How to resolve the following integration :

Question

 (x+2)/1-x^3 dx?

Answer 1

The Integral is

We can write (1 - x³) as (1-x) (x² + x + 1).

Then now re-write the Integral as .

Now we take the Integral part.

Now Equate x² terms then

A-B = 0

A = B

Equate x terms then

A + B - C = 1

B + B - C = 1.

2B - C = 1.     ........................Equation (1)

Equate Constants terms then

A + C = 2

B + C = 2.      ..........................Equation (2)

Add Equation (1) and (2)

3B = 3

B = 1

Then A =1

Then 2(1) - C = 1

C = 1

Therefore A = 1, B = 1 and C = 1.

Therefore

Now

Therefore .