hp40g+.book Page 20 Friday, December 9, 2005 1:03 AM

Example

 

 

 

Given:

 

 

 

f(x) = -------------

x

⎛x + 1⎞

2

– 1

+ LN⎝-----------x– 1⎠

x

 

 

calculate a primitive of f.

Type:

 

 

 

 

NTVX⎛

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

X

+ LN⎛X------------+ 1⎞

⎝

X

2

+ 1

⎝ X – 1⎠

 

 

 

Or, if you have stored f(x) in F, that is, if you have already typed:

TORE⎛

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

X

+ LN⎛X------------+ 1⎞

,F

⎝

X

2

– 1

⎝ X – 1⎠

 

 

 

 

 

then type:

INTVX(F)

Or, if you have used DEF to define f(x), that is, if you have already typed:

DEF(F(X) = --------------

X

⎛X + 1⎞ ⎞

2

– 1

+ LN⎝------------X– 1⎠ ⎠

X

 

 

then type:

INTVX(F(X))

The result in all cases is equivalent to:

⋅ LN⎛X + 1⎞

+

3

⋅ LN(

 

X – 1

 

) +

3

⋅ LN(

 

X + 1

 

 

 

 

 

⎝ X – 1⎠

 

2

 

 

 

 

 

2

 

 

 

 

You will obtain absolute values only in Rigorous mode. (See “CAS modes” on page 14-5 for instructions on setting and changing modes.)

Example

Calculate:

∫

 

 

2

 

 

 

 

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

dx

x

6

+ 2 ⋅ x

4

+ x

2

 

 

 

 

 

Typing:

14-20

 

 

Computer Algebra System (CAS)