3.20.21 \(\int e^{-3+e^{e^{-3+x^2} (3+e^{3-x^2} (5+x))}+x^2+e^{-3+x^2} (3+e^{3-x^2} (5+x))} (e^{3-x^2}+6 x) \, dx\)

Optimal. Leaf size=18 \[ -2+e^{e^{5+3 e^{-3+x^2}+x}} \]

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Rubi [F]  time = 0.83, 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 \exp \left (-3+e^{e^{-3+x^2} \left (3+e^{3-x^2} (5+x)\right )}+x^2+e^{-3+x^2} \left (3+e^{3-x^2} (5+x)\right )\right ) \left (e^{3-x^2}+6 x\right ) \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[E^(-3 + E^(E^(-3 + x^2)*(3 + E^(3 - x^2)*(5 + x))) + x^2 + E^(-3 + x^2)*(3 + E^(3 - x^2)*(5 + x)))*(E^(3 -
x^2) + 6*x),x]

[Out]

Defer[Int][E^(5 + E^(5 + 3*E^(-3 + x^2) + x) + 3*E^(-3 + x^2) + x), x] + 6*Defer[Int][E^(2 + E^(5 + 3*E^(-3 +
x^2) + x) + 3*E^(-3 + x^2) + x + x^2)*x, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int e^{2+e^{5+3 e^{-3+x^2}+x}+3 e^{-3+x^2}+x} \left (e^3+6 e^{x^2} x\right ) \, dx\\ &=\int \left (e^{5+e^{5+3 e^{-3+x^2}+x}+3 e^{-3+x^2}+x}+6 \exp \left (2+e^{5+3 e^{-3+x^2}+x}+3 e^{-3+x^2}+x+x^2\right ) x\right ) \, dx\\ &=6 \int \exp \left (2+e^{5+3 e^{-3+x^2}+x}+3 e^{-3+x^2}+x+x^2\right ) x \, dx+\int e^{5+e^{5+3 e^{-3+x^2}+x}+3 e^{-3+x^2}+x} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.31, size = 16, normalized size = 0.89 \begin {gather*} e^{e^{5+3 e^{-3+x^2}+x}} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[E^(-3 + E^(E^(-3 + x^2)*(3 + E^(3 - x^2)*(5 + x))) + x^2 + E^(-3 + x^2)*(3 + E^(3 - x^2)*(5 + x)))*(
E^(3 - x^2) + 6*x),x]

[Out]

E^E^(5 + 3*E^(-3 + x^2) + x)

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fricas [A]  time = 0.77, size = 13, normalized size = 0.72 \begin {gather*} e^{\left (e^{\left (x + 3 \, e^{\left (x^{2} - 3\right )} + 5\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((exp(-x^2+3)+6*x)*exp(((5+x)*exp(-x^2+3)+3)/exp(-x^2+3))*exp(exp(((5+x)*exp(-x^2+3)+3)/exp(-x^2+3)))
/exp(-x^2+3),x, algorithm="fricas")

[Out]

e^(e^(x + 3*e^(x^2 - 3) + 5))

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giac [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int {\left (6 \, x + e^{\left (-x^{2} + 3\right )}\right )} e^{\left (x^{2} + {\left ({\left (x + 5\right )} e^{\left (-x^{2} + 3\right )} + 3\right )} e^{\left (x^{2} - 3\right )} + e^{\left ({\left ({\left (x + 5\right )} e^{\left (-x^{2} + 3\right )} + 3\right )} e^{\left (x^{2} - 3\right )}\right )} - 3\right )}\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((exp(-x^2+3)+6*x)*exp(((5+x)*exp(-x^2+3)+3)/exp(-x^2+3))*exp(exp(((5+x)*exp(-x^2+3)+3)/exp(-x^2+3)))
/exp(-x^2+3),x, algorithm="giac")

[Out]

integrate((6*x + e^(-x^2 + 3))*e^(x^2 + ((x + 5)*e^(-x^2 + 3) + 3)*e^(x^2 - 3) + e^(((x + 5)*e^(-x^2 + 3) + 3)
*e^(x^2 - 3)) - 3), x)

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maple [A]  time = 0.08, size = 28, normalized size = 1.56

method	result	size
norman	\({\mathrm e}^{{\mathrm e}^{\left (\left (5+x \right ) {\mathrm e}^{-x^{2}+3}+3\right ) {\mathrm e}^{x^{2}-3}}}\)	\(28\)
risch	\({\mathrm e}^{{\mathrm e}^{\left (x \,{\mathrm e}^{-x^{2}+3}+5 \,{\mathrm e}^{-x^{2}+3}+3\right ) {\mathrm e}^{x^{2}-3}}}\)	\(32\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(-x^2+3)+6*x)*exp(((5+x)*exp(-x^2+3)+3)/exp(-x^2+3))*exp(exp(((5+x)*exp(-x^2+3)+3)/exp(-x^2+3)))/exp(-
x^2+3),x,method=_RETURNVERBOSE)

[Out]

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

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maxima [A]  time = 0.87, size = 13, normalized size = 0.72 \begin {gather*} e^{\left (e^{\left (x + 3 \, e^{\left (x^{2} - 3\right )} + 5\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((exp(-x^2+3)+6*x)*exp(((5+x)*exp(-x^2+3)+3)/exp(-x^2+3))*exp(exp(((5+x)*exp(-x^2+3)+3)/exp(-x^2+3)))
/exp(-x^2+3),x, algorithm="maxima")

[Out]

e^(e^(x + 3*e^(x^2 - 3) + 5))

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mupad [B]  time = 1.29, size = 15, normalized size = 0.83 \begin {gather*} {\mathrm {e}}^{{\mathrm {e}}^5\,{\mathrm {e}}^{3\,{\mathrm {e}}^{x^2}\,{\mathrm {e}}^{-3}}\,{\mathrm {e}}^x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp(exp(exp(x^2 - 3)*(exp(3 - x^2)*(x + 5) + 3)))*exp(x^2 - 3)*exp(exp(x^2 - 3)*(exp(3 - x^2)*(x + 5) + 3)
)*(6*x + exp(3 - x^2)),x)

[Out]

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

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sympy [A]  time = 0.59, size = 20, normalized size = 1.11 \begin {gather*} e^{e^{\left (\left (x + 5\right ) e^{3 - x^{2}} + 3\right ) e^{x^{2} - 3}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((exp(-x**2+3)+6*x)*exp(((5+x)*exp(-x**2+3)+3)/exp(-x**2+3))*exp(exp(((5+x)*exp(-x**2+3)+3)/exp(-x**2
+3)))/exp(-x**2+3),x)

[Out]

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

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