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Differentiate w.r.t. c
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\int 3+c\mathrm{d}x
Evaluate the indefinite integral first.
\left(3+c\right)x
Find the integral of 3+c using the table of common integrals rule \int a\mathrm{d}x=ax.
\left(3+c\right)\times 1-\left(3+c\right)\times 0
The definite integral is the antiderivative of the expression evaluated at the upper limit of integration minus the antiderivative evaluated at the lower limit of integration.
3+c
Simplify.