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

[frasifrasi]

[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?

 

[arildno]

Substitute u=\sqrt{x}, and see what you get.

 

[Astronuc]

If x=u², then dx = 2 u du

sqrt (x) = u, and

x+1 = u² + 1

 

[frasifrasi]

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!

 

[frasifrasi]

Ha, you rascal!