\[\int_{0}^{\pi /4}{{}}\sec x\log (\sec x+\tan x)\,dx=\]

• A. \[\frac{1}{2}{{[\log (1+\sqrt{2})]}^{2}}\]
• B. \[{{[\log (1+\sqrt{2})]}^{2}}\]
• C. \[\frac{1}{2}{{[\log (\sqrt{2}-1)]}^{2}}\]
• D. \[\frac{1}{2}{{[\log (\sqrt{2}-1)]}^{2}}\]