integral calculus: integrate x^2/ (x+1)(x-1)^2

[M TI]

please could someone help me with the following as I am a bit rusty, I need to solve the following integral x^2/ (x+1)(x-1)^2. using partial fractions and simplifying the fractions I end up with x^2=A(X-1)^2+B(x+1)(x-1)+C(x+1). please could someone help with steps as I'm not sure whether to let x=something or let the brackets =0 etc to find A,B & C and the eventually answer. kind regards matt.

 

[Deleted member 4993]

please could someone help me with the following as I am a bit rusty, I need to solve the following integral x^2/ (x+1)(x-1)^2. using partial fractions and simplifying the fractions I end up with x^2=A(X-1)^2+B(x+1)(x-1)+C(x+1). please could someone help with steps as I'm not sure whether to let x=something or let the brackets =0 etc to find A,B & C and the eventually answer. kind regards matt.

The problem you posted:

\(\displaystyle \displaystyle{\int \dfrac{x^2}{x+1}*(x-1)^2 dx}\) has only monomial as denominator - thus does not need application of partial fraction process.

May be be you meant:\(\displaystyle \displaystyle{\int \dfrac{x^2}{(x+1)*(x-1)^2} dx}\)

Anyway - I do not get how you arrived at:

x^2=A(X-1)^2+B(x+1)(x-1)+C(x+1)

Please share your work - so that we know where exactly we need to help you.