integration: int[(x+1)/(x^2 + 2x + 2)dx

[thebenji]

integrate the indefinite integral:

int[(x+1)/(x^2 + 2x + 2)dx

after doing long division, i came up with the new integral:

int[(x+1)/(x+1 + (1/x+1))dx

now what do i do? how can i simplify it (my algebra skills are much weaker than my calculus skills...)?

 

[soroban]

Re: integration

Hello, thebenji!

\(\displaystyle \L\int \frac{x\,+\,1}{x^2\,+\,2x\,+\,2}\,dx\)

Let \(\displaystyle u\:=\:x^2\,+\,2x\,+\,2\)

 

[Guest]

If your still having trouble remember the rule

\(\displaystyle \huge\int\frac{f'(x)} {f(x)}dx = \log{[f(x)]}+ c\)