# How does my book get from this step to this step?

[SOLVED] How does my book get from this step to this step?

My book went from int of dx/ ( sqrt(x)*(x+1) )

to

2arctan sqrt (x) -- WTH?

I thought the form for arctan was dx/a^2 + u^2 and I don't see that in the given integrand?

Can anyone help?

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arildno
Homework Helper
Gold Member
Dearly Missed
Substitute $$u=\sqrt{x}$$, and see what you get.

Astronuc
Staff Emeritus
If x=u2, then dx = 2 u du

sqrt (x) = u, and

x+1 = u2 + 1

astronuc, did you arrive at that by using the substitution arildno suggested?

HallsofIvy
Well, arildno said "u= $\sqrt{x}$" and Astronuc said "x= u2". Look the same to me!