3.92.74 \(\int e^{-16+e^{-16-4 x^2} (-1+x)-4 x^2} (-1-8 x+8 x^2) \, dx\)

Optimal. Leaf size=19 \[ 4-e^{e^{-16-4 x^2} (-1+x)} \]

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Rubi [F]  time = 0.38, 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^{-16+e^{-16-4 x^2} (-1+x)-4 x^2} \left (-1-8 x+8 x^2\right ) \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[E^(-16 + E^(-16 - 4*x^2)*(-1 + x) - 4*x^2)*(-1 - 8*x + 8*x^2),x]

[Out]

-Defer[Int][E^(-16 + E^(-16 - 4*x^2)*(-1 + x) - 4*x^2), x] - 8*Defer[Int][E^(-16 + E^(-16 - 4*x^2)*(-1 + x) -
4*x^2)*x, x] + 8*Defer[Int][E^(-16 + E^(-16 - 4*x^2)*(-1 + x) - 4*x^2)*x^2, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-e^{-16+e^{-16-4 x^2} (-1+x)-4 x^2}-8 e^{-16+e^{-16-4 x^2} (-1+x)-4 x^2} x+8 e^{-16+e^{-16-4 x^2} (-1+x)-4 x^2} x^2\right ) \, dx\\ &=-\left (8 \int e^{-16+e^{-16-4 x^2} (-1+x)-4 x^2} x \, dx\right )+8 \int e^{-16+e^{-16-4 x^2} (-1+x)-4 x^2} x^2 \, dx-\int e^{-16+e^{-16-4 x^2} (-1+x)-4 x^2} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.18, size = 17, normalized size = 0.89 \begin {gather*} -e^{e^{-16-4 x^2} (-1+x)} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[E^(-16 + E^(-16 - 4*x^2)*(-1 + x) - 4*x^2)*(-1 - 8*x + 8*x^2),x]

[Out]

-E^(E^(-16 - 4*x^2)*(-1 + x))

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fricas [A]  time = 0.70, size = 15, normalized size = 0.79 \begin {gather*} -e^{\left ({\left (x - 1\right )} e^{\left (-4 \, x^{2} - 16\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((8*x^2-8*x-1)*exp((x-1)/exp(4*x^2+16))/exp(4*x^2+16),x, algorithm="fricas")

[Out]

-e^((x - 1)*e^(-4*x^2 - 16))

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giac [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int {\left (8 \, x^{2} - 8 \, x - 1\right )} e^{\left (-4 \, x^{2} + {\left (x - 1\right )} e^{\left (-4 \, x^{2} - 16\right )} - 16\right )}\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((8*x^2-8*x-1)*exp((x-1)/exp(4*x^2+16))/exp(4*x^2+16),x, algorithm="giac")

[Out]

integrate((8*x^2 - 8*x - 1)*e^(-4*x^2 + (x - 1)*e^(-4*x^2 - 16) - 16), x)

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maple [A]  time = 0.08, size = 16, normalized size = 0.84

method	result	size
risch	\(-{\mathrm e}^{\left (x -1\right ) {\mathrm e}^{-4 x^{2}-16}}\)	\(16\)
norman	\(-{\mathrm e}^{\left (x -1\right ) {\mathrm e}^{-4 x^{2}-16}}\)	\(18\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((8*x^2-8*x-1)*exp((x-1)/exp(4*x^2+16))/exp(4*x^2+16),x,method=_RETURNVERBOSE)

[Out]

-exp((x-1)*exp(-4*x^2-16))

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maxima [A]  time = 0.57, size = 24, normalized size = 1.26 \begin {gather*} -e^{\left (x e^{\left (-4 \, x^{2} - 16\right )} - e^{\left (-4 \, x^{2} - 16\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((8*x^2-8*x-1)*exp((x-1)/exp(4*x^2+16))/exp(4*x^2+16),x, algorithm="maxima")

[Out]

-e^(x*e^(-4*x^2 - 16) - e^(-4*x^2 - 16))

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mupad [B]  time = 7.42, size = 24, normalized size = 1.26 \begin {gather*} -{\mathrm {e}}^{x\,{\mathrm {e}}^{-16}\,{\mathrm {e}}^{-4\,x^2}}\,{\mathrm {e}}^{-{\mathrm {e}}^{-16}\,{\mathrm {e}}^{-4\,x^2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-exp(exp(- 4*x^2 - 16)*(x - 1))*exp(- 4*x^2 - 16)*(8*x - 8*x^2 + 1),x)

[Out]

-exp(x*exp(-16)*exp(-4*x^2))*exp(-exp(-16)*exp(-4*x^2))

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sympy [A]  time = 0.34, size = 15, normalized size = 0.79 \begin {gather*} - e^{\left (x - 1\right ) e^{- 4 x^{2} - 16}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((8*x**2-8*x-1)*exp((x-1)/exp(4*x**2+16))/exp(4*x**2+16),x)

[Out]

-exp((x - 1)*exp(-4*x**2 - 16))

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