The integral ∫(4x^3)/√(x^2+4)dx can be solved using trigonometric substitution, specifically by letting x = 2tan(θ) and dx = 2sec²(θ)dθ. This leads to the transformation of the integral into ∫32tan³(θ)sec(θ)dθ. However, an alternative approach using the substitution u = x² + 4 is suggested as potentially simpler and more straightforward.
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bbroocks said: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