Integral Calculus - Trigonometric Substitution

[Myung]

Homework Statement

2
∫ dx / (x+1)√[2x(x+2)]
1

Homework Equations

Let x = tan θ if √(a^2 + x^2)
Where a = constant

The Attempt at a Solution

2
∫ dx / (x+1)√(2x)√(x+2)
1

2
1/√2 ( ∫ dx / (√x)(x+1)[√(x+2)]
1

Now make all x in terms of √x so we can apply relevant equation ( applied also to constant )

2
1/√2 ( ∫ dx / (√x)((√x)^2+1)[√(√x+2)]
1

Now before i go on I want to ask if this is possible so I can apply the rule of the tangent in substitution?

 

[lanedance]

how about noticing that
$$2x(x+2) = 2(x^2+2x) =2(x^2+2x+1-1) = 2((x+1)^2-1)$$