Constant of Integration
Since the derivative of a constant is zero, any constant may be added to an indefinite integral (i.e., antiderivative) and will still correspond to the same integral. Another way of stating this is that the antiderivative is a nonunique inverse of the derivative. For this reason, indefinite integrals are often written in the form
 |
where 
is an arbitrary constant known as the
constant of integration.
The Wolfram Language returns indefinite integrals without constants of integration. This means that, depending on the form
used for the integrand, antiderivatives 
and 
can be obtained
that differ by a constant.
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indefinite integrals