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]
[Out]
Rule 12
Rule 2209
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]
[Out]
________________________________________________________________________________________
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]
[Out]
________________________________________________________________________________________
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]
[Out]
________________________________________________________________________________________
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]
[Out]
________________________________________________________________________________________
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]
[Out]
________________________________________________________________________________________
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]
[Out]
________________________________________________________________________________________
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]
[Out]
________________________________________________________________________________________