3.47.34 \(\int \frac {1}{200 e^8} \, dx\)

Optimal. Leaf size=15 \[ \frac {1}{25} e^{7-3 (5+\log (2))} x \]

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Rubi [A]  time = 0.00, antiderivative size = 8, normalized size of antiderivative = 0.53, 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}{200 e^8} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[1/(200*E^8),x]

[Out]

x/(200*E^8)

Rule 8

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

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\frac {x}{200 e^8}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 8, normalized size = 0.53 \begin {gather*} \frac {x}{200 e^8} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[1/(200*E^8),x]

[Out]

x/(200*E^8)

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fricas [A]  time = 0.41, size = 10, normalized size = 0.67 \begin {gather*} \frac {1}{25} \, x e^{\left (-3 \, \log \relax (2) - 8\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/25*exp(2)/exp(3*log(2)+10),x, algorithm="fricas")

[Out]

1/25*x*e^(-3*log(2) - 8)

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giac [A]  time = 0.18, size = 10, normalized size = 0.67 \begin {gather*} \frac {1}{25} \, x e^{\left (-3 \, \log \relax (2) - 8\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/25*exp(2)/exp(3*log(2)+10),x, algorithm="giac")

[Out]

1/25*x*e^(-3*log(2) - 8)

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maple [A]  time = 0.02, size = 6, normalized size = 0.40

method	result	size
risch	\(\frac {{\mathrm e}^{-8} x}{200}\)	\(6\)
norman	\(\frac {{\mathrm e}^{2} {\mathrm e}^{-10} x}{200}\)	\(10\)
default	\(\frac {{\mathrm e}^{2} {\mathrm e}^{-10} x}{200}\)	\(15\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/25*exp(2)/exp(3*ln(2)+10),x,method=_RETURNVERBOSE)

[Out]

1/200*exp(-8)*x

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maxima [A]  time = 0.38, size = 5, normalized size = 0.33 \begin {gather*} \frac {1}{200} \, x e^{\left (-8\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/25*exp(2)/exp(3*log(2)+10),x, algorithm="maxima")

[Out]

1/200*x*e^(-8)

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mupad [B]  time = 0.00, size = 12, normalized size = 0.80 \begin {gather*} \frac {x\,{\mathrm {e}}^2\,{\mathrm {e}}^{-3\,\ln \relax (2)-10}}{25} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(2)*exp(- 3*log(2) - 10))/25,x)

[Out]

(x*exp(2)*exp(- 3*log(2) - 10))/25

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sympy [A]  time = 0.07, size = 5, normalized size = 0.33 \begin {gather*} \frac {x}{200 e^{8}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/25*exp(2)/exp(3*ln(2)+10),x)

[Out]

x*exp(-8)/200

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