2001-23.md

course	course_year	question_number	tags	title	year
Complex Methods	IB	23	IB 2001 Complex Methods	2.II.16E	2001

Let $R$ be a rational function such that $\lim _{z \rightarrow \infty}{z R(z)}=0$. Assuming that $R$ has no real poles, use the residue calculus to evaluate

$$\int_{-\infty}^{\infty} R(x) d x$$

Given that $n \geqslant 1$ is an integer, evaluate

$$\int_{0}^{\infty} \frac{d x}{1+x^{2 n}}$$