@tindex integ
The @kbd{a i} (@code{calc-integral}) [@code{integ}] command computes the
indefinite integral of the expression on the top of the stack with
-respect to a variable. The integrator is not guaranteed to work for
-all integrable functions, but it is able to integrate several large
-classes of formulas. In particular, any polynomial or rational function
-(a polynomial divided by a polynomial) is acceptable. (Rational functions
-don't have to be in explicit quotient form, however;
+respect to a prompted-for variable. The integrator is not guaranteed to
+work for all integrable functions, but it is able to integrate several
+large classes of formulas. In particular, any polynomial or rational
+function (a polynomial divided by a polynomial) is acceptable.
+(Rational functions don't have to be in explicit quotient form, however;
@texline @math{x/(1+x^{-2})}
@infoline @expr{x/(1+x^-2)}
is not strictly a quotient of polynomials, but it is equivalent to
integrated. Finally, rational functions involving trigonometric or
hyperbolic functions can be integrated.
+With an argument (@kbd{C-u a i}), this command will compute the definite
+integral of the expression on top of the stack. In this case, the
+command will again prompt for an integration variable, then prompt for a
+lower limit and an upper limit.
+
@ifinfo
If you use the @code{integ} function directly in an algebraic formula,
you can also write @samp{integ(f,x,v)} which expresses the resulting