mathrm e}^{2}-1}\)	\(12\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

3/(3*exp(2)-1)*x

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maxima [A]  time = 0.75, size = 11, normalized size = 1.00 \begin {gather*} \frac {3 \, x}{3 \, e^{2} - 1} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

3*x/(3*e^2 - 1)

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mupad [B]  time = 0.00, size = 11, normalized size = 1.00 \begin {gather*} \frac {3\,x}{3\,{\mathrm {e}}^2-1} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(3/(3*exp(2) - 1),x)

[Out]

(3*x)/(3*exp(2) - 1)

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sympy [A]  time = 0.05, size = 8, normalized size = 0.73 \begin {gather*} \frac {3 x}{-1 + 3 e^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

3*x/(-1 + 3*exp(2))

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