# tricky integration of a fraction

• Aug 16th 2010, 10:11 PM
wik_chick88
tricky integration of a fraction
$
\int \frac{200000}{20000P - P^2} dP
$

• Aug 16th 2010, 10:20 PM
mr fantastic
Quote:

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

Use the method of partial fraction decomposition.
• Aug 16th 2010, 10:36 PM
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!!
• Aug 16th 2010, 10:39 PM
mr fantastic
Quote:

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.
• Aug 16th 2010, 10:41 PM
pickslides
It is correct, math tags?
• Aug 16th 2010, 10:41 PM
wik_chick88
oops forgot to wrap the text!

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)
= $\frac{20000A - AP + BP}{P(20000-P)}$
= $\frac{20000A + (B-A)P}{P(20000-P)}$
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!!