Question

Intergral from P1 to P2 of P/(P+b) dP where b is a constant. I'll code it cleaner soon

Answer 1

\[\int\limits_{P_1}^{P_2}{P \over P+b}dP\]

Answer 2

try adding b-b in the numerator

Answer 3

So that would leave me with -b over P+b, then solve

Answer 4

1-b/(P+b)

Answer 5

then integrate

Answer 6

I would still have to do u-substitution for the denominator. And you're right there should be a 1 infront, thx

Answer 7

yes, but the u-sub in the denominator is trivial, because its differential is already dP

Answer 8

\[P_2-P_1-b \ln {P_2+b \over P_1+b}\]

Answer 9

without breaking out pen and paper, I think that's right

Answer 10

Thanks for your help. I forget that a problem can be manipulated by adding in "0"

Answer 11

yeah, that's right
and yeah, gotta love that +a-a trick, otherwise you're stuck doing polynomial long division... yuck