Sejam $f(x)=\ln (\cos x{)}^2$, $0\le x<\frac{\pi }{2}$ e $F(x)=\int \left[{\left(f^{\prime }(x)\right)}^2+{\mathrm{sen}}^{2}2x\right]dx$. Se $F(0)=\frac{7\pi }{8}-5$, então ${\lim }_{x\to \frac{\pi }{4}}F(x)$ vale