3.82.15 \(\int (-1-e^{2-x}) \, dx\)

Optimal. Leaf size=12 \[ -1+e^{2-x}-x \]

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Rubi [A]  time = 0.00, antiderivative size = 11, normalized size of antiderivative = 0.92, number of steps used = 2, number of rules used = 1, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {2194} \begin {gather*} e^{2-x}-x \end {gather*}

Antiderivative was successfully verified.

[In]

Int[-1 - E^(2 - x),x]

[Out]

E^(2 - x) - 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} &=-x-\int e^{2-x} \, dx\\ &=e^{2-x}-x\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.01, size = 11, normalized size = 0.92 \begin {gather*} e^{2-x}-x \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[-1 - E^(2 - x),x]

[Out]

E^(2 - x) - x

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fricas [A]  time = 0.72, size = 10, normalized size = 0.83 \begin {gather*} -x + e^{\left (-x + 2\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-exp(2-x)-1,x, algorithm="fricas")

[Out]

-x + e^(-x + 2)

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giac [A]  time = 0.13, size = 10, normalized size = 0.83 \begin {gather*} -x + e^{\left (-x + 2\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-exp(2-x)-1,x, algorithm="giac")

[Out]

-x + e^(-x + 2)

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maple [A]  time = 0.01, size = 11, normalized size = 0.92

method	result	size
default	\({\mathrm e}^{2-x}-x\)	\(11\)
norman	\({\mathrm e}^{2-x}-x\)	\(11\)
risch	\({\mathrm e}^{2-x}-x\)	\(11\)
derivativedivides	\({\mathrm e}^{2-x}+\ln \left ({\mathrm e}^{2-x}\right )\)	\(15\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-exp(2-x)-1,x,method=_RETURNVERBOSE)

[Out]

exp(2-x)-x

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maxima [A]  time = 0.37, size = 10, normalized size = 0.83 \begin {gather*} -x + e^{\left (-x + 2\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-exp(2-x)-1,x, algorithm="maxima")

[Out]

-x + e^(-x + 2)

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mupad [B]  time = 0.08, size = 10, normalized size = 0.83 \begin {gather*} {\mathrm {e}}^{2-x}-x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(- exp(2 - x) - 1,x)

[Out]

exp(2 - x) - x

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sympy [A]  time = 0.07, size = 5, normalized size = 0.42 \begin {gather*} - x + e^{2 - x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-exp(2-x)-1,x)

[Out]

-x + exp(2 - x)

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