Integrate x^4 / (1 - x^2)^(3/2)

[mat331760298]

1. Integral of (x^4)/(1-x^2)^(3/2) dx

i let x=sint so dx=costdt used the right triangle and simplified to integral of ((sint)^4)/((cost)^2) dt

 

[rock.freak667]

Now rewrite sin⁴t as (1-cos²t)² and expand.