Integrating a Tricky Differential Equation with a Square Root Fraction

[PhysicsLad]

Homework Statement

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Solve the differential equation

Homework Equations

The Attempt at a Solution

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I just can't integrate that (1+y)^(1/2)/(1+y^2)dy at the end... the other two integrals are trivial.

 

[vela]

Try the substitution $u=\sqrt{1+y}$ and see where that gets you.

 

[PhysicsLad]

I actually tried before posting. Once you make the substitution there are two ways to attempt the problem, one by doing u^2 = 1+y and then differentiating, and the other got me to 2*(1+y)^(1/2)du = dy. None of these seemed to make the integral any easier.