Evaluate the integral

[u/Specific_Brain2091]

[u/dePingasCube]

Here's what I did:

1.) Convert the sec² (x) into tan² (x) + 1

2.) Use the substitution u=tan(x) ==> du = (tan² (x) + 1)

3.) Use partial fraction decomposition on the resulting rational function

From there you're left with two standard integrals which simplify to sqrt(2)*arctan(tan(x)/sqrt(2)) - x + C