3.79.39 \(\int e^{18 e^{8 x-4 x^2}+8 x-4 x^2} (144-144 x) \, dx\)

Optimal. Leaf size=15 \[ e^{18 e^{-4 \left (-2 x+x^2\right )}} \]

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Rubi [F]  time = 0.27, 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^{18 e^{8 x-4 x^2}+8 x-4 x^2} (144-144 x) \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[E^(18*E^(8*x - 4*x^2) + 8*x - 4*x^2)*(144 - 144*x),x]

[Out]

144*Defer[Int][E^(18*E^(8*x - 4*x^2) + 8*x - 4*x^2), x] - 144*Defer[Int][E^(18*E^(8*x - 4*x^2) + 8*x - 4*x^2)*
x, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \left (144 e^{18 e^{8 x-4 x^2}+8 x-4 x^2}-144 e^{18 e^{8 x-4 x^2}+8 x-4 x^2} x\right ) \, dx\\ &=144 \int e^{18 e^{8 x-4 x^2}+8 x-4 x^2} \, dx-144 \int e^{18 e^{8 x-4 x^2}+8 x-4 x^2} x \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.15, size = 12, normalized size = 0.80 \begin {gather*} e^{18 e^{-4 (-2+x) x}} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[E^(18*E^(8*x - 4*x^2) + 8*x - 4*x^2)*(144 - 144*x),x]

[Out]

E^(18/E^(4*(-2 + x)*x))

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fricas [A]  time = 0.62, size = 13, normalized size = 0.87 \begin {gather*} e^{\left (18 \, e^{\left (-4 \, x^{2} + 8 \, x\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-144*x+144)*exp(9/exp(4*x^2-8*x))^2/exp(4*x^2-8*x),x, algorithm="fricas")

[Out]

e^(18*e^(-4*x^2 + 8*x))

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giac [A]  time = 0.14, size = 13, normalized size = 0.87 \begin {gather*} e^{\left (18 \, e^{\left (-4 \, x^{2} + 8 \, x\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-144*x+144)*exp(9/exp(4*x^2-8*x))^2/exp(4*x^2-8*x),x, algorithm="giac")

[Out]

e^(18*e^(-4*x^2 + 8*x))

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maple [A]  time = 0.04, size = 11, normalized size = 0.73

method	result	size
risch	\({\mathrm e}^{18 \,{\mathrm e}^{-4 \left (x -2\right ) x}}\)	\(11\)
norman	\({\mathrm e}^{18 \,{\mathrm e}^{-4 x^{2}+8 x}}\)	\(18\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((-144*x+144)*exp(9/exp(4*x^2-8*x))^2/exp(4*x^2-8*x),x,method=_RETURNVERBOSE)

[Out]

exp(18*exp(-4*(x-2)*x))

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maxima [A]  time = 0.50, size = 13, normalized size = 0.87 \begin {gather*} e^{\left (18 \, e^{\left (-4 \, x^{2} + 8 \, x\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-144*x+144)*exp(9/exp(4*x^2-8*x))^2/exp(4*x^2-8*x),x, algorithm="maxima")

[Out]

e^(18*e^(-4*x^2 + 8*x))

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mupad [B]  time = 0.13, size = 13, normalized size = 0.87 \begin {gather*} {\mathrm {e}}^{18\,{\mathrm {e}}^{8\,x-4\,x^2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-exp(18*exp(8*x - 4*x^2))*exp(8*x - 4*x^2)*(144*x - 144),x)

[Out]

exp(18*exp(8*x - 4*x^2))

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sympy [A]  time = 0.30, size = 12, normalized size = 0.80 \begin {gather*} e^{18 e^{- 4 x^{2} + 8 x}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-144*x+144)*exp(9/exp(4*x**2-8*x))**2/exp(4*x**2-8*x),x)

[Out]

exp(18*exp(-4*x**2 + 8*x))

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