Texas Instruments TI-89 Tip List page 232

but the correct result is
However, if symbolic values are used for the constants, the correct result is returned, that is
¶
( ax + b ) n dx
If Approx mode is used instead of Auto mode, examples [1] to [3] return correct results.
The problem also exists with definite integrals. This is shown with a definite integral of example [1]
above:
9
¶
( 7x + 4 ) 3 dx
2
but the correct result is
In Approx mode the correct result of about 2021.11 is returned.
Correct results can be obtained in Auto mode by writing the integrand in exponential form, instead of
using the square root operator. Applying this to example [1]:
3
¶
( 7x + 4 )
2
and for the definite integral of example [4]:
9
¶
( 7x + 4 ) 3 dx
2
Incorrect results will be obtained if you use substitution (the "with" operator | ) for n, for example
¶
( 7x + 4 ) n dx x n = 3
but if you evaluate the expression without the constraint n=3, and then apply the constraint to that
result, the correct integral is returned.
A similar problem also occurs with integrands of the form
1
( ax+b ) n
For integrals of this form, the correct result is returned if
The built-in differential equation solver can fail with arguments of this type, too.
(Credit to Gary Wardall, Damien Cassou, Kevin Kofler, and ES)
( 2x−3 ) ( 2x−3 ) 7
2 ( ax+b )
returns
a ( n+2 )
8978 67
returns
5
8978 67
35
correctly returns
correctly returns
returns the incorrect result of [1]
9
n
2 +1
1944 2
−
5
1944 2
−
35
5
2 ( 7x+4 ) 2
35
8978 67
1944 2
−
35 35
n [ −10
n m 10
or .
[3]
[4]
[5]
[6]
[7]
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