Manipulating Integrals in Symbolic Form
When Mathematica cannot give you an explicit result for an integral, it leaves the integral in a symbolic form. It is often useful to manipulate this symbolic form.
cannot give an explicit result for this integral, so it leaves the integral in symbolic form.
Differentiating the symbolic form gives the integrand back again.
Here is a definite integral which cannot be done explicitly.
This gives the derivative of the definite integral.
Here is a definite integral with end points that do not explicitly depend on
The partial derivative of this with respect to
There is a non-trivial total derivative, however.