3.91.76 \(\int \frac {1}{2} (4 e^{2 x}+e^{-e^x+\frac {3}{2} e^{-e^x-x+x^4}-x+x^4} (3+3 e^x-12 x^3)) \, dx\)

Optimal. Leaf size=29 \[ -1-e^{\frac {3}{2} e^{-e^x-x+x^4}}+e^{2 x} \]

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Rubi [F]  time = 0.75, 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 \frac {1}{2} \left (4 e^{2 x}+e^{-e^x+\frac {3}{2} e^{-e^x-x+x^4}-x+x^4} \left (3+3 e^x-12 x^3\right )\right ) \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(4*E^(2*x) + E^(-E^x + (3*E^(-E^x - x + x^4))/2 - x + x^4)*(3 + 3*E^x - 12*x^3))/2,x]

[Out]

E^(2*x) + (3*Defer[Int][E^(-E^x + (3*E^(-E^x - x + x^4))/2 + x^4), x])/2 + (3*Defer[Int][E^(-E^x + (3*E^(-E^x
- x + x^4))/2 - x + x^4), x])/2 - 6*Defer[Int][E^(-E^x + (3*E^(-E^x - x + x^4))/2 - x + x^4)*x^3, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{2} \int \left (4 e^{2 x}+e^{-e^x+\frac {3}{2} e^{-e^x-x+x^4}-x+x^4} \left (3+3 e^x-12 x^3\right )\right ) \, dx\\ &=\frac {1}{2} \int e^{-e^x+\frac {3}{2} e^{-e^x-x+x^4}-x+x^4} \left (3+3 e^x-12 x^3\right ) \, dx+2 \int e^{2 x} \, dx\\ &=e^{2 x}+\frac {1}{2} \int 3 e^{-e^x+\frac {3}{2} e^{-e^x-x+x^4}-x+x^4} \left (1+e^x-4 x^3\right ) \, dx\\ &=e^{2 x}+\frac {3}{2} \int e^{-e^x+\frac {3}{2} e^{-e^x-x+x^4}-x+x^4} \left (1+e^x-4 x^3\right ) \, dx\\ &=e^{2 x}+\frac {3}{2} \int \left (e^{-e^x+\frac {3}{2} e^{-e^x-x+x^4}+x^4}+e^{-e^x+\frac {3}{2} e^{-e^x-x+x^4}-x+x^4}-4 e^{-e^x+\frac {3}{2} e^{-e^x-x+x^4}-x+x^4} x^3\right ) \, dx\\ &=e^{2 x}+\frac {3}{2} \int e^{-e^x+\frac {3}{2} e^{-e^x-x+x^4}+x^4} \, dx+\frac {3}{2} \int e^{-e^x+\frac {3}{2} e^{-e^x-x+x^4}-x+x^4} \, dx-6 \int e^{-e^x+\frac {3}{2} e^{-e^x-x+x^4}-x+x^4} x^3 \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.36, size = 28, normalized size = 0.97 \begin {gather*} -e^{\frac {3}{2} e^{-e^x-x+x^4}}+e^{2 x} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(4*E^(2*x) + E^(-E^x + (3*E^(-E^x - x + x^4))/2 - x + x^4)*(3 + 3*E^x - 12*x^3))/2,x]

[Out]

-E^((3*E^(-E^x - x + x^4))/2) + E^(2*x)

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fricas [B]  time = 0.78, size = 50, normalized size = 1.72 \begin {gather*} {\left (e^{\left (x^{4} + x - e^{x}\right )} - e^{\left (x^{4} - x + \frac {3}{2} \, e^{\left (x^{4} - x - e^{x}\right )} - e^{x}\right )}\right )} e^{\left (-x^{4} + x + e^{x}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/2*(3*exp(x)-12*x^3+3)*exp(-exp(x)+x^4-x)*exp(3/2*exp(-exp(x)+x^4-x))+2*exp(2*x),x, algorithm="fric
as")

[Out]

(e^(x^4 + x - e^x) - e^(x^4 - x + 3/2*e^(x^4 - x - e^x) - e^x))*e^(-x^4 + x + e^x)

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giac [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int -\frac {3}{2} \, {\left (4 \, x^{3} - e^{x} - 1\right )} e^{\left (x^{4} - x + \frac {3}{2} \, e^{\left (x^{4} - x - e^{x}\right )} - e^{x}\right )} + 2 \, e^{\left (2 \, x\right )}\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/2*(3*exp(x)-12*x^3+3)*exp(-exp(x)+x^4-x)*exp(3/2*exp(-exp(x)+x^4-x))+2*exp(2*x),x, algorithm="giac
")

[Out]

integrate(-3/2*(4*x^3 - e^x - 1)*e^(x^4 - x + 3/2*e^(x^4 - x - e^x) - e^x) + 2*e^(2*x), x)

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maple [A]  time = 0.12, size = 23, normalized size = 0.79

method	result	size
risch	\(-{\mathrm e}^{\frac {3 \,{\mathrm e}^{-{\mathrm e}^{x}+x^{4}-x}}{2}}+{\mathrm e}^{2 x}\)	\(23\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/2*(3*exp(x)-12*x^3+3)*exp(-exp(x)+x^4-x)*exp(3/2*exp(-exp(x)+x^4-x))+2*exp(2*x),x,method=_RETURNVERBOSE)

[Out]

-exp(3/2*exp(-exp(x)+x^4-x))+exp(2*x)

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maxima [A]  time = 0.58, size = 22, normalized size = 0.76 \begin {gather*} e^{\left (2 \, x\right )} - e^{\left (\frac {3}{2} \, e^{\left (x^{4} - x - e^{x}\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/2*(3*exp(x)-12*x^3+3)*exp(-exp(x)+x^4-x)*exp(3/2*exp(-exp(x)+x^4-x))+2*exp(2*x),x, algorithm="maxi
ma")

[Out]

e^(2*x) - e^(3/2*e^(x^4 - x - e^x))

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mupad [B]  time = 0.27, size = 23, normalized size = 0.79 \begin {gather*} {\mathrm {e}}^{2\,x}-{\mathrm {e}}^{\frac {3\,{\mathrm {e}}^{-x}\,{\mathrm {e}}^{x^4}\,{\mathrm {e}}^{-{\mathrm {e}}^x}}{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(2*exp(2*x) + (exp((3*exp(x^4 - exp(x) - x))/2)*exp(x^4 - exp(x) - x)*(3*exp(x) - 12*x^3 + 3))/2,x)

[Out]

exp(2*x) - exp((3*exp(-x)*exp(x^4)*exp(-exp(x)))/2)

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sympy [A]  time = 0.48, size = 19, normalized size = 0.66 \begin {gather*} e^{2 x} - e^{\frac {3 e^{x^{4} - x - e^{x}}}{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/2*(3*exp(x)-12*x**3+3)*exp(-exp(x)+x**4-x)*exp(3/2*exp(-exp(x)+x**4-x))+2*exp(2*x),x)

[Out]

exp(2*x) - exp(3*exp(x**4 - x - exp(x))/2)

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