∫(x2+4x+4)/(x2+5x+7)(x+2)½

Dear tejas akole

∫(x²+4x+4)dx/(x²+5x+7)(x+2)½

=∫dx(x+2)²/(x²+5x+7)(x+2)½

let x+2 =t²

dx =2 tdt

=2∫dt(t)⁴/(t⁴+t²+1)

=2∫dt-2∫(t²+1)dt/(t⁴+t²+1)

=2t-2∫(1+1/t²)dt/{(t-1/t)² +3}

now put (t-1/t) =u

               (1+1/t²)dt=du

=2t-2∫du/(u²+3)   +c

now solve and put tha value ou u and t in terms of x