3.94.68 \(\int -\frac {15 e^{-3/x}}{x^2} \, dx\)

Optimal. Leaf size=9 \[ -5 e^{-3/x} \]

________________________________________________________________________________________

Rubi [A]  time = 0.02, antiderivative size = 9, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 12, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.167, Rules used = {12, 2209} \begin {gather*} -5 e^{-3/x} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[-15/(E^(3/x)*x^2),x]

[Out]

-5/E^(3/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 (15 \int \frac {e^{-3/x}}{x^2} \, dx\right )\\ &=-5 e^{-3/x}\\ \end {aligned} \end {gather*}

________________________________________________________________________________________

Mathematica [A]  time = 0.00, size = 9, normalized size = 1.00 \begin {gather*} -5 e^{-3/x} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[-15/(E^(3/x)*x^2),x]

[Out]

-5/E^(3/x)

________________________________________________________________________________________

fricas [A]  time = 0.53, size = 8, normalized size = 0.89 \begin {gather*} -5 \, e^{\left (-\frac {3}{x}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-15/x^2/exp(3/x),x, algorithm="fricas")

[Out]

-5*e^(-3/x)

________________________________________________________________________________________

giac [A]  time = 0.17, size = 8, normalized size = 0.89 \begin {gather*} -5 \, e^{\left (-\frac {3}{x}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-15/x^2/exp(3/x),x, algorithm="giac")

[Out]

-5*e^(-3/x)

________________________________________________________________________________________

maple [A]  time = 0.03, size = 9, normalized size = 1.00

method	result	size
risch	\(-5 \,{\mathrm e}^{-\frac {3}{x}}\)	\(9\)
gosper	\(-5 \,{\mathrm e}^{-\frac {3}{x}}\)	\(11\)
derivativedivides	\(-5 \,{\mathrm e}^{-\frac {3}{x}}\)	\(11\)
default	\(-5 \,{\mathrm e}^{-\frac {3}{x}}\)	\(11\)
norman	\(-5 \,{\mathrm e}^{-\frac {3}{x}}\)	\(11\)
meijerg	\(5-5 \,{\mathrm e}^{-\frac {3}{x}}\)	\(11\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-15/x^2/exp(3/x),x,method=_RETURNVERBOSE)

[Out]

-5*exp(-3/x)

________________________________________________________________________________________

maxima [A]  time = 0.35, size = 8, normalized size = 0.89 \begin {gather*} -5 \, e^{\left (-\frac {3}{x}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-15/x^2/exp(3/x),x, algorithm="maxima")

[Out]

-5*e^(-3/x)

________________________________________________________________________________________

mupad [B]  time = 5.43, size = 8, normalized size = 0.89 \begin {gather*} -5\,{\mathrm {e}}^{-\frac {3}{x}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(15*exp(-3/x))/x^2,x)

[Out]

-5*exp(-3/x)

________________________________________________________________________________________

sympy [A]  time = 0.09, size = 7, normalized size = 0.78 \begin {gather*} - 5 e^{- \frac {3}{x}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-15/x**2/exp(3/x),x)

[Out]

-5*exp(-3/x)

________________________________________________________________________________________