I am going to make the bold assumption that you are trying to work out ∫(dx/(x²√(4+x²))).
One way to do this is by substitution: x=2tanɸ, so dx=2sec²ɸdɸ.
Now we substitute into the integral:
∫(2sec²ɸdɸ/(4tan²ɸ√(4+4tan²ɸ)))=
∫(2sec²ɸdɸ/(4tan²ɸ(2secɸ)))= [because 1+tan²ɸ ≡ sec²ɸ as a trig identity]
∫(secɸdɸ/4tan²ɸ)=¼ʃ(cosɸdɸ/sin²ɸ).
Substitute again y=sinɸ, then dy=cosɸdɸ, so we have ¼ʃ(dy/y²)=-1/(4y)+C where C is the integration constant, because 1/y² is the same as y⁻² which integrates to -y⁻¹ = 1/y.
Now we go back through the substitutions:
-1/(4y)+C=-¼cosecɸ+C=-¼√(4+x²)/x+C=-√(4+x²)/(4x)+C.