3.92.68 \(\int e^{e^{e^x}+e^{e^{e^{e^x}-5 x+6 x^2}}+e^{e^{e^x}-5 x+6 x^2}-5 x+6 x^2} (-5+e^{e^x+x}+12 x) \, dx\)

Optimal. Leaf size=24 \[ e^{e^{e^{e^{e^x}+x^2+5 \left (-x+x^2\right )}}} \]

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Rubi [F]  time = 1.79, 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 (e^{e^x}+e^{e^{e^{e^x}-5 x+6 x^2}}+e^{e^{e^x}-5 x+6 x^2}-5 x+6 x^2\right ) \left (-5+e^{e^x+x}+12 x\right ) \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[E^(E^E^x + E^E^(E^E^x - 5*x + 6*x^2) + E^(E^E^x - 5*x + 6*x^2) - 5*x + 6*x^2)*(-5 + E^(E^x + x) + 12*x),x]

[Out]

-5*Defer[Int][E^(E^E^x + E^E^(E^E^x - 5*x + 6*x^2) + E^(E^E^x - 5*x + 6*x^2) - 5*x + 6*x^2), x] + Defer[Int][E
^(E^E^x + E^E^(E^E^x - 5*x + 6*x^2) + E^x + E^(E^E^x - 5*x + 6*x^2) - 4*x + 6*x^2), x] + 12*Defer[Int][E^(E^E^
x + E^E^(E^E^x - 5*x + 6*x^2) + E^(E^E^x - 5*x + 6*x^2) - 5*x + 6*x^2)*x, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-5 \exp \left (e^{e^x}+e^{e^{e^{e^x}-5 x+6 x^2}}+e^{e^{e^x}-5 x+6 x^2}-5 x+6 x^2\right )+\exp \left (e^{e^x}+e^{e^{e^{e^x}-5 x+6 x^2}}+e^x+e^{e^{e^x}-5 x+6 x^2}-4 x+6 x^2\right )+12 \exp \left (e^{e^x}+e^{e^{e^{e^x}-5 x+6 x^2}}+e^{e^{e^x}-5 x+6 x^2}-5 x+6 x^2\right ) x\right ) \, dx\\ &=-\left (5 \int \exp \left (e^{e^x}+e^{e^{e^{e^x}-5 x+6 x^2}}+e^{e^{e^x}-5 x+6 x^2}-5 x+6 x^2\right ) \, dx\right )+12 \int \exp \left (e^{e^x}+e^{e^{e^{e^x}-5 x+6 x^2}}+e^{e^{e^x}-5 x+6 x^2}-5 x+6 x^2\right ) x \, dx+\int \exp \left (e^{e^x}+e^{e^{e^{e^x}-5 x+6 x^2}}+e^x+e^{e^{e^x}-5 x+6 x^2}-4 x+6 x^2\right ) \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 1.23, size = 20, normalized size = 0.83 \begin {gather*} e^{e^{e^{e^{e^x}-5 x+6 x^2}}} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[E^(E^E^x + E^E^(E^E^x - 5*x + 6*x^2) + E^(E^E^x - 5*x + 6*x^2) - 5*x + 6*x^2)*(-5 + E^(E^x + x) + 12
*x),x]

[Out]

E^E^E^(E^E^x - 5*x + 6*x^2)

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fricas [B]  time = 0.77, size = 128, normalized size = 5.33 \begin {gather*} e^{\left ({\left ({\left (6 \, x^{2} - 5 \, x\right )} e^{x} + e^{\left ({\left ({\left (6 \, x^{2} - 5 \, x\right )} e^{x} + e^{\left (x + e^{x}\right )}\right )} e^{\left (-x\right )} + x\right )} + e^{\left (x + e^{\left ({\left ({\left (6 \, x^{2} - 5 \, x\right )} e^{x} + e^{\left (x + e^{x}\right )}\right )} e^{\left (-x\right )}\right )}\right )} + e^{\left (x + e^{x}\right )}\right )} e^{\left (-x\right )} - {\left ({\left (6 \, x^{2} - 5 \, x\right )} e^{x} + e^{\left (x + e^{x}\right )}\right )} e^{\left (-x\right )} - e^{\left ({\left ({\left (6 \, x^{2} - 5 \, x\right )} e^{x} + e^{\left (x + e^{x}\right )}\right )} e^{\left (-x\right )}\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((exp(x)*exp(exp(x))+12*x-5)*exp(1/exp(-exp(exp(x))-6*x^2+5*x))*exp(exp(1/exp(-exp(exp(x))-6*x^2+5*x)
))/exp(-exp(exp(x))-6*x^2+5*x),x, algorithm="fricas")

