Optimal. Leaf size=11 \[ e^{-\frac {8}{x^3 \log (3)}} \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.02, antiderivative size = 11, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 2, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.100, Rules used = {12, 2240}
\begin {gather*} e^{-\frac {8}{x^3 \log (3)}} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 12
Rule 2240
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {24 \int \frac {e^{-\frac {8}{x^3 \log (3)}}}{x^4} \, dx}{\log (3)}\\ &=e^{-\frac {8}{x^3 \log (3)}}\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A]
time = 0.00, size = 11, normalized size = 1.00 \begin {gather*} e^{-\frac {8}{x^3 \log (3)}} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.36, size = 11, normalized size = 1.00
method | result | size |
gosper | \({\mathrm e}^{-\frac {8}{x^{3} \ln \left (3\right )}}\) | \(11\) |
derivativedivides | \({\mathrm e}^{-\frac {8}{x^{3} \ln \left (3\right )}}\) | \(11\) |
default | \({\mathrm e}^{-\frac {8}{x^{3} \ln \left (3\right )}}\) | \(11\) |
norman | \({\mathrm e}^{-\frac {8}{x^{3} \ln \left (3\right )}}\) | \(11\) |
risch | \({\mathrm e}^{-\frac {8}{x^{3} \ln \left (3\right )}}\) | \(11\) |
meijerg | \(-1+{\mathrm e}^{-\frac {8}{x^{3} \ln \left (3\right )}}\) | \(13\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.27, size = 10, normalized size = 0.91 \begin {gather*} e^{\left (-\frac {8}{x^{3} \log \left (3\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.36, size = 10, normalized size = 0.91 \begin {gather*} e^{\left (-\frac {8}{x^{3} \log \left (3\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.04, size = 10, normalized size = 0.91 \begin {gather*} e^{- \frac {8}{x^{3} \log {\left (3 \right )}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 0.38, size = 10, normalized size = 0.91 \begin {gather*} e^{\left (-\frac {8}{x^{3} \log \left (3\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 4.16, size = 10, normalized size = 0.91 \begin {gather*} {\mathrm {e}}^{-\frac {8}{x^3\,\ln \left (3\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________