3.86.21 \(\int e^{-10-2 e^{2 x^2}} (-14 e^{10+2 e^{2 x^2}}+9 x^2-24 e^{2 x^2} x^4) \, dx\) [8521]

Optimal. Leaf size=25 \[ x-3 x \left (5-e^{-10-2 e^{2 x^2}} x^2\right ) \]

[Out]

x-3*x*(5-x^2/exp(exp(x^2)^2+5)^2)

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Rubi [F]
time = 0.29, 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^{-10-2 e^{2 x^2}} \left (-14 e^{10+2 e^{2 x^2}}+9 x^2-24 e^{2 x^2} x^4\right ) \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[E^(-10 - 2*E^(2*x^2))*(-14*E^(10 + 2*E^(2*x^2)) + 9*x^2 - 24*E^(2*x^2)*x^4),x]

[Out]

-14*x + 9*Defer[Int][x^2/E^(2*(5 + E^(2*x^2))), x] - 24*Defer[Int][x^4/E^(2*(5 + E^(2*x^2) - x^2)), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int e^{-2 \left (5+e^{2 x^2}\right )} \left (-14 e^{10+2 e^{2 x^2}}+9 x^2-24 e^{2 x^2} x^4\right ) \, dx\\ &=\int \left (-14+9 e^{-2 \left (5+e^{2 x^2}\right )} x^2-24 e^{-2 \left (5+e^{2 x^2}\right )+2 x^2} x^4\right ) \, dx\\ &=-14 x+9 \int e^{-2 \left (5+e^{2 x^2}\right )} x^2 \, dx-24 \int e^{-2 \left (5+e^{2 x^2}\right )+2 x^2} x^4 \, dx\\ &=-14 x+9 \int e^{-2 \left (5+e^{2 x^2}\right )} x^2 \, dx-24 \int e^{-2 \left (5+e^{2 x^2}-x^2\right )} x^4 \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]
time = 0.14, size = 22, normalized size = 0.88 \begin {gather*} -14 x+3 e^{-10-2 e^{2 x^2}} x^3 \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[E^(-10 - 2*E^(2*x^2))*(-14*E^(10 + 2*E^(2*x^2)) + 9*x^2 - 24*E^(2*x^2)*x^4),x]

[Out]

-14*x + 3*E^(-10 - 2*E^(2*x^2))*x^3

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Maple [A]
time = 0.57, size = 21, normalized size = 0.84

method	result	size
risch	\(-14 x +3 x^{3} {\mathrm e}^{-10-2 \,{\mathrm e}^{2 x^{2}}}\)	\(21\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((-14*exp(exp(x^2)^2+5)^2-24*x^4*exp(x^2)^2+9*x^2)/exp(exp(x^2)^2+5)^2,x,method=_RETURNVERBOSE)

[Out]

-14*x+3*x^3*exp(-10-2*exp(2*x^2))

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Maxima [A]
time = 0.34, size = 20, normalized size = 0.80 \begin {gather*} 3 \, x^{3} e^{\left (-2 \, e^{\left (2 \, x^{2}\right )} - 10\right )} - 14 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-14*exp(exp(x^2)^2+5)^2-24*x^4*exp(x^2)^2+9*x^2)/exp(exp(x^2)^2+5)^2,x, algorithm="maxima")

[Out]

3*x^3*e^(-2*e^(2*x^2) - 10) - 14*x

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Fricas [A]
time = 0.49, size = 32, normalized size = 1.28 \begin {gather*} {\left (3 \, x^{3} - 14 \, x e^{\left (2 \, e^{\left (2 \, x^{2}\right )} + 10\right )}\right )} e^{\left (-2 \, e^{\left (2 \, x^{2}\right )} - 10\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-14*exp(exp(x^2)^2+5)^2-24*x^4*exp(x^2)^2+9*x^2)/exp(exp(x^2)^2+5)^2,x, algorithm="fricas")

[Out]

(3*x^3 - 14*x*e^(2*e^(2*x^2) + 10))*e^(-2*e^(2*x^2) - 10)

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Sympy [A]
time = 1.42, size = 20, normalized size = 0.80 \begin {gather*} 3 x^{3} e^{- 2 e^{2 x^{2}} - 10} - 14 x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-14*exp(exp(x**2)**2+5)**2-24*x**4*exp(x**2)**2+9*x**2)/exp(exp(x**2)**2+5)**2,x)

[Out]

3*x**3*exp(-2*exp(2*x**2) - 10) - 14*x

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Giac [A]
time = 0.41, size = 23, normalized size = 0.92 \begin {gather*} {\left (3 \, x^{3} e^{\left (-2 \, e^{\left (2 \, x^{2}\right )}\right )} - 14 \, x e^{10}\right )} e^{\left (-10\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-14*exp(exp(x^2)^2+5)^2-24*x^4*exp(x^2)^2+9*x^2)/exp(exp(x^2)^2+5)^2,x, algorithm="giac")

[Out]

(3*x^3*e^(-2*e^(2*x^2)) - 14*x*e^10)*e^(-10)

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Mupad [B]
time = 5.48, size = 20, normalized size = 0.80 \begin {gather*} 3\,x^3\,{\mathrm {e}}^{-2\,{\mathrm {e}}^{2\,x^2}}\,{\mathrm {e}}^{-10}-14\,x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-exp(- 2*exp(2*x^2) - 10)*(14*exp(2*exp(2*x^2) + 10) + 24*x^4*exp(2*x^2) - 9*x^2),x)

[Out]

3*x^3*exp(-2*exp(2*x^2))*exp(-10) - 14*x

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