The discussion revolves around determining the indefinite integral of the function (4x+10)/(9x^2+24x+16) using the technique of partial fractions.
Some participants confirm the correctness of the initial approach to partial fractions. Guidance is offered on how to manipulate the equation further to solve for the coefficients A and B.
There is mention of a misunderstanding regarding the structure of the partial fraction decomposition, indicating a potential oversight in the participant's approach.
arl146 said:Homework Statement
determine the indefinite integral: ∫ (4x+10)/(9x^2+24x+16) dx
Homework Equations
partial fractions technique
The Attempt at a Solution
i know it's partial fractions and i thought i did it right but i got the wrong answer.
(4x+10)/(9x^2+24x+16) = (4x+10)/(3x+4)^2 = A/(3x+4) + B/(3x+4)^2
is that part right before I continue?
As others have told you that is correct. Now multiply both sides by (3x+4)^2 to get (4x+10)(3x+ 4)^2= A(3x+ 4)+ B. Taking x= -4/3 gives an easy solution for B. Take x to be any other number, say, x= 0, to get an equation for A.arl146 said:Homework Statement
determine the indefinite integral: ∫ (4x+10)/(9x^2+24x+16) dx
Homework Equations
partial fractions technique
The Attempt at a Solution
i know it's partial fractions and i thought i did it right but i got the wrong answer.
(4x+10)/(9x^2+24x+16) = (4x+10)/(3x+4)^2 = A/(3x+4) + B/(3x+4)^2
is that part right before I continue?