3.17.41 \(\int \frac {x^2+e^{e^{e^{\frac {e^{-15-5 x+25 x^2}+x^2}{x}}}+e^{\frac {e^{-15-5 x+25 x^2}+x^2}{x}}+\frac {e^{-15-5 x+25 x^2}+x^2}{x}} (x^2+e^{-15-5 x+25 x^2} (-1-5 x+50 x^2))}{x^2} \, dx\)

Optimal. Leaf size=28 \[ e^{e^{e^{\frac {e^{5 \left (-3-x+5 x^2\right )}}{x}+x}}}+x \]

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Rubi [F]  time = 4.41, 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 {x^2+\exp \left (e^{e^{\frac {e^{-15-5 x+25 x^2}+x^2}{x}}}+e^{\frac {e^{-15-5 x+25 x^2}+x^2}{x}}+\frac {e^{-15-5 x+25 x^2}+x^2}{x}\right ) \left (x^2+e^{-15-5 x+25 x^2} \left (-1-5 x+50 x^2\right )\right )}{x^2} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(x^2 + E^(E^E^((E^(-15 - 5*x + 25*x^2) + x^2)/x) + E^((E^(-15 - 5*x + 25*x^2) + x^2)/x) + (E^(-15 - 5*x +
25*x^2) + x^2)/x)*(x^2 + E^(-15 - 5*x + 25*x^2)*(-1 - 5*x + 50*x^2)))/x^2,x]

[Out]

x + Defer[Int][E^(E^E^(E^(-15 - 5*x + 25*x^2)/x + x) + E^(E^(-15 - 5*x + 25*x^2)/x + x) + E^(-15 - 5*x + 25*x^
2)/x + x), x] + 50*Defer[Int][E^(-15 + E^E^(E^(-15 - 5*x + 25*x^2)/x + x) + E^(E^(-15 - 5*x + 25*x^2)/x + x) +
E^(-15 - 5*x + 25*x^2)/x - 4*x + 25*x^2), x] - Defer[Int][E^(-15 + E^E^(E^(-15 - 5*x + 25*x^2)/x + x) + E^(E^
(-15 - 5*x + 25*x^2)/x + x) + E^(-15 - 5*x + 25*x^2)/x - 4*x + 25*x^2)/x^2, x] - 5*Defer[Int][E^(-15 + E^E^(E^
(-15 - 5*x + 25*x^2)/x + x) + E^(E^(-15 - 5*x + 25*x^2)/x + x) + E^(-15 - 5*x + 25*x^2)/x - 4*x + 25*x^2)/x, x
]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \left (1+\exp \left (e^{e^{\frac {e^{-15-5 x+25 x^2}}{x}+x}}+e^{\frac {e^{-15-5 x+25 x^2}}{x}+x}+\frac {e^{-15-5 x+25 x^2}}{x}+x\right )+\frac {\exp \left (-15+e^{e^{\frac {e^{-15-5 x+25 x^2}}{x}+x}}+e^{\frac {e^{-15-5 x+25 x^2}}{x}+x}+\frac {e^{-15-5 x+25 x^2}}{x}-4 x+25 x^2\right ) (-1+5 x) (1+10 x)}{x^2}\right ) \, dx\\ &=x+\int \exp \left (e^{e^{\frac {e^{-15-5 x+25 x^2}}{x}+x}}+e^{\frac {e^{-15-5 x+25 x^2}}{x}+x}+\frac {e^{-15-5 x+25 x^2}}{x}+x\right ) \, dx+\int \frac {\exp \left (-15+e^{e^{\frac {e^{-15-5 x+25 x^2}}{x}+x}}+e^{\frac {e^{-15-5 x+25 x^2}}{x}+x}+\frac {e^{-15-5 x+25 x^2}}{x}-4 x+25 x^2\right ) (-1+5 x) (1+10 x)}{x^2} \, dx\\ &=x+\int \exp \left (e^{e^{\frac {e^{-15-5 x+25 x^2}}{x}+x}}+e^{\frac {e^{-15-5 x+25 x^2}}{x}+x}+\frac {e^{-15-5 x+25 x^2}}{x}+x\right ) \, dx+\int \left (50 \exp \left (-15+e^{e^{\frac {e^{-15-5 x+25 x^2}}{x}+x}}+e^{\frac {e^{-15-5 x+25 x^2}}{x}+x}+\frac {e^{-15-5 x+25 x^2}}{x}-4 x+25 x^2\right )-\frac {\exp \left (-15+e^{e^{\frac {e^{-15-5 x+25 x^2}}{x}+x}}+e^{\frac {e^{-15-5 x+25 x^2}}{x}+x}+\frac {e^{-15-5 x+25 x^2}}{x}-4 x+25 x^2\right )}{x^2}-\frac {5 \exp \left (-15+e^{e^{\frac {e^{-15-5 x+25 x^2}}{x}+x}}+e^{\frac {e^{-15-5 x+25 x^2}}{x}+x}+\frac {e^{-15-5 x+25 x^2}}{x}-4 x+25 x^2\right )}{x}\right ) \, dx\\ &=x-5 \int \frac {\exp \left (-15+e^{e^{\frac {e^{-15-5 x+25 x^2}}{x}+x}}+e^{\frac {e^{-15-5 x+25 x^2}}{x}+x}+\frac {e^{-15-5 x+25 x^2}}{x}-4 x+25 x^2\right )}{x} \, dx+50 \int \exp \left (-15+e^{e^{\frac {e^{-15-5 x+25 x^2}}{x}+x}}+e^{\frac {e^{-15-5 x+25 x^2}}{x}+x}+\frac {e^{-15-5 x+25 x^2}}{x}-4 x+25 x^2\right ) \, dx+\int \exp \left (e^{e^{\frac {e^{-15-5 x+25 x^2}}{x}+x}}+e^{\frac {e^{-15-5 x+25 x^2}}{x}+x}+\frac {e^{-15-5 x+25 x^2}}{x}+x\right ) \, dx-\int \frac {\exp \left (-15+e^{e^{\frac {e^{-15-5 x+25 x^2}}{x}+x}}+e^{\frac {e^{-15-5 x+25 x^2}}{x}+x}+\frac {e^{-15-5 x+25 x^2}}{x}-4 x+25 x^2\right )}{x^2} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.21, size = 26, normalized size = 0.93 \begin {gather*} e^{e^{e^{\frac {e^{-15-5 x+25 x^2}}{x}+x}}}+x \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(x^2 + E^(E^E^((E^(-15 - 5*x + 25*x^2) + x^2)/x) + E^((E^(-15 - 5*x + 25*x^2) + x^2)/x) + (E^(-15 -
5*x + 25*x^2) + x^2)/x)*(x^2 + E^(-15 - 5*x + 25*x^2)*(-1 - 5*x + 50*x^2)))/x^2,x]

