# Thread: tricky integration of a fraction

1. ## tricky integration of a fraction

$\displaystyle \int \frac{200000}{20000P - P^2} dP$

i am so confused as to what to do, someone please help!!

2. Originally Posted by wik_chick88
$\displaystyle \int \frac{200000}{20000P - P^2} dP$

i am so confused as to what to do, someone please help!!
Use the method of partial fraction decomposition.

3. this is what i have:
\frac{1}{P(20000-P)} = \frac{A}{P} + \frac{B}{20000-P} (i brought the 200000 out the front of the integral)
= \frac{20000A - AP + BP}{P(20000-P)}
= \frac{20000A + (B-A)P}{20000-P}

equate coefficients:
20000A = 1, therefore A = \frac{1}{20000}
B - A = 0, therefore B = A = \frac{1}{20000}

therefore:
\frac{1}{P(20000-P)} = \frac{1}{20000P} + \frac{1}{20000(20000-P)}

have i gotten it right so far? i know where to go from here, as long as i havent made any mistakes!!

4. Originally Posted by wik_chick88
this is what i have:
\frac{1}{P(20000-P)} = \frac{A}{P} + \frac{B}{20000-P} (i brought the 200000 out the front of the integral)
= \frac{20000A - AP + BP}{P(20000-P)}
= \frac{20000A + (B-A)P}{20000-P}

equate coefficients:
20000A = 1, therefore A = \frac{1}{20000}
B - A = 0, therefore B = A = \frac{1}{20000}

therefore:
\frac{1}{P(20000-P)} = \frac{1}{20000P} + \frac{1}{20000(20000-P)}

have i gotten it right so far? i know where to go from here, as long as i havent made any mistakes!!
Correct.

5. It is correct, math tags?

6. oops forgot to wrap the text!

this is what i have:
$\displaystyle \frac{1}{P(20000-P)} = \frac{A}{P} + \frac{B}{20000-P}$ (i brought the 200000 out the front of the integral)
= $\displaystyle \frac{20000A - AP + BP}{P(20000-P)}$
= $\displaystyle \frac{20000A + (B-A)P}{P(20000-P)}$
equate coefficients:
20000A = 1, therefore A = $\displaystyle \frac{1}{20000}$
B - A = 0, therefore B = A = $\displaystyle \frac{1}{20000}$

therefore:
$\displaystyle \frac{1}{P(20000-P)} = \frac{1}{20000P} + \frac{1}{20000(20000-P)}$
have i gotten it right so far? i know where to go from here, as long as i havent made any mistakes!!