3.14.49 $\int -5e^{-x}dx$

Optimal. Leaf size=9 $$-4+5e^{-x}$$

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Rubi [A]  time = 0.00, antiderivative size = 7, normalized size of antiderivative = 0.78, 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} $$\begin{array}{c}5e^{-x}\end{array}$$

Antiderivative was successfully verified.

[In]

Int[-5/E^x,x]

[Out]

5/E^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

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

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Mathematica [A]  time = 0.00, size = 7, normalized size = 0.78 $$\begin{array}{c}5e^{-x}\end{array}$$

Antiderivative was successfully verified.

[In]

Integrate[-5/E^x,x]

[Out]

5/E^x

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fricas [A]  time = 0.86, size = 6, normalized size = 0.67 $$\begin{array}{c}5e^{(-x)}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

5*e^(-x)

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giac [A]  time = 0.31, size = 6, normalized size = 0.67 $$\begin{array}{c}5e^{(-x)}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

5*e^(-x)

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maple [A]  time = 0.01, size = 7, normalized size = 0.78

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-5/exp(x),x,method=_RETURNVERBOSE)

[Out]

5/exp(x)

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maxima [A]  time = 0.47, size = 6, normalized size = 0.67 $$\begin{array}{c}5e^{(-x)}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

5*e^(-x)

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mupad [B]  time = 0.01, size = 6, normalized size = 0.67 $$\begin{array}{c}5{\mathrm{e}}^{-x}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-5*exp(-x),x)

[Out]

5*exp(-x)

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sympy [A]  time = 0.04, size = 3, normalized size = 0.33 $$\begin{array}{c}5e^{-x}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-5/exp(x),x)

[Out]

5*exp(-x)

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