`int(a x+b)/(c x+d) \ dx`

Options

A. `(ax)/(c ) +log|cx +d| + C`
B. `a/c + log|cx + d| + C`
C. `(ax)/(c ) + ((bc- ad))/(c^(2)) log |cx + d| + C`
D. none of these

Answer

C

Explanation

On dividing `(ax+b)` by `(cx +d)`, we get
`int((ax + b))/((cx + d)) = int {a/c +((bc-ad))/(c(cx+d))} dx`
`= inta/c dx + ((bc-ad))/(c^(2)) .int(c )/((cx+d)) dx`
`= (ax)/(c ) + ((bc - ad))/(c^(2)) log|cx+d| + C`.