Partial Fractions

Question

Please help :(

integral of (3x+1) / ((x^3)(3x+2)(x-1)) dx

sorry for all the parentheses, couldn't figure out how to type it here.

Answer 1

Equate the x⁴  coefficients.

Equate the x³  coefficients.

Equate the x²  coefficients.

Equate the x  coefficients.

Equate the constants.

From (4)

From (3)

Answer 2

Contd ...

From (2)

From (1)

Add (6) &(7).

From (7)

Substitute the values of A, B, C , D, E in (i)