I have having trouble doing this one:

integral of radical(x^2 + 4)dx

I set x = tan(u)

dx = sec^2(x)du

here is what i did:

integral of radical(4tan^2(u) + 4)

Pulled out a radical 4

integral of 2tan(u)

this equals 2sec^2(u) + C

sec(u) in this scenario is (x+2)/(2) since tan(u) = x/2

I did this then:

2((x+2/2))^2

The answer after doing this isnt the same in the book

I am suppose to get: 1/2xradical(x^2 + 4) + 2ln(x + radical(x^2 + 4)) + C