Evaluating Cos I

Partial fraction decomposition of the integral would lead to, $$\begin {align}\int_0^1 \frac {\ln (1+x)} { (1+x) (1+x^2)} \, dx& = \frac {1} {2}\int_0^1\frac {\ln (1. Additionally, Here's another, seemingly monstrous question from a JEE Advanced preparation book. Furthermore, The integrand 1 1+x4 1 1 + x 4 is a rational function (quotient of two polynomials), so I could solve the integral if I can find the partial fraction of 1 1+x4 1 1 + x 4. Moreover, The problem is to solve: $$\lim_ {n\to\infty}\left ( \frac {\cos\frac {\pi} {2n}} {n+1}+\frac {\cos\frac {2\pi} {2n}} {n+1/2}+\dots+\frac {\cos\frac {n\pi} {2n}} {n+1. These findings regarding Evaluating Cos I provide comprehensive context for understanding this subject.