3.53.76 \(\int e^{-e^{9 x^4}-x} (2 x-x^2-36 e^{9 x^4} x^5+e^{e^{9 x^4}} (-4 x+2 x^2)) \, dx\)

Optimal. Leaf size=24 \[ e^{-x} x \left (-2 x+e^{-e^{9 x^4}} x\right ) \]

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Rubi [F]  time = 0.60, 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^{-e^{9 x^4}-x} \left (2 x-x^2-36 e^{9 x^4} x^5+e^{e^{9 x^4}} \left (-4 x+2 x^2\right )\right ) \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[E^(-E^(9*x^4) - x)*(2*x - x^2 - 36*E^(9*x^4)*x^5 + E^E^(9*x^4)*(-4*x + 2*x^2)),x]

[Out]

(-2*x^2)/E^x + 2*Defer[Int][E^(-E^(9*x^4) - x)*x, x] - Defer[Int][E^(-E^(9*x^4) - x)*x^2, x] - 36*Defer[Int][E
^(-E^(9*x^4) - x + 9*x^4)*x^5, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \left (2 e^{-e^{9 x^4}-x} x+2 e^{-x} (-2+x) x-e^{-e^{9 x^4}-x} x^2-36 e^{-e^{9 x^4}-x+9 x^4} x^5\right ) \, dx\\ &=2 \int e^{-e^{9 x^4}-x} x \, dx+2 \int e^{-x} (-2+x) x \, dx-36 \int e^{-e^{9 x^4}-x+9 x^4} x^5 \, dx-\int e^{-e^{9 x^4}-x} x^2 \, dx\\ &=2 \int e^{-e^{9 x^4}-x} x \, dx+2 \int \left (-2 e^{-x} x+e^{-x} x^2\right ) \, dx-36 \int e^{-e^{9 x^4}-x+9 x^4} x^5 \, dx-\int e^{-e^{9 x^4}-x} x^2 \, dx\\ &=2 \int e^{-e^{9 x^4}-x} x \, dx+2 \int e^{-x} x^2 \, dx-4 \int e^{-x} x \, dx-36 \int e^{-e^{9 x^4}-x+9 x^4} x^5 \, dx-\int e^{-e^{9 x^4}-x} x^2 \, dx\\ &=4 e^{-x} x-2 e^{-x} x^2+2 \int e^{-e^{9 x^4}-x} x \, dx-4 \int e^{-x} \, dx+4 \int e^{-x} x \, dx-36 \int e^{-e^{9 x^4}-x+9 x^4} x^5 \, dx-\int e^{-e^{9 x^4}-x} x^2 \, dx\\ &=4 e^{-x}-2 e^{-x} x^2+2 \int e^{-e^{9 x^4}-x} x \, dx+4 \int e^{-x} \, dx-36 \int e^{-e^{9 x^4}-x+9 x^4} x^5 \, dx-\int e^{-e^{9 x^4}-x} x^2 \, dx\\ &=-2 e^{-x} x^2+2 \int e^{-e^{9 x^4}-x} x \, dx-36 \int e^{-e^{9 x^4}-x+9 x^4} x^5 \, dx-\int e^{-e^{9 x^4}-x} x^2 \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.37, size = 33, normalized size = 1.38 \begin {gather*} -e^{-e^{9 x^4}-x} \left (-1+2 e^{e^{9 x^4}}\right ) x^2 \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[E^(-E^(9*x^4) - x)*(2*x - x^2 - 36*E^(9*x^4)*x^5 + E^E^(9*x^4)*(-4*x + 2*x^2)),x]

[Out]

-(E^(-E^(9*x^4) - x)*(-1 + 2*E^E^(9*x^4))*x^2)

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fricas [A]  time = 0.52, size = 27, normalized size = 1.12 \begin {gather*} -2 \, x^{2} e^{\left (-x\right )} + x^{2} e^{\left (-x - e^{\left (9 \, x^{4}\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((2*x^2-4*x)*exp(exp(9*x^4))-36*x^5*exp(9*x^4)-x^2+2*x)/exp(x)/exp(exp(9*x^4)),x, algorithm="fricas"
)

[Out]

-2*x^2*e^(-x) + x^2*e^(-x - e^(9*x^4))

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giac [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int -{\left (36 \, x^{5} e^{\left (9 \, x^{4}\right )} + x^{2} - 2 \, {\left (x^{2} - 2 \, x\right )} e^{\left (e^{\left (9 \, x^{4}\right )}\right )} - 2 \, x\right )} e^{\left (-x - e^{\left (9 \, x^{4}\right )}\right )}\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((2*x^2-4*x)*exp(exp(9*x^4))-36*x^5*exp(9*x^4)-x^2+2*x)/exp(x)/exp(exp(9*x^4)),x, algorithm="giac")

[Out]

integrate(-(36*x^5*e^(9*x^4) + x^2 - 2*(x^2 - 2*x)*e^(e^(9*x^4)) - 2*x)*e^(-x - e^(9*x^4)), x)

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maple [A]  time = 0.05, size = 28, normalized size = 1.17

method	result	size
risch	\(-2 x^{2} {\mathrm e}^{-x}+x^{2} {\mathrm e}^{-x -{\mathrm e}^{9 x^{4}}}\)	\(28\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((2*x^2-4*x)*exp(exp(9*x^4))-36*x^5*exp(9*x^4)-x^2+2*x)/exp(x)/exp(exp(9*x^4)),x,method=_RETURNVERBOSE)

[Out]

-2*x^2*exp(-x)+x^2*exp(-x-exp(9*x^4))

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maxima [A]  time = 0.44, size = 41, normalized size = 1.71 \begin {gather*} x^{2} e^{\left (-x - e^{\left (9 \, x^{4}\right )}\right )} - 2 \, {\left (x^{2} + 2 \, x + 2\right )} e^{\left (-x\right )} + 4 \, {\left (x + 1\right )} e^{\left (-x\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((2*x^2-4*x)*exp(exp(9*x^4))-36*x^5*exp(9*x^4)-x^2+2*x)/exp(x)/exp(exp(9*x^4)),x, algorithm="maxima"
)

[Out]

x^2*e^(-x - e^(9*x^4)) - 2*(x^2 + 2*x + 2)*e^(-x) + 4*(x + 1)*e^(-x)

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mupad [B]  time = 3.61, size = 27, normalized size = 1.12 \begin {gather*} x^2\,{\mathrm {e}}^{-x}\,{\mathrm {e}}^{-{\mathrm {e}}^{9\,x^4}}-2\,x^2\,{\mathrm {e}}^{-x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-exp(-x)*exp(-exp(9*x^4))*(exp(exp(9*x^4))*(4*x - 2*x^2) - 2*x + 36*x^5*exp(9*x^4) + x^2),x)

[Out]

x^2*exp(-x)*exp(-exp(9*x^4)) - 2*x^2*exp(-x)

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sympy [A]  time = 3.22, size = 22, normalized size = 0.92 \begin {gather*} - 2 x^{2} e^{- x} + x^{2} e^{- x} e^{- e^{9 x^{4}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((2*x**2-4*x)*exp(exp(9*x**4))-36*x**5*exp(9*x**4)-x**2+2*x)/exp(x)/exp(exp(9*x**4)),x)

[Out]

-2*x**2*exp(-x) + x**2*exp(-x)*exp(-exp(9*x**4))

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