Question

integration of x/(a+bx)​

Answer 1

Answer:

(a+bx - a×ln(a+bx) )/b²

Step-by-step explanation:

Let a+bx=t , x = t-a/b

differentiating,

dt= bdx

dx= dt/b

Therefore equation becomes,

x/a+bx dx = (t-a)/bt dt/b = 1/b² (t-a)/tdt

= 1/b² × (1-a/t) dt = 1/b² × (t- a lnt)

= (t- a lnt)/b² = (a+bx - a×ln(a+bx) )/b²