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#