Question

What is the best method to evaluate the integral of 1/(4x^2-9) dx
a) Integration by parts
b) Rewrite the integral using long division
c) Rewrite the integral using partial fractions
d) Use a substitution -----> my answer

Can you check for me, please

Answer 1

you can use a trig substitution, or partial fractions.

The trig substitution will give you a result in terms of inverse hyperbolic functions
The partial fractions will give a result using logs.

Of course, the hyperbolic functions involve exponentials, so the inverse functions involve logs.Not sure which is "better."