Question

How do you determine the indefinite integral of `(9/(4+z^2))dz`?

Answer 1

In this way, remembering that

`int(f'(x))/(1+[f(x)]^2)dx=arctgf(x)+c`:

`int(9/(4+z^2))dz=9int1/(4(1+z^2/4))dz=9/4int1/(1+(z/2)^2)dz=`

`=2*9/4int(1/2)/(1+(z/2)^2)dz=9/2arctg(z/2)+c`.