Solution: <span>1) pass: make the replacement </span>
2) pass: <span>We substitute in the integral of the statement </span>
3) pass: <span>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: </span>
<span>Make the system linear, to find the values of "a" and "c". </span>
We have:
4) pass: <span>We will use the partial fractions method, using the fraction from within the integral: </span>
5)pass: Adopt what was used above:
6) pass: <span>Now, solve it separately </span>
and
7) pass: Let's use the expression of
<span>8) pass: Now, returning to the expression as a function of x, we finally arrive at the final answer: </span>