integral(rhosqrt(1/(-msin(u)^2 + 1)),(u,0,x)) gives a wrong answer

epimetheus
31 ●3 ●6 ●11

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.

Comments

What is rho!?

vdelecroix ( 2018-01-25 23:56:07 +0100 )edit

rho is a constant

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

returns

2*x/m

epimetheus ( 2018-01-26 20:06:35 +0100 )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 ( 2018-01-29 12:20:44 +0100 )edit