Symbolics > Working with Symbolics > Calculus > To Evaluate Integrals Symbolically
To Evaluate Integrals Symbolically
1. Insert the integral operator.
2. Type the expression in the placeholder to the right of the integral sign.
3. Type the integration variable x in the placeholder to the right of the symbol d.
4. Insert the symbolic evaluation operator.
 You can only evaluate the indefinite integral using the symbolic evaluation operator.
5. To take the definite integral of the same function, from 0 through 5, type 0 in the bottom placeholder of the integral. Type 5 in the top placeholder and repeat steps 2-4.
6. To take the definite integral of the same function when at least one of the limits is an undefined variable, repeat steps 2-4. Then, insert the lower and upper limits of the integral.
When evaluating a definite integral in which at least one of the limits is undefined, the symbolic engine assumes the upper limit is greater than the lower limit.
7. To assign results of symbolic evaluation to a function, define a function as follows:
Cauchy Principal Value
The Cauchy principal value of the integral about a point c, in the interval (a,b), is defined by the following expression:
The purpose of the Cauchy principal value is to define the value of the integral when the function f has a singularity point at c. For example, the following integral has a singularity point at c=0, and the symbolic evaluation returns an error.
To find the Cauchy principal value of the integral, add the modifier cauchy.
 Symbolic evaluation of integrals that require Cauchy analysis return a result of undefined unless the cauchy keyword is specified.