integral(rho*sqrt(1/(-m*sin(u)^2 + 1)),(u,0,x)) gives a wrong answer

asked 2018-01-25 15:16:50 -0600

epimetheus gravatar image

HI everybody,

var('x u m')
assume(x>0)
assume(m>0)
assume(m<1)
integral(rho*sqrt(1/(-m*sin(u)^2 +1)),(u,0,x))

returns

2*rho*x/m

Expected answer is

elliptic_f(x,m)

Does anyone know how to fix this ?

Thank you.

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Comments

What is rho!?

vdelecroix gravatar imagevdelecroix ( 2018-01-25 16:56:07 -0600 )edit

rho is a constant

integral(sqrt(1/(-m*sin(u)^2 + 1)),(u,0,x))

returns

2*x/m
epimetheus gravatar imageepimetheus ( 2018-01-26 13:06:35 -0600 )edit

Seems a (Maxima) bug.

  • giac and fricas explicitely fail to integrate (retun the unevaluated integral and "failed" respectively

  • mathematica returns the expected result (along with (reasonable) conditions.

  • maple return a suspiciously complicated expression involving elliptic_f, which I was unable to simplify

  • sympy does not return

Worth a ticket (+ upstream bug report) ?

Emmanuel Charpentier gravatar imageEmmanuel Charpentier ( 2018-01-29 05:20:44 -0600 )edit