How do you integrate int dx/(4x^2-1)^(3/2) using trig substitutions?
1 Answer
Jun 20, 2018
Use the substitution
Explanation:
Let
I=intdx/(4x^2-1)^(3/2)
Apply the substitution
I=int(1/2secthetatanthetad theta)/(tan^3theta)
Simplify:
I=1/2intcscthetacotthetad theta
Integrate directly:
I=-1/2csctheta+C
Rewrite in terms of
I=-1/2 sectheta/tantheta+C
Reverse the substitution:
I=-x/sqrt(4x^2-1)+C