3.21.61 \(\int \frac {4}{3 e^5} \, dx\)

Optimal. Leaf size=10 \[ \frac {4 (133+x)}{3 e^5} \]

________________________________________________________________________________________

Rubi [A]  time = 0.00, antiderivative size = 8, normalized size of antiderivative = 0.80, 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 {4 x}{3 e^5} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[4/(3*E^5),x]

[Out]

(4*x)/(3*E^5)

Rule 8

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

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\frac {4 x}{3 e^5}\\ \end {aligned} \end {gather*}

________________________________________________________________________________________

Mathematica [A]  time = 0.00, size = 8, normalized size = 0.80 \begin {gather*} \frac {4 x}{3 e^5} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[4/(3*E^5),x]

[Out]

(4*x)/(3*E^5)

________________________________________________________________________________________

fricas [A]  time = 0.47, size = 5, normalized size = 0.50 \begin {gather*} \frac {4}{3} \, x e^{\left (-5\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(4/3/exp(5),x, algorithm="fricas")

[Out]

4/3*x*e^(-5)

________________________________________________________________________________________

giac [A]  time = 0.16, size = 5, normalized size = 0.50 \begin {gather*} \frac {4}{3} \, x e^{\left (-5\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(4/3/exp(5),x, algorithm="giac")

[Out]

4/3*x*e^(-5)

________________________________________________________________________________________

maple [A]  time = 0.01, size = 6, normalized size = 0.60

method	result	size
risch	\(\frac {4 x \,{\mathrm e}^{-5}}{3}\)	\(6\)
default	\(\frac {4 x \,{\mathrm e}^{-5}}{3}\)	\(8\)
norman	\(\frac {4 x \,{\mathrm e}^{-5}}{3}\)	\(8\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(4/3/exp(5),x,method=_RETURNVERBOSE)

[Out]

4/3*x*exp(-5)

________________________________________________________________________________________

maxima [A]  time = 0.43, size = 5, normalized size = 0.50 \begin {gather*} \frac {4}{3} \, x e^{\left (-5\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(4/3/exp(5),x, algorithm="maxima")

[Out]

4/3*x*e^(-5)

________________________________________________________________________________________

mupad [B]  time = 0.00, size = 5, normalized size = 0.50 \begin {gather*} \frac {4\,x\,{\mathrm {e}}^{-5}}{3} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((4*exp(-5))/3,x)

[Out]

(4*x*exp(-5))/3

________________________________________________________________________________________

sympy [A]  time = 0.01, size = 7, normalized size = 0.70 \begin {gather*} \frac {4 x}{3 e^{5}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(4/3/exp(5),x)

[Out]

4*x*exp(-5)/3

________________________________________________________________________________________