$
\frac{d}{dx}\left( \ln \left( \tan x\right) \right) ^{2}=\frac{2}{\tan x}
\frac{1}{\cos ^{2}x}\left( \ln \left( \tan x\right) \right) =\frac{2\ln
\left( \tan x\right) }{\sin x\cos x}
$
olduğundan
\[
\int\limits_{\frac{\pi }{4}}^{\frac{\pi }{3}}\frac{\ln \left( \tan x\right)
}{\sin x\cos x}dx=\left. \frac{1}{2}\left( \ln \left( \tan x\right) \right)
^{2}\right\vert _{\frac{\pi }{4}}^{\frac{\pi }{3}}=\frac{1}{2}\left( \left(
\ln \sqrt{3}\right) ^{2}-\left( \ln 1\right) ^{2}\right) =\frac{1}{8}\ln
^{2}3
\]
dir.