3.11.64 \(\int e^{9+e^{2 x}+e^x (-6-6 x)+19 x+8 x^2+x^4} (19+2 e^{2 x}+e^x (-12-6 x)+16 x+4 x^3) \, dx\)

Optimal. Leaf size=24 \[ e^{x-x^2+x^4+\left (3-e^x+3 x\right )^2} \]

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Rubi [F]  time = 1.74, 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 (9+e^{2 x}+e^x (-6-6 x)+19 x+8 x^2+x^4\right ) \left (19+2 e^{2 x}+e^x (-12-6 x)+16 x+4 x^3\right ) \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[E^(9 + E^(2*x) + E^x*(-6 - 6*x) + 19*x + 8*x^2 + x^4)*(19 + 2*E^(2*x) + E^x*(-12 - 6*x) + 16*x + 4*x^3),x]

[Out]

19*Defer[Int][E^(9 + E^(2*x) + E^x*(-6 - 6*x) + 19*x + 8*x^2 + x^4), x] - 12*Defer[Int][E^(9 + E^(2*x) + E^x*(
-6 - 6*x) + 20*x + 8*x^2 + x^4), x] + 2*Defer[Int][E^(9 + E^(2*x) + E^x*(-6 - 6*x) + 21*x + 8*x^2 + x^4), x] +
16*Defer[Int][E^(9 + E^(2*x) + E^x*(-6 - 6*x) + 19*x + 8*x^2 + x^4)*x, x] - 6*Defer[Int][E^(9 + E^(2*x) + E^x
*(-6 - 6*x) + 20*x + 8*x^2 + x^4)*x, x] + 4*Defer[Int][E^(9 + E^(2*x) + E^x*(-6 - 6*x) + 19*x + 8*x^2 + x^4)*x
^3, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \left (19 \exp \left (9+e^{2 x}+e^x (-6-6 x)+19 x+8 x^2+x^4\right )+2 \exp \left (9+e^{2 x}+e^x (-6-6 x)+21 x+8 x^2+x^4\right )+16 \exp \left (9+e^{2 x}+e^x (-6-6 x)+19 x+8 x^2+x^4\right ) x+4 \exp \left (9+e^{2 x}+e^x (-6-6 x)+19 x+8 x^2+x^4\right ) x^3-6 \exp \left (9+e^{2 x}+e^x (-6-6 x)+20 x+8 x^2+x^4\right ) (2+x)\right ) \, dx\\ &=2 \int \exp \left (9+e^{2 x}+e^x (-6-6 x)+21 x+8 x^2+x^4\right ) \, dx+4 \int \exp \left (9+e^{2 x}+e^x (-6-6 x)+19 x+8 x^2+x^4\right ) x^3 \, dx-6 \int \exp \left (9+e^{2 x}+e^x (-6-6 x)+20 x+8 x^2+x^4\right ) (2+x) \, dx+16 \int \exp \left (9+e^{2 x}+e^x (-6-6 x)+19 x+8 x^2+x^4\right ) x \, dx+19 \int \exp \left (9+e^{2 x}+e^x (-6-6 x)+19 x+8 x^2+x^4\right ) \, dx\\ &=2 \int \exp \left (9+e^{2 x}+e^x (-6-6 x)+21 x+8 x^2+x^4\right ) \, dx+4 \int \exp \left (9+e^{2 x}+e^x (-6-6 x)+19 x+8 x^2+x^4\right ) x^3 \, dx-6 \int \left (2 \exp \left (9+e^{2 x}+e^x (-6-6 x)+20 x+8 x^2+x^4\right )+\exp \left (9+e^{2 x}+e^x (-6-6 x)+20 x+8 x^2+x^4\right ) x\right ) \, dx+16 \int \exp \left (9+e^{2 x}+e^x (-6-6 x)+19 x+8 x^2+x^4\right ) x \, dx+19 \int \exp \left (9+e^{2 x}+e^x (-6-6 x)+19 x+8 x^2+x^4\right ) \, dx\\ &=2 \int \exp \left (9+e^{2 x}+e^x (-6-6 x)+21 x+8 x^2+x^4\right ) \, dx+4 \int \exp \left (9+e^{2 x}+e^x (-6-6 x)+19 x+8 x^2+x^4\right ) x^3 \, dx-6 \int \exp \left (9+e^{2 x}+e^x (-6-6 x)+20 x+8 x^2+x^4\right ) x \, dx-12 \int \exp \left (9+e^{2 x}+e^x (-6-6 x)+20 x+8 x^2+x^4\right ) \, dx+16 \int \exp \left (9+e^{2 x}+e^x (-6-6 x)+19 x+8 x^2+x^4\right ) x \, dx+19 \int \exp \left (9+e^{2 x}+e^x (-6-6 x)+19 x+8 x^2+x^4\right ) \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.77, size = 28, normalized size = 1.17 \begin {gather*} e^{9+e^{2 x}+19 x+8 x^2+x^4-6 e^x (1+x)} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[E^(9 + E^(2*x) + E^x*(-6 - 6*x) + 19*x + 8*x^2 + x^4)*(19 + 2*E^(2*x) + E^x*(-12 - 6*x) + 16*x + 4*x
^3),x]

