\(\int \frac {1}{e^7} \, dx\) [6643]

Optimal result

Integrand size = 3, antiderivative size = 5 \[ \int \frac {1}{e^7} \, dx=\frac {x}{e^7} \]

[Out]

exp(ln(x)-7)

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 5, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.333, Rules used = {8} \[ \int \frac {1}{e^7} \, dx=\frac {x}{e^7} \]

[In]

Int[E^(-7),x]

[Out]

x/E^7

Rule 8

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

Rubi steps \begin{align*} \text {integral}& = \frac {x}{e^7} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 5, normalized size of antiderivative = 1.00 \[ \int \frac {1}{e^7} \, dx=\frac {x}{e^7} \]

[In]

Integrate[E^(-7),x]

[Out]

x/E^7

Maple [A] (verified)

Time = 0.12 (sec) , antiderivative size = 5, normalized size of antiderivative = 1.00

method	result	size
risch	\({\mathrm e}^{-7} x\)	\(5\)
derivativedivides	\({\mathrm e}^{\ln \left (x \right )-7}\)	\(6\)
default	\({\mathrm e}^{\ln \left (x \right )-7}\)	\(6\)
parallelrisch	\({\mathrm e}^{\ln \left (x \right )-7}\)	\(6\)
norman	\({\mathrm e}^{-7} x\)	\(7\)

[In]

int(exp(ln(x)-7)/x,x,method=_RETURNVERBOSE)

[Out]

exp(-7)*x

Fricas [A] (verification not implemented)

none

Time = 0.43 (sec) , antiderivative size = 4, normalized size of antiderivative = 0.80 \[ \int \frac {1}{e^7} \, dx=x e^{\left (-7\right )} \]

[In]

integrate(exp(log(x)-7)/x,x, algorithm="fricas")

[Out]

x*e^(-7)

Sympy [A] (verification not implemented)

Time = 0.02 (sec) , antiderivative size = 3, normalized size of antiderivative = 0.60 \[ \int \frac {1}{e^7} \, dx=\frac {x}{e^{7}} \]

[In]

integrate(exp(ln(x)-7)/x,x)

[Out]

x*exp(-7)

Maxima [A] (verification not implemented)

none

Time = 0.18 (sec) , antiderivative size = 4, normalized size of antiderivative = 0.80 \[ \int \frac {1}{e^7} \, dx=x e^{\left (-7\right )} \]

[In]

integrate(exp(log(x)-7)/x,x, algorithm="maxima")

[Out]

x*e^(-7)

Giac [A] (verification not implemented)

none

Time = 0.29 (sec) , antiderivative size = 4, normalized size of antiderivative = 0.80 \[ \int \frac {1}{e^7} \, dx=x e^{\left (-7\right )} \]

[In]

integrate(exp(log(x)-7)/x,x, algorithm="giac")

[Out]

x*e^(-7)

Mupad [B] (verification not implemented)

Time = 0.02 (sec) , antiderivative size = 4, normalized size of antiderivative = 0.80 \[ \int \frac {1}{e^7} \, dx=x\,{\mathrm {e}}^{-7} \]

[In]

int(exp(log(x) - 7)/x,x)

[Out]

x*exp(-7)