3.41.23 $\int 10e^{-2x}dx$

Optimal. Leaf size=13 $$-4-5e^{-2x}-\log (3)$$

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Rubi [A]  time = 0.00, antiderivative size = 7, normalized size of antiderivative = 0.54, number of steps used = 2, number of rules used = 2, integrand size = 7, $\frac{\text{number of rules}}{\text{integrand size}}$ = 0.286, Rules used = {12, 2194} $$\begin{array}{c}-5e^{-2x}\end{array}$$

Antiderivative was successfully verified.

[In]

Int[10/E^(2*x),x]

[Out]

-5/E^(2*x)

Rule 12

Int[(a_)*(u_), x_Symbol] :> Dist[a, Int[u, x], x] /; FreeQ[a, x] &&  !MatchQ[u, (b_)*(v_) /; FreeQ[b, x]]

Rule 2194

Int[((F_)^((c_.)*((a_.) + (b_.)*(x_))))^(n_.), x_Symbol] :> Simp[(F^(c*(a + b*x)))^n/(b*c*n*Log[F]), x] /; Fre
eQ[{F, a, b, c, n}, x]

Rubi steps

$$\begin{array}{c}\begin{array}{rl}\text{integral}& =10\int e^{-2x}dx\\ & =-5e^{-2x}\end{array}\end{array}$$

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Mathematica [A]  time = 0.00, size = 7, normalized size = 0.54 $$\begin{array}{c}-5e^{-2x}\end{array}$$

Antiderivative was successfully verified.

[In]

Integrate[10/E^(2*x),x]

[Out]

-5/E^(2*x)

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fricas [A]  time = 0.68, size = 6, normalized size = 0.46 $$\begin{array}{c}-5e^{(-2x)}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(10/exp(x)^2,x, algorithm="fricas")

[Out]

-5*e^(-2*x)

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giac [A]  time = 0.19, size = 6, normalized size = 0.46 $$\begin{array}{c}-5e^{(-2x)}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(10/exp(x)^2,x, algorithm="giac")

[Out]

-5*e^(-2*x)

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maple [A]  time = 0.02, size = 7, normalized size = 0.54

method	result	size
gosper	$-5{\mathrm{e}}^{-2x}$	$7$
derivativedivides	$-5{\mathrm{e}}^{-2x}$	$7$
default	$-5{\mathrm{e}}^{-2x}$	$7$
norman	$-5{\mathrm{e}}^{-2x}$	$7$
risch	$-5{\mathrm{e}}^{-2x}$	$7$
meijerg	$5-5{\mathrm{e}}^{-2x}$	$9$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(10/exp(x)^2,x,method=_RETURNVERBOSE)

[Out]

-5/exp(x)^2

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maxima [A]  time = 0.36, size = 6, normalized size = 0.46 $$\begin{array}{c}-5e^{(-2x)}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(10/exp(x)^2,x, algorithm="maxima")

[Out]

-5*e^(-2*x)

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mupad [B]  time = 0.02, size = 6, normalized size = 0.46 $$\begin{array}{c}-5{\mathrm{e}}^{-2x}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(10*exp(-2*x),x)

[Out]

-5*exp(-2*x)

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sympy [A]  time = 0.04, size = 7, normalized size = 0.54 $$\begin{array}{c}-5e^{-2x}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(10/exp(x)**2,x)

[Out]

-5*exp(-2*x)

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