[Out]

E^E^E^(E^(-15 - 5*x + 25*x^2)/x + x) + x

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fricas [B]  time = 0.70, size = 154, normalized size = 5.50 \begin {gather*} {\left (x e^{\left (\frac {x^{2} + e^{\left (25 \, x^{2} - 5 \, x - 15\right )}}{x} + e^{\left (\frac {x^{2} + e^{\left (25 \, x^{2} - 5 \, x - 15\right )}}{x}\right )}\right )} + e^{\left (\frac {x^{2} + x e^{\left (\frac {x^{2} + e^{\left (25 \, x^{2} - 5 \, x - 15\right )}}{x}\right )} + x e^{\left (e^{\left (\frac {x^{2} + e^{\left (25 \, x^{2} - 5 \, x - 15\right )}}{x}\right )}\right )} + e^{\left (25 \, x^{2} - 5 \, x - 15\right )}}{x}\right )}\right )} e^{\left (-\frac {x^{2} + e^{\left (25 \, x^{2} - 5 \, x - 15\right )}}{x} - e^{\left (\frac {x^{2} + e^{\left (25 \, x^{2} - 5 \, x - 15\right )}}{x}\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((50*x^2-5*x-1)*exp(25*x^2-5*x-15)+x^2)*exp((exp(25*x^2-5*x-15)+x^2)/x)*exp(exp((exp(25*x^2-5*x-15)
+x^2)/x))*exp(exp(exp((exp(25*x^2-5*x-15)+x^2)/x)))+x^2)/x^2,x, algorithm="fricas")

[Out]

(x*e^((x^2 + e^(25*x^2 - 5*x - 15))/x + e^((x^2 + e^(25*x^2 - 5*x - 15))/x)) + e^((x^2 + x*e^((x^2 + e^(25*x^2
- 5*x - 15))/x) + x*e^(e^((x^2 + e^(25*x^2 - 5*x - 15))/x)) + e^(25*x^2 - 5*x - 15))/x))*e^(-(x^2 + e^(25*x^2
- 5*x - 15))/x - e^((x^2 + e^(25*x^2 - 5*x - 15))/x))

