Integral oddity
07-31-2016, 09:06 PM
Post: #1
 lrdheat Senior Member Posts: 857 Joined: Feb 2014
Integral oddity
Integral 1/(x^2 * sqrt(x^2 + 4)) should be (-sqrt(x^2 + 4))/4*x

The prime gives (-x -sqrt(x^2 + 4))/4*x after factorizing or after simplifying. Is this a bug?
07-31-2016, 09:07 PM
Post: #2
 lrdheat Senior Member Posts: 857 Joined: Feb 2014
RE: Integral oddity
Version 2016 04 14 (10077)
07-31-2016, 09:14 PM
Post: #3
 lrdheat Senior Member Posts: 857 Joined: Feb 2014
RE: Integral oddity
When integrating over a specific range such as pi/6 to pi/4, the exact answer converts to a correct approximate answer of ~.303

Am I missing something?
08-01-2016, 06:17 AM
Post: #4
 parisse Senior Member Posts: 1,320 Joined: Dec 2013
RE: Integral oddity
(07-31-2016 09:06 PM)lrdheat Wrote:  Integral 1/(x^2 * sqrt(x^2 + 4)) should be (-sqrt(x^2 + 4))/4*x

The prime gives (-x -sqrt(x^2 + 4))/4*x after factorizing or after simplifying. Is this a bug?

No, because antiderivatives are defined up to a constant.
08-01-2016, 10:08 PM
Post: #5
 lrdheat Senior Member Posts: 857 Joined: Feb 2014
RE: Integral oddity
I must be math challenged/rusty...is not the "-x" that Prime produced a variable? How are the 2 answers equivalent?

What has me befuddled is that when made into a definite integral, Prime reports a correct answer.
08-01-2016, 11:14 PM (This post was last modified: 08-01-2016 11:17 PM by Dieter.)
Post: #6
 Dieter Senior Member Posts: 2,397 Joined: Dec 2013
RE: Integral oddity
(08-01-2016 10:08 PM)lrdheat Wrote:  I must be math challenged/rusty...is not the "-x" that Prime produced a variable? How are the 2 answers equivalent?

If you simplify the Prime result...

Code:
   –x – sqrt(x²+4)    ---------------          4x    –x     sqrt(x²+4) =  --  –  ----------    4x         4x             sqrt(x²+4) =  –1/4  –  ----------                 4x             sqrt(x²+4) = const  –  ----------                 4x

...you get the same antiderivative plus a constant.

Dieter
08-02-2016, 02:10 AM
Post: #7
 lrdheat Senior Member Posts: 857 Joined: Feb 2014
RE: Integral oddity
Thanks!

For some reason, I was seeing the denominator as "4" instead of "4*x".
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