Math question!
show your work!

Solution: 
1) pass: make the replacement






2) pass: We substitute in the integral of the statement




3) pass: Using the Gauss Lemma, we will factor the polynomial (y⁴ + 1) knowing that there are no real roots, so we will directly try to factorize into two polynomials of degree 2:



Make the system linear, to find the values of "a" and "c".




We have:


4) pass: We will use the partial fractions method, using the fraction from within the integral:









5)pass: Adopt what was used above:





6) pass: Now, solve it separately







and







7) pass: Let's use the expression of 







8) pass: Now, returning to the expression as a function of x, we finally arrive at the final







 

The surface area would be 576 because you multiply all the numbers then multiply that number by 6