3.33.3 $\int 4e^{\frac{1}{18}(-e^3-e^5)}dx$

Optimal. Leaf size=22 $$-2+4e^{\frac{1}{18}(-e^3-e^5)}x$$

________________________________________________________________________________________

Rubi [A]  time = 0.01, antiderivative size = 17, normalized size of antiderivative = 0.77, number of steps used = 1, number of rules used = 1, integrand size = 19, $\frac{\text{number of rules}}{\text{integrand size}}$ = 0.053, Rules used = {8} $$\begin{array}{c}4e^{-\frac{1}{18}{e}^3(1+e^2)}x\end{array}$$

Antiderivative was successfully verified.

[In]

Int[4*E^((-E^3 - E^5)/18),x]

[Out]

(4*x)/E^((E^3*(1 + E^2))/18)

Rule 8

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

Rubi steps

$$\begin{array}{c}\begin{array}{rl}\text{integral}& =4e^{-\frac{1}{18}{e}^3(1+e^2)}x\end{array}\end{array}$$

________________________________________________________________________________________

Mathematica [A]  time = 0.00, size = 20, normalized size = 0.91 $$\begin{array}{c}4e^{\frac{1}{18}(-e^3-e^5)}x\end{array}$$

Antiderivative was successfully verified.

[In]

Integrate[4*E^((-E^3 - E^5)/18),x]

[Out]

4*E^((-E^3 - E^5)/18)*x

________________________________________________________________________________________

fricas [A]  time = 0.52, size = 13, normalized size = 0.59 $$\begin{array}{c}4x{e}^{(-\frac{1}{18}{e}^5-\frac{1}{18}{e}^3)}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(4/exp(1/18*exp(5)+1/18*exp(3)),x, algorithm="fricas")

[Out]

4*x*e^(-1/18*e^5 - 1/18*e^3)

________________________________________________________________________________________

giac [A]  time = 0.26, size = 13, normalized size = 0.59 $$\begin{array}{c}4x{e}^{(-\frac{1}{18}{e}^5-\frac{1}{18}{e}^3)}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(4/exp(1/18*exp(5)+1/18*exp(3)),x, algorithm="giac")

[Out]

4*x*e^(-1/18*e^5 - 1/18*e^3)

________________________________________________________________________________________

maple [A]  time = 0.04, size = 14, normalized size = 0.64

method	result	size
norman	$4{\mathrm{e}}^{-\frac{{\mathrm{e}}^5}{18}}{\mathrm{e}}^{-\frac{{\mathrm{e}}^3}{18}}x$	$14$
risch	$4x{\mathrm{e}}^{-\frac{{\mathrm{e}}^5}{18}-\frac{{\mathrm{e}}^3}{18}}$	$14$
default	$4x{\mathrm{e}}^{-\frac{{\mathrm{e}}^5}{18}-\frac{{\mathrm{e}}^3}{18}}$	$16$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(4/exp(1/18*exp(5)+1/18*exp(3)),x,method=_RETURNVERBOSE)

[Out]

4/exp(exp(5))^(1/18)/exp(exp(3))^(1/18)*x

________________________________________________________________________________________

maxima [A]  time = 0.60, size = 13, normalized size = 0.59 $$\begin{array}{c}4x{e}^{(-\frac{1}{18}{e}^5-\frac{1}{18}{e}^3)}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(4/exp(1/18*exp(5)+1/18*exp(3)),x, algorithm="maxima")

[Out]

4*x*e^(-1/18*e^5 - 1/18*e^3)

________________________________________________________________________________________

mupad [B]  time = 0.00, size = 13, normalized size = 0.59 $$\begin{array}{c}4x{\mathrm{e}}^{-\frac{{\mathrm{e}}^3}{18}-\frac{{\mathrm{e}}^5}{18}}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(4*exp(- exp(3)/18 - exp(5)/18),x)

[Out]

4*x*exp(- exp(3)/18 - exp(5)/18)

________________________________________________________________________________________

sympy [A]  time = 0.05, size = 14, normalized size = 0.64 $$\begin{array}{c}\frac{4x}{e^{\frac{e^3}{18}+\frac{e^5}{18}}}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(4/exp(1/18*exp(5)+1/18*exp(3)),x)

[Out]

4*x*exp(-exp(5)/18 - exp(3)/18)

________________________________________________________________________________________