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## Main Question or Discussion Point

I'm trying to integrate the Van der Waals equation of state for an isothermal problem, but based on my results I think I'm doing a bit of simple calculus wrong and hope someone here can help.

[tex]P = \int \frac{RT}{v-b} dv[/tex]

where R, b and T are known constants.

I tried to do a u-substitution for 1/(v-b) with u=(v-b)

so, du = 1.

Thus. [tex] P = \int \frac{RT}{u} du[/tex]

So, P = RT ln(u) = RT ln(v/b)

Any ideas where I went wrong? Thanks.

[tex]P = \int \frac{RT}{v-b} dv[/tex]

where R, b and T are known constants.

I tried to do a u-substitution for 1/(v-b) with u=(v-b)

so, du = 1.

Thus. [tex] P = \int \frac{RT}{u} du[/tex]

So, P = RT ln(u) = RT ln(v/b)

Any ideas where I went wrong? Thanks.