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I am evaluating an integral with constants that are not specified, 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,

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

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

d indicates dimensions so in this case I set for example, d=2, while a,b are constants (leave it open so I can put values later). In the end, I want to get an expression for "c" in terms of "a" (since "a" also gives "b") through evaluation of the integral.

I am evaluating an integral with constants that are not specified, 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,

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

d = 2; z = 10; b = a/z; SumConvergence[(c a^(d + 1)  y^d)/((1 - b^(d + 1) y^(d + 1)) (1 - c^2 (a y)^(2 d)))^(1/2), y] Integrate[(c a^(d + 1) y^ d)/((1 - b^(d + 1) y^(d + 1)) (1 - c^2 (a y)^(2 d)))^(1/2), {y, 0, 1}, Assumptions -> {c > 0, a > 0}] 

d indicates dimensions so in this case I set for example, d=2, while a,b are constants (leave it open so I can put values later). In the end, I want to get an expression for "c" in terms of "a" (since "a" also gives "b") through evaluation of the integral.

UPDATE: I changed the integral expression a bit compared to my first post, now I tried doing the SumConvergence command and it returns a TRUE value so this new integral that I posted converges but I do not know why it does not return the condition of convergence. Also, the Integrate command still does not return anything even though the function converges.

I am evaluating an integral with constants that are not specified, 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,

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

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

d indicates dimensions so in this case I set for example, d=2, while a,b are constants (leave it open so I can put values later). In the end, I want to get an expression for "c" in terms of "a" (since "a" also gives "b") through evaluation of the integral.

I am evaluating an integral with constants that are not specified, 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,

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

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

d indicates dimensions so in this case I set for example, d=2, while a,b are constants (leave it open so I can put values later). In the end, I want to get an expression for "c" in terms of "a" (since "a" also gives "b") through evaluation of the integral.

I am evaluating an integral with constants that are not specified, 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,

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

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

d indicates dimensions so in this case I set for example, d=2, while a,b are constants (leave it open so I can put values later). In the end, I want to get an expression for "c" in terms of "a" (since "a" also gives "b") through evaluation of the integral.

I am evaluating an integral with constants that are not specified, 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,

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

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

d indicates dimensions so in this case I set for example, d=2, while a,b are constants (leave it open so I can put values later). In the end, I want to get an expression for "c" in terms of "a" (since "a" also gives "b") through evaluation of the integral.