[Maxima-bugs] Integration bug

[Hal C. <hde...@gm...>]

Hello list,

Maxima 5.33.0-5 is integrating  (1/sqrt(c*c + x*x)) dx  incorrectly. Entering

    integrate(1/sqrt(c*c+x*x),x);

causes Maxima to spit out

    asinh(x/abs(c))

which is equal to  log((x/abs(c)) + sqrt((x*x/(c*c)) + 1)). The
correct result is

    log(x + sqrt(c*c + x*x)).

which I verified with Wolfram Alpha, by-hand, and numerically for a
few values. So there is a missing factor of |c| within the log Maxima
spits out.
----

My machine is an x86_64 running an up-to-date Arch Linux with sbcl
1.2.2. I'm interacting with Maxima through wxMaxima 13.04.2-2.

$ uname -a
Linux --- 3.16.0-2-ARCH #1 SMP PREEMPT Mon Aug 4 19:04:45 CEST 2014
x86_64 GNU/Linux

-hal