3.88.92 \(\int e^{-1-x} (-9 e^{1+x}+e^{e^{-1-x} x} (1-x)) \, dx\)

Optimal. Leaf size=25 \[ e^{e^{-1-x} x}-x-\log \left (3 e^{8 x}\right ) \]

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Rubi [F]  time = 0.33, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int e^{-1-x} \left (-9 e^{1+x}+e^{e^{-1-x} x} (1-x)\right ) \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[E^(-1 - x)*(-9*E^(1 + x) + E^(E^(-1 - x)*x)*(1 - x)),x]

[Out]

-9*x + Defer[Int][E^(-1 + (-1 + E^(-1 - x))*x), x] - Defer[Int][E^(-1 + (-1 + E^(-1 - x))*x)*x, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-9-e^{-1+\left (-1+e^{-1-x}\right ) x} (-1+x)\right ) \, dx\\ &=-9 x-\int e^{-1+\left (-1+e^{-1-x}\right ) x} (-1+x) \, dx\\ &=-9 x-\int \left (-e^{-1+\left (-1+e^{-1-x}\right ) x}+e^{-1+\left (-1+e^{-1-x}\right ) x} x\right ) \, dx\\ &=-9 x+\int e^{-1+\left (-1+e^{-1-x}\right ) x} \, dx-\int e^{-1+\left (-1+e^{-1-x}\right ) x} x \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.14, size = 15, normalized size = 0.60 \begin {gather*} e^{e^{-1-x} x}-9 x \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[E^(-1 - x)*(-9*E^(1 + x) + E^(E^(-1 - x)*x)*(1 - x)),x]

[Out]

E^(E^(-1 - x)*x) - 9*x

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fricas [A]  time = 0.54, size = 13, normalized size = 0.52 \begin {gather*} -9 \, x + e^{\left (x e^{\left (-x - 1\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-x+1)*exp(x/exp(x+1))-9*exp(x+1))/exp(x+1),x, algorithm="fricas")

[Out]

-9*x + e^(x*e^(-x - 1))

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giac [A]  time = 0.17, size = 27, normalized size = 1.08 \begin {gather*} -{\left (9 \, x e^{\left (-x\right )} - e^{\left (x e^{\left (-x - 1\right )} - x\right )}\right )} e^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-x+1)*exp(x/exp(x+1))-9*exp(x+1))/exp(x+1),x, algorithm="giac")

[Out]

-(9*x*e^(-x) - e^(x*e^(-x - 1) - x))*e^x

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maple [A]  time = 0.06, size = 14, normalized size = 0.56

method	result	size
risch	\(-9 x +{\mathrm e}^{x \,{\mathrm e}^{-x -1}}\)	\(14\)
norman	\(\left ({\mathrm e}^{x +1} {\mathrm e}^{x \,{\mathrm e}^{-x -1}}-9 x \,{\mathrm e}^{x +1}\right ) {\mathrm e}^{-x -1}\)	\(30\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((1-x)*exp(x/exp(x+1))-9*exp(x+1))/exp(x+1),x,method=_RETURNVERBOSE)

[Out]

-9*x+exp(x*exp(-x-1))

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maxima [A]  time = 0.43, size = 13, normalized size = 0.52 \begin {gather*} -9 \, x + e^{\left (x e^{\left (-x - 1\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-x+1)*exp(x/exp(x+1))-9*exp(x+1))/exp(x+1),x, algorithm="maxima")

[Out]

-9*x + e^(x*e^(-x - 1))

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mupad [B]  time = 5.45, size = 13, normalized size = 0.52 \begin {gather*} {\mathrm {e}}^{x\,{\mathrm {e}}^{-x}\,{\mathrm {e}}^{-1}}-9\,x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-exp(- x - 1)*(9*exp(x + 1) + exp(x*exp(- x - 1))*(x - 1)),x)

[Out]

exp(x*exp(-x)*exp(-1)) - 9*x

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sympy [A]  time = 0.15, size = 12, normalized size = 0.48 \begin {gather*} - 9 x + e^{x e^{- x - 1}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-x+1)*exp(x/exp(x+1))-9*exp(x+1))/exp(x+1),x)

[Out]

-9*x + exp(x*exp(-x - 1))

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