3.11.46 \(\int \frac {-1-e}{e} \, dx\)

Optimal. Leaf size=24 \[ 1-x-\frac {-2+\left (4+\frac {5 e^3}{3}\right )^2+x}{e} \]

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Rubi [A]  time = 0.00, antiderivative size = 9, normalized size of antiderivative = 0.38, number of steps used = 1, number of rules used = 1, integrand size = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {8} \begin {gather*} -\frac {(1+e) x}{e} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(-1 - E)/E,x]

[Out]

-(((1 + E)*x)/E)

Rule 8

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

Rubi steps

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

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Mathematica [A]  time = 0.00, size = 10, normalized size = 0.42 \begin {gather*} -x-\frac {x}{e} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-1 - E)/E,x]

[Out]

-x - x/E

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fricas [A]  time = 1.24, size = 10, normalized size = 0.42 \begin {gather*} -{\left (x e + x\right )} e^{\left (-1\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-(x*e + x)*e^(-1)

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giac [A]  time = 0.35, size = 9, normalized size = 0.38 \begin {gather*} -x {\left (e + 1\right )} e^{\left (-1\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-x*(e + 1)*e^(-1)

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maple [A]  time = 0.01, size = 12, normalized size = 0.50

method	result	size
norman	\(-{\mathrm e}^{-1} \left (1+{\mathrm e}\right ) x\)	\(12\)
default	\(\left (-{\mathrm e}-1\right ) {\mathrm e}^{-1} x\)	\(13\)
risch	\(-{\mathrm e}^{-1} x \,{\mathrm e}-{\mathrm e}^{-1} x\)	\(14\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-1/exp(1)*(1+exp(1))*x

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maxima [A]  time = 0.49, size = 9, normalized size = 0.38 \begin {gather*} -x {\left (e + 1\right )} e^{\left (-1\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-x*(e + 1)*e^(-1)

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mupad [B]  time = 0.00, size = 9, normalized size = 0.38 \begin {gather*} -x\,{\mathrm {e}}^{-1}\,\left (\mathrm {e}+1\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-exp(-1)*(exp(1) + 1),x)

[Out]

-x*exp(-1)*(exp(1) + 1)

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sympy [A]  time = 0.04, size = 10, normalized size = 0.42 \begin {gather*} \frac {x \left (- e - 1\right )}{e} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

x*(-E - 1)*exp(-1)

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