Optimal. Leaf size=18 \[ \frac {e^{-29-2 x+\frac {\log (x)}{\log (4)}}}{x} \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.13, antiderivative size = 16, normalized size of antiderivative = 0.89, number of steps
used = 3, number of rules used = 3, integrand size = 43, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.070, Rules used = {12, 2306, 2228}
\begin {gather*} e^{-2 x-29} x^{\frac {1}{\log (4)}-1} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 12
Rule 2228
Rule 2306
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int \frac {\exp \left (\frac {(-29-2 x) \log (4)+(1-\log (4)) \log (x)}{\log (4)}\right ) (1+(-1-2 x) \log (4))}{x} \, dx}{\log (4)}\\ &=\frac {\int e^{-29-2 x} x^{-1+\frac {1-\log (4)}{\log (4)}} (1+(-1-2 x) \log (4)) \, dx}{\log (4)}\\ &=e^{-29-2 x} x^{-1+\frac {1}{\log (4)}}\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A]
time = 0.03, size = 25, normalized size = 1.39 \begin {gather*} \frac {e^{-29-2 x} x^{-1+\frac {1}{\log (4)}} \log (16)}{2 \log (4)} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.28, size = 19, normalized size = 1.06
method | result | size |
risch | \(\frac {x^{\frac {1}{2 \ln \left (2\right )}} {\mathrm e}^{-2 x -29}}{x}\) | \(19\) |
norman | \({\mathrm e}^{\frac {\left (1-2 \ln \left (2\right )\right ) \ln \left (x \right )+2 \left (-2 x -29\right ) \ln \left (2\right )}{2 \ln \left (2\right )}}\) | \(27\) |
gosper | \({\mathrm e}^{-\frac {2 \ln \left (2\right ) \ln \left (x \right )+4 x \ln \left (2\right )-\ln \left (x \right )+58 \ln \left (2\right )}{2 \ln \left (2\right )}}\) | \(28\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.53, size = 18, normalized size = 1.00 \begin {gather*} \frac {e^{\left (-2 \, x + \frac {\log \left (x\right )}{2 \, \log \left (2\right )} - 29\right )}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.36, size = 26, normalized size = 1.44 \begin {gather*} e^{\left (-\frac {2 \, {\left (2 \, x + 29\right )} \log \left (2\right ) + {\left (2 \, \log \left (2\right ) - 1\right )} \log \left (x\right )}{2 \, \log \left (2\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 1.44, size = 17, normalized size = 0.94 \begin {gather*} \frac {x^{\frac {1}{2 \log {\left (2 \right )}}} e^{- 2 x}}{x e^{29}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 0.39, size = 18, normalized size = 1.00 \begin {gather*} e^{\left (-2 \, x + \frac {\log \left (x\right )}{2 \, \log \left (2\right )} - \log \left (x\right ) - 29\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 1.54, size = 17, normalized size = 0.94 \begin {gather*} x^{\frac {1}{2\,\ln \left (2\right )}-1}\,{\mathrm {e}}^{-2\,x}\,{\mathrm {e}}^{-29} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________