\(\int \frac {1}{4 e^{19}} \, dx\) [469]

Optimal result

Integrand size = 7, antiderivative size = 8 \[ \int \frac {1}{4 e^{19}} \, dx=\frac {x}{4 e^{19}} \]

[Out]

exp(-ln(4/exp(2)/x)-21)

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 8, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.143, Rules used = {8} \[ \int \frac {1}{4 e^{19}} \, dx=\frac {x}{4 e^{19}} \]

[In]

Int[1/(4*E^19),x]

[Out]

x/(4*E^19)

Rule 8

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

Rubi steps \begin{align*} \text {integral}& = \frac {x}{4 e^{19}} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 8, normalized size of antiderivative = 1.00 \[ \int \frac {1}{4 e^{19}} \, dx=\frac {x}{4 e^{19}} \]

[In]

Integrate[1/(4*E^19),x]

[Out]

x/(4*E^19)

Maple [A] (verified)

Time = 0.02 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.75

method	result	size
risch	\(\frac {{\mathrm e}^{-19} x}{4}\)	\(6\)
norman	\(\frac {{\mathrm e}^{-21} {\mathrm e}^{2} x}{4}\)	\(10\)
derivativedivides	\({\mathrm e}^{-\ln \left (\frac {4 \,{\mathrm e}^{-2}}{x}\right )-21}\)	\(16\)
default	\({\mathrm e}^{-\ln \left (\frac {4 \,{\mathrm e}^{-2}}{x}\right )-21}\)	\(16\)
parallelrisch	\({\mathrm e}^{-\ln \left (\frac {4 \,{\mathrm e}^{-2}}{x}\right )-21}\)	\(16\)

[In]

int(exp(-ln(4/exp(2)/x)-21)/x,x,method=_RETURNVERBOSE)

[Out]

1/4*exp(-19)*x

Fricas [A] (verification not implemented)

none

Time = 0.23 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.62 \[ \int \frac {1}{4 e^{19}} \, dx=\frac {1}{4} \, x e^{\left (-19\right )} \]

[In]

integrate(exp(-log(4/exp(2)/x)-21)/x,x, algorithm="fricas")

[Out]

1/4*x*e^(-19)

Sympy [A] (verification not implemented)

Time = 0.01 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.62 \[ \int \frac {1}{4 e^{19}} \, dx=\frac {x}{4 e^{19}} \]

[In]

integrate(exp(-ln(4/exp(2)/x)-21)/x,x)

[Out]

x*exp(-19)/4

Maxima [A] (verification not implemented)

none

Time = 0.19 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.62 \[ \int \frac {1}{4 e^{19}} \, dx=\frac {1}{4} \, x e^{\left (-19\right )} \]

[In]

integrate(exp(-log(4/exp(2)/x)-21)/x,x, algorithm="maxima")

[Out]

1/4*x*e^(-19)

Giac [A] (verification not implemented)

none

Time = 0.30 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.62 \[ \int \frac {1}{4 e^{19}} \, dx=\frac {1}{4} \, x e^{\left (-19\right )} \]

[In]

integrate(exp(-log(4/exp(2)/x)-21)/x,x, algorithm="giac")

[Out]

1/4*x*e^(-19)

Mupad [B] (verification not implemented)

Time = 0.02 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.62 \[ \int \frac {1}{4 e^{19}} \, dx=\frac {x\,{\mathrm {e}}^{-19}}{4} \]

[In]

int(exp(- log((4*exp(-2))/x) - 21)/x,x)

[Out]

(x*exp(-19))/4