Question

integrate 1/((x-2)(x+3)

Answer 1

partial fractions for this one
do you know how to do it?

Answer 2

\[\frac{1}{(x-2)(x+3)}=\frac{a}{x-2}+\frac{b}{x+3}\] solve for "a" and "b"

Answer 3

start with
\[a(x+3)+b(x-2)=1\] replace x by 2 get
\[5a=1\implies a=\frac{1}{5}\] and then replace x by -3 get
\[-5b=1\implies b=-\frac{1}{5}\] then rewrite and compute the two integrals, which will both be logs

Answer 4

you can just about do it in your head, you will get
\[\frac{1}{5}\ln(x-2)-\frac{1}{5}\ln(x+3)\]

Answer 5

thank u, u just made this so clear to me!