How to Integrate \frac{\sqrt{x+1}}{x+3} dx with a Suitable Substitution?

[Ethereal]

How does one integrate the following:
By using a suitable substitution, evaluate:
$$\int \frac{\sqrt{x+1}}{x+3} dx$$

I tried $$x=tan^2 \theta, x+1=y$$, but the whole thing got messier. Anyone knows the correct substitution to make?

 

[Tide]

Here's a start: Do it in stages using the first transformation to get rid of the +1 under the radical so the integrand becomes $\frac {\sqrt{x}}{x+2}$ then let $y = \sqrt {x}$. It should be apparent what to do next.

 

[Ethereal]

Thanks for your help. I managed to solve it, required 2 substitutions as you said!

 

[Tide]

Way to go!