Integration.

  The commands of ALGB related to integration are:

• FINT (library-command) to integrate rational fractions of x (more precisely of the variable contained in VX, I will assume that it is X). FINT accepts a function as input and returns the primitive evaluated between and x,
• risch to integrate rational expressions with exponentials and logarithms
• INT (INTG directory) to integrate rational expressions with ( and/or ) or ( and/or ) or (x and/or )
• LIN (INTG directory) to linearize trigonometric expressions.

The risch and INT programs accept functions or integrals as input and return the primitive or the evaluated primitive.

Some examples:

• '1/(X^2-4)' FINT EVAL XQ
• '1/(X^2-4)' risch
• '1/(X^2-4)' INT (hit the menu key after)
• : here you must choose risch
• : choose INT
• 1/(e^x-1): choose risch
• : choose INT or type TSIMP and risch.

The risch program should be used in conjonction with the TSIMP function to enable trigonometric functions integration. It is a partial implementation of the Risch algorithm: it works with pure transcendental extensions (i.e. no square root allowed), and exponential polynomial part must not contain logarithm ore other exponential. Examples:

are allowed, but:

are not allowed. Note that is not allowed directly, but after TSIMP with flag 13 set, risch will find the primitive. A new call to TSIMP with flag 13 cleared converts back complex exponential and logarithms to trigonometric functions.

In conjonction with TSIMP and EXPA, you should obtain some non trivial results: e.g.

(you can try INT or risch followed by TSIMP and EXPA).