\(\int \frac {3}{-1+3 e^2} \, dx\) [1737]

Optimal result

Integrand size = 11, antiderivative size = 11 \[ \int \frac {3}{-1+3 e^2} \, dx=\frac {x}{-\frac {1}{3}+e^2} \]

[Out]

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

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.09, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {8} \[ \int \frac {3}{-1+3 e^2} \, dx=-\frac {3 x}{1-3 e^2} \]

[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{align*} \text {integral}& = -\frac {3 x}{1-3 e^2} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.09 \[ \int \frac {3}{-1+3 e^2} \, dx=\frac {3 x}{-1+3 e^2} \]

[In]

Integrate[3/(-1 + 3*E^2),x]

[Out]

(3*x)/(-1 + 3*E^2)

Maple [A] (verified)

Time = 0.02 (sec) , antiderivative size = 12, normalized size of antiderivative = 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	\(\frac {3 x}{3 \,{\mathrm e}^{2}-1}\)	\(12\)
parallelrisch	\(\frac {3 x}{3 \,{\mathrm e}^{2}-1}\)	\(12\)

[In]

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

[Out]

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

Fricas [A] (verification not implemented)

none

Time = 0.23 (sec) , antiderivative size = 11, normalized size of antiderivative = 1.00 \[ \int \frac {3}{-1+3 e^2} \, dx=\frac {3 \, x}{3 \, e^{2} - 1} \]

[In]

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

[Out]

3*x/(3*e^2 - 1)

Sympy [A] (verification not implemented)

Time = 0.02 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.73 \[ \int \frac {3}{-1+3 e^2} \, dx=\frac {3 x}{-1 + 3 e^{2}} \]

[In]

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

[Out]

3*x/(-1 + 3*exp(2))

Maxima [A] (verification not implemented)

none

Time = 0.20 (sec) , antiderivative size = 11, normalized size of antiderivative = 1.00 \[ \int \frac {3}{-1+3 e^2} \, dx=\frac {3 \, x}{3 \, e^{2} - 1} \]

[In]

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

[Out]

3*x/(3*e^2 - 1)

Giac [A] (verification not implemented)

none

Time = 0.26 (sec) , antiderivative size = 11, normalized size of antiderivative = 1.00 \[ \int \frac {3}{-1+3 e^2} \, dx=\frac {3 \, x}{3 \, e^{2} - 1} \]

[In]

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

[Out]

3*x/(3*e^2 - 1)

Mupad [B] (verification not implemented)

Time = 0.00 (sec) , antiderivative size = 11, normalized size of antiderivative = 1.00 \[ \int \frac {3}{-1+3 e^2} \, dx=\frac {3\,x}{3\,{\mathrm {e}}^2-1} \]

[In]

int(3/(3*exp(2) - 1),x)

[Out]

(3*x)/(3*exp(2) - 1)