Question

State whether the following statement is true or false:

If `∫ x/((1 + x) (2 + x)) dx = ∫ (A/(1 + x) + B/(2 + x))dx` then A =1, B = 2.

Answer 1

This statement is false.

Given:

`x/((1 + x) (2 + x)) = A/(1 + x) + B/(2 = x)`

x = A(2 + x) + B(1 + x)    ...[Taking LCM]

x = (A + B)x + (2A + B)

Compare coefficients:

A + B = 1

2A + B = 0

A = −1, B = 2

Since statement says A = 1, B = 2