how do i intergrate this one? i know its easy but i am just not good....help...?

Integration can be tricky.

On this one, you want to write

P/(P + b) = 1 - b/(P + b).

(You can find this using long vision, or by noticing that P/(P + b) = (P + b - b)/(P + b) = (P + b)/(P + b) - b/(P + b) = 1 - b/(P + b).)

Now we want to integrate 1 - b/(P + b). Use the log rule. You'll get

x - b ln |P + b| + C.

(If you can't see this immediately, then try the substitution u = P + b.)

The absolute value around P + b above is important. The integral of 1/x is not ln (x) + C; it is ln |x| + C.

intergration of (P/(P+b) dP

P/P+b=1-b(P+b)

intergration of (1-b(P+b)) dP=P-b*In(P+b)+C

p/(p + b) = (p + b - b)/(p + b) = (p + b)/(p + b) - b/(p + b)

= 1 - b/(p + b)

This will integrate trivially to: p - b*ln(p + b) + C.