How do you integrate #int 1/sqrt(9x^2-18x+18) # using trigonometric substitution?
1 Answer
Mar 1, 2016
Explanation:
First of all, we complete the square/ re write in vertex form the quadratic under the square root:
So the integral can be re written as:
(Note the 9 under the square root has been factored out to the front)
Now consider the substitution
It will follow that
Now substitute this into the integral to get:
Use the identity:
Now evaluating the integral and reversing the substitution: