how to integrate this improper fraction?

I would change my variable:

A=9,8-v

dA=-dv

So i'd have:

"integrate [(-A+9,8)/A](-dA)"=

="integrate [(A-9,8)/A]dA"="integrate[(A/A)-(9,8/A)]dA"=

="integrate [1-(9,8/A)]dA"=

="integrate [1]dA"-"integrate (9,8/A)dA"=

=A-9,8*ln(A)+C

Change back:

=9,8-v-9,8*ln(9,8-v)+C

Put the first term into C:

=-v-9,8*ln(9,8-v)+K

∫v/(9.8 - v) dv => -∫v/(v - 9.8)) dv => -∫(v - 9.8 + 9.8)/(v - 9.8) dv => -∫(1 + 9.8/(v - 9.8)) dv

= -v - 9.8*ln|v - 9.8| + C

..................-1

............---------

-v + 9.8 | v + 0

.............v - 9.8

.............---------

................9.8

v/(9.8 - v) = -1 + 9.8/(9.8 - v)

∫ v/(9.8 - v) dv =

∫ -1 + 9.8/(9.8 - v) dv =

-v - 9.8ln(9.8 - v) + c