3.67.43 \(\int \frac {1}{e^7} \, dx\)

Optimal. Leaf size=5 \[ \frac {x}{e^7} \]

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Rubi [A]  time = 0.00, antiderivative size = 5, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 3, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.333, Rules used = {8} \begin {gather*} \frac {x}{e^7} \end {gather*}

Antiderivative was successfully verified.

[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 {gather*} \begin {aligned} \text {integral} &=\frac {x}{e^7}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 5, normalized size = 1.00 \begin {gather*} \frac {x}{e^7} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[E^(-7),x]

[Out]

x/E^7

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fricas [A]  time = 0.55, size = 4, normalized size = 0.80 \begin {gather*} x e^{\left (-7\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

x*e^(-7)

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giac [A]  time = 0.14, size = 4, normalized size = 0.80 \begin {gather*} x e^{\left (-7\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

x*e^(-7)

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maple [A]  time = 0.02, size = 5, normalized size = 1.00

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

exp(-7)*x

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maxima [A]  time = 0.37, size = 4, normalized size = 0.80 \begin {gather*} x e^{\left (-7\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

x*e^(-7)

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mupad [B]  time = 0.02, size = 4, normalized size = 0.80 \begin {gather*} x\,{\mathrm {e}}^{-7} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp(log(x) - 7)/x,x)

[Out]

x*exp(-7)

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sympy [A]  time = 0.05, size = 3, normalized size = 0.60 \begin {gather*} \frac {x}{e^{7}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

x*exp(-7)

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