How to Calculate Work for Isothermal Processes with a Non-Ideal Gas?

[opprobe]

Homework Statement

Gas obeys Equation of State, PV=RT/(1-bP), where b is a temperature dependent constant.
Isothermal process (T is constant)
V goes from V₁ to V₂
P goes from P₁ to P₂

Show that the amount of Work is
W=(P₁V₁-P₂V₂)+RTln[(P₂²V₂)/(P₁²V₁)

Homework Equations

W=-∫P(V)dV
ΔU=Q+W

The Attempt at a Solution

Solved PV=RT/(1-bP) for P in terms of V
P=(-1\pmSqrt[1-4bRT/V])/(2b)

I don't know how to really integrate that expression. I used Wolfram to eventually get this expression:

∫P(V)dV=-V/(2b)\pmRTln(2V(Sqrt[1-4bRT/V]+1)-4bRT)-V*Sqrt[1-4bRT/V]

I'm pretty sure that this isn't the approach to solve this problem. Can someone point me in the right direction?

Thanks in advance!

 

[Chestermiller]

Try integrating PdV by parts.

Chet

 

[opprobe]

That did it. Thanks for the help!