Question

∫dx/x2+x+1 and ∫dx/(x^2 -x) are my questions. Thanks for helping.

Answer 1

integrate using partial fraction decomposition

Answer 2

\[1/ (x^2 + x + 1) = (Ax + B)/(x^2 + x + 1) \ \ and \ \ 1/(x^2- x) = (Ax + B)/(x^2 - x) ?\]

Answer 3

Yes!

Answer 4

But for the second one, you can factor out an x:
\[\frac{ A }{ x } + \frac{ B }{ (x+1) }\]

Answer 5

Thank you!

Answer 6

Hmm I'm not sure that helps on the first one :\
We're just going to get \(\large A=0 \qquad B=1\) which is the equation we started with.
Probably need to do some completing the square business on that one.