Variant of inverse tangent derivative

[Saterial]

Homework Statement

1/(u^2+4)

Homework Equations

The Attempt at a Solution

I know that 1/(x^2+1) is the derivative of the inverse tangent function, and that is proved by using tany = x, derivative of both sides with secx=(1+tan^2x) and tan^2x = x^2.

I don't know how to use the proof of the inverse tangent derivative to calculate the integral of 1/(u^2+4). Am I approaching this in an incorrect way?

 

[Muphrid]

Think about how you can turn that 4 into a 1 without changing the value of the whole expression.