3.60.22 \(\int \frac {-7+e^{e^x} (-2+2 e^x x)}{x^2} \, dx\)

Optimal. Leaf size=15 \[ \frac {1+2 \left (3+e^{e^x}\right )}{x} \]

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Rubi [F]  time = 0.08, 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 {-7+e^{e^x} \left (-2+2 e^x x\right )}{x^2} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(-7 + E^E^x*(-2 + 2*E^x*x))/x^2,x]

[Out]

7/x - 2*Defer[Int][E^E^x/x^2, x] + 2*Defer[Int][E^(E^x + x)/x, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-\frac {7+2 e^{e^x}}{x^2}+\frac {2 e^{e^x+x}}{x}\right ) \, dx\\ &=2 \int \frac {e^{e^x+x}}{x} \, dx-\int \frac {7+2 e^{e^x}}{x^2} \, dx\\ &=2 \int \frac {e^{e^x+x}}{x} \, dx-\int \left (\frac {7}{x^2}+\frac {2 e^{e^x}}{x^2}\right ) \, dx\\ &=\frac {7}{x}-2 \int \frac {e^{e^x}}{x^2} \, dx+2 \int \frac {e^{e^x+x}}{x} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.02, size = 13, normalized size = 0.87 \begin {gather*} \frac {7+2 e^{e^x}}{x} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-7 + E^E^x*(-2 + 2*E^x*x))/x^2,x]

[Out]

(7 + 2*E^E^x)/x

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fricas [A]  time = 0.67, size = 11, normalized size = 0.73 \begin {gather*} \frac {2 \, e^{\left (e^{x}\right )} + 7}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((2*exp(x)*x-2)*exp(exp(x))-7)/x^2,x, algorithm="fricas")

[Out]

(2*e^(e^x) + 7)/x

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giac [A]  time = 0.14, size = 20, normalized size = 1.33 \begin {gather*} \frac {{\left (2 \, e^{\left (x + e^{x}\right )} + 7 \, e^{x}\right )} e^{\left (-x\right )}}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((2*exp(x)*x-2)*exp(exp(x))-7)/x^2,x, algorithm="giac")

[Out]

(2*e^(x + e^x) + 7*e^x)*e^(-x)/x

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maple [A]  time = 0.03, size = 12, normalized size = 0.80

method	result	size
norman	\(\frac {2 \,{\mathrm e}^{{\mathrm e}^{x}}+7}{x}\)	\(12\)
risch	\(\frac {7}{x}+\frac {2 \,{\mathrm e}^{{\mathrm e}^{x}}}{x}\)	\(15\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((2*exp(x)*x-2)*exp(exp(x))-7)/x^2,x,method=_RETURNVERBOSE)

[Out]

(2*exp(exp(x))+7)/x

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maxima [A]  time = 0.40, size = 14, normalized size = 0.93 \begin {gather*} \frac {2 \, e^{\left (e^{x}\right )}}{x} + \frac {7}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((2*exp(x)*x-2)*exp(exp(x))-7)/x^2,x, algorithm="maxima")

[Out]

2*e^(e^x)/x + 7/x

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mupad [B]  time = 4.44, size = 11, normalized size = 0.73 \begin {gather*} \frac {2\,{\mathrm {e}}^{{\mathrm {e}}^x}+7}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(exp(x))*(2*x*exp(x) - 2) - 7)/x^2,x)

[Out]

(2*exp(exp(x)) + 7)/x

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sympy [A]  time = 0.10, size = 10, normalized size = 0.67 \begin {gather*} \frac {2 e^{e^{x}}}{x} + \frac {7}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((2*exp(x)*x-2)*exp(exp(x))-7)/x**2,x)

[Out]

2*exp(exp(x))/x + 7/x

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