# How do you integrate #int sqrt(x^2-25)/x# using trig substitutions?

now simplifying the algebra.

but

If you are used to hyperbolic functions the substitution

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To integrate ( \int \frac{\sqrt{x^2 - 25}}{x} , dx ) using trigonometric substitution, you can let ( x = 5 \sec(\theta) ). Then, ( dx = 5 \sec(\theta) \tan(\theta) , d\theta ). Substitute these into the integral, simplify the expression using trigonometric identities, and then integrate with respect to ( \theta ). Finally, substitute back the original variable ( x ).

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