The integral ∫1/(x²+4)² can be approached using trigonometric substitution methods. The key manipulation involves recognizing that the integral resembles the form ∫dx/(x²+a²) = (1/a)arctan(x/a) + c, where a = 2. To facilitate this, the substitution u = 2tan(θ) is recommended, allowing the integral to be transformed into a solvable form. This approach effectively utilizes trigonometric identities to simplify the integral for further evaluation.
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Trig substitution is the way to go here. Do you know the substitution to use?cjarnutowski said:Homework Statement
∫1/(x2+4)2
Homework Equations
∫dx/(x2+a2)=(1/a)arctan(x/a)+c
The Attempt at a Solution
This looks like an arctan integral or a trig substitution, but in its current form neither would work without manipulation. I'm mainly looking for how to manipulate it to use one of these methods
Thanks!