INT _ _ _ _ _ _ _ _ _ _ _ _ operator

The int operator performs analytic integration on a variety of functions.

syntax:

<expression> can be any scalar expression. involving polynomials, log functions, exponential functions, or tangent or arctangent expressions. int attempts expressions involving error functions, dilogarithms and other trigonometric expressions. Integrals involving algebraic extensions (such as square roots) may not succeed. <kernel> must be a REDUCE kernel.

examples:

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

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 algint package. Alternatively, you could add a rule using the let statement to evaluate this integral.

The arbitrary constant of integration is not shown. Definite integrals can be found by evaluating the result at the limits of integration (use rounded) and subtracting the lower from the higher. Ev aluation can be easily done by the sub operator.

When int cannot find an integral it returns an expression involving formal int expressions unless the switch failhard has been set. If not all of the expression can be integrated, the switch nolnr controls whether a partially integrated result should be returned or not.