Solve the differential equation: `(dy)/(dx)=1/(x^2+4x+5)`

Explanation

`d y=frac{1}{x^{2}+4 x+4+1} d x `


`d y=frac{1}{(x+2)^{2}+1} d x`


By integrating both sides we get


y `=int frac{d t}{t^{2}+1}+c `

`=tan ^{-1}(t)+c `

y `=tan ^{-1}(x+2)+c `