File r37/lisp/csl/html/r37_0154.html artifact c64d18423d part of check-in e08999f63f

<A NAME=INT>

<TITLE>INT</TITLE></A>
<b><a href=r37_idx.html>INDEX</a></b><p><p>



<B>INT</B> _ _ _  _ _ _  _ _ _  _ _ _ <B>operator</B><P>
<P>
 
 <P>
<P>
The <em>int</em> operator performs analytic integration on a variety of 
functions. 
<P>
<P>
 <P> <H3> 
syntax: </H3>
<em>int</em>(&lt;expression&gt;,&lt;kernel&gt;) 
<P>
<P>
<P>
&lt;expression&gt; can be any scalar expression. involving polynomials, log 
functions, exponential functions, or tangent or arctangent expressions. 
<em>int</em> attempts expressions involving error functions, dilogarithms 
and other trigonometric expressions. Integrals involving algebraic 
extensions (such as square roots) may not succeed. &lt;kernel&gt; must be a 
REDUCE 
<A HREF=r37_0002.html>kernel</A>. 
<P>
<P>
 <P> <H3> 
examples: </H3>
<P><PRE><TT>
int(x**3 + 3,x); 

      3
  X*(X  + 12)
  ----------- 
       4



int(sin(x)*exp(2*x),x);
 

     2*X
    E   *(COS(X) - 2*SIN(X))
  - ------------------------ 
               5


int(1/(x^2-2),x);
 

  SQRT(2)*(LOG( - SQRT(2) + X) - LOG(SQRT(2) + X))
  ------------------------------------------------ 
                         4


int(sin(x)/(4 + cos(x)**2),x);
 

         COS(X)
    ATAN(------)
           2
  - ------------ 
         2



int(1/sqrt(x^2-x),x); 

      SQRT(X)*SQRT(X - 1)
  INT(-------------------,X)
              2
             X -X

</TT></PRE><P>Note that REDUCE couldn't handle the last integral with its defaul
t 
integrator, since the integrand involves a square root. However, 
the integral can be found using the 
<A HREF=r37_0265.html>algint</A> package. 
Alternatively, you could add a rule using the 
<A HREF=r37_0199.html>let</A> statement 
to evaluate this integral. 
<P>
<P>
The arbitrary constant of integration is not shown. Definite integrals can 
be found by evaluating the result at the limits of integration (use 

<A HREF=r37_0330.html>rounded</A>) and subtracting the lower from the higher. Ev
aluation can 
be easily done by the 
<A HREF=r37_0182.html>sub</A> operator. 
<P>
<P>
When <em>int</em> cannot find an integral it returns an expression 
involving formal <em>int</em> expressions unless the switch 

<A HREF=r37_0288.html>failhard</A> has been set. If not all of the expression 
can be integrated, the switch 
<A HREF=r37_0311.html>nolnr</A> controls whether a partially 
integrated result should be returned or not. 
<P>
<P>
<P>
<P>