Graph the function. What do you notice?

Use partial fraction decomposition to rewrite the integrand as a sum of fractions.

$\frac{2}{y^2-1}=\frac{A}{y-1}+\frac{B}{y+1}$

Use substitution.

Let $u =\operatorname{cos}^{–1}(x)$. Then $du =$ _____.

Recall that $\operatorname{cos}^2(x)-\operatorname{sin}^2(x) =\operatorname{cos}(2x).$

$\int\frac{1}{\cos(2t)}dt=\int\sec(2t)dt$

$=\frac{1}{2}\int\sec(u)du\text{ }u=2x$

$=\frac{1}{2}\ln(\tan(u)+sec(u))$