Question

Find value of ` int (dx)/((ax+b))` .

Answer 1

Substitute `(ax+b)=z` in the given function.
Also,` (d)/(dx)(ax+b)=(dz)/(dx)`
or ` a=(dz)/(dx)`
`:. " " dx=(dz)/(a)`
and ` int(dx)/((ax+b)) = int ((dz//a))/(z)`
`(1)/(a)int (dz)/(z)`
`(1)/(a) ln z+c`
Substitute back for z, we get
`int (dx)/((ax+b))=(1)/(a) ln (ax+b)+c`