Question

integration x^2/(a+bx)^3 dx​

Answer 1

Answer:

The Answer Is I = 1/b³ [(a+bx)-a²/(a+bx)-2a log (a+bx)]+C

Step-by-step explanation:

I=∫ x^2.dx/(a+bx)^2

Let a+bx=p or x=(p-a)/b so that dx=(1/b).dp

I=∫{(p-a)/b}^2.(1/b)dp/p^2.

I=∫ (1/b)^3.{ 1-a/p}^2.dp

I=∫ (1/b)^3[1–2a/p+a^2/p^2].dp

I= 1/b^3[ p-2a log p-a^2/p]+C

I=1/b^3[p-a^2/p-2a logp]+C

I=1/b^3 [(a+bx)-a^2/(a+bx)-2a log (a+bx)]+C