Master Integrals with Substitution: Simplifying Tricky Integrals in Calculus

[caljuice]

∫dx
--------------------- (divide by)
(x²+a²)^3/2

Tried integrating with substitution with U = x²+a²)
Then dU = 2xdx
x = √(U-a²)

Leaving me with dU/ (2x) (U)^3/2
= ∫dU/2
-----------------------
√(u-a²))(U)^3/2

But that doesn't help either.

Do I need to use a table? Thanks for any help.

 

[ehild]

You can use that 1/(1+tan^2(θ))=cos^2(θ)

Substitute x/a=tan(u).

ehild