[Out]

E^(9 + E^(2*x) + 19*x + 8*x^2 + x^4 - 6*E^x*(1 + x))

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fricas [A]  time = 1.16, size = 25, normalized size = 1.04 \begin {gather*} e^{\left (x^{4} + 8 \, x^{2} - 6 \, {\left (x + 1\right )} e^{x} + 19 \, x + e^{\left (2 \, x\right )} + 9\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2*exp(x)^2+(-6*x-12)*exp(x)+4*x^3+16*x+19)*exp(exp(x)^2+(-6*x-6)*exp(x)+x^4+8*x^2+19*x+9),x, algori
thm="fricas")

[Out]

e^(x^4 + 8*x^2 - 6*(x + 1)*e^x + 19*x + e^(2*x) + 9)

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giac [A]  time = 0.47, size = 27, normalized size = 1.12 \begin {gather*} e^{\left (x^{4} + 8 \, x^{2} - 6 \, x e^{x} + 19 \, x + e^{\left (2 \, x\right )} - 6 \, e^{x} + 9\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2*exp(x)^2+(-6*x-12)*exp(x)+4*x^3+16*x+19)*exp(exp(x)^2+(-6*x-6)*exp(x)+x^4+8*x^2+19*x+9),x, algori
thm="giac")

[Out]

e^(x^4 + 8*x^2 - 6*x*e^x + 19*x + e^(2*x) - 6*e^x + 9)

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maple [A]  time = 0.06, size = 27, normalized size = 1.12

method	result	size
norman	\({\mathrm e}^{{\mathrm e}^{2 x}+\left (-6 x -6\right ) {\mathrm e}^{x}+x^{4}+8 x^{2}+19 x +9}\)	\(27\)
risch	\({\mathrm e}^{x^{4}-6 \,{\mathrm e}^{x} x +8 x^{2}-6 \,{\mathrm e}^{x}+{\mathrm e}^{2 x}+19 x +9}\)	\(28\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((2*exp(x)^2+(-6*x-12)*exp(x)+4*x^3+16*x+19)*exp(exp(x)^2+(-6*x-6)*exp(x)+x^4+8*x^2+19*x+9),x,method=_RETUR
NVERBOSE)

[Out]

exp(exp(x)^2+(-6*x-6)*exp(x)+x^4+8*x^2+19*x+9)

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maxima [A]  time = 0.60, size = 27, normalized size = 1.12 \begin {gather*} e^{\left (x^{4} + 8 \, x^{2} - 6 \, x e^{x} + 19 \, x + e^{\left (2 \, x\right )} - 6 \, e^{x} + 9\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2*exp(x)^2+(-6*x-12)*exp(x)+4*x^3+16*x+19)*exp(exp(x)^2+(-6*x-6)*exp(x)+x^4+8*x^2+19*x+9),x, algori
thm="maxima")

[Out]

e^(x^4 + 8*x^2 - 6*x*e^x + 19*x + e^(2*x) - 6*e^x + 9)

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mupad [B]  time = 0.72, size = 33, normalized size = 1.38 \begin {gather*} {\mathrm {e}}^{-6\,x\,{\mathrm {e}}^x}\,{\mathrm {e}}^{19\,x}\,{\mathrm {e}}^{x^4}\,{\mathrm {e}}^9\,{\mathrm {e}}^{8\,x^2}\,{\mathrm {e}}^{{\mathrm {e}}^{2\,x}}\,{\mathrm {e}}^{-6\,{\mathrm {e}}^x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp(19*x + exp(2*x) - exp(x)*(6*x + 6) + 8*x^2 + x^4 + 9)*(16*x + 2*exp(2*x) - exp(x)*(6*x + 12) + 4*x^3 +
19),x)

[Out]

exp(-6*x*exp(x))*exp(19*x)*exp(x^4)*exp(9)*exp(8*x^2)*exp(exp(2*x))*exp(-6*exp(x))

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sympy [A]  time = 0.23, size = 29, normalized size = 1.21 \begin {gather*} e^{x^{4} + 8 x^{2} + 19 x + \left (- 6 x - 6\right ) e^{x} + e^{2 x} + 9} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2*exp(x)**2+(-6*x-12)*exp(x)+4*x**3+16*x+19)*exp(exp(x)**2+(-6*x-6)*exp(x)+x**4+8*x**2+19*x+9),x)

[Out]

exp(x**4 + 8*x**2 + 19*x + (-6*x - 6)*exp(x) + exp(2*x) + 9)

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