Definite integral with some unknown variables

[shinobi20]

TL;DR Summary

I am evaluating a definite integral with unknown variables in Mathematica.

I am trying to evaluate an integral with unknown variables $a, b, c$ in Mathematica, but I am not sure why it takes so long for it to give an output, so I just decided to cancel the running. The integral is given by,

$\int_0^1 dy \frac{ y^2 (1 - b^3 y^3)^{1/2} }{ (1 - a^4 c^2 y^4)^{1/2} }$

 

[S.G. Janssens]

Depending on the values of $a, b, c$ you can expect singularities in the integrand that may make the integral improper or even non-convergent. So, if the problem allows it, you should probably tell the software explicitly about assumptions on $a, b, c$.

For example, I would begin by defining $d := a^4 c^2$ and passing the assumption that $d < 1$.

 

[shinobi20]

Depending on the values of a,b,c you can expect singularities in the integrand that may make the integral improper or even non-convergent. So, if the problem allows it, you should probably tell the software explicitly about assumptions on a,b,c.

For example, I would begin by defining d:=a4c2 and passing the assumption that d<1.

This is my code

d=2;
z=1;
b=a/z;
h=c^2 a^2d;
Integrate[ ( y^d (1 - (b y)^(d+1))^1/2 )/(1 - h^2d y^2d)^1/2 , {y,0,1}, Assumptions -> {y>0, h<1} ]

It does not return anything.