3.22.21 \(\int e^{-1+x} \, dx\)

Optimal. Leaf size=5 \[ e^{-1+x} \]

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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 = 5, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.200, Rules used = {2194} \begin {gather*} e^{x-1} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[E^(-1 + x),x]

[Out]

E^(-1 + 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 {gather*} \begin {aligned} \text {integral} &=e^{-1+x}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 5, normalized size = 1.00 \begin {gather*} e^{-1+x} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[E^(-1 + x),x]

[Out]

E^(-1 + x)

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fricas [A]  time = 0.50, size = 4, normalized size = 0.80 \begin {gather*} e^{\left (x - 1\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(x-1),x, algorithm="fricas")

[Out]

e^(x - 1)

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giac [A]  time = 0.26, size = 4, normalized size = 0.80 \begin {gather*} e^{\left (x - 1\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(x-1),x, algorithm="giac")

[Out]

e^(x - 1)

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

method	result	size
gosper	\({\mathrm e}^{x -1}\)	\(5\)
derivativedivides	\({\mathrm e}^{x -1}\)	\(5\)
default	\({\mathrm e}^{x -1}\)	\(5\)
norman	\({\mathrm e}^{x -1}\)	\(5\)
risch	\({\mathrm e}^{x -1}\)	\(5\)
meijerg	\(-{\mathrm e}^{-1} \left (1-{\mathrm e}^{x}\right )\)	\(11\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp(x-1),x,method=_RETURNVERBOSE)

[Out]

exp(x-1)

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maxima [A]  time = 0.34, size = 4, normalized size = 0.80 \begin {gather*} e^{\left (x - 1\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(x-1),x, algorithm="maxima")

[Out]

e^(x - 1)

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mupad [B]  time = 0.02, size = 4, normalized size = 0.80 \begin {gather*} {\mathrm {e}}^{x-1} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp(x - 1),x)

[Out]

exp(x - 1)

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sympy [A]  time = 0.06, size = 3, normalized size = 0.60 \begin {gather*} e^{x - 1} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(x-1),x)

[Out]

exp(x - 1)

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