Question

integration of 1/(x^2+4x+5)

Answer 1

tan-1(x+2) is the ans
tan-1 is tan inv

Answer 2

Int 1/x2+4x+5
(Ax+B)/x2+4x+5=1/x2+4x+5
A=0 and B=1
Now x2+4x+5=x2+4x+4+1=(x+2)2+1
Integration of 1/(x+2)2+1
Let x+2=u therebfore after integration du=dx
Integration of du/u2+1
Let u= tan©, du=sec2©d©
Now integration sec2©d©/tan2©+1
Sec2©d©/sec2©=integration of d©
=©+c=taninverse u+c