Optimal. Leaf size=32 \[ \frac {1}{4} e^{-1-x+x \log (2)+x^2 \log \left (-\frac {1}{(4-x) x}\right )} \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.28, antiderivative size = 26, normalized size of antiderivative = 0.81, number of steps
used = 1, number of rules used = 1, integrand size = 69, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.014, Rules used = {6838}
\begin {gather*} 2^{x-2} e^{-x-1} \left (\frac {1}{x^2-4 x}\right )^{x^2} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 6838
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=2^{-2+x} e^{-1-x} \left (\frac {1}{-4 x+x^2}\right )^{x^2}\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A]
time = 0.58, size = 26, normalized size = 0.81 \begin {gather*} 2^{-2+x} e^{-1-x} \left (\frac {1}{-4 x+x^2}\right )^{x^2} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 2.09, size = 27, normalized size = 0.84
method | result | size |
risch | \(\frac {\left (\frac {1}{x^{2}-4 x}\right )^{x^{2}} 2^{x} {\mathrm e}^{-x -1}}{4}\) | \(25\) |
default | \(\frac {{\mathrm e}^{x^{2} \ln \left (\frac {1}{x^{2}-4 x}\right )+x \ln \left (2\right )-x -1}}{4}\) | \(27\) |
norman | \(\frac {{\mathrm e}^{x^{2} \ln \left (\frac {1}{x^{2}-4 x}\right )+x \ln \left (2\right )-x -1}}{4}\) | \(27\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.68, size = 28, normalized size = 0.88 \begin {gather*} \frac {1}{4} \, e^{\left (-x^{2} \log \left (x - 4\right ) - x^{2} \log \left (x\right ) + x \log \left (2\right ) - x - 1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.36, size = 26, normalized size = 0.81 \begin {gather*} \frac {1}{4} \, e^{\left (x^{2} \log \left (\frac {1}{x^{2} - 4 \, x}\right ) + x \log \left (2\right ) - x - 1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.18, size = 24, normalized size = 0.75 \begin {gather*} \frac {e^{x^{2} \log {\left (\frac {1}{x^{2} - 4 x} \right )} - x + x \log {\left (2 \right )} - 1}}{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 0.42, size = 25, normalized size = 0.78 \begin {gather*} \frac {1}{4} \, e^{\left (-x^{2} \log \left (x^{2} - 4 \, x\right ) + x \log \left (2\right ) - x - 1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 4.51, size = 28, normalized size = 0.88 \begin {gather*} \frac {2^x\,{\mathrm {e}}^{-x-1}\,{\left (-\frac {1}{4\,x-x^2}\right )}^{x^2}}{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________