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## Homework Statement

∫√(x^2 - t^2)dt/(xt) x > t > 0

## Homework Equations

## The Attempt at a Solution

So I noticed that the integrand had the form a^2 - b^2x^2, and I can apply trig substitution, so I did this:

t = xsin(θ), dt = xcos(θ), and therefore, x^2 - t^2 = x^2 - x^2sin(θ)^2.

The last formula can be rearranged into x^2 cos(θ)^2 (From the identity 1 - sin(θ)^2)

After simplification, I obtain the integral

∫cos(θ)^2 dθ/sinθ

From here, I don't know where to go. After rearranging multiple times, there is no integral and I keep getting (cosθ) - ∫cscθdθ.

Thank you for any clarity you can provide for me.