Optimal. Leaf size=20 \[ \log \left (2 \left (5+\log \left (\frac {25 (-2+x)^2 \log (5)}{16 e^5}\right )\right )\right ) \]
________________________________________________________________________________________
Rubi [A] time = 0.07, antiderivative size = 20, normalized size of antiderivative = 1.00, number of steps used = 5, number of rules used = 5, integrand size = 33, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.152, Rules used = {12, 6741, 2390, 2302, 29} \begin {gather*} \log \left (\log \left (\frac {25 (2-x)^2 \log (5)}{16 e^5}\right )+5\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 12
Rule 29
Rule 2302
Rule 2390
Rule 6741
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=2 \int \frac {1}{-10+5 x+(-2+x) \log \left (\frac {\left (100-100 x+25 x^2\right ) \log (5)}{16 e^5}\right )} \, dx\\ &=2 \int \frac {1}{(-2+x) \left (5+\log \left (\frac {25 (-2+x)^2 \log (5)}{16 e^5}\right )\right )} \, dx\\ &=2 \operatorname {Subst}\left (\int \frac {1}{x \left (5+\log \left (\frac {25 x^2 \log (5)}{16 e^5}\right )\right )} \, dx,x,-2+x\right )\\ &=\operatorname {Subst}\left (\int \frac {1}{x} \, dx,x,5+\log \left (\frac {25 (-2+x)^2 \log (5)}{16 e^5}\right )\right )\\ &=\log \left (5+\log \left (\frac {25 (-2+x)^2 \log (5)}{16 e^5}\right )\right )\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.05, size = 18, normalized size = 0.90 \begin {gather*} \log \left (5+\log \left (\frac {25 (-2+x)^2 \log (5)}{16 e^5}\right )\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.51, size = 18, normalized size = 0.90 \begin {gather*} \log \left (\log \left (\frac {25}{16} \, {\left (x^{2} - 4 \, x + 4\right )} e^{\left (-5\right )} \log \relax (5)\right ) + 5\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.32, size = 27, normalized size = 1.35 \begin {gather*} \log \left (2 \, \log \relax (5) - 4 \, \log \relax (2) + \log \left (x^{2} \log \relax (5) - 4 \, x \log \relax (5) + 4 \, \log \relax (5)\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.03, size = 21, normalized size = 1.05
method | result | size |
risch | \(\ln \left (\ln \left (\frac {\left (25 x^{2}-100 x +100\right ) \ln \relax (5) {\mathrm e}^{-5}}{16}\right )+5\right )\) | \(21\) |
norman | \(\ln \left (\ln \left (\frac {\left (25 x^{2}-100 x +100\right ) \ln \relax (5) {\mathrm e}^{-5}}{16}\right )+5\right )\) | \(23\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.58, size = 17, normalized size = 0.85 \begin {gather*} \log \left (\log \relax (5) - 2 \, \log \relax (2) + \log \left (x - 2\right ) + \frac {1}{2} \, \log \left (\log \relax (5)\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 1.02, size = 20, normalized size = 1.00 \begin {gather*} \ln \left (\ln \left (\frac {{\mathrm {e}}^{-5}\,\ln \relax (5)\,\left (25\,x^2-100\,x+100\right )}{16}\right )+5\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.15, size = 26, normalized size = 1.30 \begin {gather*} \log {\left (\log {\left (\frac {\left (\frac {25 x^{2}}{16} - \frac {25 x}{4} + \frac {25}{4}\right ) \log {\relax (5 )}}{e^{5}} \right )} + 5 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________