Question

could someone help me understand the process of integrating sqrt[1+{(6*y^4)-((1/24)*y^-4)}^2] ?

Answer 1

Tough one - use algebra to expand everything and then put together the expressions inside the square root. Turns out you'll end up with a perfect square in the numerator and a perfect square monomial in the denominator (before the square root, you should get "20736y^16 - 288 y^8 + 1" all over "576 y^8" .

Then, take the square root to get "144y^8 + 1" all over "24 y^4) - then break it apart into two terms and end up with, as your integrand: 6y^4 + 1/(24y^4) : then you can integrate using your basic rules of integration.