Trigonometric Substitution

Question

use the substitution x=3 sec t to evaluate the indefinite integral

(dx)/(x*sqrt(x^2-9))

appreciate any help thank you!

Answer 1

dx=3sect tant dt

so ∫ 3sect tant dt/3sect√[(3sect)^2 -9] = ∫ tant dt/√[(3sect)^2 -9] =∫ tant dt/3√[(sect)^2 -1] =

∫ tant dt/3√(tant)^2 ] = ∫dt/3 = t/3 +C

step 1 find the derivative of the substitution. step 2 - substitute. step 3 - simplify, step4 integrate