3.29.50 \(\int -\frac {8 e^{-\frac {19}{9}+\frac {8}{e^{19/9} x}}}{x^2} \, dx\)

Optimal. Leaf size=12 \[ e^{\frac {8}{e^{19/9} x}} \]

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Rubi [A]  time = 0.03, antiderivative size = 12, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 21, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.095, Rules used = {12, 2209} \begin {gather*} e^{\frac {8}{e^{19/9} x}} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(-8*E^(-19/9 + 8/(E^(19/9)*x)))/x^2,x]

[Out]

E^(8/(E^(19/9)*x))

Rule 12

Int[(a_)*(u_), x_Symbol] :> Dist[a, Int[u, x], x] /; FreeQ[a, x] &&  !MatchQ[u, (b_)*(v_) /; FreeQ[b, x]]

Rule 2209

Int[(F_)^((a_.) + (b_.)*((c_.) + (d_.)*(x_))^(n_))*((e_.) + (f_.)*(x_))^(m_.), x_Symbol] :> Simp[((e + f*x)^n*
F^(a + b*(c + d*x)^n))/(b*f*n*(c + d*x)^n*Log[F]), x] /; FreeQ[{F, a, b, c, d, e, f, n}, x] && EqQ[m, n - 1] &
& EqQ[d*e - c*f, 0]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=-\left (8 \int \frac {e^{-\frac {19}{9}+\frac {8}{e^{19/9} x}}}{x^2} \, dx\right )\\ &=e^{\frac {8}{e^{19/9} x}}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.01, size = 12, normalized size = 1.00 \begin {gather*} e^{\frac {8}{e^{19/9} x}} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-8*E^(-19/9 + 8/(E^(19/9)*x)))/x^2,x]

[Out]

E^(8/(E^(19/9)*x))

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fricas [B]  time = 0.85, size = 17, normalized size = 1.42 \begin {gather*} e^{\left (-\frac {{\left (19 \, x e^{\frac {19}{9}} - 72\right )} e^{\left (-\frac {19}{9}\right )}}{9 \, x} + \frac {19}{9}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-8*exp(8/x/exp(19/9))/x^2/exp(19/9),x, algorithm="fricas")

[Out]

e^(-1/9*(19*x*e^(19/9) - 72)*e^(-19/9)/x + 19/9)

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giac [A]  time = 0.47, size = 8, normalized size = 0.67 \begin {gather*} e^{\left (\frac {8 \, e^{\left (-\frac {19}{9}\right )}}{x}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-8*exp(8/x/exp(19/9))/x^2/exp(19/9),x, algorithm="giac")

[Out]

e^(8*e^(-19/9)/x)

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maple [A]  time = 0.06, size = 9, normalized size = 0.75

method	result	size
risch	\({\mathrm e}^{\frac {8 \,{\mathrm e}^{-\frac {19}{9}}}{x}}\)	\(9\)
gosper	\({\mathrm e}^{\frac {8 \,{\mathrm e}^{-\frac {19}{9}}}{x}}\)	\(11\)
derivativedivides	\({\mathrm e}^{\frac {8 \,{\mathrm e}^{-\frac {19}{9}}}{x}}\)	\(11\)
default	\({\mathrm e}^{\frac {8 \,{\mathrm e}^{-\frac {19}{9}}}{x}}\)	\(11\)
norman	\({\mathrm e}^{\frac {8 \,{\mathrm e}^{-\frac {19}{9}}}{x}}\)	\(11\)
meijerg	\(-1+{\mathrm e}^{\frac {8 \,{\mathrm e}^{-\frac {19}{9}}}{x}}\)	\(11\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-8*exp(8/x/exp(19/9))/x^2/exp(19/9),x,method=_RETURNVERBOSE)

[Out]

exp(8/x*exp(-19/9))

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maxima [A]  time = 0.53, size = 8, normalized size = 0.67 \begin {gather*} e^{\left (\frac {8 \, e^{\left (-\frac {19}{9}\right )}}{x}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-8*exp(8/x/exp(19/9))/x^2/exp(19/9),x, algorithm="maxima")

[Out]

e^(8*e^(-19/9)/x)

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mupad [B]  time = 1.70, size = 8, normalized size = 0.67 \begin {gather*} {\mathrm {e}}^{\frac {8\,{\mathrm {e}}^{-\frac {19}{9}}}{x}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(8*exp((8*exp(-19/9))/x)*exp(-19/9))/x^2,x)

[Out]

exp((8*exp(-19/9))/x)

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sympy [A]  time = 0.11, size = 8, normalized size = 0.67 \begin {gather*} e^{\frac {8}{x e^{\frac {19}{9}}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-8*exp(8/x/exp(19/9))/x**2/exp(19/9),x)

[Out]

exp(8*exp(-19/9)/x)

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