# Thread: Integration and complex nos

1. ## Integration and complex nos

Thanx
Edgar

a)Evaluate the integral

integral from minus infintiy to infinity of 1/(1+x)^4 dx

b)Where are the poles of 1/(1+z)^4 ?

2. Originally Posted by edgar davids

a)Evaluate the integral

integral from minus infintiy to infinity of 1/(1+x)^4 dx
You need to find,
$\displaystyle \int_{\infty}^{\infty} \frac{1}{(1+x)^4}dx$
The function has a vertical asymptote at $\displaystyle x=-1$
Thus you need to do,
$\displaystyle \int_{-\infty}^{-1^-} \frac{1}{(1+x)^4} dx+\int_{-1^+}^{\infty} \frac{1}{(1+x)^4} dx$
Which is,
$\displaystyle (-1/5)(1+x)^{-5}|_{-\infty}^{-1^-}+(-1/5)(1+x)^{-5}|_{-1^+}^{\infty}$
That looks unbounded to me.
b)Where are the poles of 1/(1+z)^4 ?
$\displaystyle z=-1$ of order 4.