3.5.69 \(\int \frac {1}{4 e^{19}} \, dx\)

Optimal. Leaf size=8 \[ \frac {x}{4 e^{19}} \]

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Rubi [A]  time = 0.00, antiderivative size = 8, normalized size of antiderivative = 1.00, 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}{4 e^{19}} \end {gather*}

Antiderivative was successfully verified.

[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 {gather*} \begin {aligned} \text {integral} &=\frac {x}{4 e^{19}}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 8, normalized size = 1.00 \begin {gather*} \frac {x}{4 e^{19}} \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

x/(4*E^19)

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fricas [A]  time = 1.22, size = 5, normalized size = 0.62 \begin {gather*} \frac {1}{4} \, x e^{\left (-19\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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giac [A]  time = 0.28, size = 5, normalized size = 0.62 \begin {gather*} \frac {1}{4} \, x e^{\left (-19\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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maple [A]  time = 0.02, size = 6, normalized size = 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	\({\mathrm e}^{-\ln \left (\frac {4 \,{\mathrm e}^{-2}}{x}\right )-21}\)	\(16\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

1/4*exp(-19)*x

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maxima [A]  time = 0.40, size = 5, normalized size = 0.62 \begin {gather*} \frac {1}{4} \, x e^{\left (-19\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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mupad [B]  time = 0.02, size = 5, normalized size = 0.62 \begin {gather*} \frac {x\,{\mathrm {e}}^{-19}}{4} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

(x*exp(-19))/4

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sympy [A]  time = 0.05, size = 5, normalized size = 0.62 \begin {gather*} \frac {x}{4 e^{19}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

x*exp(-19)/4

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