Evaluate
-\frac{tN^{2}}{1000}+10t+С
Differentiate w.r.t. N
-\frac{Nt}{500}
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\frac{10000-N^{2}}{1000}t
Find the integral of \frac{10000-N^{2}}{1000} using the table of common integrals rule \int a\mathrm{d}t=at.
\frac{\left(10000-N^{2}\right)t}{1000}
Simplify.
\frac{\left(10000-N^{2}\right)t}{1000}+С
If F\left(t\right) is an antiderivative of f\left(t\right), then the set of all antiderivatives of f\left(t\right) is given by F\left(t\right)+C. Therefore, add the constant of integration C\in \mathrm{R} to the result.
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