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

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Answer 1 · 2018-02-03T10:38:26

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

#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" #