Partial Fractions: Integrate (4x+10)/(9x^2+24x+16)

[arl146]

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?

 

[Ray Vickson]

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?

Yes, that is the right idea.

RGV

 

[voko]

Yes, that's right.

 

[HallsofIvy]

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]

ohhhh .. i see what i did. ok .. so i was doing A(3x+ 4)^2 + B(3x+4) not realizing the denominator difference. stupid mistake. thanks!