hp40g+.book Page 19 Friday, December 9, 2005 1:03 AM

IBP returns the AND of u(x) ⋅ v(x) and of –v(x) ⋅ u'(x)

that is, the terms that are calculated when performing a partial integration.

It remains then to calculate the integral of the second term of the AND, then add it to the first term of the AND to obtain a primitive of u(x) ⋅ v'(x) .

Typing:

IBP(LN(X),X)

gives:

X·LN(X) AND - 1

The integration is completed by calling INTVX:

INTVX(X·LN(X)AND - 1)

which produces the result: X·LN(X) - X

N O T E : If the first IBP (or INTVX) parameter is an AND of two

 

elements, IBP concerns itself only with the second element

 

of the AND, adding the integrated term to the first element

 

of the AND (so that you can perform multiple IBP in

 

succession).

INTVX

 

Primitive and defined integral

 

INTVX has one argument: an expression.

INTVX calculates a primitive of its argument with respect to the variable stored in VX.

Example

Calculate a primitive of sin(x) × cos(x).

Typing:

INTVX(SIN(X)·COS(X))

gives in step-by-step mode:

 

COS(X)·SIN(X)

 

 

 

Int[u’∗F(u)] with u=SIN(X)

 

 

 

Pressing OK then sends the result to the Equation Writer:

 

 

 

sin(x)2

 

 

 

-----------------

 

 

 

 

 

 

2

 

 

 

 

 

 

 

 

 

 

 

 

 

Computer Algebra System (CAS)

14-19