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Differentiate w.r.t. x
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\left(ax+a\right)t
Find the integral of ax+a using the table of common integrals rule \int a\mathrm{d}t=at.
\left(ax+a\right)t+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.