solving integrals

Question

∫ ( (x+3)/√(1-x²) )dx=_____________

Answer 1

It can be broken in two parts-

 

1.  Integral (x/sqrt(1-(x^2))) dx

 

Substituting--     (1-x^2)=t

                            -2xdx=dt

 

Plugging in back

 

Integral (-1/2)(t^(-1/2))dt

 

       =(-1/2)*2*sqrt(t)

 

       =-sqrt(1-(x^2))

 

2. Integral (3/sqrt(1-(x^2))

 

              =3*arcsin(x)

 

So, the complete answer is---

 

  = -sqrt(1-(x^2)) +3*arcsin(x)