Trig substitution ∫(4x^3)/√(x^2+4)

[bbroocks]

Homework Statement

∫(4x^3)/√(x^2+4)dx

Homework Equations

The Attempt at a Solution

So, I let x= 2tanθ
dx= 2sec^2θ dθ
So, √(4tan^2(θ)+4)=2secθ
∫(4x^3)/√(x^2+4)dx=∫((32tan^3(θ))/(2secθ))2sec^2(θ)dθ.

Would it go to ∫16tan^3(θ)2sec(θ)dθ
or ∫32tan^3(θ)sec(θ)dθ

 

[ehild]

Homework Statement

∫(4x^3)/√(x^2+4)dx

Homework Equations

The Attempt at a Solution

So, I let x= 2tanθ
dx= 2sec^2θ dθ
So, √(4tan^2(θ)+4)=2secθ
∫(4x^3)/√(x^2+4)dx=∫((32tan^3(θ))/(2secθ))2sec^2(θ)dθ.

Would it go to ∫16tan^3(θ)2sec(θ)dθ
or ∫32tan^3(θ)sec(θ)dθ

It is correct so far.

ehild

 

[Dick]

I don't think you really need a trig substitution here. Try u=x^2+4 first.