By recognizing that non-negative terms such as (x^(2)+k)^(n) could be written in terms of a radical, in this case (sqrt(x^(2)+k))^(2n), we could evaluate other types of similar integrals with this "triangle method" of inverse substitution. Use this technique to evaluate int (1)/((x^(2)+1)^(2))dx.
(Hint: You will need the identity sin(2 heta )=2sin( heta )cos( heta ).)
4. By recognizing that non-negative terms such as (x2 + k)n could be written in terms of a radical, in this case (x2+ k)2n we could evaluate other types of similar integrals with this "triangle method" of inverse substitution. Use this technique to evaluate (x2+1)2dx
(Hint: You will need the identity sin(20)= 2 sin(0) cos(0).)