Question

Help please, easy question I think, but I don't know how to do it :(. Question attached in the comment/reply.

Answer 1

factor the denominator of the integrand as (x+2) (x+3)....
to find A and B, you'll need to do a partial fractions decomposition....

Answer 2

I got the (x+2) and (x+3) but I don't know how to do the rest.

Answer 3

you have a choice of ways. in this case the simplest way is to view this as
\[\frac{9x}{(x+2)(x+3)}\] and if you want the coefficient of the term over the \(x+2\) replace \(x\) by \(-2\) and ignore that factor in the denominator
you get
\[\frac{9\times -2}{-2+3}=-18\]

Answer 4

similarly for the coefficient over the \(x+3\) term, ignore that factor and replace \(x\) b \(-3\) to get
\[\frac{9\times -3}{-3+2}=27\]