Integral oddity - Printable Version +- HP Forums (https://www.hpmuseum.org/forum) +-- Forum: HP Calculators (and very old HP Computers) (/forum-3.html) +--- Forum: HP Prime (/forum-5.html) +--- Thread: Integral oddity (/thread-6637.html) Integral oddity - lrdheat - 07-31-2016 09:06 PM 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? RE: Integral oddity - lrdheat - 07-31-2016 09:07 PM Version 2016 04 14 (10077) RE: Integral oddity - lrdheat - 07-31-2016 09:14 PM 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? RE: Integral oddity - parisse - 08-01-2016 06:17 AM (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. RE: Integral oddity - lrdheat - 08-01-2016 10:08 PM 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. RE: Integral oddity - Dieter - 08-01-2016 11:14 PM (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 RE: Integral oddity - lrdheat - 08-02-2016 02:10 AM Thanks! For some reason, I was seeing the denominator as "4" instead of "4*x".