What is the integral of this and how to get to the answer? (substitution method)
#(12x)/(x^2-1)^4#
The substitution method confuses me :( I have seen the answer but don't understand it :(
The substitution method confuses me :( I have seen the answer but don't understand it :(
1 Answer
May 1, 2018
To simplify the denominator let us substitute
#u=(x^2-1)#
Differentiating both sides with respective variables we get
#du=2x\ dx#
#=> dx=du 1/(2x)#
Integral becomes
#I=int\ (12x)/u^4 1/(2x)\ du#
#=>I=6int\ u^-4\ du#
Integrating using power rule we get
#I=6xx u^(-4+1)/(-4+1)#
#=>I=6xx u^(-3)/(-3)#
#=>I=-2/ u^(3)#
Undo substitution and add a constant of integration
#I=-2/ (x^2-1)^(3)+C#
