Help me with this math problem?
How to integrate this integral? I've tried the partial fraction decomposition method but it doesn't seem to work at all. Please show all your work. Thanks.
- atsuoLv 61 year agoFavourite answer
x^2+4x+4 = (x+2)^2 , so let x+2 = u and dx = du .
∫ 6x/(x^2+4x+4) dx
= ∫ (6(x+2)-12)/((x+2)^2) dx
= ∫ (6u-12)/(u^2) du
= ∫ 6/u - 12/u^2 du
= 6ln|u| + 12/u + C
= 6ln|x+2| + 12/(x+2) + C