Question

I got stuck on this integral how do i take the integral on the left side?

Answer 1

`int (1+v)/(v^2-3v+2) dv = ln| (v-2)^3 / (v-1)^2 | + "constant"`

Explanation:

`int (1+v)/(v^2-3v+2) dv = int(1+v)/( (v-1)(v-2) )dv`

Partial fractions...

`(1+v)/( (v-1)(v-2) ) = A/(v-1) + B/(v-2)`

`1+v = A(v-2) + B(v-1)`

Let `v = 2`

`3 = B`

Let `v = 1`

`2 = -A => A = -2`

`=> int -2/(v-1) + 3/(v-2) dv`

`= -2ln|v-1| + 3ln|v-2| + "constant"`

`color(red)(= ln| (v-2)^3 / (v-1)^2 | + "constant"`