Integral of 1/cos(x) in CAS
10-12-2016, 02:47 PM
Post: #6
 John P Member Posts: 219 Joined: Dec 2013
RE: Integral of 1/cos(x) in CAS
(10-10-2016 05:53 AM)parisse Wrote:  I will investigate, note that
a:=int(1/cos(x)); simplify(a)
returns almost immediatly ln((sin(x)^2+2*sin(x)+1)/(sin(x)^2-2*sin(x)+1))/4
If you are computing an integral with symbolic boundaries that are disjoints, then you should compute the antiderivative and rewrite it at this step then make the difference at the boundaries. This is way more efficient than rewriting the difference of the antiderivatives at the boundaries because you have one less variable and an expression that is twice smaller (there is nothing in simplify that checks for the difference of a same expression at two different points).

Why the XCAS doesn't use the same approach as you described. Wouldn't that be more efficient and simple?
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 Messages In This Thread Integral of 1/cos(x) in CAS - Nigel (UK) - 10-09-2016, 08:01 PM RE: Integral of 1/cos(x) in CAS - parisse - 10-10-2016, 05:53 AM RE: Integral of 1/cos(x) in CAS - Nigel (UK) - 10-10-2016, 07:50 PM RE: Integral of 1/cos(x) in CAS - John P - 10-12-2016 02:47 PM RE: Integral of 1/cos(x) in CAS - parisse - 10-11-2016, 05:55 AM RE: Integral of 1/cos(x) in CAS - Nigel (UK) - 10-12-2016, 08:16 AM RE: Integral of 1/cos(x) in CAS - parisse - 10-12-2016, 06:44 PM

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