Question

integral x+2 / x^2+2x+2

Answer 1

since the derivative of denominator is 2x+2
i suggest you write numerator as
(1/2) (2x+2 +2)
then separate out the denominator.

Answer 2

did u get what adjustment i did ?

Answer 3

so first term you will get the form as
int f'(x)/f(x) dx which is log |f(x)| +c
and 2nd term, you'll have as 1/x^2+2x+2
which is of the form 1/(x^2+a^2) [by completing the square in denominator] and you will get the form of tan inverse function

Answer 4

{(x^2+a^2) by completing the square } do this step

Answer 5

x^2+2x+2 = x^2+2x+1 +1 = (x+1)^1 +1^2
form ---->x^2+a^2----->1/a tan inverse (x/a)
(x+1)^1 +1^2 ------> tan inverse (x+1)

and don't forget the 1/2 as the co-efficient :)

Answer 6

x^2+2x+2 = x^2+2x+1 +1 = (x+1)^1 +1^2
please explain this step

Answer 7

i just split 2 as 1+1
because we know that x^2+2x+1 is a perfect square.

Answer 8

ohhhhhh sorry my mistake
i didn't see it correctly

Answer 9

tell me if you get stuck :)

Answer 10

no thank you
you are my savior

Answer 11

you're welcome ^_^