Optimal. Leaf size=23 \[ e^{3+x \left (-8-e^{\left .\frac {1}{4}\right /x}+\log \left (x^2\right )\right )} \]
________________________________________________________________________________________
Rubi [A] time = 0.56, antiderivative size = 25, normalized size of antiderivative = 1.09, number of steps used = 2, number of rules used = 2, integrand size = 65, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.031, Rules used = {12, 6706} \begin {gather*} e^{-e^{\left .\frac {1}{4}\right /x} x-8 x+3} \left (x^2\right )^x \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 12
Rule 6706
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{4} \int \frac {e^{-8 x-e^{\left .\frac {1}{4}\right /x} x+x \log \left (x^2\right )} \left (e^{3+\frac {1}{4 x}} (1-4 x)-24 e^3 x+4 e^3 x \log \left (x^2\right )\right )}{x} \, dx\\ &=e^{3-8 x-e^{\left .\frac {1}{4}\right /x} x} \left (x^2\right )^x\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.55, size = 25, normalized size = 1.09 \begin {gather*} e^{3-8 x-e^{\left .\frac {1}{4}\right /x} x} \left (x^2\right )^x \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.92, size = 34, normalized size = 1.48 \begin {gather*} e^{\left ({\left (x e^{3} \log \left (x^{2}\right ) - 8 \, x e^{3} - x e^{\left (\frac {12 \, x + 1}{4 \, x}\right )}\right )} e^{\left (-3\right )} + 3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.31, size = 21, normalized size = 0.91 \begin {gather*} e^{\left (-x e^{\left (\frac {1}{4 \, x}\right )} + x \log \left (x^{2}\right ) - 8 \, x + 3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.34, size = 24, normalized size = 1.04
method | result | size |
default | \({\mathrm e}^{3} {\mathrm e}^{x \ln \left (x^{2}\right )-x \,{\mathrm e}^{\frac {1}{4 x}}-8 x}\) | \(24\) |
norman | \({\mathrm e}^{3} {\mathrm e}^{x \ln \left (x^{2}\right )-x \,{\mathrm e}^{\frac {1}{4 x}}-8 x}\) | \(24\) |
risch | \({\mathrm e}^{3-\frac {i \pi \mathrm {csgn}\left (i x^{2}\right )^{3} x}{2}+i \pi \mathrm {csgn}\left (i x^{2}\right )^{2} \mathrm {csgn}\left (i x \right ) x -\frac {i \pi \,\mathrm {csgn}\left (i x^{2}\right ) \mathrm {csgn}\left (i x \right )^{2} x}{2}+2 x \ln \relax (x )-x \,{\mathrm e}^{\frac {1}{4 x}}-8 x}\) | \(73\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.40, size = 20, normalized size = 0.87 \begin {gather*} e^{\left (-x e^{\left (\frac {1}{4 \, x}\right )} + 2 \, x \log \relax (x) - 8 \, x + 3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 6.89, size = 22, normalized size = 0.96 \begin {gather*} {\mathrm {e}}^{-8\,x}\,{\mathrm {e}}^3\,{\mathrm {e}}^{-x\,{\mathrm {e}}^{\frac {1}{4\,x}}}\,{\left (x^2\right )}^x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.57, size = 22, normalized size = 0.96 \begin {gather*} e^{3} e^{- x e^{\frac {1}{4 x}} + x \log {\left (x^{2} \right )} - 8 x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________