No easy way.
Just stick with trig. sub. ... or (better yet) use hyperbolic substitution.
sec^2(x) - 1 =tan^2(x) . . . . ... . . . cosh^2(x) - 1 = sinh^2(x) .
Look, stuck man, I donot think there is any way to find the integral from the 2 fractions. Even wolfram alpha solves it using trigonometric substitution. You can see it here if you like. link. If required you can also use hyperbolic substitution.