3.5.9 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.

Mathematica cannot give an explicit result for this integral, so it leaves the integral in symbolic form.

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Differentiating the symbolic form gives the integrand back again.

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Here is a definite integral which cannot be done explicitly.

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This gives the derivative of the definite integral.

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Here is a definite integral with end points that do not explicitly depend on x.

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The partial derivative of this with respect to u is zero.

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There is a non-trivial total derivative, however.

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