Evaluate: ∫(2x + 1)/(4 - 3x - x^2)dx ​

Question

Evaluate:

\(\int\frac{(2x+1)}{(4-3x-x^2)}dx\) 

∫(2x + 1)/(4 - 3x - x²)dx

Answer 1

Let I = \(\int\frac{(2x+1)}{(4-3x-x^2)}dx\)

A(4 + x) + B(1 - x) = 2x + 1 

Now put 1 - x = 0 

Therefore, x = 1 

A(5) + B(0) = 3 

A = 3/5

Now put 4 + x = 0 

Therefore, x = - 4 

A(0) + B(5) = - 8 +1 = -7

B = -7/5

Now From equation (1) we get,