[Out]

e^(((6*x^2 - 5*x)*e^x + e^(((6*x^2 - 5*x)*e^x + e^(x + e^x))*e^(-x) + x) + e^(x + e^(((6*x^2 - 5*x)*e^x + e^(x
+ e^x))*e^(-x))) + e^(x + e^x))*e^(-x) - ((6*x^2 - 5*x)*e^x + e^(x + e^x))*e^(-x) - e^(((6*x^2 - 5*x)*e^x + e
^(x + e^x))*e^(-x)))

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giac [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int {\left (12 \, x + e^{\left (x + e^{x}\right )} - 5\right )} e^{\left (6 \, x^{2} - 5 \, x + e^{\left (6 \, x^{2} - 5 \, x + e^{\left (e^{x}\right )}\right )} + e^{\left (e^{\left (6 \, x^{2} - 5 \, x + e^{\left (e^{x}\right )}\right )}\right )} + e^{\left (e^{x}\right )}\right )}\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((exp(x)*exp(exp(x))+12*x-5)*exp(1/exp(-exp(exp(x))-6*x^2+5*x))*exp(exp(1/exp(-exp(exp(x))-6*x^2+5*x)
))/exp(-exp(exp(x))-6*x^2+5*x),x, algorithm="giac")

[Out]

integrate((12*x + e^(x + e^x) - 5)*e^(6*x^2 - 5*x + e^(6*x^2 - 5*x + e^(e^x)) + e^(e^(6*x^2 - 5*x + e^(e^x)))
+ e^(e^x)), x)

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maple [A]  time = 0.08, size = 16, normalized size = 0.67

method	result	size
risch	\({\mathrm e}^{{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{x}}+6 x^{2}-5 x}}}\)	\(16\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(x)*exp(exp(x))+12*x-5)*exp(1/exp(-exp(exp(x))-6*x^2+5*x))*exp(exp(1/exp(-exp(exp(x))-6*x^2+5*x)))/exp
(-exp(exp(x))-6*x^2+5*x),x,method=_RETURNVERBOSE)

[Out]

exp(exp(exp(exp(exp(x))+6*x^2-5*x)))

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maxima [A]  time = 0.83, size = 15, normalized size = 0.62 \begin {gather*} e^{\left (e^{\left (e^{\left (6 \, x^{2} - 5 \, x + e^{\left (e^{x}\right )}\right )}\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((exp(x)*exp(exp(x))+12*x-5)*exp(1/exp(-exp(exp(x))-6*x^2+5*x))*exp(exp(1/exp(-exp(exp(x))-6*x^2+5*x)
))/exp(-exp(exp(x))-6*x^2+5*x),x, algorithm="maxima")

[Out]

e^(e^(e^(6*x^2 - 5*x + e^(e^x))))

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mupad [B]  time = 7.74, size = 17, normalized size = 0.71 \begin {gather*} {\mathrm {e}}^{{\mathrm {e}}^{{\mathrm {e}}^{-5\,x}\,{\mathrm {e}}^{6\,x^2}\,{\mathrm {e}}^{{\mathrm {e}}^{{\mathrm {e}}^x}}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

exp(exp(exp(-5*x)*exp(6*x^2)*exp(exp(exp(x)))))

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sympy [A]  time = 55.77, size = 17, normalized size = 0.71 \begin {gather*} e^{e^{e^{6 x^{2} - 5 x + e^{e^{x}}}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((exp(x)*exp(exp(x))+12*x-5)*exp(1/exp(-exp(exp(x))-6*x**2+5*x))*exp(exp(1/exp(-exp(exp(x))-6*x**2+5*
x)))/exp(-exp(exp(x))-6*x**2+5*x),x)

[Out]

exp(exp(exp(6*x**2 - 5*x + exp(exp(x)))))

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