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giac [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {x^{2} + {\left (x^{2} + {\left (50 \, x^{2} - 5 \, x - 1\right )} e^{\left (25 \, x^{2} - 5 \, x - 15\right )}\right )} e^{\left (\frac {x^{2} + e^{\left (25 \, x^{2} - 5 \, x - 15\right )}}{x} + e^{\left (\frac {x^{2} + e^{\left (25 \, x^{2} - 5 \, x - 15\right )}}{x}\right )} + e^{\left (e^{\left (\frac {x^{2} + e^{\left (25 \, x^{2} - 5 \, x - 15\right )}}{x}\right )}\right )}\right )}}{x^{2}}\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((50*x^2-5*x-1)*exp(25*x^2-5*x-15)+x^2)*exp((exp(25*x^2-5*x-15)+x^2)/x)*exp(exp((exp(25*x^2-5*x-15)
+x^2)/x))*exp(exp(exp((exp(25*x^2-5*x-15)+x^2)/x)))+x^2)/x^2,x, algorithm="giac")

[Out]

integrate((x^2 + (x^2 + (50*x^2 - 5*x - 1)*e^(25*x^2 - 5*x - 15))*e^((x^2 + e^(25*x^2 - 5*x - 15))/x + e^((x^2
+ e^(25*x^2 - 5*x - 15))/x) + e^(e^((x^2 + e^(25*x^2 - 5*x - 15))/x))))/x^2, x)

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maple [A]  time = 0.09, size = 25, normalized size = 0.89

method	result	size
risch	\(x +{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{\frac {{\mathrm e}^{25 x^{2}-5 x -15}+x^{2}}{x}}}}\)	\(25\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((50*x^2-5*x-1)*exp(25*x^2-5*x-15)+x^2)*exp((exp(25*x^2-5*x-15)+x^2)/x)*exp(exp((exp(25*x^2-5*x-15)+x^2)/
x))*exp(exp(exp((exp(25*x^2-5*x-15)+x^2)/x)))+x^2)/x^2,x,method=_RETURNVERBOSE)

[Out]

x+exp(exp(exp((exp(25*x^2-5*x-15)+x^2)/x)))

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maxima [A]  time = 0.82, size = 22, normalized size = 0.79 \begin {gather*} x + e^{\left (e^{\left (e^{\left (x + \frac {e^{\left (25 \, x^{2} - 5 \, x - 15\right )}}{x}\right )}\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((50*x^2-5*x-1)*exp(25*x^2-5*x-15)+x^2)*exp((exp(25*x^2-5*x-15)+x^2)/x)*exp(exp((exp(25*x^2-5*x-15)
+x^2)/x))*exp(exp(exp((exp(25*x^2-5*x-15)+x^2)/x)))+x^2)/x^2,x, algorithm="maxima")

[Out]

x + e^(e^(e^(x + e^(25*x^2 - 5*x - 15)/x)))

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mupad [B]  time = 1.24, size = 24, normalized size = 0.86 \begin {gather*} x+{\mathrm {e}}^{{\mathrm {e}}^{{\mathrm {e}}^{\frac {{\mathrm {e}}^{-5\,x}\,{\mathrm {e}}^{-15}\,{\mathrm {e}}^{25\,x^2}}{x}}\,{\mathrm {e}}^x}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((x^2 - exp(exp((exp(25*x^2 - 5*x - 15) + x^2)/x))*exp(exp(exp((exp(25*x^2 - 5*x - 15) + x^2)/x)))*exp((exp
(25*x^2 - 5*x - 15) + x^2)/x)*(exp(25*x^2 - 5*x - 15)*(5*x - 50*x^2 + 1) - x^2))/x^2,x)

[Out]

x + exp(exp(exp((exp(-5*x)*exp(-15)*exp(25*x^2))/x)*exp(x)))

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sympy [A]  time = 14.72, size = 22, normalized size = 0.79 \begin {gather*} x + e^{e^{e^{\frac {x^{2} + e^{25 x^{2} - 5 x - 15}}{x}}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((50*x**2-5*x-1)*exp(25*x**2-5*x-15)+x**2)*exp((exp(25*x**2-5*x-15)+x**2)/x)*exp(exp((exp(25*x**2-5
*x-15)+x**2)/x))*exp(exp(exp((exp(25*x**2-5*x-15)+x**2)/x)))+x**2)/x**2,x)

[Out]

x + exp(exp(exp((x**2 + exp(25*x**2 - 5*x - 15))/x)))

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