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Differentiate w.r.t. P
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\frac{P}{1+r^{2}}p
Find the integral of \frac{P}{1+r^{2}} using the table of common integrals rule \int a\mathrm{d}p=ap.
\frac{Pp}{1+r^{2}}
Simplify.
\frac{Pp}{1+r^{2}}+С
If F\left(p\right) is an antiderivative of f\left(p\right), then the set of all antiderivatives of f\left(p\right) is given by F\left(p\right)+C. Therefore, add the constant of integration C\in \mathrm{R} to the result.