Having trouble understanding this integration

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The discussion focuses on the integration of the expression ∫ R/(x^2 + R^2)^(3/2) dx, which arises from a physics problem involving the conditions r = √(x^2 + R^2) and sin(θ) = R/√(x^2 + R^2). The integration is simplified using the substitution x = R tan(θ), leading to the result x/R(x^2 + R^2)^(1/2). This substitution is crucial for transforming the integral into a more manageable form.

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Stochastic13
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I am reading through this physics book and have trouble understanding how they integrated one of the problems the conditions are

Conditions: // ignoring the constant for simplicity

r = √(x^2 + R^2)
sin(θ) = R/√(x^2 + R^2)

Integration:

∫ R/(x^2 + R^2)^3/2 dx

and the result is: x/R(x^2 + R^2)^1/2

Could someone please explain to me how the integration part was done in more detail?
 
Last edited:
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Nevermind, I had to use a substitution x = R tan (theta)
 

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