\(\int \frac {1}{200 e^8} \, dx\) [4634]

Optimal result

Integrand size = 7, antiderivative size = 15 \[ \int \frac {1}{200 e^8} \, dx=\frac {1}{25} e^{7-3 (5+\log (2))} x \]

[Out]

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

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.53, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.143, Rules used = {8} \[ \int \frac {1}{200 e^8} \, dx=\frac {x}{200 e^8} \]

[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{align*} \text {integral}& = \frac {x}{200 e^8} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.53 \[ \int \frac {1}{200 e^8} \, dx=\frac {x}{200 e^8} \]

[In]

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

[Out]

x/(200*E^8)

Maple [A] (verified)

Time = 0.01 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.40

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

[In]

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

[Out]

1/200*x*exp(-8)

Fricas [A] (verification not implemented)

none

Time = 0.28 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.67 \[ \int \frac {1}{200 e^8} \, dx=\frac {1}{25} \, x e^{\left (-3 \, \log \left (2\right ) - 8\right )} \]

[In]

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

[Out]

1/25*x*e^(-3*log(2) - 8)

Sympy [A] (verification not implemented)

Time = 0.02 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.33 \[ \int \frac {1}{200 e^8} \, dx=\frac {x}{200 e^{8}} \]

[In]

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

[Out]

x*exp(-8)/200

Maxima [A] (verification not implemented)

none

Time = 0.19 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.33 \[ \int \frac {1}{200 e^8} \, dx=\frac {1}{200} \, x e^{\left (-8\right )} \]

[In]

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

[Out]

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

Giac [A] (verification not implemented)

none

Time = 0.27 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.67 \[ \int \frac {1}{200 e^8} \, dx=\frac {1}{25} \, x e^{\left (-3 \, \log \left (2\right ) - 8\right )} \]

[In]

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

[Out]

1/25*x*e^(-3*log(2) - 8)

Mupad [B] (verification not implemented)

Time = 0.00 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.80 \[ \int \frac {1}{200 e^8} \, dx=\frac {x\,{\mathrm {e}}^2\,{\mathrm {e}}^{-3\,\ln \left (2\right )-10}}{25} \]

[In]

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

[Out]

(x*exp(2)*exp(- 3*log(2) - 10))/25