integration - Compute $intfrac{1-x}{(x-2)(x+3)}$ and $intfrac{cos(3x)}{sin(3x)}$

Compute $\int\frac{1-x}{(x-2)(x+3)}$ and $\int\frac{cos(3x)}{sin(3x)}$. I have no idea how to solve these 2 integrals, I've run out of ideas. The first one especially, I can't even start, not sure how to do it. I've done this for the second one:

I introduced a new variable $t$, $3x = t$, therefore $dx = \frac{dt}{3}$

Inserted into the integral: $\frac13\int\frac{cost}{sint}dt$, which leaves me with $\frac13\int cot(t)dt$ and then it stops for me, I tried Per-Partes, but couldn't come up with anything useful.

How do I solve these 2 integrals? They're driving me nuts.

Answer

Hints : For the first one use partial fractions, noting that
$$\frac{1-x}{(x-2)(x+3)}=\frac{-1}{5x-10}-\frac{4/5}{x+3}.$$

For the second one there is an obvious change of variable.