how should I integrate 1/(x^2 +1)^5

Question

drwls · Answer

According to my table of integrals, this one is a real mess.

I had to use a recursion relation. This is equivalent to using integration by parts several times. The first step yields

INT of 1/(x^2 +1)^5

= x/[8(x^2+1)^4]
+ (1/4) INT of 1/(x^2 +1)^4

In the next step you reduce the second integral to another function of x plus the integral of 1/(x^2 +1)^3 etc.

There will be a log or hyperbolic tangent term in the last step

Ann · Answer

Drwls, how did you derive the first step so that I can continue with the remainder of the steps?