How can Arctan and ln be used to simplify the integral of (x+1)/(x^2+4x+5)?

[TheTimeTraveler]

∫(x+1)/(x^2 + 4x +5) dx
Anyone can help me doing it using Arctan and ln

 

[blue_leaf77]

Let's first hear out your own idea to solve this problem? What strategy you have in mind?

 

[TheTimeTraveler]

Let's first hear out your own idea to solve this problem? What strategy you have in mind?

∫(x+1)/(x^2+4x+5) dx = 1/2∫ (2x+2)/(x^2+4x+5) dx = 1/2∫(2x+4)/(x^2+4x+5) dx + 1/2∫(-2)/(1+(x+2)^2) dx
[1/2 ln l(x^2+4x+5)l ] - arctan(x+2)
SO??

 

[HallsofIvy]

Don't forget the "constant of integration".

 

[TheTimeTraveler]

Don't forget the "constant of integration".

Thaanks

 

[phion]

Try re-writing the original expression into something more manageable.