1. ## partial fractions #2

Similarly, to my previous problem. I solved the problem and got an answer, but it says it's the incorrect answer.

The problem is:

I set the equation to be:

x^3 + 17 = A(x+1) + B(x+3)

I solved for A first and got 5.

I then went back and solved for B and got 8.

This would result in the partial fraction of:

I then integrated and got:

5 ln |x+1| + 8 ln |x+3|

Can anyone show me how it is correctly done?

Thank you.

2. Originally Posted by abilitiesz
Similarly, to my previous problem. I solved the problem and got an answer, but it says it's the incorrect answer.

The problem is:

I set the equation to be:

x^3 + 17 = A(x+1) + B(x+3)

I solved for A first and got 5.

I then went back and solved for B and got 8.

This would result in the partial fraction of:

I then integrated and got:

5 ln |x+1| + 8 ln |x+3|

Can anyone show me how it is correctly done?

Thank you.
note that if you add those two fractions, you will not get an $\displaystyle x^3$ term in the numerator.

start by doing long division ...

$\displaystyle \frac{x^3+17}{x^2+4x+3} = x - 4 + \frac{13x+29}{x^2+4x+3}$

now do partial fractions with the last term.

3. Originally Posted by skeeter
note that if you add those two fractions, you will not get an $\displaystyle x^3$ term in the numerator.

start by doing long division ...

$\displaystyle \frac{x^3+17}{x^2+4x+3} = x - 4 + \frac{13x+29}{x^2+4x+3}$