HP 40gs - Manual (Page 201)

Computer Algebra System (CAS) 14-19
IBP returns the AND of and of
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
.
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:
u x ( ) v x ( ) ⋅ v – x ( ) u' x ( ) ⋅
u x ( ) v' x ( ) ⋅
x ( ) 2
sin
2
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