Evaluate: ∫ (1-3x)/(3x^2+4x+2)dx

Question

Evaluate:\(\int\cfrac{(1-3x)}{(3x^2+4x+2)}dx\)

∫ (1-3x)/(3x²+4x+2)dx

Answer 1

To find:\(\int\cfrac{(1-3x)}{(3x^2+4x+2)}dx\)

Formula Used:

Rewriting the given equation,

Using partial fractions,

3x – 1 = A (6x + 4) + B 

Equating the coefficients of x, 

3 = 6A

A = \(\cfrac{1}{2}\)

Also, -1 = 4A + B

⇒ B = -3

Substituting in the original equation,