Optimal. Leaf size=17 \[ -13-e^x+2 x-\log (x)+\log (\log (x)) \]
________________________________________________________________________________________
Rubi [A] time = 0.30, antiderivative size = 16, normalized size of antiderivative = 0.94, number of steps used = 9, number of rules used = 5, integrand size = 24, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.208, Rules used = {6742, 2194, 43, 2302, 29} \begin {gather*} 2 x-e^x-\log (x)+\log (\log (x)) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 29
Rule 43
Rule 2194
Rule 2302
Rule 6742
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-e^x+\frac {1-\log (x)+2 x \log (x)}{x \log (x)}\right ) \, dx\\ &=-\int e^x \, dx+\int \frac {1-\log (x)+2 x \log (x)}{x \log (x)} \, dx\\ &=-e^x+\int \left (\frac {-1+2 x}{x}+\frac {1}{x \log (x)}\right ) \, dx\\ &=-e^x+\int \frac {-1+2 x}{x} \, dx+\int \frac {1}{x \log (x)} \, dx\\ &=-e^x+\int \left (2-\frac {1}{x}\right ) \, dx+\operatorname {Subst}\left (\int \frac {1}{x} \, dx,x,\log (x)\right )\\ &=-e^x+2 x-\log (x)+\log (\log (x))\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.02, size = 16, normalized size = 0.94 \begin {gather*} -e^x+2 x-\log (x)+\log (\log (x)) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.51, size = 15, normalized size = 0.88 \begin {gather*} 2 \, x - e^{x} - \log \relax (x) + \log \left (\log \relax (x)\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.19, size = 15, normalized size = 0.88 \begin {gather*} 2 \, x - e^{x} - \log \relax (x) + \log \left (\log \relax (x)\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.03, size = 16, normalized size = 0.94
method | result | size |
default | \(\ln \left (\ln \relax (x )\right )+2 x -\ln \relax (x )-{\mathrm e}^{x}\) | \(16\) |
norman | \(\ln \left (\ln \relax (x )\right )+2 x -\ln \relax (x )-{\mathrm e}^{x}\) | \(16\) |
risch | \(\ln \left (\ln \relax (x )\right )+2 x -\ln \relax (x )-{\mathrm e}^{x}\) | \(16\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.36, size = 15, normalized size = 0.88 \begin {gather*} 2 \, x - e^{x} - \log \relax (x) + \log \left (\log \relax (x)\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 9.26, size = 15, normalized size = 0.88 \begin {gather*} 2\,x+\ln \left (\ln \relax (x)\right )-{\mathrm {e}}^x-\ln \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.26, size = 14, normalized size = 0.82 \begin {gather*} 2 x - e^{x} - \log {\relax (x )} + \log {\left (\log {\relax (x )} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________