Can i solve using partial fractions?

[johann1301]

Homework Statement

∫(x+1)/(x²+2x+3)dx

The Attempt at a Solution

This problem was under partial fractions in my book. I solved it using u-substitution where u=x²+2x+3, but i can't see how it can be solved using partial fractions?

can it?

 

[SteamKing]

Yeah, you could, but it's a lot of extra work.

Hint: Complete the square in the denominator.

 

[johann1301]

(x^2+2x+3)=(x+3)(x+1)?

 

[johann1301]

no, i see that's not right..

 

[johann1301]

I get that (x^2+2x+3) = (-1-√2i)(-1+√2i).

 

[johann1301]

but their complex... will this work?

 

[johann1301]

sorry, (x^2+2x+3) = (x+1+√2i)(x+1-√2i).

 

[SteamKing]

You need to familiarize yourself with 'completing the square' for a quadratic polynomial.

http://www.purplemath.com/modules/sqrquad.htm