3.59.52 \(\int \frac {e^{e^x} (-8+8 e^x x)}{x^2} \, dx\)

Optimal. Leaf size=15 \[ \frac {x+8 \left (e^{e^x}+x\right )}{x} \]

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Rubi [A]  time = 0.04, antiderivative size = 10, normalized size of antiderivative = 0.67, number of steps used = 1, number of rules used = 1, integrand size = 17, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.059, Rules used = {2288} \begin {gather*} \frac {8 e^{e^x}}{x} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(E^E^x*(-8 + 8*E^x*x))/x^2,x]

[Out]

(8*E^E^x)/x

Rule 2288

Int[(y_.)*(F_)^(u_)*((v_) + (w_)), x_Symbol] :> With[{z = (v*y)/(Log[F]*D[u, x])}, Simp[F^u*z, x] /; EqQ[D[z,
x], w*y]] /; FreeQ[F, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\frac {8 e^{e^x}}{x}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.01, size = 10, normalized size = 0.67 \begin {gather*} \frac {8 e^{e^x}}{x} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^E^x*(-8 + 8*E^x*x))/x^2,x]

[Out]

(8*E^E^x)/x

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fricas [A]  time = 0.56, size = 8, normalized size = 0.53 \begin {gather*} \frac {8 \, e^{\left (e^{x}\right )}}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((8*exp(x)*x-8)*exp(exp(x))/x^2,x, algorithm="fricas")

[Out]

8*e^(e^x)/x

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giac [A]  time = 0.16, size = 8, normalized size = 0.53 \begin {gather*} \frac {8 \, e^{\left (e^{x}\right )}}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((8*exp(x)*x-8)*exp(exp(x))/x^2,x, algorithm="giac")

[Out]

8*e^(e^x)/x

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maple [A]  time = 0.02, size = 9, normalized size = 0.60

method	result	size
norman	\(\frac {8 \,{\mathrm e}^{{\mathrm e}^{x}}}{x}\)	\(9\)
risch	\(\frac {8 \,{\mathrm e}^{{\mathrm e}^{x}}}{x}\)	\(9\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((8*exp(x)*x-8)*exp(exp(x))/x^2,x,method=_RETURNVERBOSE)

[Out]

8*exp(exp(x))/x

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maxima [A]  time = 0.39, size = 8, normalized size = 0.53 \begin {gather*} \frac {8 \, e^{\left (e^{x}\right )}}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((8*exp(x)*x-8)*exp(exp(x))/x^2,x, algorithm="maxima")

[Out]

8*e^(e^x)/x

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mupad [B]  time = 4.05, size = 8, normalized size = 0.53 \begin {gather*} \frac {8\,{\mathrm {e}}^{{\mathrm {e}}^x}}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(exp(x))*(8*x*exp(x) - 8))/x^2,x)

[Out]

(8*exp(exp(x)))/x

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sympy [A]  time = 0.10, size = 7, normalized size = 0.47 \begin {gather*} \frac {8 e^{e^{x}}}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((8*exp(x)*x-8)*exp(exp(x))/x**2,x)

[Out]

8*exp(exp(x))/x

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