Optimal. Leaf size=26 \[ 36 \left (3 x+\frac {1}{4} e^{-1/x} \left (e^x+x\right )\right ) \log \left (x^2\right ) \]
________________________________________________________________________________________
Rubi [B] time = 1.02, antiderivative size = 56, normalized size of antiderivative = 2.15, number of steps used = 8, number of rules used = 3, integrand size = 68, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.044, Rules used = {6742, 2295, 2288} \begin {gather*} 9 e^{-1/x} x \log \left (x^2\right )+108 x \log \left (x^2\right )+\frac {9 e^{x-\frac {1}{x}} \left (x^2 \log \left (x^2\right )+\log \left (x^2\right )\right )}{\left (\frac {1}{x^2}+1\right ) x^2} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 2288
Rule 2295
Rule 6742
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (\frac {9 e^{-1/x} \left (2 x+24 e^{\frac {1}{x}} x+\log \left (x^2\right )+x \log \left (x^2\right )+12 e^{\frac {1}{x}} x \log \left (x^2\right )\right )}{x}+\frac {9 e^{-\frac {1}{x}+x} \left (2 x+\log \left (x^2\right )+x^2 \log \left (x^2\right )\right )}{x^2}\right ) \, dx\\ &=9 \int \frac {e^{-1/x} \left (2 x+24 e^{\frac {1}{x}} x+\log \left (x^2\right )+x \log \left (x^2\right )+12 e^{\frac {1}{x}} x \log \left (x^2\right )\right )}{x} \, dx+9 \int \frac {e^{-\frac {1}{x}+x} \left (2 x+\log \left (x^2\right )+x^2 \log \left (x^2\right )\right )}{x^2} \, dx\\ &=\frac {9 e^{-\frac {1}{x}+x} \left (\log \left (x^2\right )+x^2 \log \left (x^2\right )\right )}{\left (1+\frac {1}{x^2}\right ) x^2}+9 \int \left (12 \left (2+\log \left (x^2\right )\right )+\frac {e^{-1/x} \left (2 x+\log \left (x^2\right )+x \log \left (x^2\right )\right )}{x}\right ) \, dx\\ &=\frac {9 e^{-\frac {1}{x}+x} \left (\log \left (x^2\right )+x^2 \log \left (x^2\right )\right )}{\left (1+\frac {1}{x^2}\right ) x^2}+9 \int \frac {e^{-1/x} \left (2 x+\log \left (x^2\right )+x \log \left (x^2\right )\right )}{x} \, dx+108 \int \left (2+\log \left (x^2\right )\right ) \, dx\\ &=216 x+9 e^{-1/x} x \log \left (x^2\right )+\frac {9 e^{-\frac {1}{x}+x} \left (\log \left (x^2\right )+x^2 \log \left (x^2\right )\right )}{\left (1+\frac {1}{x^2}\right ) x^2}+108 \int \log \left (x^2\right ) \, dx\\ &=108 x \log \left (x^2\right )+9 e^{-1/x} x \log \left (x^2\right )+\frac {9 e^{-\frac {1}{x}+x} \left (\log \left (x^2\right )+x^2 \log \left (x^2\right )\right )}{\left (1+\frac {1}{x^2}\right ) x^2}\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.34, size = 26, normalized size = 1.00 \begin {gather*} 9 e^{-1/x} \left (e^x+x+12 e^{\frac {1}{x}} x\right ) \log \left (x^2\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.66, size = 23, normalized size = 0.88 \begin {gather*} 9 \, {\left (12 \, x e^{\frac {1}{x}} + x + e^{x}\right )} e^{\left (-\frac {1}{x}\right )} \log \left (x^{2}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.34, size = 37, normalized size = 1.42 \begin {gather*} 9 \, x e^{\left (-\frac {1}{x}\right )} \log \left (x^{2}\right ) + 108 \, x \log \left (x^{2}\right ) + 9 \, e^{\left (\frac {x^{2} - 1}{x}\right )} \log \left (x^{2}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [B] time = 0.13, size = 84, normalized size = 3.23 \[-9 \left (-\frac {\ln \left (x^{2}\right )+2 \ln \left (\frac {1}{x}\right )}{x}+\frac {2 \ln \left (\frac {1}{x}\right )}{x}\right ) {\mathrm e}^{-\frac {1}{x}} x^{2}+\frac {9 \left (\ln \left (x^{2}\right )-2 \ln \relax (x )\right ) x \,{\mathrm e}^{x -\frac {1}{x}}+18 x \,{\mathrm e}^{x -\frac {1}{x}} \ln \relax (x )}{x}+108 x \ln \left (x^{2}\right )\]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} 216 \, x \log \relax (x) + 18 \, e^{\left (x - \frac {1}{x}\right )} \log \relax (x) + 18 \, \Gamma \left (-1, \frac {1}{x}\right ) + 9 \, \int \frac {2 \, {\left (x + 1\right )} e^{\left (-\frac {1}{x}\right )} \log \relax (x)}{x}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [F] time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \int \frac {{\mathrm {e}}^{-\frac {1}{x}}\,\left (\ln \left (x^2\right )\,\left (9\,x+108\,x^2\,{\mathrm {e}}^{1/x}+{\mathrm {e}}^x\,\left (9\,x^2+9\right )+9\,x^2\right )+216\,x^2\,{\mathrm {e}}^{1/x}+18\,x\,{\mathrm {e}}^x+18\,x^2\right )}{x^2} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.45, size = 36, normalized size = 1.38 \begin {gather*} 108 x \log {\left (x^{2} \right )} + 9 x e^{- \frac {1}{x}} \log {\left (x^{2} \right )} + 9 e^{- \frac {1}{x}} e^{x} \log {\left (x^{2} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________